Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019) [1st ed. 2020] 978-981-15-0473-0, 978-981-15-0474-7

Table of contents :
Front Matter ....Pages i-xv
An Improved Image Registration Method for Infrared and Visible Images (Ningning Ding, Jingchang Zhuge, Shujian Xing, Yang Wang)....Pages 1-9
Study on a Dual Mode Switching Technology of Multi-energy Ship Microgrid (Weiqiang Liao, Jiangbo Lü, Rencheng Zhang, Xianyue Liu)....Pages 11-21
Economic Dispatch of Wind Farm Cluster Integrated Power System Considering High Energy Load (Xiaoying Zhang, Shun Liao, Kun Wang, Xiaolan Wang, Wei Chen)....Pages 23-32
Physical Layer Encryption Based on Hyper-Chen Chaos in Universal Filtered Multi-carriers System (Yongtao Huang, Pengqi Yin, Jie Ma, Rui Wang)....Pages 33-39
Verification Research on On-line Monitoring Method of Aircraft ARINC825 Bus Cable Fault Based on SSTDR (Xudong Shi, Xiangyang Xu, Yang Liu, Tao Jing)....Pages 41-51
Research on Motion Control System of 6-DOF Robotic Arm (Minglei Liu, Hongbo Zhou, Aiping Pang)....Pages 53-61
A Novel Capacitor Voltage Balancing Control Strategy for Modular Multilevel Converters (Jian Li, Zhuo Chen, Aiping Pang, Qingfang Zhang, Zhanbao Wang, Jiawei Ma et al.)....Pages 63-74
Research on Face Recognition Technology Based on PCA and SVM (Shu Zhang, Zi-Yue Li, Yu-Chao Liu)....Pages 75-85
A Study on PD-like Fuzzy Logic Control Based Active Noise Control for Narrowband Noise Cancellation with Acoustic Feedback and Distance Ratio (Tongrui Peng, Quanmin Zhu, Tokhi M. Osman, Yufeng Yao)....Pages 87-98
Sliding-Mode Control of STENA DRILLMAX Drillship with Environmental Disturbances for Dynamic Positioning (C. S. Chin, C. S. Lio)....Pages 99-111
Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas (Qing Xiao, Shao-Wu Zhou)....Pages 113-121
The Study of Air Supply Ways Effects on the Aircraft Cabin Thermal Environment (Xudong Shi, Di Chao, Yu Zhang, Hongxu Zhao)....Pages 123-131
Identification of the Wiener System Based on Instrumental Variables (Shaoxue Jing, Tianhong Pan)....Pages 133-140
Cervical Histopathology Image Clustering Using Graph Based Unsupervised Learning (Chen Li, Zhijie Hu, Hao Chen, Dan Xue, Ning Xu, Yong Zhang et al.)....Pages 141-152
Study on Analysis and Avoidance of Unstable Control for Flexible System Design (G. Q. Zhai, R. Y. K. Zhang, F. W. Meng, Z. Y. Liu, S. Liu, X. R. Yan)....Pages 153-164
Eigenvalue Sensitivity Analysis of Aircraft Power System (Jianying Liu, Jin Cai, Jiawang Huang, Zhangang Yang)....Pages 165-172
Modeling and Simulation of Closed-Loop Control Circuit of Aircraft Fuel Metering Valve (Xudong Shi, Shaoshuai Yuan, Yakun Wang, Xu Wang)....Pages 173-184
A Static Gesture Recognition Algorithm Based on DAG-SVMs (Mengxin Li, Tongwei Jiang, Rui Xu, Baifeng Lin)....Pages 185-193
Semiconductor Bonding Equipment Grouping Model Based on Processing Task Matching (Zhijun Gao, Wen Si, Zhonghua Han, Jiayu Peng, Hongzhi Zheng)....Pages 195-204
Research on the Improved Dragonfly Algorithm-Based Flexible Flow-Shop Scheduling (Zhonghua Han, Jingyuan Zhang, Shuo Lin, Chunguang Liu)....Pages 205-214
Modeling and Adaptive Control for Tower Crane Systems with Varying Cable Lengths (Menghua Zhang, Yongfeng Zhang, Huimin Ouyang, Changhui Ma, Xingong Cheng)....Pages 215-226
EEG Recognition with Adaptive Noise Reduction Based on Convolutional LSTM Network (Hengxing Lv, Xuemei Ren, Yongfeng Lv)....Pages 227-237
Peaking Reduction of CRM-Based Adaptive Control via a Modified Adaptive Law (Yafei Liu, Jun Yang, Jing Na, Guanbin Gao, Shubo Wang, Qiang Chen)....Pages 239-248
Unbalance Suppression for Active Magnetic Bearing Rotor System Based on Disturbance Observer (Zhuangzhuang Yue, Huimin Ouyang, Guangming Zhang, Lei Mei, Xin Deng)....Pages 249-261
Investigation of Pilot Flight Technology Based on Exploratory Factor Analysis (Peipei Zeng, Zhonghua Li, Yan Chen)....Pages 263-272
Study on Crack Propagation of Rivet Stiffened Plate Containing MSD Structure in Corrosive Environment (Yuan Zhao, Jinfang Zhao)....Pages 273-279
H∞ Phase Control for Flexible Systems (Junfeng Yang, Muzhou Yu, Yanjie Niu, Wenjie Zhang, Fanwei Meng)....Pages 281-296
Mixed Sensitivity Design of Magnetic Suspension System (Muzhou Yu, Junfeng Yang, Fanwei Meng, Yanjie Niu)....Pages 297-304
Unmanned Autonomous Helicopter Integral Sliding Mode Control and Its Stability Analysis (Haojia Zhang, Aijun Li, Yu Wang)....Pages 305-313
UAVs Formation Control Based on Artificial Potential Functions with the Orientation Considered (Jiawei Li, Wei Wang, Aijun Li, Bojian Liu)....Pages 315-324
Automatic Image Annotation with Deep Model Trained by Dynamic Loss Function (Ze Si, Dongmei Fu, Yang Liu, Xinshi Liu)....Pages 325-334
Fuzzy Neural Network PID Control of Quadrotor Unmanned Aerial Vehicle Based on PSO-GA Optimization (Xia Li, Shuaihua Zhang, Fang Zheng, Bingyuan Wang)....Pages 335-345
Risk Analysis of Information System Security Based on the Evidence Distance (Jinhua LingHu, Ping Pan, Yaoyao Du)....Pages 347-358
Fault Diagnosis of the Motor of Electro-Mechanical Transmission of the High Speed Rotorcraft (Yue Ma, Lu Lin, Fei Qi)....Pages 359-371
Backstepping Sliding Mode Control for the Displacement Tracking of Permanent Magnet Linear Synchronous Motor Based on Nonlinear Disturbance Observer (Hong-jiao Song, Le Liu, Man-jun Cai, Nuan Shao)....Pages 373-382
An Edge Extraction Method Based on Gray Lever-Gradient Two-Dimensional Maximum Entropy Threshold Method for Footprint Inspection (Mengxin Li, Wenlong Pei, Meiling Li, Rui Xu)....Pages 383-391
Target Feature Extraction and Recognition of SAR Images Based on PCANet (Pucheng Li, Junchen Li, Wen Yin, Lei Yang)....Pages 393-400
Evaluation on Symbiotic Performance of Regional Technological Entrepreneurship Ecosystem (Chunxiao Sun, Chunyan Li, Jianhua Zhang)....Pages 401-411
Fixed-Time Terminal Sliding Mode Control for Quadrotor Aircraft (Jie Wang, Xiao Ma, Gaowei Zhang, Yan Zhang, Qing Miao)....Pages 413-421
Nonlinear Observer Based Fault Diagnosis for an Innovative Intensified Heat-Exchanger/Reactor (Xue Han, Zetao Li, Boutaib Dahhou, Michel Cabassud, Menglin He)....Pages 423-432
Research on Rudder Roll Stabilization Motion Control Based on Adaptive LQR (Yanwen Liu, Changsheng Zhou, Yinlin Liu, Guangqing Zhai)....Pages 433-442
Study on Non-local Cubic Spline Function Based on Peridynamics (Jincai Chang, Jiecheng Wang, Dan Jian, Zhuo Wang, Jianhua Zhang)....Pages 443-453
Weakly Supervised Semantic Segmentation Based on Deep Learning (Binxiu Liang, Yan Liu, Linxi He, Jiangyun Li)....Pages 455-464
Real-Time Human Body Detection Based on YOLOv2 Network (Xiaopeng Liu, Yan Liu, Hong Wang, Jiangyun Li)....Pages 465-473
Research on the Temperature Field and Thermal Roll Shape of Cold Rolling Model (Zichao Sun, Weicun Zhang, Yan Liu)....Pages 475-484
Optimized Control System Design for Two-Wheeled Inverted Pendulums (Haifei Si, Yizhi Wang, Xingliu Hu, Zhong Yang)....Pages 485-495
A Retinal Vessel Segmentation Algorithm with Convolutional Neural Network (Leiming Liu, Jiahao Li, Weicun Zhang, Dongmei Fu)....Pages 497-502
A Detection and Isolation of Faults Technique in Automotive Engines Using a Data-Driven and Model-Based Approach (Yingmin Wang, Dong Cui, Feng Guo)....Pages 503-520
Decomposition-Based Gradient Iterative Estimation for Input Nonlinear Model by Using the Kalman Filter (Qiuling Fei, Junxia Ma, Weili Xiong, Jing Chen)....Pages 521-530
Modeling of Asymmetric Cylinder Electro-hydraulic System Based on Backstepping Control Method (Yun-fei Wang, Ji-yun Zhao, Hai-gang Ding, Jia-xiang Man)....Pages 531-540
An AUV Adaptive Front-Tracking Algorithm Based on Data-Driven (Xiangyu Qu, Yiping Li, Gaofei Xu)....Pages 541-554
Parameter Identification of MR Damper Model Based on Particle Swarm Optimization (Yonggang Yang, Youchuang Ding, Shixing Zhu)....Pages 555-563
State Observer-Based Prescribed Performance Control for MDF Continuous Hot Pressing System (Liangkuan Zhu, Yugang Zhou, Xinrui Chen)....Pages 565-574
Optimization Approaches for Parameters of SVM (Jinxiang Chen, Yilan Yin, Lu Han, Feng Zhao)....Pages 575-583
The Staffing Optimization Problem for the M-Design Multi-Skill Call Center Based on Queuing Model (Chunyan Li, Chunxiao Sun, Jianhua Zhang)....Pages 585-595
Adaptive Sliding Mode Trajectory Tracking Control of Quadrotor UAV with Unknown Control Direction (Lijun Wang, Wencong Deng, Jinkun Liu, Rong Mei)....Pages 597-607
An Aeroengine Adaptive Inverse Control Method Based on U-Model (Jiajie Chen, Zhongzhi Hu, Jiqiang Wang, Weicun Zhang)....Pages 609-618
The Active Fault-Tolerant Control of Reconfigurable Manipulator Based on Iterative Fault Observer (Wenfeng Ren, Yanli Du)....Pages 619-629
Prediction for Time Series with CNN and LSTM (Xuebo Jin, Xinghong Yu, Xiaoyi Wang, Yuting Bai, Tingli Su, Jianlei Kong)....Pages 631-641
CO2 Pipeline Transportation System Optimization Design Based on Multiple Population Genetic Algorithm (Qunhong Tian, Aiqin Sun, Kan Shi, Fengde Wang)....Pages 643-651
A Train Integrity Monitoring Method Based on GNSS Moving Baseline Resolution (Wei Jiang, Yongqiang Liu, Dan Liu, Baigen Cai, Jian Wang)....Pages 653-662
Generalized Extended Stochastic Gradient Algorithm Implemented Parameter Identification for Complex Multivariable-Systems (Wei Wang)....Pages 663-673
Reinforcement Learning on Robot with Variational Auto-Encoder (Yiwen Chen, Chenguang Yang, Ying Feng)....Pages 675-684
A Multi-Center PSO Algorithm with Memory Ability and Its Application to the Online Modelling of an Underwater Vehicle Thruster (Gaofei Xu, Guanqun Wang, Yiping Li, Xiaohui Wang, Xiangyu Qu)....Pages 685-695
Trajectory Tracking of Mobile Robots Based on Fuzzy Control and Extended State Observer (Dan Su, Jian Huang, Daqian Yang)....Pages 697-706
Design of Wireless Body Area Network with Motion Sensors Using New Materials (Guodong Wang, Yanxiao Zhao, Yichun Ding, Jack Yang, Zhengtao Zhu)....Pages 707-717
The Depth Estimation Method Based on Double-Cues Fusion for Light Field Images (Xinshi Liu, Dongmei Fu, Chunhong Wu, Ze Si)....Pages 719-726
Fuzzy Gain Scheduler Based Path Tracking on Image Plane for XY/Z Partitioned IBVS System (Jie Zhong, Tao Wang, Lianglun Cheng)....Pages 727-735
Valve Control System with Mechanical Feedback (Hao Yan, Bowen Jiang, Zheqing Zuo)....Pages 737-746
The Algorithm for UAV Obstacle Avoidance and Route Planning Based on Reinforcement Learning (Jiantong Liu, Zhengjie Wang, Zhide Zhang)....Pages 747-754
Cascade Improved Visual Detection and Distance Estimation in Formation of Micro Unmanned Aerial Vehicles (Jiankun Sun, Yanxuan Wu, Xutan Lu, Yunduo Feng)....Pages 755-765
Saturated Adaptive Backstepping Control for Uncertain Nonlinear Active Suspension Systems with Prescribed Performance (Gang Wang, Feng Liu, Zhenghao Sun)....Pages 767-776
High Gain Finite-Time Trajectory Tracking Control of Pneumatic Muscle Actuator (Tong Shen, Jian Huang)....Pages 777-787
Research on Reversing Radar Based on Linear Structured Light (Xinliang Tang, Yang Li, Jianhua Zhang)....Pages 789-799
Multi-objective Minimal Time Optimal Control Based Path Planning of Mobile Robots (Siqi Tu, Shurong Li, Zhe Liu, Derui Zeng)....Pages 801-810
Modeling and Simulation in Distributed Cooperative Simulation Platform of Aircraft Fuel System (Zhiyong Fan, Da Teng, Zhexu Liu)....Pages 811-820
Adaptive Neural Network Dynamic Surface Control Algorithm for Pneumatic Servo System (Gang Liu, Guihai Li, Zhengyang Peng, Huihui Pan)....Pages 821-829
Data Aggregation Point Placement in Energy Harvesting Powered Smart Meter Networks (Asif Hassan, Lina Pu, Yu Luo, Guodong Wang, Yanxiao Zhao)....Pages 831-841
Bipartite Consensus Control for Coupled Harmonic Oscillators Using Sampled Data with Measurement Noise (Jun Liu, Hengyu Li, Jun Luo)....Pages 843-849
Adaptive Sliding Model Controller Design of Carlike Robot Speed and Steering Angle Based on Characteristic Model (Zhen Xu, Mingchu Xu, Qingwei Chen)....Pages 851-862
Inventory Control Strategy on High-Value Aviation Spares at Line Maintenance (Shiwei Zhao, Guihang Liu, Peng Zhang)....Pages 863-873
Experimental Modeling of Rotary Traveling-Wave Ultrasonic Motor (Qingquan Liu, Xin Huo, Weijia Shi, Hui Zhao)....Pages 875-885
Time-Domain System Identification for Long-EZ Fixed-Wing Aircraft Based on Flight Test Data (Danyang Xu, Chi Yuan, Youmin Zhang)....Pages 887-896
Fault Prediction of Fan Cooling System for Aircraft Weather Radar (Liu Guihang, Zhao Shiwei)....Pages 897-905
Research on Harmonic Current Functional Analysis of AC Arc Furnaces and Evaluation of Harmonic Level (Pu Deng, Shi Zeng, Yongzhong Li, Xiaojun Peng, Jing Nong, Zhuo Chen et al.)....Pages 907-916
Minimax Optimization for Capacitors Composited with Two Kinds of Series Reactance Rates (Pu Deng, Tinghao Lei, Fengyuan Wang, Zhuo Chen, Aiping Pang)....Pages 917-925
GRU-Based Estimation Method Without the Prior Knowledge of the Noise (Xuebo Jin, Aiqiang Yang, Tingli Su, Jianlei Kong)....Pages 927-935
Research on Optimization Method of LEACH Routing Protocol (Fan Chao, Zhiqin He, Xiumin Hu, Hongbo Zhou, Aiping Pang)....Pages 937-946
Stochastic Road Condition Identification for Electromagnetic Active Suspension Based on Support Vector Regression (Zepeng Gao, Sizhong Chen, Yuzhuang Zhao, Zhicheng Wu, Lin Yang, Jiang Hu et al.)....Pages 947-957
Research on Noise Suppression and Edge Reading Algorithms in X-Ray Image Detection (Xiumin Hu, Zhiqin He, Fan Chao, Aiping Pang)....Pages 959-967
Research on Water Monitoring Information Acquisition System of UAV Based on Wireless Sensor Network (Junjie Ge, Fan Chao, Zhiqin He, Wenye Shi)....Pages 969-977
Recursive Estimation Method for Bilinear Systems by Using the Hierarchical Identification Principle (Ling Xu, Xiao Zhang, Feng Ding)....Pages 979-987
PSO Rapid Ascending Trajectory Planning Method Based on Neural Network Trajectory Surrogate Model (Yuhang Zeng, Ye Yang, Yongji Wang, Lei Liu)....Pages 989-1000
A Two-Stage Design of Formation Control for Underactuated Surface Vessels (Xiaofei Yang, Chunxiao Ge, Hui Ye, Shuyi Shao)....Pages 1001-1010
Research on 3D Space Target Following Method of Mobile Robot Based on Binocular Vision (Xitong Zhao, Lei Cheng, Rui Peng, Chan Li, Xiaoqi Nong, Huaiyu Wu et al.)....Pages 1011-1024
Control Allocation Reconstruction of Launch Vehicle Based on Neural Network (Zhu Li, Yaokun Zhang, Zhaowei Liang, Zhongtao Cheng, Lei Liu, Ye Yang)....Pages 1025-1033
An EEC Dual Channel Switching Algorithm Based on Engine Thrust Sensitivity (Xiuqi Wang, Jie Shen, Zhongzhi Hu)....Pages 1035-1045
A U-Model Sliding Mode Control Design for Discrete Nonlinear Systems (Jianhua Zhang, Yang Li, Xiaoyun Xu, Xinling Dou, Xueli Wu, Feng Zhu)....Pages 1047-1054
Adaptive Fast Finite-Time Consensus for Second-Order Multi-agent Systems (Jiabo Ren, Baofang Wang, Mingjie Cai)....Pages 1055-1067
Industrial Robot Control Systems: A Review (Li Xiao, Jin Gong, Jinbao Chen)....Pages 1069-1082
The Research on Aircraft Anti-skid Braking Switching Control with Road Online Identification Based on Fuzzy Algorithm (Jie Gao, Bing Gao)....Pages 1083-1093
Automatic Sleep Staging Based on XGBOOST Physiological Signals (Xiangfa Zhao, Panxiang Rong, Guobing Sun, Bin Zhang)....Pages 1095-1106
Research on Unmanned Aerial Vehicle Water Combined Quality Detection and Early-Warning System (Han Cao, Lei Cheng, Bei Wu, GuoQiang Gao)....Pages 1107-1117
An Improved Lidar Data Segmentation Algorithm Based on Euclidean Clustering (Zhengyang Sun, Ziyue Li, Yuchao Liu)....Pages 1119-1130
RLV Guidance and Control System Design for Terminal Area Energy Management Phase (Lingxia Mu, Xiang Yu, Youmin Zhang)....Pages 1131-1138
A Compound Attitude Control System for a High Coupling Reentry Vehicle (Jiaping Zhang, Xu Li, Qianwei He, Zihao Huang, Ye Yang, Lei Liu)....Pages 1139-1150
An Improved FCM Algorithm Based on the Firework Algorithm for Liquid Rocket Engine Fault Detection (Liang Zhaowei, Huang Zihao, Li Zhu, Zhang Jiaping, Lei Liu)....Pages 1151-1162
Two-Stage Least Squares Based Iterative Parameter Identification Method for Time-Delay Systems (Ya Gu, Huigang Xu, Yongxin Chou, Jicheng Liu, Peiyi Zhu)....Pages 1163-1170
Trajectory Tracking of Unmanned Ground Vehicle Based on Iterative Learning Model Predictive Control (Chaofang Hu, Lingxue Zhao, Na Wang)....Pages 1171-1180
Attack-Time Cooperative Guidance of Multi-missile System Based on Bessel Curve (Yiwen Liu, Xuejing Lan, Wenbiao Xu)....Pages 1181-1191
Flight Control Experimental Platform of Transport Aircraft Based on FlightGear/Matlab (Yue Wang, Shuguang Zhang, Pengqi Yin, Shiguang Guo)....Pages 1193-1204
A Dynamic Buffer Reservation Method Based on Markov Chain to Solve Deadlock Problem in Scheduling (Zhonghua Han, Yuehan Liu, Haibo Shi, Xutian Tian)....Pages 1205-1213
Robust Adaptive Position/Force Control for Flexible-Link with Flexible-Joint Manipulator (Baigeng Wang, Shurong Li, Zhe Liu)....Pages 1215-1227
Identification of Flowrates and Pressures in HVAC Distribution Network Based on Collective Intelligence System (Zhen Yu, Huai Li)....Pages 1229-1237
Neural Network Sliding Mode Control for Pneumatic Servo System Based on Particle Swarm Optimization (Gang Liu, Guihai Li, Haoyue Song, Zhengyang Peng)....Pages 1239-1248
Delay Efficient D2D Communications over 5G Edge-Computing Mobile Networks (Xiaohua Xu, Yuanfang Chen, Yanxiao Zhao, Shuibing He, Houbing Song)....Pages 1249-1260
Data Optimization for Spatial Data Mining and Classification in Marine Geochemical Exploration (Haihong Wang, Li Liu, Jingjing Wang, Yanming Gao)....Pages 1261-1270
Single Machine Due Date Assignment Scheduling with Deterioration and Learning Effect (Weiwei Liu, Chong Jiang)....Pages 1271-1279
EM Algorithm-Based Combined Distribution of Mold on the Mold Table (Fangjun Luan, Shuai Wang, Zhonghua Han, Hongbin Cui)....Pages 1281-1290
Multi-rotor UAV Track Planning Based on Improved Artificial Potential Field (Liying Yang, Kaiyuan Bi, Yuqing He, Zhonghua Han)....Pages 1291-1302
Tracking Control Design for a Class of Mobile Robot with a Single Trailer via Differential Flatness Approach (Chunxiao Wang, Huajun Fu, Zhongcai Zhang)....Pages 1303-1312
On Interconnected Observer Design for Nonlinear System (Mei Zhang, Ze-tao Li, Michel Cabassud, Boutaïeb Dahhou)....Pages 1313-1323
Development and Research of Grid Short-Circuit Capacity Tester (Wei Chen, Pu Deng, Zhenghang Hao, Zhuo Chen, Aiping Pang)....Pages 1325-1334
A 3-D Deployment and Coverage Algorithm for Aircraft Cargo (Rui Wang, Chengrui Bai, Lei Gao, Hui Sun)....Pages 1335-1343
Optimal Tilt Integral Derivative Controller with Filter Design for Quadrotor Based on Adaptive Particle Swarm Optimization (Yimin Zhou, Bo Han, Kranthi Kumar Deveerasetty, Junhai Cao)....Pages 1345-1357
Apron-Aware Network Congestion Control Strategy Based on Opportunistic Transmission (Weixing Chen, Meihan Meng, Jingfang Su)....Pages 1359-1369
Bearing Fault Diagnosis Based on Improved Denoising Auto-encoders (Weixing Chen, Chaochen Cui, Xiaojing Li)....Pages 1371-1381
Back Matter ....Pages 1383-1387

Citation preview

Lecture Notes in Electrical Engineering 582

Rui Wang Zengqiang Chen Weicun Zhang Quanmin Zhu   Editors

Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019)

Lecture Notes in Electrical Engineering Volume 582

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Lab, Karlsruhe Institute for Technology, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martin, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Lab, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Rui Wang Zengqiang Chen Weicun Zhang Quanmin Zhu •

•

•

Editors

Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019)

123

Editors Rui Wang College of Electronic Information and Automation Civil Aviation University of China Tianjin, China Weicun Zhang Department of Automation University of Science and Technology Beijing Beijing, China

Zengqiang Chen Department of Automation Nankai University Tianjin, China Quanmin Zhu Department of Engineering Design and Mathematics University of the West of England Bristol, UK

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-15-0473-0 ISBN 978-981-15-0474-7 (eBook) https://doi.org/10.1007/978-981-15-0474-7 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Contents

An Improved Image Registration Method for Infrared and Visible Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ningning Ding, Jingchang Zhuge, Shujian Xing and Yang Wang

1

Study on a Dual Mode Switching Technology of Multi-energy Ship Microgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weiqiang Liao, Jiangbo Lü, Rencheng Zhang and Xianyue Liu

11

Economic Dispatch of Wind Farm Cluster Integrated Power System Considering High Energy Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaoying Zhang, Shun Liao, Kun Wang, Xiaolan Wang and Wei Chen

23

Physical Layer Encryption Based on Hyper-Chen Chaos in Universal Filtered Multi-carriers System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yongtao Huang, Pengqi Yin, Jie Ma and Rui Wang

33

Verification Research on On-line Monitoring Method of Aircraft ARINC825 Bus Cable Fault Based on SSTDR . . . . . . . . . . . . . . . . . . . Xudong Shi, Xiangyang Xu, Yang Liu and Tao Jing

41

Research on Motion Control System of 6-DOF Robotic Arm . . . . . . . . Minglei Liu, Hongbo Zhou and Aiping Pang A Novel Capacitor Voltage Balancing Control Strategy for Modular Multilevel Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jian Li, Zhuo Chen, Aiping Pang, Qingfang Zhang, Zhanbao Wang, Jiawei Ma and Fei Liu Research on Face Recognition Technology Based on PCA and SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shu Zhang, Zi-Yue Li and Yu-Chao Liu

53

63

75

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Contents

A Study on PD-like Fuzzy Logic Control Based Active Noise Control for Narrowband Noise Cancellation with Acoustic Feedback and Distance Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tongrui Peng, Quanmin Zhu, Tokhi M. Osman and Yufeng Yao

87

Sliding-Mode Control of STENA DRILLMAX Drillship with Environmental Disturbances for Dynamic Positioning . . . . . . . . . C. S. Chin and C. S. Lio

99

Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qing Xiao and Shao-Wu Zhou

113

The Study of Air Supply Ways Effects on the Aircraft Cabin Thermal Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xudong Shi, Di Chao, Yu Zhang and Hongxu Zhao

123

Identification of the Wiener System Based on Instrumental Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shaoxue Jing and Tianhong Pan

133

Cervical Histopathology Image Clustering Using Graph Based Unsupervised Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chen Li, Zhijie Hu, Hao Chen, Dan Xue, Ning Xu, Yong Zhang, Xiaoyan Li, Qian Wang and He Ma Study on Analysis and Avoidance of Unstable Control for Flexible System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Q. Zhai, R. Y. K. Zhang, F. W. Meng, Z. Y. Liu, S. Liu and X. R. Yan Eigenvalue Sensitivity Analysis of Aircraft Power System . . . . . . . . . . Jianying Liu, Jin Cai, Jiawang Huang and Zhangang Yang Modeling and Simulation of Closed-Loop Control Circuit of Aircraft Fuel Metering Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xudong Shi, Shaoshuai Yuan, Yakun Wang and Xu Wang A Static Gesture Recognition Algorithm Based on DAG-SVMs . . . . . . Mengxin Li, Tongwei Jiang, Rui Xu and Baifeng Lin

141

153 165

173 185

Semiconductor Bonding Equipment Grouping Model Based on Processing Task Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhijun Gao, Wen Si, Zhonghua Han, Jiayu Peng and Hongzhi Zheng

195

Research on the Improved Dragonfly Algorithm-Based Flexible Flow-Shop Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhonghua Han, Jingyuan Zhang, Shuo Lin and Chunguang Liu

205

Contents

Modeling and Adaptive Control for Tower Crane Systems with Varying Cable Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Menghua Zhang, Yongfeng Zhang, Huimin Ouyang, Changhui Ma and Xingong Cheng

vii

215

EEG Recognition with Adaptive Noise Reduction Based on Convolutional LSTM Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hengxing Lv, Xuemei Ren and Yongfeng Lv

227

Peaking Reduction of CRM-Based Adaptive Control via a Modified Adaptive Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yafei Liu, Jun Yang, Jing Na, Guanbin Gao, Shubo Wang and Qiang Chen

239

Unbalance Suppression for Active Magnetic Bearing Rotor System Based on Disturbance Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhuangzhuang Yue, Huimin Ouyang, Guangming Zhang, Lei Mei and Xin Deng

249

Investigation of Pilot Flight Technology Based on Exploratory Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peipei Zeng, Zhonghua Li and Yan Chen

263

Study on Crack Propagation of Rivet Stiffened Plate Containing MSD Structure in Corrosive Environment . . . . . . . . . . . . . . . . . . . . . . Yuan Zhao and Jinfang Zhao

273

H∞ Phase Control for Flexible Systems . . . . . . . . . . . . . . . . . . . . . . . . Junfeng Yang, Muzhou Yu, Yanjie Niu, Wenjie Zhang and Fanwei Meng

281

Mixed Sensitivity Design of Magnetic Suspension System . . . . . . . . . . . Muzhou Yu, Junfeng Yang, Fanwei Meng and Yanjie Niu

297

Unmanned Autonomous Helicopter Integral Sliding Mode Control and Its Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haojia Zhang, Aijun Li and Yu Wang

305

UAVs Formation Control Based on Artificial Potential Functions with the Orientation Considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiawei Li, Wei Wang, Aijun Li and Bojian Liu

315

Automatic Image Annotation with Deep Model Trained by Dynamic Loss Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ze Si, Dongmei Fu, Yang Liu and Xinshi Liu

325

Fuzzy Neural Network PID Control of Quadrotor Unmanned Aerial Vehicle Based on PSO-GA Optimization . . . . . . . . . . . . . . . . . . . . . . . Xia Li, Shuaihua Zhang, Fang Zheng and Bingyuan Wang

335

viii

Contents

Risk Analysis of Information System Security Based on the Evidence Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jinhua LingHu, Ping Pan and Yaoyao Du

347

Fault Diagnosis of the Motor of Electro-Mechanical Transmission of the High Speed Rotorcraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yue Ma, Lu Lin and Fei Qi

359

Backstepping Sliding Mode Control for the Displacement Tracking of Permanent Magnet Linear Synchronous Motor Based on Nonlinear Disturbance Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hong-jiao Song, Le Liu, Man-jun Cai and Nuan Shao An Edge Extraction Method Based on Gray Lever-Gradient Two-Dimensional Maximum Entropy Threshold Method for Footprint Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mengxin Li, Wenlong Pei, Meiling Li and Rui Xu

373

383

Target Feature Extraction and Recognition of SAR Images Based on PCANet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pucheng Li, Junchen Li, Wen Yin and Lei Yang

393

Evaluation on Symbiotic Performance of Regional Technological Entrepreneurship Ecosystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chunxiao Sun, Chunyan Li and Jianhua Zhang

401

Fixed-Time Terminal Sliding Mode Control for Quadrotor Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jie Wang, Xiao Ma, Gaowei Zhang, Yan Zhang and Qing Miao

413

Nonlinear Observer Based Fault Diagnosis for an Innovative Intensified Heat-Exchanger/Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . Xue Han, Zetao Li, Boutaib Dahhou, Michel Cabassud and Menglin He

423

Research on Rudder Roll Stabilization Motion Control Based on Adaptive LQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yanwen Liu, Changsheng Zhou, Yinlin Liu and Guangqing Zhai

433

Study on Non-local Cubic Spline Function Based on Peridynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jincai Chang, Jiecheng Wang, Dan Jian, Zhuo Wang and Jianhua Zhang

443

Weakly Supervised Semantic Segmentation Based on Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binxiu Liang, Yan Liu, Linxi He and Jiangyun Li

455

Real-Time Human Body Detection Based on YOLOv2 Network . . . . . Xiaopeng Liu, Yan Liu, Hong Wang and Jiangyun Li

465

Contents

ix

Research on the Temperature Field and Thermal Roll Shape of Cold Rolling Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zichao Sun, Weicun Zhang and Yan Liu

475

Optimized Control System Design for Two-Wheeled Inverted Pendulums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haifei Si, Yizhi Wang, Xingliu Hu and Zhong Yang

485

A Retinal Vessel Segmentation Algorithm with Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leiming Liu, Jiahao Li, Weicun Zhang and Dongmei Fu

497

A Detection and Isolation of Faults Technique in Automotive Engines Using a Data-Driven and Model-Based Approach . . . . . . . . . . Yingmin Wang, Dong Cui and Feng Guo

503

Decomposition-Based Gradient Iterative Estimation for Input Nonlinear Model by Using the Kalman Filter . . . . . . . . . . . . . . . . . . . . Qiuling Fei, Junxia Ma, Weili Xiong and Jing Chen

521

Modeling of Asymmetric Cylinder Electro-hydraulic System Based on Backstepping Control Method . . . . . . . . . . . . . . . . . . . . . . . . Yun-fei Wang, Ji-yun Zhao, Hai-gang Ding and Jia-xiang Man

531

An AUV Adaptive Front-Tracking Algorithm Based on Data-Driven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiangyu Qu, Yiping Li and Gaofei Xu

541

Parameter Identification of MR Damper Model Based on Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yonggang Yang, Youchuang Ding and Shixing Zhu

555

State Observer-Based Prescribed Performance Control for MDF Continuous Hot Pressing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liangkuan Zhu, Yugang Zhou and Xinrui Chen

565

Optimization Approaches for Parameters of SVM . . . . . . . . . . . . . . . . Jinxiang Chen, Yilan Yin, Lu Han and Feng Zhao

575

The Staffing Optimization Problem for the M-Design Multi-Skill Call Center Based on Queuing Model . . . . . . . . . . . . . . . . . . . . . . . . . Chunyan Li, Chunxiao Sun and Jianhua Zhang

585

Adaptive Sliding Mode Trajectory Tracking Control of Quadrotor UAV with Unknown Control Direction . . . . . . . . . . . . . . . . . . . . . . . . Lijun Wang, Wencong Deng, Jinkun Liu and Rong Mei

597

An Aeroengine Adaptive Inverse Control Method Based on U-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiajie Chen, Zhongzhi Hu, Jiqiang Wang and Weicun Zhang

609

x

Contents

The Active Fault-Tolerant Control of Reconfigurable Manipulator Based on Iterative Fault Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wenfeng Ren and Yanli Du Prediction for Time Series with CNN and LSTM . . . . . . . . . . . . . . . . . Xuebo Jin, Xinghong Yu, Xiaoyi Wang, Yuting Bai, Tingli Su and Jianlei Kong

619 631

CO2 Pipeline Transportation System Optimization Design Based on Multiple Population Genetic Algorithm . . . . . . . . . . . . . . . . . Qunhong Tian, Aiqin Sun, Kan Shi and Fengde Wang

643

A Train Integrity Monitoring Method Based on GNSS Moving Baseline Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Jiang, Yongqiang Liu, Dan Liu, Baigen Cai and Jian Wang

653

Generalized Extended Stochastic Gradient Algorithm Implemented Parameter Identification for Complex Multivariable-Systems . . . . . . . . Wei Wang

663

Reinforcement Learning on Robot with Variational Auto-Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yiwen Chen, Chenguang Yang and Ying Feng

675

A Multi-Center PSO Algorithm with Memory Ability and Its Application to the Online Modelling of an Underwater Vehicle Thruster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaofei Xu, Guanqun Wang, Yiping Li, Xiaohui Wang and Xiangyu Qu Trajectory Tracking of Mobile Robots Based on Fuzzy Control and Extended State Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dan Su, Jian Huang and Daqian Yang Design of Wireless Body Area Network with Motion Sensors Using New Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guodong Wang, Yanxiao Zhao, Yichun Ding, Jack Yang and Zhengtao Zhu

685

697

707

The Depth Estimation Method Based on Double-Cues Fusion for Light Field Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinshi Liu, Dongmei Fu, Chunhong Wu and Ze Si

719

Fuzzy Gain Scheduler Based Path Tracking on Image Plane for XY/Z Partitioned IBVS System . . . . . . . . . . . . . . . . . . . . . . . . . . . Jie Zhong, Tao Wang and Lianglun Cheng

727

Valve Control System with Mechanical Feedback . . . . . . . . . . . . . . . . Hao Yan, Bowen Jiang and Zheqing Zuo

737

Contents

xi

The Algorithm for UAV Obstacle Avoidance and Route Planning Based on Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiantong Liu, Zhengjie Wang and Zhide Zhang

747

Cascade Improved Visual Detection and Distance Estimation in Formation of Micro Unmanned Aerial Vehicles . . . . . . . . . . . . . . . . Jiankun Sun, Yanxuan Wu, Xutan Lu and Yunduo Feng

755

Saturated Adaptive Backstepping Control for Uncertain Nonlinear Active Suspension Systems with Prescribed Performance . . . . . . . . . . . Gang Wang, Feng Liu and Zhenghao Sun

767

High Gain Finite-Time Trajectory Tracking Control of Pneumatic Muscle Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tong Shen and Jian Huang

777

Research on Reversing Radar Based on Linear Structured Light . . . . Xinliang Tang, Yang Li and Jianhua Zhang

789

Multi-objective Minimal Time Optimal Control Based Path Planning of Mobile Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siqi Tu, Shurong Li, Zhe Liu and Derui Zeng

801

Modeling and Simulation in Distributed Cooperative Simulation Platform of Aircraft Fuel System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhiyong Fan, Da Teng and Zhexu Liu

811

Adaptive Neural Network Dynamic Surface Control Algorithm for Pneumatic Servo System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gang Liu, Guihai Li, Zhengyang Peng and Huihui Pan

821

Data Aggregation Point Placement in Energy Harvesting Powered Smart Meter Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asif Hassan, Lina Pu, Yu Luo, Guodong Wang and Yanxiao Zhao

831

Bipartite Consensus Control for Coupled Harmonic Oscillators Using Sampled Data with Measurement Noise . . . . . . . . . . . . . . . . . . . Jun Liu, Hengyu Li and Jun Luo

843

Adaptive Sliding Model Controller Design of Carlike Robot Speed and Steering Angle Based on Characteristic Model . . . . . . . . . . . . . . . Zhen Xu, Mingchu Xu and Qingwei Chen

851

Inventory Control Strategy on High-Value Aviation Spares at Line Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shiwei Zhao, Guihang Liu and Peng Zhang

863

Experimental Modeling of Rotary Traveling-Wave Ultrasonic Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qingquan Liu, Xin Huo, Weijia Shi and Hui Zhao

875

xii

Contents

Time-Domain System Identification for Long-EZ Fixed-Wing Aircraft Based on Flight Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . Danyang Xu, Chi Yuan and Youmin Zhang

887

Fault Prediction of Fan Cooling System for Aircraft Weather Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liu Guihang and Zhao Shiwei

897

Research on Harmonic Current Functional Analysis of AC Arc Furnaces and Evaluation of Harmonic Level . . . . . . . . . . . Pu Deng, Shi Zeng, Yongzhong Li, Xiaojun Peng, Jing Nong, Zhuo Chen and Aiping Pang

907

Minimax Optimization for Capacitors Composited with Two Kinds of Series Reactance Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pu Deng, Tinghao Lei, Fengyuan Wang, Zhuo Chen and Aiping Pang

917

GRU-Based Estimation Method Without the Prior Knowledge of the Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xuebo Jin, Aiqiang Yang, Tingli Su and Jianlei Kong

927

Research on Optimization Method of LEACH Routing Protocol . . . . . Fan Chao, Zhiqin He, Xiumin Hu, Hongbo Zhou and Aiping Pang Stochastic Road Condition Identification for Electromagnetic Active Suspension Based on Support Vector Regression . . . . . . . . . . . . . . . . . Zepeng Gao, Sizhong Chen, Yuzhuang Zhao, Zhicheng Wu, Lin Yang, Jiang Hu, Yong Chen and Baoku Liu

937

947

Research on Noise Suppression and Edge Reading Algorithms in X-Ray Image Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiumin Hu, Zhiqin He, Fan Chao and Aiping Pang

959

Research on Water Monitoring Information Acquisition System of UAV Based on Wireless Sensor Network . . . . . . . . . . . . . . . . . . . . . Junjie Ge, Fan Chao, Zhiqin He and Wenye Shi

969

Recursive Estimation Method for Bilinear Systems by Using the Hierarchical Identification Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . Ling Xu, Xiao Zhang and Feng Ding

979

PSO Rapid Ascending Trajectory Planning Method Based on Neural Network Trajectory Surrogate Model . . . . . . . . . . . . Yuhang Zeng, Ye Yang, Yongji Wang and Lei Liu

989

Contents

xiii

A Two-Stage Design of Formation Control for Underactuated Surface Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001 Xiaofei Yang, Chunxiao Ge, Hui Ye and Shuyi Shao Research on 3D Space Target Following Method of Mobile Robot Based on Binocular Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011 Xitong Zhao, Lei Cheng, Rui Peng, Chan Li, Xiaoqi Nong, Huaiyu Wu, Ling Xiong and Yang Chen Control Allocation Reconstruction of Launch Vehicle Based on Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025 Zhu Li, Yaokun Zhang, Zhaowei Liang, Zhongtao Cheng, Lei Liu and Ye Yang An EEC Dual Channel Switching Algorithm Based on Engine Thrust Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035 Xiuqi Wang, Jie Shen and Zhongzhi Hu A U-Model Sliding Mode Control Design for Discrete Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047 Jianhua Zhang, Yang Li, Xiaoyun Xu, Xinling Dou, Xueli Wu and Feng Zhu Adaptive Fast Finite-Time Consensus for Second-Order Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055 Jiabo Ren, Baofang Wang and Mingjie Cai Industrial Robot Control Systems: A Review . . . . . . . . . . . . . . . . . . . . 1069 Li Xiao, Jin Gong and Jinbao Chen The Research on Aircraft Anti-skid Braking Switching Control with Road Online Identification Based on Fuzzy Algorithm . . . . . . . . . 1083 Jie Gao and Bing Gao Automatic Sleep Staging Based on XGBOOST Physiological Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095 Xiangfa Zhao, Panxiang Rong, Guobing Sun and Bin Zhang Research on Unmanned Aerial Vehicle Water Combined Quality Detection and Early-Warning System . . . . . . . . . . . . . . . . . . . . . . . . . . 1107 Han Cao, Lei Cheng, Bei Wu and GuoQiang Gao An Improved Lidar Data Segmentation Algorithm Based on Euclidean Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119 Zhengyang Sun, Ziyue Li and Yuchao Liu RLV Guidance and Control System Design for Terminal Area Energy Management Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131 Lingxia Mu, Xiang Yu and Youmin Zhang

xiv

Contents

A Compound Attitude Control System for a High Coupling Reentry Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139 Jiaping Zhang, Xu Li, Qianwei He, Zihao Huang, Ye Yang and Lei Liu An Improved FCM Algorithm Based on the Firework Algorithm for Liquid Rocket Engine Fault Detection . . . . . . . . . . . . . . . . . . . . . . 1151 Liang Zhaowei, Huang Zihao, Li Zhu, Zhang Jiaping and Lei Liu Two-Stage Least Squares Based Iterative Parameter Identification Method for Time-Delay Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1163 Ya Gu, Huigang Xu, Yongxin Chou, Jicheng Liu and Peiyi Zhu Trajectory Tracking of Unmanned Ground Vehicle Based on Iterative Learning Model Predictive Control . . . . . . . . . . . . . . . . . . . . 1171 Chaofang Hu, Lingxue Zhao and Na Wang Attack-Time Cooperative Guidance of Multi-missile System Based on Bessel Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181 Yiwen Liu, Xuejing Lan and Wenbiao Xu Flight Control Experimental Platform of Transport Aircraft Based on FlightGear/Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1193 Yue Wang, Shuguang Zhang, Pengqi Yin and Shiguang Guo A Dynamic Buffer Reservation Method Based on Markov Chain to Solve Deadlock Problem in Scheduling . . . . . . . . . . . . . . . . . . . . . . . 1205 Zhonghua Han, Yuehan Liu, Haibo Shi and Xutian Tian Robust Adaptive Position/Force Control for Flexible-Link with Flexible-Joint Manipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1215 Baigeng Wang, Shurong Li and Zhe Liu Identification of Flowrates and Pressures in HVAC Distribution Network Based on Collective Intelligence System . . . . . . . . . . . . . . . . . 1229 Zhen Yu and Huai Li Neural Network Sliding Mode Control for Pneumatic Servo System Based on Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . 1239 Gang Liu, Guihai Li, Haoyue Song and Zhengyang Peng Delay Efficient D2D Communications over 5G Edge-Computing Mobile Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249 Xiaohua Xu, Yuanfang Chen, Yanxiao Zhao, Shuibing He and Houbing Song Data Optimization for Spatial Data Mining and Classification in Marine Geochemical Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . 1261 Haihong Wang, Li Liu, Jingjing Wang and Yanming Gao

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Single Machine Due Date Assignment Scheduling with Deterioration and Learning Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1271 Weiwei Liu and Chong Jiang EM Algorithm-Based Combined Distribution of Mold on the Mold Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1281 Fangjun Luan, Shuai Wang, Zhonghua Han and Hongbin Cui Multi-rotor UAV Track Planning Based on Improved Artificial Potential Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1291 Liying Yang, Kaiyuan Bi, Yuqing He and Zhonghua Han Tracking Control Design for a Class of Mobile Robot with a Single Trailer via Differential Flatness Approach . . . . . . . . . . . 1303 Chunxiao Wang, Huajun Fu and Zhongcai Zhang On Interconnected Observer Design for Nonlinear System . . . . . . . . . . 1313 Mei Zhang, Ze-tao Li, Michel Cabassud and Boutaïeb Dahhou Development and Research of Grid Short-Circuit Capacity Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1325 Wei Chen, Pu Deng, Zhenghang Hao, Zhuo Chen and Aiping Pang A 3-D Deployment and Coverage Algorithm for Aircraft Cargo . . . . . 1335 Rui Wang, Chengrui Bai, Lei Gao and Hui Sun Optimal Tilt Integral Derivative Controller with Filter Design for Quadrotor Based on Adaptive Particle Swarm Optimization . . . . . 1345 Yimin Zhou, Bo Han, Kranthi Kumar Deveerasetty and Junhai Cao Apron-Aware Network Congestion Control Strategy Based on Opportunistic Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359 Weixing Chen, Meihan Meng and Jingfang Su Bearing Fault Diagnosis Based on Improved Denoising Auto-encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1371 Weixing Chen, Chaochen Cui and Xiaojing Li Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383

An Improved Image Registration Method for Infrared and Visible Images Ningning Ding, Jingchang Zhuge, Shujian Xing and Yang Wang

Abstract Aiming at solve the problem that it is difficult to match the infrared and visible image of aircraft surface in the same scene, an improved registration algorithm is proposed. It is aiming to obtain more complementary information of residual ice. Firstly, the infrared image enhanced by the image enhancement algorithm based on fuzzy logic, so that the details and the contour become more clear. It also effectively reduces the number of feature points to be extracted. Secondly, in order to solve the problem of high mismatch rate of speeded up robust features (SURF) algorithm, the constraint condition of slope consistency has been used to eliminate the number of mismatch points. Finally, the RANSAC algorithm is used to further improve the matching speed and accuracy. Experimental results show that the proposed method has better rapidity and accuracy. Keywords Image registration · Fuzzy logic · SURF algorithm · Slope consistency

1 Introduction Using image registration, the optimal image transformation relationship between different images can be find, and the spatial consistency of the matched image at the corresponding point can be achieved [1]. Residual ice detection for aircraft skin remains a vital task in the field of civil aviation. Infrared images can present the contour of the target, and the different radiation on the surface of the object will also highlight the residual ice information on the plane’s surface. But due to its own imaging principle, there are large noise, low resolution, and other weakness in the resulting image. These disadvantages are precisely remedied, relying on the characteristics of better spatial resolution, texture and edge characteristics of visible N. Ding (B) · J. Zhuge · S. Xing College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] Y. Wang Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_1

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Infrared image A

Fuzzy logic enhancement

Enhanced image C

SURF description

Feature point matching Visible image B

Fine registration

SURF description

Fig. 1 Registration process

images [2]. Through the improvement of the registration algorithm of infrared and visible images, the sharpness and reliability of the fusion images are improved [3]. In this case, the image enhancement algorithm based on fuzzy logic is used to preprocess the infrared image firstly, and the contour details and sharpness of the image are enhanced. The SURF algorithm will produce a lot of mismatch points [4] but it is more simple and fast to eliminate the mismatch point by detecting the slope [5]. The process is shown in Fig. 1.

2 The Related Principles 2.1 Fuzzy Enhancement Algorithm On the basis of gray scale transformation method, it applies fuzzy control logic to image enhancement. After the image is blurred, fuzzy enhancement is carried out through the formulation of fuzzy rules. Finally, anti-fuzzy processing is carried out to obtain the enhancement images. After it processed, the contrast of infrared image is improved, and the infrared target is more clear and obvious, which is easier for the subsequent image registration.

2.2 Fuzzy Logic Enhancement Processing The process of fuzzy enhancement is shown in Fig. 2. After detecting a large number of experiments on scene images, the results show that the fuzzy enhancement method can make the edge contour of the image clearer. The biggest advantage of fuzzy logic is that it does not require the training steps of supervised pattern recognition technology, nor does it have the unsupervised machine learning algorithm used in the process of multi-objective parameter optimization, which is simple and convenient [6].

An Improved Image Registration Method for Infrared …

Fuzzy input

Perform any required fuzzy logic operations

Using an Inference method

3

Application of aggregation method to fuzzy sets

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Fig. 2 Fuzzy logic enhancement process

2.3 SURF Algorithm The SURF algorithm is a kind of local feature description algorithm with good efficiency and high robustness, which not only has strong adaptability to image rotation and scaling, but also maintain a certain degree of stability in the case of illumination change, angle of view change, affine transformation and noise in the image environment [7]. The process of SURF algorithm processing is shown in Fig. 3.

2.3.1

Feature Point Detection

The matching image has different spatial scales [8], and the image pyramid can solve the original image in different scale space to meet the matching requirements. In the classical SIFT algorithm, the pyramid model of the image is first established, then the potential feature points are found by difference of Gaussian filtering on each layer at the bottom of the pyramid, but the establishment of each layer have to wait until the previous layer is constructed, which reduce the speed [9]. The SURF algorithm uses the Hessian matrix determinant approximation image, and each pixel point can solve a Hessian matrix as follows:   L x x(x, σ ) L x y(x, σ ) H (x, σ ) = (1) L x y(x, σ ) L yy(x, σ ) Lxx, Lxy, Lyy is the convolution of the input image and the second derivative of Gaussian filter function g(σ ). In the process of solving the Hessian matrix, the discrete image is realized by the convolution of the template. It uses the box filter approximation instead of the Erigos filter, and the integral image is used to accelerate the convolution to improve the calculation speed. In order to balance the error, the

Scale space Feature Point Detection

Positioning feature points

Fig. 3 SURF algorithm processing process

Determine the orientation of the feature point

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Dxy is given a weighted average coefficient, the general assignment is 0.9, and the determinant expression of H is as follows: det(H ) = Dx x Dyy − (0.9Dx y)2

(2)

By constructing the multi-scale image pyramid, in each order, the 4-layer scale image is selected, and the extremum is obtained by using the Hessian matrix, compared with the other 26 points in the upper and lower scale space, the feature point can be used only under the condition that the extreme value is obtained at this point.

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Determining the Direction of the Feature Points

In order for these feature points have rotational invariance, the main direction of each feature point must be determined. First, selecting the circular region with the feature point as the center, 6 s (s as the scale of the feature point) as the radius, and count the Haar wavelet response of all points in the x and y direction. After that, a fan sliding window with an angle of 60° is used to rotate the area continuously at a step of 12°, and the response value dx and dy of the Harr wavelet transform in the fan region are accumulated. Eventually, the vector (m w , θw ) can be obtained. mw =



dx +

w

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Centered on the feature point, the axis is rotated to the main direction. The rectangular region with the edge length of 20 s (s as the scale of the feature point) is selected according to the main direction, the window area is divided into 16 sub-regions, the Haar wavelet features of pixels in each region are counted, and the response value of each pixel point is multiplied by the weight coefficient, in order to increase the to the set transformation, thus forming a 4-dimensional vector. v =

 robustness d x |d x| dy |dy| . Therefore, for each feature point, a 64-d description Vector is formed.

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2.4 Improvement of Matching Algorithm In the process of matching feature points of SURF algorithm, the minimum value obtained is used as the best match of feature points. Only the European distance between the sub-vectors of each feature is referenced. In this way, when the matching points of similar shapes are encountered, a large number of mismatches are generated. The feature points are matched by the prior knowledge of the slope consistency between the correct matching points. In this paper, the constraint conditions of slope range are used to conduct secondary screening to eliminate the mismatched points.

2.4.1

Slope Range Filter Again

On the basis of European distance measurement, the slope of two feature points wiring is used as the constraint condition, and the mismatch points are removed by setting the range of slope. Firstly, the slope of the feature point connection is calculated, and the range of slope should be obtained by trial in range F[−0.57, 0.57], and the mismatch points should be eliminated by comparing the slope value of match points.

3 The Experimental Results and Evaluation 3.1 Registration Experimental Results In order to verify the effectiveness and accuracy of the algorithm proposed in this paper, infrared and visible images of the aircraft skin have been carried out registration experiments. In the following experiments, considering the image resolution and computational complexity, the infrared image is enhanced with fuzzy logic firstly, the normal image as shown in Fig. 4, and the enhanced image as shown in Fig. 5. Fig. 4 Original infrared image

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Fig. 5 Enhanced infrared image

Fig. 6 Original match results

Subsequently, the feature points of two images are detected, the position and direction are calibrated. After constructing the feature point descriptor, the original matching results are obtained by matching the feature points, as shown in Fig. 6. There are plenty of mismatch points, which not only affects the matching accuracy, but also increases the complexity of the calculation. Besides, it also reduces the running speed of the algorithm. By limiting the slope range of the matching point, the mismatch points are eliminated, second matching results are obtained as shown in Fig. 7. After removing the mismatch points, the RANSAC algorithm is used, and the best match is finally obtained as shown in Fig. 8.

3.2 Evaluation of Registration Results The experimental results demonstrate that the contrast and sharpness of the infrared image are improved and the contour is more accomplish after fuzzy logically strengthened. In order to measure the validity of the algorithm objectively, this paper makes

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Fig. 7 Second matching results

Fig. 8 Final match results

an objective evaluation of the registration image by using the following objective indexes: the number of feature points, the matching accuracy rate and the algorithm time consuming. As can be seen from Table 1, compared with the original algorithm, the improved algorithm improves the accuracy of algorithm matching and reduces the algorithm Table 1 Algorithm experimental results Number of feature points

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time by about 0.2 s. It reveals that this algorithm has a good effect in the registration process of infrared and visible image, and it has strong adaptability to the feature point extraction of the heterologous image. The improved registration algorithm proposed in this paper achieves better registration of infrared image and visible image.

4 Conclusion According to the characteristics of visible image and infrared image, an improved infrared and visible image registration algorithm is proposed. The fuzzy logic enhancement of infrared image is carried out firstly, which highlights its contrast and detail information well. Therefore, it is beneficial to extract feature points, and greatly reduces the difficulty of image registration. Controlling the slope of the mismatch points, the false matching points are eliminated, which enhances the running speed of the algorithm. It also increases the possibility of application in practical engineering and improves the precision of residual ice detection. Admittedly, the algorithm studied is only applicable to the research in the context of the residual ice detection of aircraft skin in this paper. There are still many problems in the image registration system, and a good registration effect can facilitate image fusion, which is also a problem worthy of further study. Acknowledgements This work was supported in part by the Open Fund of Tianjin Key Lab for Advanced Signal Processing under Grant 2017 ASP-TJ02, the National Natural Science Foundation of China under Grant 61405246, and CAUC Fund under Grant 3122017005.

References 1. Zhang, Z., Blum, R.S.: A hybrid image registration technique for camera image fusion application. J. Inf. Fus. 2(2), 135–149 (2001) 2. Li, H., Liu, L., Huang, W., Yue, C.: An improved fusion algorithm for infrared and visible images based on multi-scale transform. J. Infrared Phys. Technol. 74, 28–37 (2016) 3. Liu, S., Piao, Y., Tahir, M.: Research on fusion technology based on low-light visible image and infrared image. J. Opt. Eng. 55(12), 123104 (2016) 4. Bay, H., Ess, A., Tuytelaars, T., Gool, L.V.: SURF: speed up robust features. J. Comput. Vis. Image Underst. 110(3), 346–359 (2008) 5. Xu, J.-x., Lu, Q.-w., Yun-peng, M.A., Qian, R.: Registration method between infrared and visible images of electrical equipment based on slope consistency. J. Optoelectron. Laser 28(07), 794–802 (2017) 6. Rahman, M.A., Liu, S., Wong, C.Y., et al.: Multi-focal image fusion using degree of focus and fuzzy logic. J. Dig. Sig. Process. 1(185), 1–19 (2016) 7. Hu, M. ,Chen, J., Shi, C.: Three-dimensional mapping based on SIFT and RANSAC for mobile robot. In: 2015 IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), pp. 139–144. Shenyang Institute of Automation, Shenyang 2015

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8. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. J. Int. J. Comput. Vis. 60(2), 91–110 (2004) 9. Lowe, D.G.: Object recognition from local scale-invariant features. In: Proceedings of International Conference on Computer Vision, pp. 1150–1157 (1999)

Study on a Dual Mode Switching Technology of Multi-energy Ship Microgrid Weiqiang Liao, Jiangbo Lü, Rencheng Zhang and Xianyue Liu

Abstract In this paper, a multi-energy ship microgrid system is taken as an object, and a dual-mode switching technology is proposed to solve the problem of reliable switching under different power supply modes. First, the requirements and principles of smooth switching of marine microgrid are clarified; Secondly, the control strategies of different operation modes are designed, and the performance of voltage and current loop is improved; Finally, the simulation model is established, and the simulation results of different operation modes are verified. The simulation results show that the designed switching technology can meet the dynamic performance of the ship microgrid. Keywords Ship microgrid · Inverter · Dual mode · Switching technology

1 Introduction In view of the complexity of marine operation, considering energy saving and emission reduction, multi-energy ship microgrid needs to switch between different power supply states [1–4]. At the same time, a large number of power electronics technologies are used in the multi-energy ship microgrid, the most important of which is the inverter [5]. These advanced power electronics technologies are the key to the conversion, transmission, storage and power supply state transformation of the whole multi-energy ship microgrid [6]. Among them, the smooth switching of the inverters play a vital role in the safe and reliable operation of the ships under various power supply conditions, such as the combined supply by diesel generator and new energy power generation system or independent supply by new energy generation system. Therefore, according to the characteristics of ships, this paper studied a kind of dual mode switching technology suitable of multi-energy ship microgrid. W. Liao · R. Zhang Key Laboratory of Process Monitoring and System Optimization for Mechanical and Electrical Equipment (Huaqiao University), Fujian Province University, Xiamen 361021, China W. Liao · J. Lü (B) · X. Liu School of Marine Engineering, Jimei University, Xiamen 361021, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_2

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2 Principle and Design of Dual Mode Switching Technology According to the structure and characteristics of multi-energy ship microgrid, there are two modes: grid-connected operation and independent operation [7]. This involves the switching between different operation modes, and its switching control logic block diagram is shown in Fig. 1. When the power of the inverters can not meet the load requirement, the diesel generator runs normally, and the dual-mode inverters in the micro-grid work in the grid-connected state, the optional switch is to switch to the grid-connected controller, and the grid-connected switch is closed at the same time. When the power of the inverters can meet the load demand or the diesel generator breaks down, the optional switch and grid-connected switch can be switched to the opposite direction immediately, and the diesel generator can be cut off from the micro-power generation system to supply the load separately, so as to ensure the stable operation of the ship, and at the same time, the energy can be used more reasonably [8].

2.1 Control Strategies for the Two Different Operation Modes When the marine micro-grid operates in the independent mode, the voltage and frequency stability of the grid is supported by the inverter power supply. The inverters are controlled by constant voltage and constant frequency, i.e. V/F control. The output voltage and frequency of the inverters are maintained within a certain range. According to the V/F control principle, voltage loop and current loop control are adopted respectively, and the control schematic diagram is shown in Fig. 2 [9]. When the ship is running in grid-connected mode, the inverters adopt constant power control, i.e. P/Q control, which means to maintain the constant output power according to the given power output of the system. Its principle is to adopt single current loop control. Under this mode, the voltage and frequency of the system power grid are supported by diesel generators. Its control schematic diagram is shown in Fig. 3 [10].

Fig. 1 Switching control logic block diagram

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K i p s + K ii s

(1)

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iLdq ∗

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1 Ts + 1

Fig. 4 Control block diagram of current loop

1 |Hi ( j2π · 1000)|

Kpwm Ts + 15.0

(2)

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(3)

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K i p = 0.02

(4)

K ii = 0.163

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+

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+1

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According to the above, the Bode diagram of the open-loop transfer function before compensation, the compensation network and the open-loop transfer function after compensation can be drawn as shown in Fig. 5. Figure 5 shows that before adding PI controller compensation network, the lowband gain of open-loop transfer function of current loop is 92.13 dB, and the phase margin is only 8°. By introducing compensation controller, the amplitude-frequency characteristic curve of open-loop transfer function of current loop crosses zero decibel line at a slope of −20 dB/dec, and the crossing frequency is 1000 Hz. The phase margin is 48.6°. The voltage loop control block diagram is shown in Fig. 6. The

Study on a Dual Mode Switching Technology … uodq∗ Kvp +

K vi s

1 Ts + 1

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uodq

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Fig. 6 Control block diagram of voltage loop

compensation transfer function of the voltage loop PI controller is: Hv (s) =

K v p s + K vi s

(6)

The bandwidth of the open-loop transfer function of the compensated voltage loop is 1/5 of that of the current loop. That is to say, the frequency of the voltage loop should be set at 200 Hz. It can be obtained as the Eq. (7): |G v0 ( j2π · 200)| =

1 |Hi ( j2π · 200)|

(7)

The zero frequency corresponding to the compensation network should be less than the crossover frequency. In this paper, 100 Hz is selected with the Eq. (8) [12]: Kv p 1 = K vi 2π · 100

(8)

Combination Eqs. (7) and (8) can obtain the voltage loop PI controller parameters as the Eq. (9): 

K v p = 0.046 K vi = 14.612

(9)

According to the above, Bode diagram of open-loop transfer function, compensation transfer function and open-loop transfer function after compensation can be drawn as shown in Fig. 7. Figure 7 shows that the open-loop transfer function crossing frequency of the system before compensation is 1150 Hz. When PI controller is added to compensate, the low-frequency gain increases. The slope of the voltage loop amplitude-frequency characteristic curve passes through the zero decibel line at 200 Hz, and the phase margin is 45°. This makes the compensated open-loop transfer function have good stability and dynamic performance.

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Phase (deg)

Magnitude (dB)

Bode Diagram 100 50 0 -50 -100 -150 0 -45 -90 -135 -180 -225 -270 100

101

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Fig. 7 Bode diagram before and after compensation for voltage loop

3 Simulation and Verification of Dual Mode Switching 3.1 Simulation Model Building of Dual Mode Switching Technology According to the above, the simulation model of dual-mode switching technology is built by using MATLAB/Simulink. The diesel generator system and the inverter are connected in parallel. The overall structure simulation model is shown in Figs. 8 and 9.

Fig. 8 Overall structure of dual mode switching simulation

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Fig. 9 Optional switch module

3.2 Simulation Results of Dual Mode Switching Technology According to the operation mode of multi-energy ship microgrid, it can be divided into four modes: grid-connected operation mode, independent operation mode, gridconnected switching to independent operation and independent operation switching to grid-connected operation. The simulation time is set to 1 s: (a) grid-connected operation mode The diesel generator runs in parallel with the inverters. The load 1 is 50 kw, the load 2 is 10 kw and the load 3 is 20 kw. The given power of the inverters is set as Pref = 50 kw and Qref = 0; During the period of 0–0.4 s, put into load 1 and load 3, the load 2 is put into at the 0.4 s, and the load 3 is cut off when the steady operation at 0.7 s. The voltage, current and frequency of the system and the output power of each power supply are shown in Fig. 10. From Fig. 10, it can be seen that the voltage and frequency of the diesel generator supporting the power grid, the output voltage and current wave forms of the power grid track the load changes steadily; during the load switching process, the fluctuation range of voltage and frequency is only about 0.05 Hz, and the change of frequency is very small; and the total output power of the marine microgrid tracks the load changes steadily. At this time, the inverters are controlled by P/Q, so the output power of the inverters follows the given power Pref = 50 kW steadily, and the insufficient power is supplemented by diesel generators. (b) Independent operation mode The inverters operate independently. The given voltage and frequency of the inverters are set as Uref = 311 V and Fref = 50 Hz; During the period of 0–0.4 s, put into load 1 and load 3, the load 2 is put into at the 0.4 s, and the load 3 is cut off when the steady operation at 0.7 s. The voltage, current and frequency of the system and the output power of each power supply are shown in Fig. 11. As shown in the figure, at this time, because the diesel generator is cut off, the inverters are controlled by V/F. The voltage amplitude and frequency of the power grid are stable to track the given

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Fig. 11 Bode diagram in independent mode

values Uref = 311 V and Fref = 50 Hz, which ensures the stability of the power grid voltage; and the output voltage and current are stable to track the load changes. (c) grid-connected switching to independent operation Combining the above two operation modes, the simulation analysis of grid-connected switching to independent operation mode is carried out. At 0 s system is started, input load 1 and load 2; During the period of 0–0.2 s system adopts grid-connected operation mode, At 0.2 s the optional switch is switching, and the system is converted to independent operation mode. The voltage, current and frequency of the system and the output power of each power supply are shown in Fig. 12. From Fig. 12, can be see that the switch mode is switched at 0.2 s and the operation mode of the

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400 200

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(b) frequency and output power of each power

Fig. 12 Switching from grid-connected to independent mode’s bode diagram

system is changed. At 0.2 s, the system’s voltage and current oscillate, three-phase unbalance occurs, and the voltage and current restore stability in one cycle or so; during the switching process, the frequency of the power grid drops by about 0.3 Hz, and the stability restores in one cycle or so; Before switching, the inverter track the given power of 50 kw, the diesel generator outputs 10 kw; and at 0.2 s, the output power of the inverters is suddenly reduced by around 10 kw. However, the output power gradually increased to 60 kW in one cycle. At 0.2 s, the output power of diesel generator gradually decreased to 0 kW due to the cut-off. (d) independent operation switching to grid-connected Mode switching is performed in 0.7 s. The output voltage, current, frequency and output power of the system are shown in Fig. 13. According to Fig. 13, the switch is selected for switching at 0.7 s, and the system is converted from independent mode to grid-connected mode. The output voltage and current of the system are distorted due to the change of the support power supply and recovery after 0.07 s; After switching, the control strategy of the inverter converted from V/F to P/Q, the inverter output according to the set power, and reaches the set value after 0.05 s. The diesel generator follow the load change of the system and output power 10 kW. According to the above simulation results, it can be seen that the dual-mode switching technology can operate stably in grid-connected mode and independent mode, ensuring the stability of system’s voltage, current and frequency. In the process of switching between gridconnected and off-grid, the frequency and voltage of grid are distorted to a certain extent, but they can meet the standard requirements of ship power grid. In the process of switching, inverter can choose different control strategies according to different operation modes.

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(b) frequency and output power of each power

Fig. 13 Switching from independent mode to grid-connected’s bode diagram

4 Conclusion According to the operation characteristics of ships, this paper proposes a dual mode switch technology for micro-grid, which enables the ship power grid to operate in the grid-connected and off-grid state according to the actual operation conditions, so as to achieve the purpose of energy saving and emission reduction. According to the simulation results, the performance indicators of the proposed switching technology can meet the requirements of the ship power grid in four operation modes. During the switching process, the performance indicators of the power grid will fluctuate and need to be further improved. Acknowledgements The authors acknowledge the support provided the Fujian Province Natural Science Foundation of China (No. 2017J01703), the National Natural Science Foundation of China (No. 51679106), the Fujian Industry-University Cooperation Science & Technology Major Project (No. 2016H6014) and the fundamental research funds for the central universities of China (No. JB-JC1008).

References 1. Bartelt, R., Oettmeier, M., Heising, C., et al.: Scenario-based stability-assessment of converterfed DC-ship grids loaded with pulsed power. In: Proceedings of the Electric Ship Technologies Symposium (ESTS), 2011 IEEE, F10–F13 Apr. 2011 2. Jusoh, A., Baamodi, H., Mekhilef, S.: Active damping network in DC distributed power system driven by photovoltaic system. Sol. Energy 87, 254–267 (2013) 3. Zahedi, B., Norum, L.E.: Modeling and simulation of hybrid electric ships with DC distribution systems. In: 2013 15th European Conference on Proceedings of the Power Electronics and Applications (EPE), F2–F6 Sept. 2013

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4. Zahedi, B., Norum, L.E.: Efficiency analysis of shipboard dc power systems. In: IECON 201339th Annual Conference of the IEEE Proceedings of the Industrial Electronics Society, F10–F13 Nov. 2013 5. Majumder, R., Chaudhuri, B., Ghosh, A., et al.: Improvement of stability and load sharing in an autonomous microgrid using supplementary droop control loop. IEEE Trans. Power Syst. 25(2), 796–808 (2010) 6. Wenwei, Zhan: Analysis of application of solar photovoltaic system to ships. Mar. Electr. 01, 16–20 (2015) 7. Quanhu, Yu.: Summarization of research and development on solar powered ships. Mar. Electr. 38(2), 30–34 (2018) 8. Zhou, L., Xing, J.A.: Smooth control mode switching strategy of inverters based on fuzzy control. In: Chinese Control and Decision Conference, pp. 6198–6202. IEEE 9. Zhuo, C.: The constant voltage constant frequency control strategy for three-phase SPWM inverter. Electr. Eng. 12, 24–26 (2010) 10. Aixia, W.: Design of micro-source inverter control system in grid-connected mode based on constant power control. Power Syst. Clean Energy 03, 48–53 (2014) 11. Kan, J., Xiao, H., Guo, L., Xie, S.: Study of control strategy for grid-connected inverters based on dropped PLL. Proc. CSEE 18, 21–26 (2011) 12. Ci, T.: Four design methods for proportional-integral controller of grid-connected inverter with LCL output filter. Power Syst. Technol. 11, 3268–3275 (2013)

Economic Dispatch of Wind Farm Cluster Integrated Power System Considering High Energy Load Xiaoying Zhang, Shun Liao, Kun Wang, Xiaolan Wang and Wei Chen

Abstract It is difficult to realize the economic dispatch for the large-scale wind power integration system. This paper thus presents a more comprehensive economic dispatch scheme, which considers the high energy load as a schedulable resource. The coordinated dispatch is achieved with the high energy load and wind farm cluster through the coordination layer. The multiple target mathematical models of the economic dispatch are established for the wind integrated power system. In this method, the income of the colony coordination layer maximization and the cost of control center minimization are assumed as the objective functions on the condition of output restriction, with power system security and output power of wind farm. The multi-objective cuckoo algorithm is used to perform the optimal solution. Finally, the mathematical models and the optimization algorithm are simulated respectively. The results verify the correctness of the proposed dispatch scheme and the effectiveness of the algorithm. Keywords High energy load · Wind power integration · Economic dispatch scheme · Multi-objective cuckoo algorithm

1 Introduction With the rapid development of wind generation, there are many issues occurred in the conventional power system because of the un-adapted demand for large-scale wind power transmission. In order to reduce the fluctuation of wind output power under the existing dispatch scheme, the conventional units generally provide enough X. Zhang (B) · X. Wang · W. Chen College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, China e-mail: [email protected] S. Liao Liangshan Power Supply Corporation, State Grid Sichuan Electric Power Company, Chengdu, China K. Wang Electric Science Institute, State Grid Gansu Provincial Power Company, Lanzhou, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_3

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backup service to the old pattern, however it can increase the cost of the units and is even hard to achieve the economic efficiency. Literature [1] studied the incorporation scene between the battery energy storage systems and the wind farms, in order to achieve economic dispatch for the wind power generators. In this scene, the multi-energy generation from the angle of differences according to the mismatches between the actual and allocated wind and photovoltaic power and pumped storage is considered in [2, 3]. Literature [4] proposed a model with the constraints to regulating characteristics of units, aiming to minimize the total cost of generation and reserve capacity of all units. Literature [5] proposed a security-constrained bi-level economic dispatch model for the integrated electro-gas hybrid systems considering the wind power and power-to-gas process. Obviously, the traditional idea coming from the above literatures holds that the switching is the primary form of load operation and load is not involved in normal regulation of power system. With the further development of power demand side management, the adjustable ability of the load has attracted more and more attention. The changing characteristic of loads is considered as an effective tuning point to solve the problem of wind power consumption. Literature [6] adopted energy management system to shave the peak load and reduce the users’ electricity tariff. For the economic dispatch of the largescale wind power grid-connected system, the schedule of the high energy load with the adjustable and interruptible characteristics is widely concerned. Literature [7] studied the model of the high energy load, the former took account into the modeling in long-term and short-term time scale, and the latter established the load model with the high energy load involved in the wind dispatching based on the characteristics of the high energy load. From the above literatures, it is obvious that there is no study taking into consideration of establishing a new dispatching pattern that incorporated the high energy load. Therefore, in order to overcome the deficiencies of those studies, this paper proposes a new scheduling mode for the economic dispatching of wind farm grid-connected system incorporating the high energy load. In the proposed scheduling mode, the high energy load is incorporated into the wind farm grid-connected system as a kind of scheduling resources, and the coordination layer is set up to coordinate the high energy load and the wind farm. Finally, a bi-level optimal model is proposed to coordinate the dispatch cost and the cluster coordination layer.

2 Dispatch Scheme for Wind Farm Integrated Power System with High Energy Load The cluster coordination layer is set up to coordinate the high energy load and the wind farm, the economic dispatch mode of the wind farm grid-connected system with high energy load is shown in Fig. 1. In this scheduling mode, the dispatching center is no longer faced with a single wind farm and the high energy load, but only for the cluster coordination layer,

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conventional generators

scheduling center

cluster coordination layer 1

Wind farm 1

Wind farm 2

Wind farm N1

high energy load1

cluster coordination layer J

high energy Load M1

Wind farm 1

Wind farm 2

Wind farm NJ

high energy Load 1

high energy Load MJ

Fig. 1 Economic dispatching mode of wind farm cluster integrated system with high energy load

which greatly reduces the scheduling target for the dispatch center, thus improving the scheduling efficiency. The cluster coordination layer is based on the wind power cluster system, in which the high energy load in the layer can be zero i.e. the layer contains only wind farms. In this layer, the high energy load can be considered as the most appropriate selection for taking in the output power of wind farm. When the characteristics of the high energy load is combined with cluster coordination layer, the whole layer can be regarded as a storage battery. In other words, while the power grid purchases power from the coordination layer, it is equivalent to the discharge of the battery. When the coordination layer purchases power from the power grid, it is equivalent to battery charging.

3 Mathematical Models of the Economic Dispatching 3.1 The Upper Level Optimization Model The aim of the economic dispatching for the dispatch center is to maximize the total benefit of the electricity dispatching system. The objective function is formulated as: min F = FG + FXg FG =

NG T  

(1)

UGi,t [αi (PGi,t )2 + βi PGi,t + γi ]

t=1 i=1

+ UGi,t (1 − UGi,t−1 )[ψ0i + ψ1i (1 − eτ/ τi )]

(2)

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FXg =

T  J 

λ j,t PXG j,t

(3)

t=1 j=1

where: FG is the generation cost of the conventional units, including the operating cost and start-up/shut-down cost. FXg is the total cost of the cluster coordination layer. J is the amount of the cluster coordination layer. T is the dispatch cycle. αi , βi and γi are the operating cost parameters of the conventional units. UGi,t is the start-up/shutdown state of the conventional units, UGi,t = 1 represents starting up, UGi,t = 0 means shut-down. ψoi , ψ1i and τi are the parameters of the start-up/shut-down cost. τ is the downtime of conventional units. NG is the number of the conventional units. PGi,t is the active power output of the conventional units i during interval t. PXG j,t is the active power output of the cluster coordination layer during interval t, PXG j,t > 0 implies that the cluster coordination layer sell power to the grid, and vice versa; λ j,t is the price of purchase electricity between the cluster coordination layer and the power grid. Constraints of the upper level are shown as follows: (1) Power balance constraint NG  i=1

UGi,t PGi,t +

K 

PX G j,t = PL ,t

(4)

j=1

where PL ,t indicates the normal load of dispatching system during interval t. (2) Generation limit constraint of the cluster coordination layer The scope of dispatching output could be represented as: PX G j,t min ≤ PX G j,t ≤ PX G j,t max

(5)

where, PX G j,t max and PX G j,t min are the upper and lower limit constraints of output forecast of the cluster coordination layer j during interval t, respectively. PX G j,t max = PX G j,t f −

Mj 

PX G jm,t min

(6)

PX G jm,t max

(7)

m=1

PX G j,t min = PX G j,t f −

Mj  m=1

where PX G j,t f is the output forecast of all wind farms of the cluster coordination layer j during interval t, PX G jm,t max and PX G jm,t min are the maximum and minimum electricity use of the high energy load m of the cluster coordination layer j during interval t.

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(3) The output constraint of the conventional generators PGi min ≤ PGi ≤ PGi max

(8)

where PGi max and PGi min are the maximum and minimum output power which can be generated by the conventional generators respectively. (4) The reserve capacity constraint of the system ⎧N G ⎪ ⎪ ⎨ UGi,t (PGi,t − PGi,t min ) ≥ RG,tdown + RXG,tdown i=1

NG  ⎪ ⎪ ⎩ UGi,t (PGi,t max − PGi,t ) ≥ RG,tup + RXG,tup

(9)

i=1

where RG,tup and RG,tdown are the plus-minus spinning reserve capacity for the forecasting error of load during interval t; RXG,tup and RXG,tdown are the positive and negative spinning reserve respond for the forecasting error of the cluster coordination layer during interval t. (5) The ramp rate constraint of the conventional generators 

UGi,t PGi,t − UGi,t−1 PGi,t−1 ≤ PGi,up UGi,t−1 PGi,t−1 − UGi,t PGi,t ≤ PGi,down

(10)

where PGi,up and PGi,down are the maximum up and down ramp rate limits of the ith conventional generator in the unit time, respectively.

3.2 The Lower Level Optimization Model In the process of quadratic optimization, the objective function is described as: maxCXG j =

T  t=1

(λ j,t PXG j,t + r j,t PXG j0,t )−

M j Nm  

ν j,t S jmk,t P jmk

(11)

m=1 k=1

where: PXG j0,t is the electricity consumption of the high energy load from the j cluster coordination layer during interval t. r j,t is the price of electricity which is sold to the high energy load by the cluster coordination layer j during interval t. ν j,t is the sum of the compensation for the decrease of electricity consumption and the cost of purchase electricity from the cluster coordination layer of the high energy load company during interval t. S jmk,t = 1 shows the high energy load cutting off, S jmk,t = 0 shows the high energy load putting into. Constraints of the lower level are shown as follows:

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(1) The power balance constraint of the cluster coordination layer j PXG j,t + PXG j0,t = PXG j f,t +

M j Nm  

(1 − S jmk,t )P jmk

(12)

m=1 k=1

where PXG j f,t is the active power output of wind farm of the cluster coordination layer j during interval t. (2) The output constraint of wind farm PXG j f,t ≤ PXG j,t f

(13)

(3) The times constraint of switching 0≤

T  S jmk,t − S jmk,t−1 ≤W jmk

(14)

t=1

(4) The up/down time constraint of the conventional units 

Ton j,m t ≥ Ton j,m min Toff j,m t ≥ Toff j,m min

(15)

where Ton j,m t and Toff j,m t are the duration of putting into and removing of the high energy load m of the cluster coordination layer j, respectively; Ton j,m min and Toff j,mmin are the minimum duration of putting into and removing of the high energy load m of the cluster coordination layer j.

4 The Cuckoo Optimization Algorithm Cuckoo search algorithm (CSA) is a recently proposed metaheuristic algorithm to solve optimization problems. In literature [8], CSA was adopted to solve the multistage hybrid flow shop scheduling problems. For improving CSA performance both on the efficiency of searching and the speed of convergence, literature [9] proposed an improved CSA based on the teaching-learning strategy. To simplify, cuckoo optimization algorithm is based on three ideal rules [10]: (1) A cuckoo bird lays only one egg at a time, and randomly selects one bird’s nest to place. (2) The best nest and high-quality bird eggs will be preserved for the next generation. (3) The total number of available nests is fixed, and the probability that the host bird finding a foreign bird egg is Pa∈[0,1]. For the multi-objective optimization problems, the first and third rules of the original cuckoo’s idealization rule need to be modified: Rule 1: each cuckoo randomly

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produces K eggs, and the egg corresponds to the solution of the k target problem; Rule 3: each nest host bird will have the probability Pa to find the cuckoo’s egg, then nest in a new position is based on the similarities/differences between the K bird’s eggs. Some random mixtures will be used to produce some diversity.

5 Simulation Analysis In this section, a total of 10 conventional generators and two cluster coordination layers are contained in the study. The coordination layer 1 contains high energy load. There is no high energy load in the cluster coordination layer 2. At the same time, the conventional generators unit 1, unit 3 and unit 4 have a climbing rate and the up and down rates of three units are 40 MW/h. The system’s conventional load forecasting and the active power output prediction of the wind power cluster are shown in Figs. 2 and 3 respectively.

5.1 Scheduling Output of Conventional Generator The scheduling results between the available traditional scheduling mode and the scheduling mode proposed in this study are compared when we analyzed the dispatching output of conventional units. The corresponding dispatching output results are shown in Fig. 4a, b. Based on the analysis of Fig. 4a, b, it can be known that the conventional generators unit 8, unit 9 and unit 10 have the dispatching output only during the peak load period, and their output are discontinuous, the output time is less. For example, unit 8 only has five output time periods as the longest running unit of all these four units. After setting the cluster coordination layer to coordinate the high energy load and the Fig. 2 Power system traditional load forecasting

1400

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100

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6

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Fig. 3 Cluster coordination layer forecasting

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unit1 unit2 unit3 unit4 unit5 unit6 unit7 unit8 unit9 unit10

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(a)

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unit1 unit2 unit3 unit4 unit5 unit6 unit7 unit8 unit9 unit10

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Fig. 4 Dispatching outputs of conventional units under traditional mode and proposed mode

wind farm, the outputs of the conventional generators unit 8, unit 9 and unit 10 are zero in the dispatching time. This is because the dispatching center can only use the installed capacity of the conventional generator which are set as the reserve capacity of the dispatching system when the high energy load is not involved in the scheduling. Therefore, in the peak load the dispatch center can only start the corresponding units to meet the needs of the load power consumption, which makes some conventional generators have to start and stop frequently. After the cluster coordination layer is set up, the dispatch center can dispatch the output power of the coordination layer according to the constraints of the coordination layer to reduce the output of the conventional generator, the cluster coordination layer can reduce the energy consumption of the high energy load by removing the high energy load when the wind power cannot meet the dispatching output, thus increasing the active power of the coordination layer output or reducing the power consumption of the coordination layer from the system.

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Table 1 Scheduling cost of system Scheduling mode

Conventional unit power generation cost (Yuan)

High load capacity compensation cost (Yuan)

Total cost (Yuan)

Conventional

516,292

0

516,292

This text

503,065

5000

508,065

5.2 Cost Analysis The system scheduling costs are shown in Table 1. Table 1 analysis shows that the scheduling mode of the high energy load removal costs incurred 5000 RMB Yuan, but the total operation cost decreased by 8227 RMB Yuan. The reason is that the high energy load can play its schedulable benefits, so that conventional generator sets run at a more economical level of output. In summary, the cluster coordination layer is set up for the high energy load and the wind power cluster, as a result, the load compensation cost of the high load energy is increased and the scheduling of the entire system is reduced.

6 Conclusion The scheduling mode constructed in this paper fully considers the uncertainty of wind power and the controllability of the high energy load. By setting up the coordination layer of cluster to coordinate the high energy load and the wind farms, the economic dispatch model of the wind farm grid-connected system with the high energy load is established. The new scheduling model fully reflects the economic performance of the high energy load to participate in the power grid dispatching, which makes the power grid dispatching obtain a great economic benefit. The multi-objective cuckoo algorithm is used to perform the optimal solution, the minimum cost of dispatch center and maximum income of the coordination layer are obtained. Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51867015 and 51767017). Innovation group project of basic research of Gansu province (No. 18JR3RA133) and Synergistic innovation team project of Gansu province university.

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References 1. Yuan, Y., Zhang, X., Ju, P., et al.: Determination of economic dispatch of wind farm-battery energy storage system using Genetic Algorithm. Int. Trans. Electr. Energy Syst. 24, 264–280 (2014) 2. Mohy-Ud-Din, G.: Hybrid dynamic economic emission dispatch of thermal, wind, and photovoltaic power using the hybrid backtracking search algorithm with sequential quadratic programming. J. Renew. Sustain. Energy 9(1), 015502 (2017) 3. Nazari, M.E., Ardehali, M.M.: Optimal coordination of renewable wind and pumped storage with thermal power generation for maximizing economic profit with considerations for environmental emission based on newly developed heuristic optimization algorithm. J. Renew. Sustain. Energy 8(6), 065905 (2016) 4. Jiang, Y., Xu, J., Sun, Y., et al.: Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system. Appl. Energy 190, 1126–1137 (2017) 5. Li, G., Zhang, R., Jiang, T., et al.: Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process. Appl. Energy (2016) 6. Li, Y., Min Yang, Q.: Optimal storage sizing of energy storage for peak shaving in presence of uncertainties in distributed energy management systems. Int. J. Modell. Ident. Control. 31, 72–80 (2019) 7. He, G., Cao, N., Jiang, L.I., et al.: Research on peak-load regulating with participation of high-use industrial consumers in wind power rich area. Renew. Energy Resour. 33(4), 491–496 (2015) 8. Marichelvam, M.K., Tosun, Ö.: Using Cuckoo search algorithm for hybrid flow shop scheduling problems under makespan criterion. Int. J. Modell. Ident. Control 40, 819–827 (2018) 9. Liu, J., Zeng, M., Ge, Y., Wu, C., Wang, X.: Improved Cuckoo search algorithm for numerical function optimization. Int. J. Comput. Appl. Technol. 142, 34–39 (2018) 10. Khalil, M., Wibowo, R.S., Penangsang, O.: Combined economic emission dispatch with cubic criterion function using Cuckoo search algorithm. In: 2018 International Conference on Information and Communications Technology, 36–40 (2018)

Physical Layer Encryption Based on Hyper-Chen Chaos in Universal Filtered Multi-carriers System Yongtao Huang, Pengqi Yin, Jie Ma and Rui Wang

Abstract We propose four dimensions (4D) Hyper-Chen chaos to achieve a better security performance of physical-layer in Universal Filtered Multi-Carriers (UFMC) systems. Four dimensions are related to XOR operation, frequency domain chaotic constellation mapping and subcarriers scrambling respectively. In our proposed multifold encryption scheme, quadrature amplitude modulation 16 (QAM16) symbols are scrambled and distributed onto the noisy-like complex plane independently. An encrypted UFMC data transmission is successfully emulated demonstrated over wireless multipath channel. The proposed encryption scheme has key space of 5.25×10354 and can combat exhaustive attacks effectively. Keywords Universal filtered multi-carrier · Physical layer encryption · Hyper-Chen chaos

1 Introduction With the rapid development of wireless intelligent terminals and mobile Internet, the data traffic, represented by IP increased dramatically in recent years. Orthogonal Frequency Division Multiplexing (OFDM) [1, 2] based 4G mobile communication no longer meets the ever growing communication needs, 5G era based on non-orthogonal waveforms has come recently. Non-orthogonal waveforms such as Universal Filtered Multi Carrier (UFMC) [3–7] has attracted wide publicity. Due to sub-band filter, UFMC have better out-band suppression characteristics, more flexible allocation of spectrum resources, more robust to carrier frequency offset (CFO) than conventional OFDM [8]. So UFMC has become one of the popular candidate waveforms for 5G. However, in multi carrier transmission line, an illegal carrier can easily attack other carrier by brute force, choose plaintext attack and so on. Different from OFDM Y. Huang (B) · P. Yin · J. Ma Beijing University of Posts and Telecommunications, Beijing, China e-mail: [email protected] R. Wang Civil Aviation University of China, Beijing, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_4

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system, an illegal sub-band can also eavesdrop in UFMC systems. Therefore, when use a UFMC system, it is significant to solve the illegal eavesdropper problem. Chaotic encryption has many characteristic for its uncertainty. A small change in the initial value may have a greater impact on the results, and the process can’t be predicted. So the encryption process is very covert. Meanwhile, in order to improve the security of transmission, each sub-band should be encrypted. Numerous chaos encryption method have been discussed in [9–12]. In [9], subcarriers scrambling method based on chaotic logistic map is designed for IEEE 802.11i. In [10], Dr. Zhang proposed phase of QAM symbols encryption based on 2D logistic chaos. Chaotic ZCMT precoding Matrix can not only Encryption OFDM data but also reduce the peak-to-average power ratio (PAPR) [11]. And [12] proposed a novel piecewise linear (PWL) maps chaotic modulation scheme based on the symbolic sequence associated to the chaotic map and backward iteration. But few security scheme proposed for UMFC systems now. A new chaotic encryption scheme is put forward in this paper to discuss the issue of dynamic mapping of QAM constellation. Unlike previous ones, four dimensions are used. One dimension (x) is used as XOR operation, two dimensions (y, z) are used as frequency domain chaotic constellation mapping and the other dimension (w) is used as subcarriers scrambling. Owing to initial value sensitivity of HyperChen chaotic system, a tiny change (10−20 ) of initial value will result in failure of decryption.

2 Operation Principle 2.1 Physical Layer Encryption Method Based on Chen Chaos in UFMC In our scheme, 4D Hyper-Chen chaos is used to obtain 4 independent chaotic sequences x, y, z, w, ⎧ dx = −ax + ay + w ⎪ dt ⎪  ⎨ dy = d x − x z A + cy dt  dz ⎪ = x y A − bz ⎪ dt  ⎩ dw = yz A − r w dt

(1)

where a = 35, b = 3, c = 12, d = 7, r = 0.58 and A = 0.08. Hyper-Chen chaos will be discussed in detail in the following Sect. 2.2. The proposed 4D Hyper-Chen chaos encryption scheme as Fig. 1 shown is explained as follows. Firstly, we get binary sequence from chaotic sequence x, and then use it to operate XOR with PRBS (Pseudo Random Bit Sequence). Secondly, after 16QAM mapping and UFMC coder, chaotic sequence y, z are used for chaotic mapping. In no encryption UFMC systems, time domain signal is generated from

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Fig. 1 a Conventional mapping in 16-QAM, b chaotic mapping in 16-QAM

frequency domain using the inverse discrete Fourier transform (IDFT) operation as follows: si (n) =

1   2πnk S (k)e j N , n = 0, 1 . . . M − 1 N k=B i

(2)

i

where i-th sub-band Bi means i-th resource block (RB) and each RB contains M subcarriers. We define Si (k) = Si I (k) + j Si Q (k), so constellation chaotic mapping can be expressed as:   Si (k) = f (Si (k)) = (Si I (k) ± I ) + j Si Q (k) ± Q

(3)

where Si (k) is Quadrature Amplitude Modulation 16 (QAM16) signal and I and Q are generated from chaotic sequence y and z: (Fig. 2) I = 3 × mod(y, f loor (abs(y)))

Fig. 2 Schematic of UFMC system utilizing Hyper-Chen chaotic encryption

(4)

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Q = 3 × mod(z, f loor (abs(z)))

(5)

The original 16QAM mapping and chaotic mapping are shown in Fig. 1a, b. After chaotic shifting, the original information is hidden. Lastly, we use chaotic sequence w to generate time domain scrambling matrix for each sub-band. When an UFMC symbol’s length have B sub-bands and each sub-band have M subcarriers, we obtain B sequence of length M from chaotic sequence w. Then the sort index is obtained: index = sor t(w)

(6)

Now we create B M × M scrambling matrixes Wi from the index. The i-th row and index(i)-th column of Wi are 1 and the others elements are 0. So the symbol of UFMC is: y(n) =

B 

[ci (n)[Wi si (n) ∗ f i (n)]]

(7)

i=1

2.2 Hyper-Chen Chaos Equation (1) is classical 4D Hyper-Chen system’s state Eq. (4) D Hyper-Chen chaos system has extremely initial values and control parameters. The nonlinear dynamical behavior and topological structure of 4D Hyper-Chen chaos is complex. High dimensional hyper-chaotic system has greater key space. Balanced computational complexity with key space, we decide to use 4D Hyper-Chen system to perform chaotic encryption. In the circumstances of chaotic state, a, b, c, d, r and A can slightly change to enhance the key space. Fourth and fifth-order Runge-Kutta method is used to solve the nonlinear differential equation as Eq. (1). The 4D Hyper-Chen chaos system’s x-y and z-w phase diagrams are shown in Fig. 3a, b.

3 Simulation Result In this paper we conduct three simulation experiments to verify the performance of proposed chaotic encryption scheme for UFMC systems. We carry out our simulation setup for B = 14, M = 16 and FFT size of N = 256. The length of guard band interval at both ends is 16 each. We use a Dolph-Chebyshev window with 40 dB stop-band attenuation and the filter length L fir = 17. So an UFMC symbol length is N + L fir − 1 = 272. We set the normalized CFO as 0.01 and multipath environment is h = [1, −0.3, 0.2]T in our simulation work. Correspondingly, the transmitter and receiver perform chaotic encryption and decryption as described in Sect. 2 (Fig. 4).

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Fig. 3 Hyper-Chen chaos system phase diagram, a x-y phase diagram, b z-w phase diagram

Fig. 4 BER versus SNR with/without right key

We conduct 4D Hyper-Chen chaos encryption for difference signal-to-noise ratio (SNR) transmission case. The initial value (Key) is set as {0.01, −0.01, 0.01, 0}. If the legal receiver get the right key, BER is 3.1 × 10−3 at SNR = 15 dB, which means the encrypted UFMC signals can be decrypted correctly. But without right Key, BER is 0.5 at all SNR, which means it is unable to extract any valid information. In our encryption, any tiny discrepancy (10−18 ) from one of the initial value (x0 , y0 , z 0 , w0 ) would bring incorrect decryption result. Figure 5 shows the system BER performance versus difference initial value error in different dimension. An illegal receiver, whose initial value is 0.01 + 10−18,

−18 , 0.01, 0 , 0.01, −0.01, 0.01 + 10−18 , 0 −0.01, + 10 

0.01, 0}, 0.01, −0.01−18 can’t decrypt the UFMC signals (BER ~ 0.5). and 0.01, −0.01, 0.01, 0 + 10 Now let’s discuss how the system will affect if some chaotic sequences are eavesdropped. Figure 6 shows the simulation results in this case. In Fig. 6, although the sequences of the three dimensions are eavesdropped, the original information still cannot be decoded accurately (BER ~ 0.5). This shows that our scheme is very effective. If you want to decode correctly, you must know the key completely, or the deviation of these keys is very small (10−18 ).

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Fig. 5 BER versus initial value error

Fig. 6 BER versus SNR when some chaotic sequences are eavesdropped

Finally, 4D Hyper-Chen chaotic based frequency domain shifting and subcarriers scrambling encryption system’s key space is analyzed. In our simulation work, there are 256 subcarriers with 4 bits (16-QAM). So the key space can be calculated by 24∗256 = 21024 . Assumed that decryption failure can be produced from a 10−9 (10−18 ) deviation to the initial value. Now as we have four dimensions,  4 then the total key space for the initial value is beyond 109 = 1036 . In the 14 sub-bands, each sub-band has 16! = 2.09 × 1013 scrambling matrix, which is created according to chaos sequence w. So the key space for our encryption system is 21024 × 14 × 16! × 1032 = 5.25 × 10354 at least, no considering a, b, c, d, r and A’s slightly change in Eq. (1). In such an encryption scheme with large secret space, brute force can hardly produce any impact. This result leads to a perfect confidential communication in the physical layer.

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39

4 Conclusions We propose a novel chaotic encryption scheme that exploring dynamic mapping of QAM constellation for UFMC. Our operation mainly contains three parts, which are XOR operation, frequency domain chaotic constellation mapping and subcarriers scrambling. They run on four dimensions separately. Owing to initial value sensitivity of Hyper-Chen chaotic system, a tiny change (10−20 ) of initial value will result in failure of decryption. But our scheme has a very large key space. Therefore, our scheme has a better robustness and gain a better performance when meet brute force due to the large key space. Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC, No. 61531007, 61821001, 61875239) and BUPT Excellent Ph.D. Students Foundation (CX2019124).

References 1. Batariere, M., Baum, K., Krauss, T.P.: Cyclic prefix length analysis for 4G OFDM systems. In: IEEE 60th Vehicular Technology Conference. VTC2004-Fall, pp. 543–547. IEEE Press (2004) 2. Osseiran, A., Logothetis, A.: A new full rate relaying method for 4G OFDM systems. IEEE Trans. Wirel. Commun. 8(8), 3996–4003 (2009) 3. Frank, S., Thorsten, W., Yejian, C.: Waveform contenders for 5G–suitability for short packet and low latency transmissions. In: Vehicular Technology Conference, pp. 1–5. IEEE Press (2014) 4. Gerhard, W., Peter, J., Martin, K., et. al.: 5GNOW: Non-orthogonal asynchronous waveforms for future mobile applications. IEEE Commun. Mag. 52(2), pp. 97–105 (2014) 5. Gerhard, W., Martin, K., Stephan, T.B., Frank, S., et al.: 5GNOW: challenging the LTE design paradigms of orthogonality and synchronicity. In: 2013 IEEE 77th Vehicular Technology Conference (VTC Spring), pp. 1–5 (2013) 6. Vida, V., Thorsten, W., Frank, S, Stephan, T.B., et al.: Universal-filtered multi-carrier technique for wireless systems beyond LTE. In: 2013 IEEE Globecom Workshops (GCWkshps), pp. 223–228 (2013) 7. Frank, S., Thorsten, W.: Waveform contenders for 5G—OFDM vs. FBMC versus UFMC. In: 2014 6th International Symposium on Communications, Control and Signal Processing, pp. 457–460. IEEE Press (2014) 8. Chen, L., Yu, J.G.: Interference cancelation scheme with variable bandwidth allocation for universal filtered multicarrier systems in 5G networks. EURASIP J. Wirel. Commun. Network., 1–10 (2018) 9. Khan, M.A., Asim, M., Jeoti, V., Manzoor, R.S.: On secure OFDM system: Chaos based constellation scrambling. In: 2007 International Conference on Intelligent and Advanced Systems, pp. 484–488 (2007) 10. Wang, Y., Zhang, X., Zeng, J., Wang, Y.: Secure OFDM transmission scheme based on twostage chaos mapping. J. Commun. 37(7), 13–139 (2016) 11. Chen, H., Yang, X., Sun, W., Hu, W.: Physical-layer OFDM data encryption using chaotic ZCMT precoding matrix. In: 2017 19th International Conference on Transparent Optical Networks, pp. 1–4 (2017) 12. Luengo, D., Santamaria, I.: Secure communications using OFDM with chaotic modulation in the subcarriers. In: 2005 IEEE 61st Vehicular Technology Conference, pp. 1022–1026 (2005)

Verification Research on On-line Monitoring Method of Aircraft ARINC825 Bus Cable Fault Based on SSTDR Xudong Shi, Xiangyang Xu, Yang Liu and Tao Jing

Abstract The online monitoring method based on the spread spectrum time domain reflectometry (SSTDR) theory is studied to detect the intermittent fault of the aircraft ARINC825 bus cable. Firstly, the impedance characteristics and reflection characteristics of the aircraft ARINC825 bus cable fault are analyzed, and the online monitoring method model is constructed. Secondly, the frequency and amplitude of the monitoring signal is designed according to the ARINC825 protocol and airworthiness standard. Finally, the experimental platform is built to verify the proposed method. On-line monitoring experiments are carried out with multiple sets of ARINC825 bus cables. The results show that the positioning accuracy and fault type judgment accuracy of fault online monitoring are very high. Therefore, the method has proved to be feasible. Keywords ARINC825 · SSTDR · Online monitoring · Airworthiness standard

1 Introduction The rapid development of multi-electric aircraft technology has realized the unified management of the aircraft’s electrical, hydraulic, mechanical and other systems [1]. This makes the connection between the various systems of the aircraft closer, and at the same time, the number and variety of aviation buses will be even larger. The cables for the aircraft bus are distributed over multiple areas of the aircraft, including avionics cabin, engine pods, and interior wall of cabin. As a kind of data bus widely used in aircraft, the reliability of the ARINC825 bus cable is particularly important [2]. Regardless of the routine maintenance or the overhaul, the troubleshooting of the aircraft bus cable can only be taken offline [3, 4]. In other word, detection can only be carried out after the aircraft bus has been powered down. Intermittent failure of an aircraft bus cable is manifested by an instantaneous open or short circuit during the X. Shi (B) · X. Xu · Y. Liu · T. Jing College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_5

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flight of the aircraft. Off-line detection methods such as time domain reflectometry (TDR) and time frequency domain reflectometry (TFDR) are difficult to detect intermittent faults that are only exposed during the flight of the aircraft. Therefore, there is a need for a method of online monitoring of the ARINC 825 bus while the aircraft is flying. The spread spectrum time domain reflectometry (SSTDR) technology uses a sine wave as a carrier to spread-modulate the pseudo-noise code [5]. It has strong anti-interference ability and can be superimposed on the working signal to be recognized. It is an excellent selection for online monitoring of the aircraft ARINC825 bus cable fault. Based on the SSTDR principle, this paper designs a monitoring signal suitable for the aircraft ARINC825 bus, and then builds an experimental verification platform for the ARINC825 bus cable online monitoring system. Whether there is interference between the ARINC825 signal and the monitoring signal is confirmed by experiments. At the same time, the accuracy of the online monitoring method is also obtained through experiments.

2 Theory Analysis 2.1 Monitoring Principle Cable faults generally manifest as sudden changes in impedance [6]. The electrical signal will reflect at a sudden change in cable impedance, as shown in Fig. 1. In Fig. 1, Z 0 is the characteristic impedance of the ARINC825 bus cable, and Z x is the equivalent impedance of the fault location. The electrical signal will reflect at the fault location due to impedance mismatch. The voltage and current relationship at this position are as shown in Eq. (1).

Fig. 1 The schematic of reflection in ARINC825 bus cable fault position

Verification Research on On-line Monitoring Method …



Vx = Vin + Vr e f Ix = Iin + Ir e f

43

(1)

In Eq. (1), the relationship between the electrical signal and the impedance is as shown in Eq. (2). ⎧ ⎨ Vin = Iin Z 0 V = −Ir e f Z 0 ⎩ ref Vx = Ix Z x

(2)

The reflection coefficients of the fault location can be derived by combining Eqs. (1) and (2) as shown in Eq. (3). =

Vr e f Zx − Z0 = Vin Zx + Z0

(3)

When the cable is open-circuited, the fault position Z x is abruptly changed to ∞, and Γ = 1. When the cable is short-circuited, Z x is abruptly changed to 0, and Γ = −1. If the propagation velocity v of the electrical signal in the cable and the delay time τ of the reflected signal are known, the fault distance x can be obtained by the Eq. (4). x=

1 vτ 2

(4)

In order to realize on-line monitoring of ARINC825 bus cable faults, it is necessary to design a monitoring signal that meets the following conditions. After the monitoring signal is superimposed with the ARINC825 bus signal, it cannot interfere with the acceptance and recognition of the ARINC825 bus signal, and it should be easy to be separated and identified. Based on the SSTDR method, the PN sequence and the sine wave are selected to generate the monitoring signal through BPSK modulation. The PN sequence has a white noise characteristic with a mean value of zero. After being superimposed on the ARINC825 bus, it will not interfere with the operation of the original signal. BPSK modulation improves the anti-interference so that the monitoring signal can be separated from the mixed signal by high-pass filtering. To perform BPSK modulation on the PN sequence, it is first necessary to convert the PN sequence from unipolar to bipolar as shown in Eq. (5) [7]. Mb = 2Mu − 1

(5)

In the Eq. (5), M u is a unipolar PN sequence, and M b is a PN sequence which has been converted into a bipolar. The bipolar PN sequence can be spread-modulated according to Eq. (6). Sin = Mb sin(2π f t + ϕ)

(6)

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In Eq. (6), f is the frequency of the sine wave carrier. In order to ensure that the detection signal has the best correlation characteristics, f is set equal to the chip frequency of the PN sequence. Therefore, f = 1/t c , where t c is the chip time of the PN sequence. The process of recognizing the reflected signal needs to be done by means of correlation function operations. Since the waveform data collected by hardware is discrete, an algorithm that uses discrete sequence correlation operations is required to perform correlation function operations. The algorithm is shown in Eq. (7) [8, 9]. R(τ ) =

T 1  Si (t − τ )Sr (t) T n=1

(7)

In a period T, the value of the correlation |R(τ)| changes over time. When the correlation |R(τ)| reaches a maximum, the corresponding delay time τ is the time that the detection signal passes through the round-trip fault point from the transmission point in the cable [10]. Substituting the delay time τ into Eq. (4) can calculate the fault distance x. The sign of the correlation maximum is used for determine the type of fault. The positive will be judged to be an open circuit fault, and the negative will be judged to be a short circuit fault.

2.2 Parameter Design of Monitoring Signals The amplitude of the signal voltage specified by the ARINC825 bus protocol is shown in Fig. 2. The parameter of the monitoring signal is designed based on the ARINC825 protocol and airworthiness standard. According to CCAR-25, Regulations of Chinese Civil Aviation, No. 25.1431, the installation of radio and electronic equipment must Dominant ≈ 3.5V Recessive ≈ 2.5V

CANH CANL

Dominant ≈ 1.5V

Recessive ≈ 2.5V

Dominant ≈ 2V Recessive ≈ 0V

Vdiff=CANH-CANL Dominant = logical 0

Recessive = logical 1

Fig. 2 Signal characteristics specified by the ARINC825 bus protocol

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45

take into account critical environmental conditions. Moreover, electronic equipment must be installed in such a way that the simultaneous operation of other radio and electronic components is not adversely affected. Since the online monitoring method essentially superimposes the noise signal in the ARINC825 bus signal, it must be ensured that the monitoring signal does not adversely affect the ARINC825 bus signal. The ARINC825 bus uses differential signals, and the effective signal of a single line is at least V s = 1.5 V. DO-160 “Environmental Conditions and Test Procedures for Airborne Equipment” specifies the noise margin of airborne equipment. Therefore, the signal to noise ratio should be higher than 20 dB, which is as shown in Eq. (8).    Vs  S N R = 20 lg  > 20 dB Vn

(8)

In Eq. (8), V s is the amplitude of the effective signal and V n is the amplitude of the noise signal. Therefore, the noise amplitude V n < 0.15 V can be calculated. In summary, the monitoring signal amplitude can be set to 0.1 V. When the delay time τ is greater than the period T, multiple reflections will occur, which will affect subsequent data analysis. On the other hand, when the delay time τ is less than the signal chip time t c , the transmitted detection signal is confused with the reflected signal, which will affect the determination of the fault location. Therefore, the range of the delay time τ is as shown in Eq. (9). tc ≤ τ ≤ ntc

(9)

Combining Eqs. (4) and (9), an effective measurement range of the detection signal can be obtained as shown in Eq. (10). 1 1 vtc ≤ x ≤ vntc 2 2

(10)

The ARINC825 bus uses the aerospace-specific data bus cable produced by Nexans. The distribution parameters in the working state are: resistance value is 124 /km, capacitance value is 36 pF/m, and inductance value is 0.543 μH/m. The propagation speed of the high-frequency signal on the ARINC825 bus cable is as shown in Eq. (11). v=√

1 LC

=√

1 0.543 ×

10−6

× 36 × 10−12

≈ 2.261 × 108 (m/s)

(11)

The ARINC825 bus signal with a transmission rate of 83.33 kbit/s is selected as the research sample. In order to facilitate the separation of the reflected signal, the carrier frequency of the monitoring signal is set to 100 MHz. At the same time, the chip time of the PN code can be determined to t c = 1×10−8 s. Considering the

X. Shi et al. 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5

Sine Wave

PN Sequence

1.5

Amplitude/V

Amplitude/V

46

1

0.5 0 -0.5

0

0.5

1

1.5

2

2.5

3.5

3

4

0

1.5

2

2.5

3

3.5

4 -6

x 10

Time/s

(a) Waveform of M-sequence

(b) Waveform of sine wave carrier

SSTDR signal

Autocorrelation

1 0.8 0.6

0.4 0.3 0.2

Amplitude/V

Amplitude/V

1

x 10

Time/s

0.5

0.5

-6

0.1 0 -0.1 -0.2 -0.3

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

-0.4 -0.5 0

0.5

1

1.5

2

2.5

3

4

3.5

Time/s

-1 -1

-0.8 -0.6 -0.4 -0.2

-6

(c) Waveform of monitoring signal

0

0.2

Time/s

x 10

0.4

0.6

0.8 1 -6 x 10

(d) Autocorrelation coefficient distribution

Fig. 3 Monitoring signal and autocorrelation coefficient distribution

common length of the ARINC825 bus cable, set the length of the PN code to n = 63. In summary, according to Eq. (9), the effective fault location range is 1.131 m < x < 71.222 m. The parameters are set as follows: t c = 1×10−8 s, n = 63, f = 100 MHz, and V s = 0.1 V. Then the monitoring signal of SSTDR and the distribution of autocorrelation coefficients are obtained by using MATLAB. The m-sequence in Fig. 3a determines the period and code bit width of the monitoring signal, and the sine wave carrier in Fig. 3b determines the amplitude and frequency of the monitoring signal. After BPSK modulation, the monitoring signal waveform shown in Fig. 3c can be obtained. The normalized autocorrelation coefficient distribution of the monitoring signal is shown in Fig. 3d, which peak is clearly easy to identify.

3 Experiment and Analysis 3.1 Design of the Experimental Scheme The experimental scheme is shown in Fig. 4. After the PN sequence is spreadmodulated, a monitoring signal is generated and sent to the ARINC825 bus cable

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47 Fault location

Cross-correlation operation

PN code BPSK modulation

Monitoring signal

Reflected signal

Signal separation

Mixed signal of reflected signal and working signal

Sine wave Monitoring signal

ARINC 825 bus cable in the state of transmitting signals fault

Fig. 4 Experiment scheme of ARINC825 bus cable fault online monitoring

in live operation. The reflected signal generated at the fault location is extracted by signal isolation, and a correlation function is performed with the reference signal to obtain corresponding fault information.

3.2 Construction of Experimental System The experimental system consists of two parts: the online monitoring device and the ARINC825 bus. Both parts are based on PXI bus technology for hardware construction. Hardware selection is shown in Table 1. The online monitoring device uses the AMC58234 PXI smart tablet as the host computer and writes software based on the LABVIEW platform. NI PXI-5422 is used for waveform generation and NI PXIe-5162 is used for data acquisition. NI PXIe-1065 and NI PXI-8513 are used for build the ARINC825 bus system. And the software uses the system’s own self-transceiver program. The filter connecting the online monitoring device to the ARINC825 bus system uses an RC high-pass filter circuit. Table 1 Hardware selection

Hardware type

Function

AMC58234 smart tablet

Host computer

NI PXI-5422

Waveform generator

NI PXIe-5162

Data collector

NI PXI-8513

ARINC825 signal generator

High pass filter

Filter

NI PXIe-1065

Bus experiment platform

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(a) ARINC825 signal

(b) Mixed signal of ARINC825 and SSTDR

Fig. 5 ARINC825 signal and mixed signal of ARINC825 and SSTDR

3.3 Analysis of Signal Effects ARINC825 signal and mixed signal of ARINC825 and SSTDR are collected by oscilloscope. The waveforms are shown in Fig. 5. Figure 5a is the working signal of the ARINC825 bus received by the oscilloscope, and Fig. 5b is the mixed signal of ARINC825 bus working signal and SSTDR monitoring signal received by the oscilloscope. The effective value of the ARINC825 signal voltage and the effective value of the noise voltage can be substituted into Eq. (8). After calculation, the minimum signalto-noise ratio of the ARINC825 signal in Fig. 5a is 27.96 dB before the SSTDR monitoring signal is superimposed. After superimposing the SSTDR detection signal, the minimum signal-to-noise ratio of the ARINC825 signal in Fig. 5b is 24.44 dB. Before and after superimposing the SSTDR detection signal, the signal-to-noise ratio of the ARINC825 signal is always greater than 20 dB, which satisfies the requirements of DO-160.

3.4 Experimental Verification As shown in Fig. 6, the ARINC825 bus experiment system is connected for online monitoring experiments, in which the impedance change is set at the interface between the ARINC825 bus cable and the PXI-8513 interface. As shown in Fig. 6, during the operation of the monitoring device, the indicator light of the ARINC825 bus self-transceiver remains green, indicating that the ARINC825 signal transmission is correct. It is proved that the monitoring signal transmitted by the monitoring device does not interfere with the normal operation of the ARINC825 bus and meets the requirements of CCAR-25. At the same time, the detection device measured a sudden change in impedance between the ARINC825 bus cable and the PXI-8513 interface, and the positioning error was less than 0.1 m.

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Fig. 6 Experiment of ARINC825 bus online monitoring

The indicator light turns green to indicate that the ARINC825 bus signal transmission is correct.

ARINC825 self-transceiver program

PXI-8513

Monitoring device

Filter

Take an ARINC825 bus cable with a line length of 45.24 m as the experimental object and use the experimental system to monitor it online. First disconnect the ARINC825 bus cable from the NI PXI-8513 PORT2 to form an open circuit fault. The reflected signal is collected as shown in Fig. 7a. Then short the end of the ARINC825 bus cable and collect the reflected signal as shown in Fig. 7b. After the correlation function operation processing, the correlation coefficient of the open circuit fault reflection signal can be obtained as shown in Fig. 8a, and the correlation coefficient distribution of the short circuit fault is as shown in Fig. 8b. The propagation velocity v has been input to directly convert the abscissa into the fault distance in meters. After the peak detection and subtraction, the open circuit fault location can be obtained by 45.22 m, and the short circuit fault location is 45.17 m. Fault location error is less than 0.1 m. Then prepare three groups of ARINC825 bus cables as experimental samples. The two ends of each ARINC825 bus cable are connected to the transmitting port PORT1 and receiving port PORT2 of the NI PXI-8513. Each group of experimental

(a) Reflection waveform of open circuit fault

Fig. 7 Acquired fault waveform

(b) Reflection waveform of short circuit fault

X. Shi et al. Correlation coefficient distribution diagram of open circuit fault

1

45.22m

0.8 0.6 0.4 0.2 0 -0.2 -0.4

0

1

2

3

4

5

Time/s

6

7

8

Normalized correlation coefficient

Normalized correlation coefficient

50

Correlation coefficient distribution diagram of short circuit fault

1

45.17m

0.5

0

-0.5

0

1

3

2

-7

x 10

(a) Open circuit fault

4

5

6

8

7

-7

x 10

Time/s

(b) Short circuit fault

Fig. 8 Correlation coefficient distribution obtained by the monitoring device

Table 2 Experimental result Number of experiments

Fault distance setting (m)

100

5.12

Position result (m)

Error rate (%)

Fault type setting

4.884–5.356

≤4.6

Short-circuit

100

5.12

4.925–5.314

≤3.7

Open-circuit

100

24.93

24.556–25.303

≤1.5

Short-circuit

100

24.93

24.653–25.203

≤1.1

Open-circuit

100

45.10

44.332–45.867

≤1.7

Short-circuit

100

45.10

44.513–45.690

≤1.3

Open-circuit

samples is subjected to 100 times of short-circuit and open-circuit fault monitoring experiments. The monitoring results are shown in Table 2. The experimental results show that the positioning error of online monitoring of ARINC825 bus cable fault based on SSTDR is less than 4.6%.

4 Conclusion The SSTDR monitoring signal is designed for the ARINC825 bus and applied to the experiment. And the experimental verification platform for ARINC825 bus fault online monitoring is built. Then the experimental results show that the SSTDR monitoring signal has little effect on ARINC825 and meets ARINC825 protocol and DO-160 requirements. In summary, the online monitoring method has a small position error and a high accuracy of the fault type judgment, and the method is feasible. Acknowledgements The research is supported by the Innovation Team Cultivation Plan of Colleges and Universities in Tianjin (TD13-5071) and the Fundamental Research Funds for the Central Universities (3122018D004).

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References 1. Fan, Z., Tan, Z., Liu, T.: Research on fault transmission modes for electrical system of more electric aircraft. Mod. Electron. Tech. 41(24), 48–51 + 56 (2018) 2. Xiao, B., Wang, W., Wang, D., et al.: Research on calibration method for ARINC825 bus. Metrol. Measur. Technol. 36(3), 49–51 (2016) 3. Wang, F., Jiang, L.: Analysis of typical failures for aircraft cable. Aviat. Maintenance Eng. 6, 89–90 (2017) 4. Shi, X., Pei, H., Jing, T., et al.: Aircraft cable fault diagnosis based on time-frequency reflection. Inf Control 39(1), 77–81 (2010) 5. Smith, P., Furse, C., Gunther, J.: Fault location on aircraft wiring using spread spectrum time domain reflectometry. IEEE Sens. J. 5(6), 1496–1478 (2005) 6. Hong, B., Wang, L., Mao, J., et al.: An online detection and locating method for spacecraft bus faults. Trans. China Electrotech. Soc. (2016) 7. Dong, Z.: Study and Implementation of BPSK Modem Algorithm Based on FPGA. Harbin Engineering University (2016) 8. P. Venkatesh Kumar, P., Rajeswari, R.: A recursive discrete Kalman filter for the generation of reference signal to UPQC with unbalanced and distorted supply conditions. Int. J. Modell. Ident. Control (2019) 9. Chen, C., Tseng, K.-K., Zhang, X.: A real-world online signature verification system based on correlation algorithm. Int. J. Comput. Appl. Technol. (2018) 10. Wang M., Sun, X., Xing, H., Zheng, H.: Online fault detection for networked control system with unknown network-induced delays. Int. J. Modell. Ident. Control (2018)

Research on Motion Control System of 6-DOF Robotic Arm Minglei Liu, Hongbo Zhou and Aiping Pang

Abstract Robot control technology is developing rapidly on a global scale with the way of interaction between human and robot towards two directions of convenience and intuition. In this paper, the operator’s arm position and motion state are represented by the motion sensing, which providing the necessary information for the robot motion control. This paper studies the interactive 6-DOF robotic arm control system that combining visual and wearable leap motion device. This system uses human body’s rotation angle of the shoulders and elbows to control the 6 joints of the robotic arm, and the gestures to claw. This experiment platform was built with data and instructions were transmitted wirelessly. The experimental results show that the interactive robot with integrated visual and wearable leap motion device can effectively and intuitively control the robotic arm for object grabbing. Keywords Robot control · Motion sensing · Motion control · 6-DOF robotic arm control system

1 Introduction With the rapid development of intelligent technology, robot applications continue to expand and deepen. The interactive control system based on virtual reality technology enables the robot to remotely control the operator in harsh environments. The friendly human-machine interface for human senses and control in special environments, creating the first vision of the robot’s working environment without someone on site. Visual sensors and wearables have developed rapidly in recent years and have been widely used in medical treatment, education and training, animation entertainment, games, exhibitions and other industries. Visual sensors can collect depth images of human body, while wearable sensors can acquire human muscle potential [1–3]. In this paper, visual and wearable leap motion technology are applied to combine the user’s natural motion with the robot motion. By extracting the spatial position M. Liu · H. Zhou · A. Pang (B) Guizhou University, School of Electronical Engineering, Huaxi Avenue, Guiyang 550025, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_6

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data of the human arm joints and the information of the arm motion state, the user’s arm movement can be simulated to realize the control of the robotic arm.

2 Motion Control System Design The motion control system of 6-DOF robotic arm studied in this paper consists of the motion information acquisition and analysis part, as well as the robotic arm control part [4]. The visual sensor, wearable sensor, and computer complete the motion information acquisition and analysis. The robotic arm control part is composed of an embedded controller and a 6-DOF robotic arm. The structure block diagram as shown in Fig. 1. The motion information acquisition and analysis subsystem in the upper part of the figure and the robotic arm control subsystem in the lower part can be connected by wired or wireless methods. Robots and control systems are usually located on the industrial site or at the site where operations are required, typically using an embedded control platform as their controller [5, 6]. The Raspberry Pi selected for the paper is an ARM-based controller with an internal operating system and Python as a development platform. The visual sensor is mainly used to obtain the depth and infrared information of the arm, and the 25 bone point data of the human body can be obtained. The model is Microsoft’s Kinect Xbox One (Kinect), which is mainly composed of 1080P color camera, depth camera, infrared emitter, infrared camera and microphone matrix. The main technical indicators are shown in Table 1. The wearable sensor uses the Myo armband of Thalmic Labs. The armband consists of a microprocessor (ARM Cortex M4), a medical grade stainless steel electromyogram (EMG) sensor, and a high-sensitivity nine-axis inertial measuring unit Fig. 1 The 6-DOF robotic arm motion control system block diagram

Visual sensor Wearable sensor

PC

Motion information acquisition and analysis system

Embedded controller 6-DOF robotic arm Robotic arm control system

Research on Motion Control System of 6-DOF Robotic Arm Table 1 Kinect Xbox one main technical indicators

55

Parameters

Value

RGB image resolution/(pixels)

1920 × 1080

RGB image frame rate/(frame s−1 )

30/15

Infrared image resolution/(pixels)

512 × 424

Infrared image frame rate/(frame s−1 )

30

Depth data measurement range/(m)

0.5–4. 5

Number of human body indexes/(a)

6

Detect the number of human bones/(a)

25

(IMU) with a built-in three-axis gyroscope, a three-axis accelerometer, and a threeaxis magnetometer. The Myo gesture detection principle is based on the muscle electrical signal. It works closely against the arm. It has 8 muscle pulse detection modules and a metal contact on the inside for close to the arm to detect muscle impulses.

3 Motion Detection and Angle Analysis 3.1 Arm Joint Data Sampling Kinect sensor data includes color images, depth of field data streams, skeletal data streams, and infrared data streams. First, the Kinect sensor is calibrated to record basic information such as the length of the human body [7–9]. (1) According to the system prompts, the human body moves in front of the Kinect sensor to set the optimal collection distance and viewing angle. (2) According to the system prompts, the human body’s right (or left) arm is in the state of horizontal extension and horizontal bending, so that the sensor records data. The built-in acquisition program dynamically acquires the upper arm and forearm moving image, and internally analyzes and calculates the arm joint points in the threedimensional space in the two-dimensional coordinate system X-Y, Y-Z and X-Z as shown in Fig. 2. According to the above-described projection relationship of the arm joint point in the plane, the horizontal rotation angle and the vertical rotation angle of the upper arm relative to the human body trunk and the rotation angle of the forearm perpendicular to the upper arm can be solved. The definition range of α1 in the X-Y plane direction vector is 0–180°. The twodimensional vector is defined by the difference between the wrist point X-Y coordinates and the elbow point X-Y coordinates. After the direction vector is defined, the angle can be derived using the mathematical Formula (1) shown below.

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Z

Fig. 2 Arm joint angle calculation model

1

O Y

X 2

A 3 4 5

 α1 =

  ◦ ◦ β arctan YX  Y  0 ◦< α1 < 90 ◦ 180 − β arctan X 90 < α1 < 180

(1)

where β = 57.1 is related to the arm length of the mechanical arm, which needs to be measured and calculated manually. According to the Fig. 3, α1 α2 and α3 are represented by three angles respectively. The method used for calculation is vector analysis. For α2 and α3 , two-dimensional inverse kinematics is used to calculate the angle. By solving α1 and transforming the problem into a two-dimensional plane, twodimensional inverse kinematics can be used to solve α2 and α3 . Due to its complexity, detailed analysis methods are ignored. The general modeling of the method is shown in Fig. 3. In the figure, θ1 corresponds to α2 , and θ2 corresponds to α3 . (x,y)

Fig. 3 Two-dimensional inverse kinematics mathematical model

y

θ2

θ1

(0,0)

x

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Fig. 4 Gesture diagram

3.2 Grasp the Control Angle Through the Armband The Myo armband collects the current signal released by the muscles during arm movement, transmits it to the computer for analysis and processing through Bluetooth 4.0, and recognizes seven gesture states such as displacement, double-click, fist, finger spread, wrist left swing, wrist right swing and arm rotation. As shown in Fig. 4. In the label 5, the state of wrist left swing causes the angle α5 to be accumulated. In the label 6, the state of wrist right swing causes the angle α5 to be successively decremented. In the label 2, the state of double-click to pause the angle α5 to the current position. In the label 3, the state of fist controls grips the claw. In the label 4, the gesture finger spread controls the claw to open.

4 Software Testing of Robotic Control System The angle calculated by the Kinect sampling and the data obtained by the Myo armband are transmitted remotely via Wi-Fi, and the PWM data is obtained by the embedded controller to control the servo motor on the robotic arm [10, 11]. The algorithm applies the inverse kinematics principle. Since the algorithm is oriented by the human arm posture, the actual angle of the servo motor is not necessarily equal to or close to the true angle between the human body’s upper arm and the forearm. This shows that the angle calculated by Kinect determines the position of the end effector, not the actual position of the human arm. The three-dimensional spatial data returning to the six joint points is detected by the geomagnetic sensor installed at the end of the actuator to optimize the final posture of the robotic arm. This control system uses the C++ programming language, the writing tool is Visual Studio 2017, and the authoring environment is .NetFrameWork 4.5 and Kinect sdk2.0 toolkit. The control system software flow is as follows. Initialize all objects first, then get the Kinect and Myo armband data, process them through the PC, and draw joint points and display related data on the GUI panel. Finally, the data is transmitted to the main controller for verification analysis to drive the entire robot arm. Press the keyboard Ctrl+C to terminate the program. The UI interface of the control system software is shown in Fig. 5. The system tests in this paper are divided into visual sensing subsystem and wearable motion subsystem. The two subsystems passed nearly one hundred tests, and the state was stable with an error of 5%, which was within the allowable range. Table 2 shows some excellent test results of the visual sensing system. Wearable

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Fig. 5 System software UI interface Table 2 Visual sensing subsystem testing data Test number and angle value

Position description

Test No. 1

Arm extended to the right

Angle 1 Angle 2

Test No. 2

Angle 1

Test No. 3

Angle 1

Angle 2 Angle 2

Test No. 4

Angle 1

Test No. 5

Angle 1

Angle 2 Angle 2 Test No. 6

Angle 1 Angle 2

Test No. 7

Angle 1 Angle 2

Test No. 8

Angle 1 Angle 2

Arm extended to the left Arm bent forward, forearm perpendicular to ground Arm bent, forearm parallel to ground

Physical measurement (°)

Arm measurement (°)

0

0

0

10

130

140

20

20

90

90

−30

−30

90

85

45

60

Bend your arm to the right

55

45

5

10

Bend your arm to the left

135

130

−5

20

Forearm parallel to ground in front of chest

120

125

15

20

Slight bent arm to the right

35

35

40

40

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sensing subsystem test in Fig. 6 shows such as the fist, the wrist left swing, and the data test of the arm rotation. In order to ensure the stable operation of the whole system after the integration of the two subsystems, the test delay index can determine whether the load can run normally. The delay test curve is shown in Fig. 8. It can be seen that the potential

Fig. 6 Wearable sensing subsystem testing

Fig. 7 System testing

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Fig. 8 Delay testing curve

delay of the system is very low, which ensures the normal operation of the whole system. The test results of the whole system are shown in Fig. 7.

5 Conclusion By acquiring the joint coordinate data α1 α2 and α3 of the human skeleton from the visual sensor and acquiring the motion information of the arm and the wrist by the wearable sensor, the 6-DOF robot is finally controlled. Thereby, the natural human-computer interaction mode of the motion control is realized to improve the interaction mode between the human and the robot. Through the experimental data, it can be seen that the GUI interaction mode using the visual sensor and the wearable sensor can realize the precise control of the robot arm, greatly improving the efficiency of human-computer interaction, and greatly simplifying the interaction between the human and the robot. Moreover, the implementation is simple, and it has very important significance for the future medical rehabilitation, bomb disposal, and aerospace remote control. Acknowledgements This work was supported partly by district science foundation program of a study on soft grab method based on active excitation and state recognition of manipulator system (60663005) and talent introduction scientific research project of Guizhou University named a research on H-inf comprehensive control of moving objects (201801).

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References 1. Zhong, J., Cao, J.S.: Implementation of the 6-dof mechanical arm control system based on kinect V2. J. Mach. Tools Hydraul. 9, 81–85 (2018) 2. Li, H.B., Li, S.S., Sun, H.Y.: Methods of human motion and gesture recognition based on Kinect bone data. J. Comput. Eng. Des. 4, 969–975 (2016) 3. Xin, Y.Z., Xing, Z.F.: Methods of human motion recognition based on kinect. J. Comput. Eng. Des. 4, 1056–1061 (2016) 4. Xin, J., Guo, J.L., Ma, X.M., Huang, K.: The perspective of mobile machine people based on kinect. J. Robot. 5, 560–568 (2014) 5. Pan, S.Y.: Interactive system and control behavior design of live interactive art—taking Myo wristband as an example. J. Chin. Media Technol. 3, 75–77 (2018) 6. Wu, G.B.: Kinect Human-Computer Interaction Development Practice. People Post and Telecommunications Press (2013) 7. Han, Z., Liu, H.P., Huang, W.B.: Robot arm target grabbing based on Kinect. J. Intell. Syst. 2, 149–155 (2013) 8. Yu, T.: Practical Application Development of Kinect and Dialogue with Machine in the Most Natural Way. Mechanical Industry Press (2013) 9. Gordon, M., Tang, Y.: A Guide to Arduino Robotics. Science Press (2014) 10. Gaber, A., Faher, M.F., Waned, M.A.: Automated grading of facial paralysis using the kinect V2: a proof of concept study. In: Virtual Rehabilitation Proceedings (ICVR), pp. 258–264. IEEE, Spain (2015) 11. International Federation of Robotics.: IFR forecast: 1.7 million new robots to transform the world’s factories by 2020. R. Frankfurt (2017)

A Novel Capacitor Voltage Balancing Control Strategy for Modular Multilevel Converters Jian Li, Zhuo Chen, Aiping Pang, Qingfang Zhang, Zhanbao Wang, Jiawei Ma and Fei Liu

Abstract In engineering applications, there are hundreds of sub-modules in modular multilevel converter high-voltage direct-current (MMC-HVDC) transmission system. Voltage equalization of SM capacitors is always a key technical problem for stable operation of MMC. In order to solve the problem of traditional capacitor voltage sorting, this paper adopts the idea of integer factorization to group the bridge arm modules. Due to the voltage imbalance between groups, a inter group voltage balancing method is proposed. And according to the number of grouping groups, different sorting methods are selected, so then the sorting operation and the requirement for the hardware of the system are reduced. Aiming at the problem of large switching loss caused by repeated switching of IGBT SM in traditional voltage equalization method, this paper introduces the retention coefficient to reduce the switching frequency and the loss of SM. Finally, a double-ended MMC-HVDC supplying active networks is built in Matlab/Simulink to verify the correctness and effectiveness of the proposed capacitor voltage equalization method. Keywords MMC-HVDC · Integer factorization · Interblock voltage balancing method · Retention coefficient · Switching frequency J. Li · Z. Chen (B) · A. Pang · Q. Zhang · Z. Wang · J. Ma · F. Liu College of Electrical Engineering, Guizhou University, Guiyang 550025, Guizhou, China e-mail: [email protected] J. Li e-mail: [email protected] A. Pang e-mail: [email protected] Q. Zhang e-mail: [email protected] Z. Wang e-mail: [email protected] J. Ma e-mail: [email protected] F. Liu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_7

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1 Introduction The MMC is a new topological construction applied to voltage source DC transmission. It not only has the characteristics of voltage source converter, but also has many advantages. For example, its highly modular structure design can be extended to different voltage levels, its many output level numbers makes the output voltage quality high, and MMC has a good fault protection to work in three-phase unbalanced state [1]. Therefore, MMC-HVDC has become a research hotspot in the field of high voltage and high-power multilevel transmission. In practical engineering applications, the number of SMs is very large, each time the capacitor voltage must be sorted, and the amount of calculation is large, which brings a huge challenge to the hardware system. In addition, frequent switching of traditional methods will lead to high converter loss and reduce the service life of switching devices. Therefore, in order to reduce the number of sorting and switching losses, it is particularly important to improve the SM capacitor voltage equalization method. An improved method for MMCs is proposed,which can keep the capacitance voltage balance and reduced the height of the staircase output voltage by 50% than the carrier phase shifted width modulation, but it is not suitable for large power transmission systems [2]. A general framework for the capacitor voltage balancing of an MMC is proposed to reduce the unnecessary switching transitions, but it does not consider the number of capacitor voltages sorting [3]. An improved quick sort algorithm is applied to MMC-HVDC, by this method, the calculation efficiency has been greatly enhanced and the hardware requirements is reduced [4]. Aiming at the large number of MMC SMs in practical engineering, in order to reduce the number of sorting times and the switching frequency of SMs. Firstly, this paper adopts the idea of integer factorization to group the SMs, a group voltage balancing method is proposed to solve the voltage imbalance between groups. Then, according to the number of grouping groups, different sorting methods are selected, so as to improve the calculation speed. Aiming at the problem of large switching loss, this paper introduces the retention coefficient to reduce the switching frequency and the loss of SM. Finally, Two-terminal MMC-HVDC is built based on Matlab/Simulink to verify the reliability and correctness of the proposed capacitor voltage equalization method.

2 The Traditional Capacitor Voltage Balancing Strategy 2.1 The Working Principle of MMC The topology of three-phase MMC is shown in Fig. 1, which consists of 6 bridge arms. Each phase include upper and lower arms, and a single arm has N identical SMs and an inductance L0. In Fig. 1, Usm (m = a, b, c, the same below) is the equivalent potential of the M phase. Rm and L m are the resistance and inductance of the AC

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SM 1

SM 1

SM1

SM 2

SM 2

SM 2

SM n

SM n

SM n

P I dc

Udc /2 Usa

Ra

La

Rb

Lb

L0

Ia Usb Usc

L0

+

L0

Ib

Udc

−

Ic Rc

Lc

L0

L0

L0

SM 1

SM 1

SM 1

SM2

SM 2

SM2

SM n

SMn

SM n

O

Udc /2

N

Fig. 1 The topology of three-phase MMC

system, respectively. The output voltage and current on the DC side are represented by Udc and Idc respectively, and O represents the center point on the DC side. A single SM consists of two IGBTs, two reverse parallel diodes and a capacitor, and the structure is shown in Fig. 2. Each SM has three working states: locking, cutting and switching. The SMs are connected to the main circuit topology by cascade method. In the MMC topology, the upper and lower arms of each phase form a phase unit. In regular work, half of the SMs of each phase unit are put into operation to ensure the stability of DC voltage. The desired AC side voltage can be obtained by changing the distribution relationship between the upper and lower arm of each phase unit [5].

+

Fig. 2 The structure of a single SM

T1

D1

iSM C

SMn

uSM T2

−

D2

UC

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2.2 Voltage Balancing Method Based on Traditional Sorting In MMC-HVDC system, SM’s capacitance is independent of each other. The capacitance value, charge-discharge and loss of each SM will affect the voltage value of capacitor and seriously endanger the normal operation of MMC. In MMC-HVDC, the number of sub modules Non to be put into which is calculated according to the NLM. When the bridge arm current charges the SMs, the capacitance voltage of each bridge arm is monitored, and the capacitance voltage is sorted from low to high, and the first Non SMs are put in, and the remaining SMs are cut off. When the bridge arm current discharges to the SM, the capacitor voltage is sorted from high to low, and the first Non SM is put in, and the remaining SM is cut off. Take bubble sorting method, as an example to illustrate the sorting of capacitor voltage of N SMs, the number of capacitor voltage sorting is T = (n − 1) + (n − 2) + · · · + 1 =

n2 − n 2

(1)

Formula (1) When the number of SMs in the phase unit is large, the number of sorting times per time will increase by square, and the amount of sorting calculation is very large. At the same time, each rescheduling results in frequent switching of IGBT increases system attrition. To solve these problems, this paper proposes an optimized capacitor voltage equalization control strategy, which can ensure the effect of capacitor voltage equalization and reduce the number of sorting to avoid frequent switching of SMs.

3 Optimized Capacitance Voltage Balance Strategy 3.1 Integer Factorization Grouping Sorting Algorithm The main idea of Integer factorization grouping sorting algorithm is to analogize the idea of integer prime factor decomposition and group the bridge arm modules. Mathematical proof shows that grouping which according to the Integer factorization from big to small can greatly reduce the number of capacitor voltage sorting and improve the efficiency of sorting. Assume that the number of individual bridge arm SMs is N, Multi-layer grouping which sorts from big to small based on Integer factorization, we get: N = n 1 × n 2 × n 3 × . . . × n k . . . × n h ,Where,n h is the number of groups contained in the k level, n 1 > n 2 > n 3 · · · > n k · · · > n h . Take 250 SMs as an example to illustrate the multi-layer grouping, which is divided into four layers, 250 = 5 * 5 * 5 * 2, as shown in Fig. 3a. Figure 3b is a result graph of a multi-layer grouping with Integer factorization. According to the complexity based on quick sort method

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5 groups 5 groups 5 groups 2 groups

(a) Grouping method

(b) a result graph of a multi-layer grouping

Fig. 3 Diagrammatic sketch of integer factorization

T (n) = O(n log2 n)

(2)

We get integer factorization ranking times T which is adopted quick sort. T = n 1 log2 n 1 + n 1 · n 2 log2 n 2 + · · · + (n 1 n 2 . . . n k ) log2 n k ⎡⎛ ⎞ ⎤ k i   ⎣⎝ n j ⎠ log2 n i ⎦ = i=1

(3)

j=1

Suppose T1 is the times of Integer factorization with bubble method, T2 is the times of Integer factorization with fast sorting, the difference between the two sorting times ⎛⎛ ⎞ ⎛⎛ ⎞ ⎞ ⎞ k i k i     n − 1 ⎝⎝ n j ⎠ i ⎝⎝ n j ⎠log2 n i ⎠ ⎠− T = T1 − T2 = 2 i=1 j=1 i=1 j=1 ⎛ ⎞

 k i  ⎝ n i − 1 − log2 n i = n j⎠ (4) 2 i=1 j=1 Through analysis, it is concluded that: (1) x ∈ (0, 2In2), y  < 0, y monotonically decrease; (2) x ∈ (2In2, +∞), y  > 0 y monotonically increase. Based on the above analysis, the bubble sorting algorithm is used when the number of groups n k < 7, and the fast sorting algorithm is used when the number of groups n k ≥ 7. According to the above analysis, different groups need to use different sorting algorithms, which can reduce the number of capacitor voltage sorting, and improve the operational ability of the calculator. Packet sorting solves the problem of capacitor voltage balance in each group, but it also causes the problem of capacitor voltage imbalance among groups. In order to solve the problem of voltage imbalance between two groups, a method of inter group voltage balancing is proposed. The idea is to monitoring the capacitance voltage and summing the capacitance voltage in each

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group. According to the number of groups, select the appropriate sorting algorithm to sort the sum of the capacitance voltage in each group. By using the number of sub modules required at this time divided by the number of groups, the quotient X and the remainder y are obtained. The quotient x is the cardinal number of the SMs in each group, and the remainder y is assigned to the first Y group in turn according to the order of the total voltage.

3.2 Optimized Trigger Mode Compared with the traditional sorting method, the Integer factorization grouping sorting algorithm mentioned above can significantly reduce the number of sorting calculations and reduce the sorting complexity. But, the above method will lead to frequent switching of sub modules and increase the loss of sub modules. Aiming at this problem, this paper introduces the retention coefficient on the basis of mixed sorting, which increases the input probability of the sub module in the next action. In this way, we reduce the number of sorting while avoiding frequent switching of sub modules. The steps are as follows: (1) When the bridge arm current charges the input SM capacitor, the original input SM voltage is divided by a retaining coefficient which slightly more than 1. Then, according to the multilayer grouping sorting, the switching of sub modules is determined. (2) When the bridge arm current discharges the input SM capacitor, the original input SM voltage is multiplied by a retaining coefficient which slightly more than 1. Then, according to the multilayer grouping sorting, the switching of sub modules is determined.

3.3 A Voltage Balancing Control Flow Chart for Multilayer Grouping Sorting The multi-layer grouping of SM capacitance voltage and the method of introducing retention coefficient can significantly reduce the number of sorting. n the whole system operation process, it can not only ensure the equalization effect of the capacitor voltage of the SM, but also reduce the frequent switching of the IGBT. The specific actualization process are as follows: (1) The number of bridge arm SM N is resolved by integer factorization, it contains a total of H layers. The capacitance voltage of each SM is monitored and the number of M SMs which need to be put into is determined. Then the charge and discharge of the sub module capacitor is determined according to the current direction.

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(2) For the first layer, they are divided into n1 groups, and the sum of the capacitance voltages in each group is calculated. If the arm current Iarm > 0, the original input SM voltage is divided by a retaining coefficient which slightly more than 1. If the arm current Iarm < 0, the original input SM voltage is multiplied by a retaining coefficient which slightly more than 1. Then, according to whether the number of the groups n1 is less than 7, the sorting method for the total voltage of each group is determined. According to the positive and negative currents of the bridge arm, the sorting order of capacitor voltage is determined. Finally, the number of sub modules N is divided by n1, the quotient X and the residue y are worked out. The number of sub modules in each group can be obtained by the capacitor voltage balancing method. (3) For the k (1 < k < h) layer, the sum of the capacitance voltage of each group is calculated respectively. Then the sorting method is determined by whether the number of group groups is less than 7. Finally, according to the method of capacitor voltage balance between groups, the number of sub modules should be determined in each group. (4) For the last layer, that is, layer h. Whether the number of sub modules which allocated by this group is less than 7 determines to use the quick sorting algorithm or bubble sorting algorithm. Finally, the sub module needed to be input in the bridge arm is determined. Taking the first layer as an example, the process is introduced through the flowchart, as shown in Fig. 4.

4 Simulation Results 4.1 Simulation Model and Parameter Introduction In order to verify the feasibility and effectiveness of the proposed sub module capacitor voltage balancing strategy in this paper, a double-ended 89-level MMC-HVDC supplying active networks simulation system is built in Matlab/Simulink, the system diagram is shown in Fig. 5. The simulation uses two identical parameters of the converter station, the main parameters of the system are shown in Table 1. The rectifier part MMC1 adopts constant DC voltage and constant reactive power control, the reference values are set to 10,120 V and 0 Var respectively. The inverter part MMC2 adopts constant active power and constant reactive power control, the reference values are set to 105 V and 104 Var respectively.

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J. Li et al. Start multilayer grouping using integer factorization for the first layer, the sum of the total voltage of each group is calculated NO

I arm

YES

0

The original input SM voltage is divided by a slightly more than 1

The original input SM voltage is multiplied by a slightly more than 1 NO

n

n

7

bubble method to sort from big to small

Quotient x

YES bubble method to sort from big to small

Remainder y quick sort methodto sort from big to small

quick sort methodto sort from big to small

Take the front x SM to Turn on in each group

NO

7

The number of SMs to be input is divided by the number of groups in the layer

YES

YES

Take the front x SM to Turn on in each group

NO

Sequence number 0. A typical Lyapunov function [21] can be expressed as follows: V (t) =

1 T s Ms 2

(40)

The control input can be defined as τ = Te Ke ue where the control input ue is expressed as: −1 −1 ue = −T+ e Ke {Mo R [K sp sgn(s) + K si s + K sd v ˙ + κ η] ˙ − Dv} + Rv

(41)

where K sp , K si , K sd are the adjustable control gains, T+ = (TT T)−1 TT is the Moore–Penrose pseudoinverse and sgn(s) is defined as:  sgn(s) =

+1, for s ≥ 0 −1, for s < 0

(42)

By substituting ue back into τ = Te Ke ue then into V˙ yields: V˙ (t) ≤ sT M[−K sp sgn(s/) − K si s − K sd v] ≤ 0

(43)

The control gains [21] K sp , K si and K sd are chosen to be large enough such that V˙ (t) ≤ 0. Notice that, V˙ ≤ 0 implies V (t) ≤ V (0), and therefore that s is bounded. It also implies that V¨ is bounded and V˙ must be uniformly continuous. With Barbalat’s ˜ implies the lemma, it shows that s → 0 gives η˙˜ + κ η˜ = 0, and thus η(t) ˜ = e−κt η(0) position error, η(t) ˜ converge to zero exponentially as t → ∞. Hence, the system is therefore asymptotically stable.

7 Dynamic Positioning Simulation and Discussion In this section, a DP system for the STENA DRILLMAX Drillship was created in MATLAB and Simulink [22]. The controllers such as the PID and SMC will

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Table 2 Parameters used in DP simulation Parameters

Values

λ

0.26

X u˙ , Yv˙

{−4.8500 × 106 , −1.6268 × 108 }

Yr˙ , Nv˙ , Nr˙

{0, 0, −7.0544 × 1011 }

X u , Yv

{21.100, 259.80}

Yr , Nv , Nr

855.40, 855.40, 6130.5}

xg

0m

A Fw , A Lw

{969.0, 2978.4} m2

A Fc , A Fc

[504.0, 2736.0] m2

ρ, ρ a

1030, 1.204 kg/m3

cXw , cYw , cNw

{0.700, 0.825, 0.125}

V w, V c

45, 2.5 m/s

cXc , cYc , cNc

{0.480, 0.650, 0.035}

Ke

[1 0 1 0 1 0 1 0 1 0 1 0; 0 1 0 1 0 1 0 1 0 1 0 1; −18.8 110 −18.8 110 0 101 − 18.8 61 −18.8 61 0 96]

M

Diag{101.8 × 106 , 259.6 × 106 , 705.4 × 109 } ⎞ ⎛ −21.1 0 0 ⎟ ⎜ ⎜ 0 −259.8 −855.4 ⎟ ⎠ ⎝ 0 −855.4 −6130.5

D

compare and discuss. In addition to Tables 1 and 2 shows the parameters used in the simulation. In the DP system, the actual position vector η, is subtracted from ηd in order to compute the position error. A switch allows the user to choose the types of controller. The controller determines the control input to the thrusters located in the middle of the diagram. The upper part of the diagram shows the current, wave and wind acting on the STENA DRILLMAX drillship model. The maximum forces and moment for the wave, wind and current are namely: 7700 × 102 kN, 7420 × 103 kN and 4190 × 105 k Nm, respectively. The thruster model generates the thrust to maneuver the drillship. The transformation matrix provides the transformation from body-fixed to earth-fixed coordinate to obtain the surge, sway and heading angle. The desired drilling position and heading are: x = 5 m, y = 4 m, and ψ = 20°. The wind speed (V w ) was 45 m/s at 30° wind direction, current speed (V c ) was set to 2.5 m/s in the same direction as the wind. Simulation time of 1000 s was used. The responses in position and velocity can be seen in Fig. 1. The PID control parameters were obtained via the PID Tuner. On the other hand, the SMC control parameters were obtained by examining the asymptotical stability of output responses. The parameters of the PID and SMC are tabulated as shown in Table 3. Note that the gains used in the controllers are quite high in order to attenuate the external disturbances. Both controllers exhibit good steady-state responses in the position and velocity as seen in Fig. 1. The SMC requires more time to reach a steady-state position as

Sliding-Mode Control of STENA DRILLMAX Drillship … Position Response

PID SMC

2 0 0

100

200

300

400

500

600

700

Velocity Response

4

4

u(m/s)

x(m)

6

109

800

900

0

2

4

6

8

v(m/s)

y(m)

4 2

14

16

18

20

0

100

200

300

400

500

600

700

800

900

12

14

16

18

20

12

14

16

18

20

0 -5

1000

0

2

4

6

8

10

Time(s)

Time(s) 40

0.4

\r(rad/s)

(deg)

12

5

6

20 0

10

Time(s)

Time(s)

0

SMC

0 -2

1000

PID

2

0

100

200

300

400

500

600

700

800

900

1000

0.2 0 -0.2

0

2

4

6

Time(s)

8

10

Time(s)

Fig. 1 Position (left) and velocity (right) response of STENA DRILLMAX at x = 5 m, y = 4 m, and ψ = 20° under external disturbances

Table 3 Controllers’ parameters for each DoF Controller

Control parameters for each DoF Surge

Sway

Yaw

PID

K P = 1.9 × Ki = 8.9 × 105 K D = 9.9 × 107

SMC

K sp = 1.9 × 107 , K si = 4.9 × 107 , K sd = 7 × 1010 , κ = 10,  = 0.5

107 ,

K P = 4.8 × Ki = 2.2 × 106 K D = 2.5 × 108 107 ,

K P = 1.3 × 1011 , K i = 6.1 × 109 K D = 6.8 × 1011

compared to the PID controller. The rate of change in the position or velocity is lower when compared to the PID controller. The PID has a higher overshoot in the velocity as compared to SMC. It is due to the sudden increase in velocity to move the drillship to the desired position. On the other hand, the steady state error in surge and sway direction are quite similar except for the yaw angle. As deduced in Fig. 1, the steady state error of the yaw angle is higher than the SMC. Further increase in the control gains for the yaw angle may be required. However, it can cause the time to reach the steady-state value to increase. As seen in Fig. 2, the trajectory of the drill ship can be plotted. The PID takes a longer path to reach the desired position as compared to the SMC. In summary, the PID performs quite well as seen in the position response. As compared to PID, SMC takes a shorter path to reach the target position. Figure 2 shows that the DP model can maintain the target position within the standard deviation of 15 m for the drilling operation and 30 m for the standby condition.

8 Conclusions This paper presented the dynamic positioning simulation of STENA DRILLMAX drillship. The sliding-mode control (SMC) were simulated and compared with proportional-integral-derivative (PID) controller subjected to environmental forces

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Fig. 2 Trajectory of STENA DRILLMAX Drillship under external disturbances

from wind, wave and current. From the simulation results, the PID controller achieved better yaw control as compared to SMC. However, the rate of change in the position is higher in PID than SMC. The results showed the SMC performed better in velocity regulation than PID. Future works will include intelligent means to tune the controller gains and predict the trajectory of the drillship under varying external disturbances. More detailed comparisons will be performed with other controllers. Acknowledgements The authors are grateful to Newcastle University in Singapore.

References 1. Zheng, M., Zhou, Y., Yang, S., Li, L., Suo, Y.: Design of robust H∞ controller for dynamic positioning ships based on sampled-data control. In: 32nd Youth Academic Annual Conference of Chinese Association of Automation, Anhui, China, pp. 1106–1110 (2017) 2. Fu, M., Sun, J., Wang, D.: Research on thrust allocation of dynamic positioning ship with cycloidal propeller. In: 37th Chinese Control Conference (CCC), Wuhan, China, pp. 620–624 (2018) 3. Zhang, Z., Wu, D. Operator panel design for dynamic positioning simulator. In: 2018 Chinese Automation Congress (CAC), Xi’an, China, pp. 1020–1023 (2018) 4. Chen,Y., Yang, X., Liu, R.: A nonlinear sate estimate for dynamic positioning based on improved particle filter. In: 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference, Chongqing, China, pp. 880–884 (2018) 5. Xie, D., Jia, B., Ren, Y.: Control System Design for Dynamic Positioning Ships Using Nonlinear Passive Observer Backstepping, 2018 Chinese Automation Congress (CAC), pp. 4221–4226. Xi’an, China (2018) 6. Chas, C.S., Ferreiro, R.: Introduction to ship dynamic positioning systems. J. Marit. Res. V(1), 79–96. Santander, Spain (2008) 7. Balchen, J.G., Jenssen, N.A., Saelid, S.: A dynamic positioning system based on Kalman filtering and optimal control. Int. J. Model. Ident. Control (IJMIC) 1(3), 135–163 (1980)

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8. Saelid, S., Jenssen, N.A., Balchen, J.G.: Design and analysis of a dynamic positioning system based on Kalman filtering and optimal control. IEEE Trans. Autom. Control 28(3), 331–339 (1983) 9. Agostinho, A.C., Moratelli Jr., L., Tannuri, E.A., Morishita, H.M.: Sliding mode control applied to offshore dynamic positioning systems. In: Proceedings of the IFAC International Conference on Manoeuvring, Guarujá, Brazil (2009) 10. Ho, W.H., Chen, S.H., Chou, J.H.: Optimal control of Takagi-Sugeno fuzzy-model-based systems representing dynamic ship positioning systems. Appl. Soft Comput. 13, 3197–3210 (2013) 11. Yin, Y., Xia, L., Song, L., Ren, Z.: The ship IPMS networked control system modelling and design. Int. J. Model. Ident. Control (IJMIC) 20(3), 234–241 (2013) 12. Du, J., Yang, Y., Wang, D., Guo, C.: A robust adaptive neural networks controller for maritime dynamic positioning system. Neurocomputing 110, 128–136 (2013) 13. Fang, M.C., Lee, Z.Y.: Application of neuro-fuzzy algorithm to portable dynamic positioning control system for ships. Int. J. Naval Archit. Ocean Eng. 8, 38–52 (2016) 14. Wang, Y., Guo, C., Sun, F., Shen, Z., Guo, D.: Dynamic neural-fuzzified adaptive control of ship course with parametric modelling uncertainties. Int. J. Model. Ident. Control (IJMIC) 13(4), 251–258 (2011) 15. Wang, M., Li, H.S., Qing, M., Rong, B.G.: Intelligent control algorithm for ship dynamic positioning. Arch. Control Sci. 24(LX), 4, 479–497 (2014) 16. Chang, W.J., Ku, C.C., Huang, B.J.: Multi-constrained fuzzy intelligent control for uncertain discrete systems with complex noises: an application to ship steering systems. J. Mar. Eng. Technol. 16(1), 11–21 (2017) 17. IMCA M 198. Dynamic Positioning Station Keeping Incidents—Incidents Reported for 2007 (2009) 18. Society of Naval Architects and Marine Engineers (SNAME), Principles of Naval Architecture, Vol. III, pp. 41, Section 3—Ship Responses to Regular Waves (1989) 19. Lio, C.S.: Development of a Control System for the Dynamic Positioning of Ships. Dissertation for Bachelor of Engineering in Marine Engineering, School of Marine Science and Technology, Newcastle University (2017) 20. Fossen, T.I.: Handbook of Marine Craft Hydrodynamics and Motion Control. Wiley, UK (2011) 21. Chin, C.S., Lin, W.P.: Robust genetic algorithm and fuzzy inference mechanism embedded in sliding-mode controller for uncertain underwater robot. IEEE/ASME Trans. Mechatron. 23(2), 655–666 (2018) 22. Chin, C.S., Lau, M.W.S., Low, E., Seet, G.G.: Software for modelling and simulation of a remotely operated vehicle. Int. J. Simul. Model. 5(3), 114–125 (2006)

Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas Qing Xiao and Shao-Wu Zhou

Abstract In this paper, the statistical features of correlated wind speeds at multiple sites are characterized by marginal distributions and Archimedean copulas. Firstly, the generalized lambda distribution (GLD), kappa distribution and Weibull distribution are employed to recover the quantile function of wind speed at each site. Then, three new Archimedean copula models are constructed to characterize the dependence structure of historical wind speed data. Based on Rosenblatt transformation, a generic algorithm is presented to produce sample realizations of correlated wind speeds, which would have the same statistical features as historical wind speed data. Finally, numerical examples are given to illustrate the proposed methods. Keywords Correlated wind speeds · Generalized lambda distribution · Kappa distribution · Weibull distribution · Archimedean copula · Rosenblatt transformation

1 Introduction In recent years, renewable energy sources like wind power have been increasingly integrated into the electric grid [2, 6]. One decisive factor for the output of wind turbines is the wind speed, which is often modeled as a random variable due to changeable weather conditions at wind farms [17]. Because wind speeds at neighbouring sites are non-normally distributed and dependent of each other, when anaQ. Xiao · S.-W. Zhou (B) School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, Hunan Province, China e-mail: [email protected] Q. Xiao e-mail: [email protected] Q. Xiao College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, Hunan Province, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_11

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lyzing the impact of wind power on power system operation, statistic models should be employed to represent correlated wind speeds. Let X = (X1 , . . . , Xi , . . . , Xm ) denote wind speeds at m sites. Because X is not an independent random vector, it is difficult to directly construct the joint cumulative distribution function (CDF) of X, and researchers often resort to copula theory [9], whereby the joint CDF of X can be constructed as follows: (1) Transform each random variable Xi to a standard uniform variable: Ui = Fi (Xi ), i = 1, . . . , m,

(1)

where Fi (·) is the CDF of Xi . (2) Create the joint CDF of U = (U1 , . . . , Ui , . . . , Um ): C(U) = C(U1 , . . . , Ui , . . . , Um ),

(2)

where C(·) is the CDF of U. (3) Construct the joint CDF of X by: F(X) = C(U1 , . . . , Ui , . . . , Um ) = C(F1 (X1 ), . . . , Fi (Xi ), . . . , Fm (Xm )),

(3)

where F(X) is the joint CDF of X. Given a set of historical wind speed data, analytical expressions of Fi (Xi ) (i = 1, . . . , m) in Eq. (1) are generally unknown, and Weibull distribution is often recommended to fit wind speed data [1, 12]. However, in some cases, more flexible models should be employed to recover the probability distributions of wind speeds [15]. Along with Weibull distribution, three different statistic models are presented in Table 1, where GLD denotes the generalized lambda distribution, Kappa is the kappa distribution. Because quantile functions of these models are in closed form, it can facilitate generating samples of wind speeds by inversing the transformation in Eq. (1): (4) Xi = Fi−1 (Ui ), where Fi−1 (·) is the inverse CDF of Xi . With marginal distributions of Xi (i = 1, . . . , m), copula models can be introduced to construct C(U) in Eq. (2), then the joint CDF of correlated wind speeds can be recovered by Eq. (3). The elliptical copulas can capture the mutual dependence structure of wind speeds, and are relatively easy to be sampled [3, 8, 13]. Compared to elliptical copulas, Archimedean copulas are the high flexibility, and can represent different types of dependence structures with different generators [16, 20]. The major disadvantage of Archimedean copulas is that it is not convenient to generate samples. In [10], a Laplace transform based method is developed to sample Archimedean copulas, which is very efficient and convenient. However, this method

Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas Table 1 A summary of probability distributions Distribution U = F(X ) GLDa Kappab Weibull a The b The

−   1/k 1/h 1 − h X −a  b  b  1 − exp − Xa

115

X = F −1 (U ) U λ3 −(1−U )λ4  λh2 k + b 1−U h

λ1 + a

1

a [−ln(1 − U )] b

procedures for parameterizing GLD can be found in [18] procedures for parameterizing the kappa distribution can be found in [19]

requires to perform inverse Laplace transform on the generator to obtain a probability distribution, from which random deviates are generated to transform independent standard uniform variables to samples of Archimedean copulas, and it is applicable to a few Archimedean copulas [4, 5]. This paper sets out to develop three Archimedean models to model correlated wind speeds at multiple sites, and the contribution is two-fold: (1) it develops three new Archimedean copula models; (2) based on Rosenblatt transformation, it presents a generic algorithm to generate samples of the proposed Archimedean copulas, which can be further transformed to samples of correlated wind speeds. The following part of the paper is outlined as follows: Sect. 2 derives new Archimedean copula models using trigonometric generators. Section 3 presents the algorithm for sampling Archimedean copulas. In Sect. 4, case studies are conducted to illustrate the proposed algorithms. Section 5 gives some conclusions.

2 Trigonometric Archimedean Copulas In this paper, the Fully nested Archimedean copula (FNAC) is employed to represent the dependence structure of wind speeds, and it constructs C(U) as follows:  Cm (U1 , U2 , . . . , Um ) = ψ1 ψ1−1 (U1 ) + ψ1−1 (Cm−1 (U2 , . . . , Um−1 )) .

(5)

For example, if m = 3, it has: C3 (U1 , U2 , U3 ) = ψ1 (ψ1−1 (U1 ) + ψ1−1 (C2 (U2 , U3 ))) = ψ1 (ψ1−1 (U1 ) + ψ1−1 (ψ2 [ψ2−1 (U2 ) + ψ2−1 (U3 )])),

(6)

where ψ(·) is the generator of Archimedean copula [11]. In [14], five different generators are developed using cotangent and cosecant functions. Because the fourth and fifth generators are limited to highly correlated dependence structures, where the Kendall’s tau should be no less than 0.5, and they are discarded. The other three generators are presented in Table 2. Following Eq. (6), the analytical expressions of C3 (U1 , U2 , U3 ) are given in Table 3.

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Table 2 Three different generator functions Family θ ψ(t)

 

ψ −1 (t)   cotθ π2 t   cot π2 t θ

cot-I

[1, ∞)

cot-II

[1, ∞)

1 2 θ π arccot t 1 2 θ π arccot(t)

[0.5, ∞)

 π   θ 1 2 θ csc 2 t − 1 π arccsc 1 + t

csc

Kendall’s τ 1−

8 π2θ

1−

1 4 πθ

1+

sin(π t θ ) dt 0 t θ−1 16[ln(2)−1] π2θ

Table 3 Three Archimedean copula models (θ2 ≥ θ1 ) Family C3 (U1 , U2 , U3 ) 

1 π   θ π   π  θ1 θ1 2 θ θ θ2 1 2 2 cot-I cot 2 u1 + cot 2 u2 + cot 2 u3 π arccot  cot-II

csc

 2 π arccot

θ1  2 u1 + cot

π

 π 2



2 π arccot



 θ1

 π θ2  θ2  2 u2 + cot 2 u3

π

θ2



1 θ1

cot cot ⎧ 1⎫  ⎨  θ1    π   θ2   π  θ2  θθ21 θ1 ⎬  π  2 csc 2 u1 − 1 + csc 2 u2 − 1 + csc 2 u3 − 1 π arccsc ⎩1 + ⎭

If Kendall’s tau is used to quantify the dependence structure of FNA in Eq. (6), it would give the following correlation matrix: ⎛

⎞ 1 τ1,2 τ1,3 RU = ⎝ τ1,2 1 τ2,3 ⎠ . τ1,3 τ2,3 1

(7)

where RU is the correlation coefficient matrix of U = (U1 , U2 , U3 ). τi,j is the correlation coefficient between Ui and Uj . For example, if the “cot-I” generator is used to construct copula models, RU should be ⎛

⎞ 1 1 − π 28θ1 1 − π 28θ1 1 1 − π 28θ2 ⎠ . RU = ⎝ 1 − π 28θ1 1 − π 28θ1 1 − π 28θ2 1

(8)

Therefore, the parameters θ1 and θ2 of copula models in Table 3 can be determined using the rank correlation matrix of wind speeds. Although all Archimedean copulas in Table 3 can match the correlation matrix of correlated wind speeds, they are constructed by different generators, and thus yield different dependence structures. When these copulas are used to model correlated wind speeds, a goodness of fit should be conducted to select the optimal copula model. In Sect. 4, the P-P plot is employed to check the performance of each copula model.

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3 Generating Samples of Correlated Wind Speeds Because it is difficult to perform inverse Laplace transform on generators in Table 2, Rosenblatt transformation is therefore introduced in this paper to sample Archimedean copulas, which employs conditional marginal distributions of Ui (i = 1, . . . , m) to relate U to V [7]: V1 = C1 (U1 ) V2 = C2|1 (U2 |U1 ) .. . Vi = Ci|1,2,...,i−1 (Ui |U1 , . . . , Ui−1 ) .. . Vm = Cm|1,2,...,m−1 (Um |U1 , . . . , Um−1 ),

(9)

where V = (V1 , . . . , Vi , . . . , Vm ) is an independent standard uniform vector. In Eq. (9), Ci|1,2,...,i−1 (Ui |U1 , . . . , Ui−1 ) is the conditional marginal distribution of Ui , which can be calculated by following steps: (1) Set Uj = 1 (j = i + 1, . . . , m), obtain the joint distribution of (U1 , . . . , Ui ): Ci (U1 , . . . , Ui ) = C(U1 , . . . , Ui , 1, . . . , 1),

(10)

(2) Calculate (i − 1)th-order mixed partial derivative of C i (U1 , . . . , Ui ) and C i−1 (U1 , . . . , Ui−1 ): ∂ (i−1) C i (U1 , . . . , Ui ) , ∂U1 · · · ∂Ui−1

∂ (i−1) C i−1 (U1 , . . . , Ui−1 ) . ∂U1 · · · ∂Ui−1

(11)

(3) Obtain the conditional marginal distribution of Ui : Ci|1,2,...,i−1 (Ui |U1 , . . . , Ui−1 ) =

∂ (i−1) C i (U1 ,...,Ui ) ∂U1 ···∂Ui−1 ∂ (i−1) C i−1 (U1 ,...,Ui−1 ) ∂U1 ···∂Ui−1

.

(12)

Denote samples of V as v k = (v1,k , . . . , vi,k , . . . , vm,k ) (k = 1, . . . , n), denote samples of U as uk = (u1,k , . . . , ui,k , . . . , um,k ) (k = 1, . . . , n). According to Eq. (9), v k can be transformed to uk by inverse functions of Ci|1,2,...,i−1 (Ui |U1 , . . . , Ui−1 ) (i = 1, . . . , m):

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Table 4 Parameters of GLD, Kappa distribution and Weibull distribution Distribution Sample λ1 λ2 λ3 GLD

Distribution Kappa

Distribution Weibull

1 2 3 Sample 1 2 3 Sample 1 2 3

10.5246 2.6374 7.0942 a 13.2766 19.9320 15.4031 a 8.1348 6.4357 8.2989

0.0829 0.0683 0.1214 b −7.8255 −16.5096 −8.6920 b 3.0159 2.6444 4.3620

0.4757 0.0290 0.1726 h 0.3177 0.4893 0.0294 – − − −

λ4 0.0551 0.3132 0.2558 k 0.6444 0.2291 0.2654 – − − −

u1,k = C1−1 (v1,k ) −1 (v2,k |U1 = u1,k ) u2,k = C2|1

.. . −1 (vi,k |U1 = u1,k , U2 = u2,k , . . . , Ui−1 = ui−1,k ) ui,k = Ci|1,2,...,i−1

(13)

.. . −1 (vm,k |U1 = u1,k , U2 = u2,k , . . . , Um−1 = um−1,k ), um,k = Ci|1,2,...,m−1

In most cases, inverse functions of Ci|1,2,...,i−1 (Ui ) (i = 1, . . . , m) cannot be given in closed form, and numerical methods are invoked to determine ui,k , then, uk can be transformed to samples of correlated wind speeds by quantile functions in Table 1.

4 Case Study Here, the proposed methods are tested for three sets of historical wind speed data, which are denoted as Sample-1, Sample-2 and Sample-3 respectively. The generalized lambda distribution (GLD), kappa distribution and Weibull distribution in Table 1 are employed to recover marginal distribution functions, the parameters of these distributions are summarized in Table 4, the probability distribution functions (PDFs) are depicted in Fig. 1. As can be seen, GLD and kappa distribution give a better representation of marginal distributions than Weibull distribution. The Kendall rank correlation matrix of wind data is:

Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas Sample−1 0.15

119

Sample−2 Histogram GLD Kappa Distribution Weibull distribution

Sample−3 Histogram GLD Kappa Distribution Weibull distribution

0.2 0.15

0.1

PDF

PDF

Histogram GLD Kappa Distribution Weibull distribution

0.2 0.15

PDF

0.1

0.1

0.05 0.05 0

0

5

10

0

15

0.05

0

2

4

X (m/s)

6

8

0 0

10 12 14 16

5

10

15

X (m/s)

X (m/s)

1

3

2

Fig. 1 The PDFs of wind speeds Table 5 The performance of Archimedean copulas Family θ1 θ2 Minimum 2.007 3.599 1.232

cot−I Copula

0

0.2

0.4

0.6

0.8

1

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

7.63 × 10−6 3.81 × 10−6

Mean

Maximum

0.014 0.020 0.016

0.033 0.068 0.073

cot−II Copula

Copula

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1.140 1.383 0.699

Copula

Copula

cot-I cot-II csc

2.29 × 10−6

0

0.2

Empirical distribution

0.4

0.6

0.8

1

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

csc Copula

0

Empirical distribution

0.2

0.4

0.6

0.8

1

Empirical distribution

Fig. 2 The P-P plots

⎛

⎞ 1 0.359 0.409 RU = R = ⎝ 0.359 1 0.641 ⎠ . 0.409 0.641 1 Using the correlation coefficient matching method, θ1 and θ2 are obtained (see Table 5). Following Eq. (3), the joint CDF of wind speeds is recovered, which is denoted as F(·). In order to assess the performance of each copula model, the theoretical distribution function F(·) is compared against the empirical joint distribution of wind speed samples:   εk = F(x1,k , x2,k , x3,k ) − F e (x1,k , x2,k , x3,k ) ,

(14)

where F e (·) is the empirical joint CDF of wind speeds, (x1,k , x2,k , x3,k ) is the k−th sample of wind speed, Table 5 presents the minimum value, mean value and maximum value of εk (k = 1, . . . , n). Figure 2 presents the P-P plots, and the copula model of “cot-I” family gives a better representation for wind speed data.

Q. Xiao and S.-W. Zhou cot−I Copula

cot−II Copula

0.8 0.7 0.6 0.5

Copula

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Copula

Copula

120

0.4 0.3 0.2 0.1

0

0.2

0.4

0.6

0.8

Empirical distribution

1

0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

csc Copula

0

Empirical distribution

0.2

0.4

0.6

0.8

1

Empirical distribution

Fig. 3 The P-P plots of samples generated by Rosenblatt transformation

In order to check the algorithm in Sect. 3, 103 samples are generated for each copula model in Table 3. Using C(U1 , U2 , U3 ) in Table 3 and empirical distribution of samples, the P-P plots are drawn. An observation of Fig. 3 indicates that dependence structures of samples can well match those of Archimedean copula models.

5 Conclusion Using trigonometric generators, three new Archimedean copula models are constructed to represent the dependence structure of wind speeds. Along with GLD and kappa distribution, the joint distribution of correlated wind speeds is recovered. The case study shows that Rosenblatt transformation can generate samples with a dependence structure defined by copula model. Acknowledgements This research is partially supported by National Natural Science Foundation of China (Grant No. 51577057).

References 1. Akgül, F.G., Seno˘ ¸ glu, B., Arslan, T.: An alternative distribution to Weibull for modeling the wind speed data: inverse Weibull distribution. Energ. Convers. Manage. 114, 234–240 (2016) 2. Asiabanpour, B., Almusaied, Z., Rainosek, K., Davidson, K.: A comparison between simulation and empirical methods to determine fixed versus sun-tracking photovoltaic panel performance. Int. J. Comput. Appl. Technol. 60(1), 37–50 (2019) 3. Hagspiel, S., Papaemannouil, A., Schmid, M., Andersson, G.: Copula-based modeling of stochastic wind power in Europe and implications for the Swiss power grid. Appl. Energy 96, 33–44 (2012) 4. Hofert, M.: Sampling Archimedean copulas. Comput. Stat. Data. Anal. 52(12), 5163–5174 (2008) 5. Hofert, M.: Efficiently sampling nested Archimedean copulas. Comput. Stat. Data. An. 55(1), 57–70 (2011) 6. Khooban, M.-H., Dehghani, M., Dragiˇcevi´c, T.: Hardware-in-the-loop simulation for the testing of smart control in grid-connected solar power generation systems. Int. J. Comput. Appl. Trans. 58(2), 116–128 (2018)

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7. Lebrun, R., Dutfoy, A.: Do Rosenblatt and Nataf isoprobabilistic transformations really differ? Probabilist. Eng. Mech. 24(4), 577–584 (2009) 8. Lojowska, A., Kurowicka, D., Papaefthymiou, G., van der Sluis, L.: Stochastic modeling of power demand due to EVs using copula. IEEE Trans. Power Syst. 27(4), 1960–1968 (2012) 9. Louie, H.: Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures. Wind Energy 17(2), 225–240 (2014) 10. McNeil, A.J.: Sampling nested Archimedean copulas. J Stat. Comput. Sim. 78(6), 567–581 (2008) 11. McNeil, A.J., Neslehova, J.: Multivariate Archimedean copulas, d -monotone functions and 1 -norm symmetric distributions. Ann. Stat. 37(5B), 3059–3097 (2009) 12. Ozay, C., Celiktas, M.S.: Statistical analysis of wind speed using two-parameter Weibull distribution in alaçatı region. Energ. Convers. Manage. 121, 49–54 (2016) 13. Papaefthymiou, G., Kurowicka, D.: Using copulas for modeling stochastic dependence in power system uncertainty analysis. IEEE Trans. Power. Syst. 24(1), 40–49 (2009) 14. Pirmoradian, A.: A New One Parameter Family of Archimedean Copula and Its Extensions. Ph.D. thesis, University of Malaya (2013) 15. Samal, R.K., Tripathy, M.: Estimating wind speed probability distribution based on measured data at Burla in Odisha, India. Energ. Sour. Part. A 41(8), 918–930 (2019) 16. Stephen, B., Galloway, S.J., McMillan, D., Hill, D.C., Infield, D.G.: A copula model of wind turbine performance. IEEE Trans. Power. Syst. 26(2), 965–966 (2011) 17. Wang, Y., Ming, Y., Tang, X.: Study on licence plate location algorithm in complex weather. Int. J. Comput. Appl. Trans. 57(2), 85–93 (2018) 18. Xiao, Q.: Modeling uncertainties in power system by generalized lambda distribution. Int. J. Electr. Pow. Syst. 15(3), 195–203 (2014) 19. Xiao, Q., Zhou, S.: Probabilistic power flow computation considering correlated wind speeds. Appl. Energy 231, 677–685 (2018) 20. Xie, K., Li, Y., Li, W.: Modelling wind speed dependence in system reliability assessment using copulas. IET Renew. Power. Gen. 6(6), 392–399 (2012)

The Study of Air Supply Ways Effects on the Aircraft Cabin Thermal Environment Xudong Shi, Di Chao, Yu Zhang and Hongxu Zhao

Abstract The purpose of this study is to fully understand the effects of air supply positions and angles on the cabin thermal environment and improve the thermal environment quality. Firstly, the cabin model is established based on the Boeing 737 cabin structure and the grid independence is verified, which proves that the number of grids no longer affects the simulation results and the result has high credibility. On this basis, PMV-PPD values, temperature non-uniformity indices and the velocity non-uniformity indices under different air supply positions and angles in the cabin are compared and analyzed. Finally, the relationship between air supply ways and thermal comfort is obtained. The simulation results provide theoretical basis for the optimization of airflow distribution in aircraft cabin, and ultimately achieve optimal thermal comfort and energy-saving. Keywords Aircraft cabin · Thermal environment · PMV-PPD · Non-uniformity

1 Introduction With the vigorous development of the civil aviation industry and the improvement of people’s living standards, more and more people prefer to choose the aircraft travel, which is efficient and convenient. The comfort level of the cabin environment not only affects the passenger’s travel experience and health, but also affects the crew’s working status. Therefore, in order to improve the comfort of the cabin environment, it is particularly important to optimize the air supply ways of the cabin [1]. In recent years, some studies have shown that the cabin environment can be optimized by changing the air supply ways [2]. Y. Z. Zhang evaluated the performance of different ventilation systems in the cabin model. After comprehensive comparison of mixed ventilation and displacement ventilation, he proposed that displacement ventilation has higher ventilation efficiency [3]. Y. X. Wu analyzed the effects of X. Shi (B) · D. Chao · Y. Zhang · H. Zhao College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_12

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Fig. 1 Cabin model

different air supply volumes and air supply temperatures on the thermal comfort of the human body under the personalized air supply ways in the winter cabin [4]. Although these studies provided meaningful results, their studies have only focused on the influence of the air supply methods on the thermal environment of the cabin. The effects of the air supply position and the air supply angle on the cabin thermal environment is rarely studied. For further improvement of the cabin air quality, this article proposes a comprehensive evaluation index (DAQ) for the cabin thermal environment by combining the thermal environment evaluation index (PMV-PPD) [5], temperature and velocity non-uniformity indices. Based on this thermal environment quality index, the effects of the air supply position and the air supply angle on the thermal environment is studied. By comparing the cabin thermal environment under different air supply ways, a relatively reasonable cabin air supply ways can be obtained.

2 Research Methods 2.1 Cabin Model and Meshing This paper establishes the aircraft cabin model based on the real Boeing 737-200 front cabin structure, and simulates the cabin flow field in the cabin full state in summer flight conditions. The cabin geometry model is shown in Fig. 1. The front cabin model is 5.8 m long, 3.53 m wide and 2.15 m high. The cabin seat layout is 3–3, a total of 7 rows, and the middle is the front cabin aisle. The human body model refers to the standard human body height and is set to 1.2 m in the sitting position.

2.2 Grid Independence Verification The number of grids should be sufficient to ensure a reasonable description of the cabin airflow process. When its number exceed a certain value, computing resources and time are wasted. Therefore, it is necessary to verify the model grid independence.

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Fig. 2 Grid independence verification

In the simulation, the number of grids increases from 7.13 millions to 8.65 millions and 10.4 millions. As the number of grids increases, the air velocity data of 6 different sampling points before and after grid encryption are shown in Fig. 2. The velocity of the monitoring point is basically the same after the second encryption, so it can be considered that the 8.65 million grid has met the calculation requirements and the grid is independent. Therefore, under the premise of ensuring the calculation accuracy and considering the calculation resources, the number of grids can predict the flow pattern more accurately.

2.3 Analysis Method of Cabin Environment According to the ASHRAE standard requirements, monitoring points are set in the comfort sensitive area of the passengers in the cabin area (0.1 m for the ankle, 0.61 m for the waist, 1.09 m for the head). Take a section at 10 cm in front of each row of passengers, and set observation points on the section. The air supply position includes three kinds which are ceiling, sidewall, ceiling and sidewall, and similarly the three air supply angles are 45°, 60°, 75°. So there are 9 kinds of combined air supply ways. The flow diagram of the airflow under different air supply positions is shown in Fig. 3, and the air supply angle setting is shown in Fig. 4.

2.3.1

Thermal Comfort Evaluation Index PMV-PPD

PMV model combines six factors affecting human thermal comfort in human variables and environmental variables [6]. It is the most comprehensive and precise thermal environment evaluation index at present, so PMV is selected as the evaluation thermal comfort index in this paper. The PMV formula is shown in (1).

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Ceiling inlet

Sidewall inlet

Bottom outlet

Bottom outlet

Sidewall inlet

Bottom outlet

Bottom outlet

Sidewall inlet

Sidewall inlet

Bottom outlet

Bottom outlet

(b) Sidewall supply

(a) ceiling supply

(c) ceiling &sidewall supply

Fig. 3 Sketch of airflow under different air supply positions

θ

θ

θ

θ

Fig. 4 Air supply angle setting diagram

  P M V = 0.303 exp(−0.036M) + 0.028 {M − W − 3.05 × 10−3 [5733 − 6.96(M − W ) − Pa ] − 0.42(M − W − 58.2) − 0.0173M(5.867 − Pa ) − 0.0014M(34 − t) − 3.96 × 10−8 f cl [(tcl + 273)4 − (ts + 273)4 ] − f cl hc(tcl − t)}

(1)

In the formula: M is the energy metabolism rate of the human body, which is determined by the amount of activity of the human body, W/m2 ; W is the mechanical work done by the human body, W/m2 ; t cl is the surface temperature of the human body after dressing, °C; t is ambient air Temperature, °C; t s is the average radiant temperature, °C. The quantitative relationship between PMV and PPD is obtained by probability analysis method, which is shown in Formula (2). P P D = 100 − 95 exp[−(0.03353P M V 4 + 0.2179P M V 2 )]

(2)

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2.3.2

127

Temperature Non-uniformity Index

The temperature non-uniformity index is used for evaluation, and The root mean square deviation (3).  δt =

(ti − t¯)2 n

(3)

where t i is the temperature of point, m/s; t¯ is the area-averaged temperature values, m/s; n is the number of sampling points. And the temperature non-uniformity index (N t ) is calculated as follows (4). Nt =

δt t¯

(4)

The velocity non-uniformity calculation can refer to the above calculation process, which is omitted here.

3 Results and Analysis 3.1 Airflow Field Distribution As shown in Fig. 5, the air supply angle is set to 60°, and there are temperature and velocity field distribution of ceiling air supply, sidewall air supply, ceiling and sidewall air supply. It is convectively mixed in the passenger area, and is discharged outside the cabin through the floor return air outlet. Considering the heat transfer of the human body model and the radiation of the inner wall of the cabin, the air temperature in different areas is obviously stratified. It can be seen that under different air supply ways, due to the symmetrical structure of the cabin and the symmetric distribution of the air outlets, the flow field is symmetrically distributed but the flow field distribution is obviously different. The temperature around passengers is relatively high, and people can enjoy a relatively comfortable environment after convective heat transfer. In the ceiling air supply ways (C), the velocity in the aisle area is high reaching about 0.6 m/s while the velocity around the passenger area is relatively low. In the sidewall (S) or mixed air supply (CS) mode, the airflow distribution in the cabin is relatively uniform. In the ceiling and sidewall mixed air supply ways (CS), except for a small part of the area temperature exceeding 297 k, most of the area temperature is suitable and the velocity of the passenger area is about 0.2 m/s. As shown in Fig. 6, these are the temperature field in the ceiling air supply ways at different air supply angles. The flow field distribution maps are given at 45°, 60°, and 75°. Observing the flow field distribution in the figure, it can be seen that the air

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Temperature/k

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(b1) Sidewall supply

(c1) Ceiling & Sidewall supply

Velocity/(m/s)

(a1) Ceiling supply

(a2) Ceiling supply

(b2) Sidewall supply

(c2) Ceiling &Sidewall supply

Fig. 5 Flow field distribution under different air supply position Temerature/k

(a) 45

o

(b) 60

o

(c) 75

o

Fig. 6 Temperature field distribution under different air supply angles

supply angle has an obvious influence on the temperature field of the cabin. As the air supply angle increases, the influence on the temperature field distribution gradually decreases.

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Table 1 Thermal sensation versus human PMV values Thermal feeling

Hot

Warm

Slightly hot

Neutral

Slightly cool

Cool

Cold

PMV values

+3

+2

+1

0

−1

−2

−3

Table 2 PMV values under different air supply ways Air supply position

Supply angle/°

Ankle PMV

Waist PMV

Head PMV

Average PMV

PPD values

C

45

−0.11

−0.09

−0.14

−0.11

5.94

C

60

−1.33

−0.26

0.11

−0.50

10.61

C

75

−1.30

−0.03

0.06

−0.42

9.22

S

45

−0.45

−0.05

−0.02

−0.18

6.00

S

60

−1.27

−0.02

0.10

−0.40

8.75

S

75

−1.17

−0.05

0.10

−0.38

8.38

CS

45

−0.87

−0.04

0.16

−0.25

6.51

CS

60

−1.08

−0.09

0.15

−0.34

7.95

CS

75

−1.17

−0.10

0.18

−0.36

8.24

3.2 PMV-PPD Values Under Different Air Supply Ways The relationship between thermal sensation and PMV values is shown in Table 1. The PMV values of different parts are calculated, as shown in Table 2. According to the PMV values of different parts, the human body can obtain a more comfortable state in the ceiling and 45° air supply ways, and the human body has a slight cold feeling under the ceiling and 60° air supply ways. The PPD values are also shown in Table 2. It can be seen that the C45, S45, and CS45 have lower dissatisfaction rates under the air supply ways, while the C60 air supply ways has the highest dissatisfaction rate.

3.3 Cabin Environmental Non-uniformity As shown in Fig. 7, the comparison shows that under different air supply ways, the temperature non-uniformity is small, and difference is obvious. The velocity nonuniformity is the largest under the ceiling and 45° air supply ways (C45). The value is the smallest under ceiling, sidewall and 45° air supply condition.

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Fig. 7 Temperature and velocity non-uniformity

3.4 Cabin Thermal Environment Assessment Take the sum of them as a new comprehensive indicator. This judgment indicator can select which type of air supply ways is superior. D AQ = p + tnu + vnu

(5)

Among them, P is the dissatisfactory rate (PPD) of thermal comfort of the cabin; t nu is temperature non-uniformity; vnu is velocity non-uniformity; DAQ is the dissatisfactory air quality index. Figure 8 shows that the value is highest in C60 supply ways, and it is relatively low under C45, S45 and CS45. Besides, the cabin can obtain a relatively good thermal environment according to DAQ index. However, combining the Fig. 8, the velocity non-uniformity is highest in the C45 air supply ways, S45 is second, and CS is the lowest. Therefore, it shows that more comfortable cabin thermal environment can be obtained under CS45 air supply ways after the comprehensive comparison.

10 5 0 C45 C60 C75 S45 S60 S75 CS45 CS60 CS75

Environmental unsatisfactory values

15

Fig. 8 Environmental dissatisfactory values

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4 Conclusion The conclusions can be concluded as follows: Under different air supply positions and angles, the comparison shows that the difference of temperature non-uniformity is relatively small, but the difference of the velocity non-uniformity is obvious. After comparison of the PMV-PPD values and non-uniformity of the cabin in different air supply ways, ceiling, sidewall and 45° (CS45) air supply way can obtain a relatively satisfied thermal environment. The performance of ceiling and 60° air supply is relatively dissatisfied. In order to optimize the thermal environment of the cabin, in addition to changing the air supply temperature and velocity, the air supply position and the air supply angle can also be changed to achieve the goal. Acknowledgements The research is supported by the Innovation Team Cultivation Plan of Colleges and Universities in Tianjin (TD13-5071).

References 1. Pang, L.P., et al.: Thermal comfort assessment in civil aircraft cabins. Chin. J. Aeronaut. 27(2), 210–216 (2014) 2. Zhang, Y.Z., Jun-jie, L., Jing-jing, P., et al.: Statistical analysis of turbulent thermal convection in a cabin mockup. Build. Environ. 115, 34–41 (2017) 3. Zhang, Y., Liu, J., Pei, J., et al.: Performance evaluation of different air distribution systems in an aircraft cabin mockup. Aerosp. Sci. Technol. 70 (2017) 4. Wu, Y.X.: Research on Nozzle Air Supply in Winter Engine Room Based on Human Comfort. Chongqing University (2017) 5. Cui, W.L., Qin, O.Y., et al.: Thermal environment and passengers’ comfort in aircraft cabin. Lect. Notes Electr. Eng. 261, 321–328 (2014) 6. Nadlamani, K., Jadhav, G., Jadhav, K.: Environment monitoring system using Raspberry-Pi. IJCAT, 463–468 (2015)

Identification of the Wiener System Based on Instrumental Variables Shaoxue Jing and Tianhong Pan

Abstract The Wiener system consists of a linear model followed in series with a nonlinear static element. The parameter estimation of a Wiener system, whose linear part is a finite impulse response function and nonlinear inverse function a polynomial, is considered in this paper. The system is polluted by a process noise. Traditional algorithms cost heavy computation because of the parameter product term and give a biased estimate owing to the correlation between the information vector and the noise. To solve these problems, a two-stage input prediction error algorithm is proposed. In the first stage, a least squares estimate is obtained by minimizing the input prediction error. However, this estimate is biased. To get an unbiased estimate, the estimated output of the linear part is taken as an instrumental variable. And an instrumental variable estimate is obtained unbiasedly. A numerical simulation verified the proposed algorithm. Keywords Parameter estimation · Wiener system · Process noise · Input prediction error · Instrumental variable

1 Introduction In recent decades, identification and control of nonlinear systems have attracted wide attention [3, 16, 18]. many Wiener system involves a linear dynamic subsystem in series with a static nonlinearity. In recent decades, the Wiener system has been widely used in modeling and control [4, 12, 13]. The identification of the Wiener system is S. Jing (B) School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian 223000, Jiangsu, China e-mail: [email protected] T. Pan School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_13

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very difficult because the system contains output nonlinearity. The existing parameter identification methods for the Wiener system are as follows. (1) Optimization algorithms such as neural networks algorithm [5], brainstorming optimization algorithm [15], particle swarm algorithm [19], genetic algorithm [2] and evolutionary algorithm [9], et al. are widely used in the identification of Wiener systems. (2) The least-squares (LS) algorithm and various algorithms derived from LS are often adopted to identify Wiener systems [6, 10, 21]. (3) Iterative identification algorithms, such as Newton iterative algorithm [7], gradient iterative algorithm [22] are often applied to parameter identification of Wiener systems. Although these algorithms work well for different types of Wiener system, there are still some issues. (1) Most algorithms directly identify the overparameterized Wiener system to get the parameter estimate of parameter product terms (PPT). The single parameter is separated from the PPT. However, identification of the PPT with a high dimension leads to great computational burden. (2) The separation of the PPT using the averaging method or singular value decomposition sometimes faces with the numerical problem. (3) For the Wiener system with a process noise, LS algorithm will give a biased estimate because the information vector correlates with the process noise. To solve the mentioned problems, a two-stage algorithm based on LS and IV algorithm is proposed in this work. The rest of this work is organized as follows. The estimation problem is described in Sect. 2. A two-stage parameter estimation algorithm based on input prediction error is proposed in Sect. 3. A numerical example is used to validate the proposed method in Sect. 4. The main conclusions are summarized in Sect. 5.

2 Problem Description Consider a Wiener system depicted in Fig. 1, where u(k) and y(k) are the input and output of the system, respectively. B(z −1 ) is a linear dynamic model described by an FIR function. N (•) is the static nonlinear function, whose inverse function is a polynomial. And, x1 (k) and x2 (k) are unmeasurable intermediate variables. The Wiener system is polluted by a process noise v(k) with mean zero.

Fig. 1 Block diagram of a Wiener system

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It can be seen from Fig. 1 that x1 (k) = B(z −1 )u(k) = b1 u(k − 1) + b2 u(k − 2) + · · · + bn b u(k − n b ) =

(1)

ϕ BT (k)θ B ,

where the order of the FIR, n b , is supposed to be known and 

T  θ B = b1 , b2 , . . . , bn b ∈ Rn b ×1 , ϕ B (k) = [u(k − 1), u(k − 2), . . . , u(k − n b )]T ∈ Rn b ×1 .

(2)

One problem in the traditional algorithms is that the Wiener system is parameterized as PPT of the linear part and nonlinearity. The PPT greatly increases the dimension of parameter vectors, which leads to a huge computational burden. To avoid the PPT, the inverse function of the original nonlinear function is parameterized and expressed by the following polynomial [1, 20]: x2 (k) = N −1 (y(k)) = β1 y(k) + β2 y 2 (k) + · · · + βn β y n β (k)

(3)

= ϕβT (k)θβ , where the degree n β is known and 

T  θβ = β1 , β2 , . . . , βn β ∈ Rn β ×1 ,  T ϕβ (k) = y(k), y 2 (k), . . . , y n β (k) ∈ Rn β ×1 .

(4)

Then, the identification of the Wiener system shown in Fig. 1 can be transformed L into the estimation of the parameters θ B , θβ based on the observations {u(k), y(k)}k=1 , where L is the data length.

3 Recursive Two-Stage Input Prediction Error Parameter Estimation Algorithm In Fig. 1, it’s seen that x2 (k) = x1 (k) + v(k)

(5)

Letting b1 = 1 to obtain a unique parameter estimate. Considering Eqs. (1) and (3), Eq. (5) is rewritten as u(k − 1) = ϕ T (k)θ1 + w(k),

(6)

where the parameter vector θ1 and the information vector ϕ(k) are defined as follows:

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⎧

T ⎪ T T ⎪ ϕ(k) = −ϕ (k), ϕ (k) ∈ Rn×1 , ⎪ β b ⎪ ⎪ 

⎪ T ⎪ T T ⎪ ⎪ ∈ Rn×1 , ⎨ θ1 = θb , θβ ϕb (k) = [u(k − 2), u(k − 3), . . . , u(k − n b )]T ∈ R(n b −1)×1 , ⎪ T  ⎪ ⎪ θb = b2 , b3 , . . . , bn b ∈ R(n b −1)×1 , ⎪ ⎪ ⎪ ⎪ w(k) = −v(k), ⎪ ⎪ ⎩ n = n b + n β − 1,

(7)

and ϕβ (k), θβ can be found in Eq. (4) Minimizing the criterion V =

L 2 1

u(k − 1) − ϕ T (k)θˆ1 (k) L k=1

(8)

to obtain an LS estimate θˆ1 (k) by the following equations [14]: θˆ1 (k) = θˆ1 (k − 1) + L(k)[u(k − 1) − ϕ T (k)θˆ1 (k − 1)],

(9)

P(k − 1)ϕ(k) , 1 + ϕ T (k)P(k − 1)ϕ(k)

(10)

P(k) = [I − L(k)ϕ T (k)]P(k − 1).

(11)

L(k) =

However, the y i (k) included in the information vector ϕ(k) is contaminated by the process noise v(k) [(see Eqs. (7) and (4)]. In other words, the information vector is correlated to the noise. The LS estimate given by Eqs. (9)–(11) is biased. To obtain unbiased estimate, instrumental variable (IV) idea is adopted [11, 17]. The output of the linear part, i.e. x1 (k), is taken as the IV. But x1 (k) is unmeasurable. A feasible way is to calculate the unknown IV, i.e. xˆ1 (k), by the following equation: xˆ1 (k) = ϕbT (k)θˆ1l (L) + u(k − 1),

(12)

where θˆ1l (L) is the linear part of the LS estimate:

T θˆ1l (L) = bˆ2 (L), bˆ3 (L), . . . , bˆn b (L) ∈ R(n b −1)×1 .

(13)

Replacing the y i (k) in Eq. (4) with xˆ1i (k) and rewriting Eq. (7) give a new information vector as follows:  T n ϕ2 (k) = −u(k − 2), . . . , −u(k − n b ), xˆ1 (k), xˆ12 (k), . . . , xˆ1 β (k) .

(14)

Identification of the Wiener System Based on Instrumental Variables

Let

⎧ k ⎪ ⎪ ⎨ P−1 (k) = ϕ2 (i)ϕ T (i), i=1 ⎪ ⎪ ⎩ L(k) = P(k)ϕ2 (k),

137

(15)

an IV estimate θˆ2 (k) can be obtained by following recursive IV equations [8] θˆ2 (k) = θˆ2 (k − 1) + L(k)[u(k − 1) − ϕ T (k)θˆ2 (k − 1)],

(16)

P(k − 1)ϕ2 (k) , 1 + ϕ T (k)P(k − 1)ϕ2 (k)

(17)

P(k) = [I − L(k)ϕ T (k)]P(k − 1).

(18)

L(k) =

The proposed algorithm estimates the parameters of the Wiener system by two stages and minimizes the input prediction error in each stage. Thus, the proposed algorithm is named the “recursive two-stage input prediction error” (RTS-IPE) algorithm. The RTS-IPE algorithm can be summarized as follows. Step 1: initialize parameters 

bˆi (0) = 10−6 , (i = 2, 3, . . . , n b ), βˆi (0) = 10−6 , i = 1, 2, . . . , n β . Step 2: collect the input and output data u(k) and y(k). Step 3: estimate θˆ1 (k) using Eqs. (11)–(13). Step 4: let k = k + 1, if k < L, go to Step 2; otherwise, goto Step 5. Step 5: separate θˆ1l (L) from θˆ1 (L) using Eq. (13). Step 6: calculate xˆ1 (k) by Eq. (12). Step 7: construct ϕ2 (k) by Eq. (14). Step 8: estimate θˆ2 (k) using Eqs. (16)–(18). Step 9: let k = k + 1, if k < L, go to Step 6; otherwise, iteration terminates.

4 Numerical Example Consider the Wiener system depicted in Fig. 1 with following transfer functions:  B(z −1 ) = z −1 − 1.1z −2 + 0.66z −3 , (19) x2 (k) = y(k) + y 3 (k), where the input u(k) obeys uniform distribution between [1.0, 3.0]. A process noise v(k) with mean zero was added to the system. The proposed RTS-IPE algorithm was used to identify the parameters of the system (19). The estimation results were shown in Table 1, where the noise variance

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Table 1 Results using RTS-IPE algorithm k 50 200 400 b2 b3 β1 β2 β3 δ(%)

−1.0988 0.6564 1.0058 0.0000 0.9895 0.6587

−1.1010 0.6600 1.0025 −0.0065 1.0009 0.3705

Fig. 2 The estimation errors using RTS-IPE under different noise levels

−1.0993 0.6592 1.0023 0.0025 0.9944 0.3485

600

800

TrueValues

−1.0988 0.6587 1.0010 0.0021 0.9962 0.2506

−1.0992 0.6590 0.9999 −0.0003 1.0000 0.0697

−1.1000 0.6600 1.0000 0.0000 1.0000

10 σ2=0.012 σ2=0.052

9

σ2=0.102

8 7

δ (%)

6 5 4 3 2 1 0

0

100

200

300

400

500

600

700

800

k

    σ 2 = 0.012 and the estimation error δ is defined as: δ = θˆ2 (k) − θ0  / θ0  × 100 and θ0 denotes the true value of the parameters. The parameter estimation errors were shown in Fig. 2 (solid line). Also, the estimation errors when the variance of the noise is 0.052 and 0.102 were shown in Fig. 2. It’s seen from Table 1 and Fig. 2 that: (1) With the increase of the data length k, the estimation errors decrease rapidly to zero. In other words, the parameter estimates converge rapidly to the true value. (2) The estimation error increases with the increase of the noise level. (3) It’s found in Table 1 that the estimation error was very small (0.0697%) when 800 observations were used. The estimate obtained by the proposed algorithm is very accurate.

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5 Conclusions To estimate the parameter of a Wiener system polluted by a process noise, a recursive two-stage algorithm was proposed. Firstly, the system was parameterized based on an FIR function and a polynomial function. Secondly, a criterion based on the input prediction error was minimized to parameter estimation. Thirdly, a two-stage algorithm was presented to get an unbiased estimate. A numerical example validated the proposed algorithm. Acknowledgements This work is supported by National Nature Science Foundation under Grant 61873113, Industry-University Cooperation Project of Jiangsu Province (BY2018231), and Natural Science Research Project of Jiangsu higher school, China (19KJD510001).

References 1. Ahmed-Ali, T., Tiels, K., Schoukens, M., Giri, F.: Sampled-data based state and parameter estimation for state-affine systems with uncertain output equation. IFAC-PapersOnLine 51(15), 491–496 (2018) 2. Al-Duwaish, H.N.: Identification of wiener model using genetic algorithms. In: 2009 5th IEEE GCC Conference & Exhibition, pp. 1–4. IEEE (2009) 3. Benamor, A., Messaoud, H.: A new adaptive sliding mode control of nonlinear systems using volterra series: application to hydraulic system. Int. J. Model. Ident. Control 29(1), 44–52 (2018) 4. Chen, H.F.: Recursive identification for wiener model with discontinuous piece-wise linear function. IEEE Trans. Autom. Control 51(3), 390–400 (2006) 5. De-hui, W.: Identification method for nonlinear dynamic system using wiener neural network. Control Theor. Appl. 11, 002 (2009) 6. Ding, F., Liu, X., Liu, M.: The recursive least squares identification algorithm for a class of wiener nonlinear systems. J. Franklin Inst. 353(7), 1518–1526 (2016) 7. Ding, F., Ma, J., Xiao, Y.: Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1–2), 21–30 (2013) 8. Fang, C., Xiao, D.: Process Identification. Tsinghua University Press, Beijing (1988) 9. Hatanaka, T., Uosaki, K., Koga, M.: Evolutionary computation approach to block oriented nonlinear model identification. In: 5th Asian Control Conference, vol. 1, pp. 90–96. IEEE (2004) 10. Hu, Y., Liu, B., Zhou, Q., Yang, C.: Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circ. Syst. Sig. Process. 33(2), 655–664 (2014) 11. Janczak, A.: Instrumental variables approach to identification of a class of mimo Wiener systems. Nonlinear Dyn. 48(3), 275–284 (2007) 12. Jing, S., Pan, T., Li, Z.: Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise. Nonlinear Dyn. 90(4), 2293–2303 (2017) 13. Liu, D., Wu, J., Li, S.: Wiener model of pressure management for water distribution network. Int. J. Modell. Ident. Control 30(2), 73–82 (2018) 14. Ljung, L.: System Identification: Theory for the User. Prentice-Hall, Upper Saddle (1987) 15. Pal, P.S., Kar, R., Mandal, D., Ghoshal, S.P.: Parametric identification with performance assessment of Wiener systems using brain storm optimization algorithm. Circ. Syst. Sig. Process. 36(8), 3143–3181 (2017)

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16. Retes, P.F.L., Aguirre, L.A.: Narmax model identification using a randomised approach. Int. J. Model. Ident. Control 31(3), 205–216 (2019) 17. Söderström, T., Stoica, P.: Instrumental variable methods for system identification. Circ. Syst. Sig. Process. 21(1), 1–9 (2002) 18. Tamboli, D., Chile, R.: Multi-model approach for 2-dof control of nonlinear CSTR process. Int. J. Model. Ident. Control 30(2), 143–161 (2018) 19. Tang, Y., Qiao, L., Guan, X.: Identification of Wiener model using step signals and particle swarm optimization. Expert Syst. Appl. 37(4), 3398–3404 (2010) 20. Tiels, K., Schoukens, J.: Wiener system identification with generalized orthonormal basis functions. Automatica 50(12), 3147–3154 (2014) 21. Wang, D., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Sig. Process. 91(5), 1182–1189 (2011) 22. Zhou, L., Li, X., Pan, F.: Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling. Nonlinear Dyn. 76(1), 627–634 (2014)

Cervical Histopathology Image Clustering Using Graph Based Unsupervised Learning Chen Li, Zhijie Hu, Hao Chen, Dan Xue, Ning Xu, Yong Zhang, Xiaoyan Li, Qian Wang and He Ma

Abstract In order to apply the important topological information to solve a Cervical Histopathology Image Clustering (CHIC) problem, a Graph Based Unsupervised Learning (GBUL) approach is proposed in this paper. First, the GBUL method applies color features and k-means clustering for a first-stage “coarse” clustering. Then, a Skeletonization Based Node Generation (SBNG) approach is introduced to approximate the distribution of cervical cell nuclei. Thirdly, based on the SBNG nodes, a minimum spanning tree graph is constructed. Next, graph features and additional geometrical features are extracted based on the constructed graph. Finally, the k-means clustering is applied again for the second-stage clustering. In the experiment, a practical cervical histopathology image dataset with ten whole scanned images is tested, obtaining a promising CHIC result and showing a huge potential in the cancer risk prediction field. Keywords Cervical cancer · Histopathology image · Clustering · Unsupervised learning · Skeletonization · Graph theory

C. Li · Z. Hu · H. Chen · D. Xue · H. Ma (B) Microscopic Image and Medical Image Analysis Group, MBIE College, Northeastern University, Shenyang, China e-mail: [email protected] C. Li e-mail: [email protected] N. Xu Liaoning Shihua University, Fushun, China Y. Zhang · X. Li · Q. Wang Liaoning Hospital & Institute, Shenyang, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_14

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1 Introduction Cervical cancer is a common and worldwide cancer among women, ranking only second to breast cancer, which is the most common cause of death among middleaged women [16]. Therefore, research on cervical cancer is particularly important. When the lesion of cervical cancer occurs, a lot of morphological transforms of the cell nuclei happen synchronously, e.g., the sizes of cell nuclei expand abnormally, the shapes of cell nuclei become irregular, cell distribution in tissues, and the topological structures of the tissue also change accordingly [14]. So, the morphological transforms of cell nuclei is an important clue to discover and diagnose cervical cancer. Traditionally, to assess the morphological transforms, histopathologists always analyse the histopathology images of cervical cancer under a microscope by their naked eyes, and manually evaluate the case based on their medical knowledge. However, this analysing process is usually time consuming, subjective and only qualitative, leading to a considerable variability in the final diagnostic results. Furthermore, because histopathologists always have high strength in their practical work, the diagnostic accuracy is also unstable. To this end, more and more effective Computer Aided Diagnosis (CAD) techniques are introduced to the cervical cancer histopathology image analysis field, helping histopathologists to increase their diagnosis speed and improve the accuracy. Among various CAD tasks, Cervical Histopathology Image Clustering (CHIC) plays a novel role to assist histopathologists to monitor and discover suspected risk of malignant tissues in an image. However, due to the complexity of contents of cervical histopathology images, the CHIC task is a challenging work. To this end, a Graph Based Unsupervised Leaning (GBUL) approach is proposed in this paper, where graph features are used to describe the structure information of different tissues in the histopathological images [13], and two stages of unsupervised leaning processes are applied to group the tissues into relevant types. Especially, because cell nuclei positions are used as nodes to generate graphs in an image, but current techniques are not effective to detect nuclei of high-viscosity cells, we introduce a Skeletonization Based Node Generation (SBNG) approach to approximately represent the distribution of the cell nuclei. In Fig. 1, the workflow of the proposed GBUL clustering method is shown. In Fig. 1, Step (a): We extract RGB color features and apply k-means method for the first-stage clustering, where sparse cell nuclei are clustered clearly, but the highviscosity cell nuclei are clustered jointly. Step (b): Based on our SBNG approach, the distribution of the cell nuclei are approximately represented by the generated skeleton nodes. Step (c): Using the generated nodes, we apply minimum spanning tree (MST) to construct graphs, depicting the density, proximity and spatial arrangement of the various nodes relative to each other. Step (d): A series of statistical values of the constructed graphs are calculated and used as graph features to represent the topological information of the image. Step (e): Based on the extracted graph features, the k-means method is applied again for the second-stage clustering, where the tissues grouped by the first-stage clustering is further clustered with more detailed differences.

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(c) Graph Construction

(e) Second-stage Clustering

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(d) Graph Feature Extraction

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Fig. 1 Workflow of the proposed GBUL clustering method

2 Related Work Cervical Caner: Uterine malignancy is a common cancer in the female reproductive system. Cervical cancer is one of the most representative types of all uterine malignancies. In recent years, its incidence increases in the world [10]. In addition, due to the high survival rate and cure rate of cervical cancer, researchers pay more and more attention to it [16]. In the study of tumour, the diagnosis of pathology is very important, where cervical cancer sections are observed under a microscope by histopythologists and manually analyses based on their prior medical knowledge to analyse the characteristics and properties of the tissues [7, 9]. However, the objectivity of this manual analysis process is unstable, depending on the experience, workload and mood of the histopathologists. CAD Techniques for Cervical Cancer: In recent decades, many CAD techniques are applied to improve the objectivity and quantification of cervical histopathological research, including pattern recognition, machine learning and image processing approaches [1, 5, 15]. For example, in [12], color features of histopathology images are used for an unsupervised learning process. In [17, 19], novel segmentation methods are proposed to cancer detection application fields. In [2], proposes an efficient fuzzy-firefly clustering by integrating the merits of firefly and fuzzy clustering. The proposed method is compared with other swarm optimisation based clustering algorithms. Applications of Graph Theory in CHIC: As a new research hotspot, graph theory technology involves a lot of theoretical knowledge. A graph theory method is introduced in [3] to describe the spatial relationship between cells, where a MST and a zone of influence subdivision map are established, and various statistical values are calculated through the tree and graph structure to represent density and cell

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distribution. In [13], a threshold-based local segmentation method is used to detect nuclei, and a graph theory method is used to describe the structure of cervical cancer. Based on the Voronoi diagram and its subgraphs, 27 structural features are developed and tested. In the work of [6], a neighborhood graph is constructed based on the results of the segmentation of the nucleus. Then calculate the feature vector and describe the structural information of the pathological image of the cervical tissue. In [4], local and global features are extracted to evaluate histopathology images. It also proposes that that the global graph is easier to distinguish feature differences than the local graph, and the MST in the global graph has the highest discrimination. Hence, we select the MST method in our work.

3 Our Method 3.1 Basic Knowledge of Unsupervised Learning and Graph Theory Unsupervised Learning: Unsupervised learning is a machine learning method used to discover patterns in data. The data input to the unsupervised algorithm has no tags, that is, only the input variables are provided for the algorithm and there is no corresponding output variable [11]. Unsupervised learning is often used in association, clustering, and dimensionality reduction. The clustering algorithm mainly includes two types: Partitioning and hierarchical methods. Typical partitioning clustering algorithms are k-means and k-medoids; typical hierarchical clustering algorithms include BIRCH and DBSCAN. Among them, because k-means is easy to implement and fast in convergence, it is often applied [8]. The idea of k-means is to determine the constant k in advance, and the constant k represents the final number of cluster categories. In this paper, we apply the k-means clustering in two stages: First, we extract RGB color features and use it for the first-stage “coarse” clustering. Second, we extract graph features and use k-means again for the second-stage “delicate” clustering. Graph Theory: A graph is a collection of multiple nodes V and edges E, which can be represented as ordered pairs of G = (V, E). Graph based methods all involve identifying the spatial location of a single core and then constructing the graph as a set of connected kernel nodes (or vertices), so a graph can describe the topological (or structural or spatial) information of an image [6]. Furthermore, quantitative descriptors can be mined from these graphs that describe the density and spatial arrangement of individual nuclei relative to each other [18]. Usually, the graph generation methods are grouped into global and local two types. Global graphs (such as Voronoi diagram, Delaunay triangulation, and MST) tend to study the structure of all nodes in an image. In contrast, local graphs (Cell Cluster Graphs and Nearest Neighbor Graphs) tend to observe the node structure in the local neighborhood. Especially, based on the result in [4], we choose the MST method in our work, which is the

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Fig. 2 An example of the generated MST graph. a Is an original image, b shows the corresponding MST graph

minimal connected subgraph of Delaunay triangulation, and contains all the nodes in the original graph, and the sum of the weights is the smallest. MST can be obtained by the Kruskal algorithm or the Prim algorithm, which can be used to calculate the lowest cost. An example of the constructed MST graph is shown in Fig. 2.

3.2 The Proposed GBUL Clustering First-stage Clustering: First, we extract the RGB pixel values as our color features. Then, we set k = 2, and apply the k-means algorithm to group the tissues in a cervical histopathology image into two clusters. Graph Node Generation: From the first-stage clustering result, we can find that sparse cell nuclei can be clustered well, but nuclei of high-viscosity cells (overlapping and adherent cells) are difficult to identify. In addition, the clustering results are affected by sharpness and staining methods heavily. In this case, it is very hard to discover the nuclei positions in an image to generate the graph nodes. Hence, we propose a skeletonization based node generation (SBNG) approach to approximately represent the nuclei distribution. First, a skeletonization process is carried out on the first-stage clustering result. Then, a refinement process is done to the skeletonization result for a further skeleton structure. In general, the skeleton of each cell produces two nodes and the spatial distribution of the skeleton nodes and the nucleus is similar. The redundant nodes are deleted and the remaining nodes are used to approximately represent the distribution of cell nuclei. Graph Construction: First, we divide the nuclei in the first-stage clustering result into two types: One type is the sparse cell nuclei, and another type is the nuclei of high-viscosity cells. This separate processing can facilitate the distinction between

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different types of tissues. Then, the SBNG nodes in each tissue type are used to construct a graph. Graph Feature Extraction: According to the graph generated by the MST, various statistical values are calculated and used as the graph features to represent different tissues. The extracted graph features include the mean, variance, skewness, and kurtosis of the edge lengths and angles in each graph. In addition, some geometrical features are also extracted, including the perimeters of the tissues and the independent fitting of the nodes within each tissue. Mean is the number of trends that represent a set of datasets and is an indicator of trends in the dataset. It is defined as Eq. (1). x = (x1 + x2 + x3 + · · · + xn )/n,

(1)

where x is the average and n is the number of data. Variance is a measure of the degree of dispersion when measuring a set of data, and it is defined as Eq. (2). n (xi − x)2 )/(n − 1), σ 2 = (Σi=1

(2)

where σ 2 is the variance. Skewness is a measure of the direction and extent of statistical data skew and is expressed by Eq. (3). Sk =

μ2 3 2

μ2

=

1 n Σ (x − x)3 μ3 n i=1 i = 3 , 1 n σ3 ( n−1 Σi=1 (xi − x)2 ) 2

(3)

where Sk represents skewness; μ3 represents a 3rd-order center moment; σ represents a standard deviation. Normally, the kurtosis is defined by dividing the fourth-order center moment by the square of the probability distribution variance and subtracting three, and it is defined as Eq. (4). γ2 =

1 n Σ (x − x)4 μ4 n i=1 i − 3 = − 3, n σ4 ( n1 Σi=1 (xi − x)2 )2

(4)

where γ2 represents kurtosis; μ4 represents a fourth-order center moment. Second-stage Clustering: Sparse cells are discovered after the first-stage clustering, so we focus on the subsequent processing for nuclei of high-viscosity cells. Based on the extracted graph features and additional geometrical features, we use the k-means clustering again, where we set the k value for two types of tissues, separately. Then, more detailed results are obtained by the second-stage clustering process to predict the cancer risk of the tissues.

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4 Experiments 4.1 Experimental Setting In the experiment, a practical cervical histopathology image dataset is provided by two histopathologists from the Liaoning Cancer Hospital & Institute, Shenyang, China. The details of the dataset are as follows. Staining method: Hematoxylineosin (H&E) staining; Microscope: Olympus digital scanning microscope; Images: ten images with 40× magnification are included, the size of each image is between 200 M and 2024 M, and the pixel number is between 30,000 × 30,000 and 60,000 × 60,000; Image pre-processing: Because the size of each scanned image is very big, we crop each image into 500 sub-images.

4.2 Evaluation of First-Stage Clustering and SBNG Performance In Fig. 3, an example of the first-stage clustering and the generated nodes by the SBNG method is shown. From Fig. 3c, d, we can find that the redundant nodes are removed from the skeletons. Furthermore, a comparison between the real nuclei positions (nuclei center) and the proposed SBNG mode potions is shown in Fig. 4. In Fig. 4, ground truth images provided by the histopathologists are first used to calculate the real nuclei positions (nuclei center). Then, the real positions are compared with the SBNG nodes within a radius of 12 pixels. Finally, the test results show that the overlapping rate between the real nuclei and SBNG node positions reaches 90%. Hence, the proposed SNBG nodes can approximate the distribution of the real nuclei well, showing the feasibility of our method.

Fig. 3 An example of the first-stage clustering and the SBNG nodes. a Shows an original image, b shows the first-stage clustering result, c shows their skeletons, and d shows the generated nodes

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Fig. 4 An comparison between real nuclei and SBNG node positions. Red dots indicate the real nuclei positions (nuclei center). Yellow dots indicate the SBNG node positions

4.3 Evaluation of Graph Feature and Second-Stage Clustering In this section, the graph features are evaluated with two types of cervical tissues, respectively. Because the tissues with nuclei of high-viscosity cells present more visible structural information, in the same cervical histopathology image, the number of them is less than that of sparse nuclei. An example of the extracted graph features is shown in Fig. 5. From Fig. 5, we can find that the mean values of the lengths and angles of the high-viscosity tissues are relatively stable and show no significant difference, but the differences in variance, skewness and kurtosis are obvious. Hence, the high-viscosity tissues can be divided into two to three categories by k-means. In contrast, the mean value of the lengths and angles of the sparse tissues exhibit a certain fluctuation, where the variance, skewness and kurtosis are more pronounced. The sparse tissues can also be divided into two to three categories by k-means. The extracted graph and geometrical features are first used with the k-means clustering for a further clustering. Then, the clustering results are further processed with a voting strategy to obtain the second-stage clustering result. Furthermore, an example of the structure of the tissue clustering result is shown in Fig. 6, where the cells are grouped into different clusters based on their graph theory characteristics. In addition, we use an effective and feasible evaluation method, namely silhouette plot, to further analyse the clustering results. This effective evaluation is used to illustrate how close each data point in one cluster is to other data points in its neighboring clusters. If this average value is high, the overall performance is good. Otherwise,

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Fig. 5 An example of the graph features. The top row shows the mean, variance, skewness, kurtosis of the length of the high-viscosity tissues, respectively; the second row represents the mean, variance, skewness, kurtosis of the length of the sparse tissues, respectively; the third row denotes the mean, variance, skewness, kurtosis of the angle of the high-viscosity tissues, respectively; the bottom row shows the mean, variance, skewness, kurtosis of the angle of the sparse tissues, respectively

Fig. 6 An example of the clustering result. a, b Represent two types of high-adhesion tissues, while c, d represent two types of sparse tissues

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Fig. 7 Silhouette plots with clustering and graph features based at k = 4 and k = 6. a is k = 4 and b is k = 6. The horizontal axis shows the contour value and the vertical axis denotes the cluster number. In a 1 and 2 on the vertical axis represent two types of high-adhesion tissues; 3 and 4 represent two types of sparse tissues. In b 1, 2 and 3 on the vertical axis represent three types of high-adhesion tissues; 4, 5 and 6 represent three types of sparse tissues

the overall performance is bad. The visualized results of silhouette evaluation are shown in Fig. 7. From Fig. 7, we can find that because we use practical medical data in this paper, the numbers of different types of tissues are greatly different, and the uniformity of

Fig. 8 An comparison between the first- and second-stage clustering using the proposed GBUL method. a Shows the first-stage clustering result; b represents the corresponding second-stage clustering result. Red denotes the high-viscosity tissues, and blue denotes the sparse tissues. The color the darker, the tissues have more high-viscosity cells inside. The line segment in the tissue represents the MST graphs

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clustering cannot be guaranteed. When k = 4, the clustering result is better. With the increasing of k, the result becomes worse. At last, a comparison of the first-stage and second-stage clustering is shown in Fig. 8, where the sparse and high-viscosity tissues are marked with different colors. From Fig. 8, we can find that both the high-viscosity and sparse tissues are subdivided into two types (marked by darker and lighter colors), respectively. The darker the color, the tissue has a more complex topological structure. This result shows the effectiveness of our GBUL clustering method for the cervical histopathology image clustering approach. It can provide an assistant for doctors in their medical diagnosis, where a tissue has a more complex structure, it has a much more higher risk of cancer.

5 Conclusion and Future Work In this paper, a graph based unsupervised learning approach is proposed to solve a cervical histopathology image clustering task in the cancer risk predication field. Especially, a skeletonization based node generation method is introduced to approximately represent the cell nuclei distribution in an image. Finally, the proposed method jointly applies color, graph and geometrical information and two k-means clustering processes to finish the clustering task. In the experiment, a practical image dataset is tested to prove the effectiveness and future potential of our method. Acknowledgements We thank the funds supported by the “National Natural Science Foundation of China” (No. 61806047), the “Fundamental Research Funds for the Central Universities” (No. N171903004), and the “Scientific Research Launched Fund of Liaoning Shihua University” (No. 2017XJJ-061). We also thank Zhijie Hu, due to his contribution is considered as important as the first author in this paper.

References 1. Alpaydin, E.: Introduction to Machine Learning (2009) 2. Banu, P.N., Azar, A.T., Inbarani, H.H.: Fuzzy firefly clustering for tumour and cancer analysis. Int. J. Model. Ident. Control 27(2), 92–103 (2017) 3. Chaudhuriand, B., Rodenacker, K., Burger, G.: Characterization and featuring of histological section images. Patt. Recogn. Lett. 7(4), 245–252 (1988) 4. Cruz-Roa, A., Xu, J., Madabhushi, A.: A note on the stability and discriminability of graphbased features for classification problems in digital pathology. In: Proceedings of SPIE 9287, p. 928703 (2015) 5. Gonzalez, R., Woods, E., Eddins, S., et al.: Digital Image Processing Using MATLAB, vol. 624 (2004) 6. Miranda, G., Barrera, J., Soares, E., et al.: Structural analysis of histological images to aid diagnosis of cervical cancer. Proc. SIBGRAPI 2012, 316–323 (2012) 7. Otali, D., Fredenburgh, J., Oelschlager, D., et al.: A standard tissue as a control for histochemical and immunohistochemical staining. Biotech. Histochem. 91(5), 309–326 (2016)

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8. Peng, Y., Park, M., Xu, M., et al.: Clustering nuclei using machine learning techniques. In: Proceedings of IEEE/ICME International Conference, pp. 52–57 (2010) 9. Ramos-Vara, J.: Principles and methods of immunohistochemistry. In: Gautier, J. (ed.) Drug Safety Evaluation, pp. 83–96 (2011) 10. Siegel, R., Miller, K., Jemal, A.: Cancer statistics. CA: A Cancer J. Clin. 67(1), 7–30 (2017) 11. Sornapudi, S.: Nuclei Segmentation of Histology Images Based on Deep Learning and Color Quantization and Analysis of Real World Pill Images (2017) 12. Sornapudi, S., Stanley, R., Stoecker, W., et al.: Deep learning nuclei detection in digitized histology images by superpixels. J. Pathol. Inf. 9 (2018) 13. Sudbø, J., Marcelpoil, R., Reith, A.: Caveats: numerical requirements in graph theory based quantitation of tissue architecture. Anal. Cell. Pathol. 21(2), 59–69 (2000) 14. Sukumarand, P., Gnanamurthy, R.: Computer aided detection of cervical cancer using pap smear images based on adaptive neuro fuzzy inference system classifier. J. Med. Imaging Health Inf. 6(2), 312–319 (2016) 15. Theodoridis, S., Pikrakis, A., Koutroumbas, K., et al.: Introduction to Pattern Recognition: A Matlab Approach. America (2010) 16. Torre, L., Bray, F., Siegel, R., et al.: Global cancer statistics. CA: A Cancer J. Clin. 65(2), 87–108 (2015) 17. Wang, X., Li, S., Li, J., Wang, J.: An adaptive and selective segmentation model based on local and global image information. Int. J. Model. Ident. Control 28(2), 114–124 (2017) 18. Wuand, Z., Leahy, R.: An optimal graph theoretic approach to data clustering: theory and its spplication to image segmentation. IEEE Trans. Patt. Anal. Mach. Intell. 15(11), 1101–1113 (1993) 19. Xiao, Y., Cao, Y., Yu, W., Tian, J.: Multi-level threshold selection based on artificial bee colony algorithm and maximum entropy for image segmentation. Int. J. Comput. Appl. Technol. 43(4), 343–350 (2012)

Study on Analysis and Avoidance of Unstable Control for Flexible System Design G. Q. Zhai, R. Y. K. Zhang, F. W. Meng, Z. Y. Liu, S. Liu and X. R. Yan

Abstract It is difficult to design the control law for flexible systems with multiple lightly damped modes. Particularly, when there exist parameter perturbations, for example, resonant frequency or damping ratio etc., the stability of the system cannot be guaranteed. Conventionally, the control design of the flexible system is only stabilization design, without considering the performance requirement of the system. For the H∞ control, even the famous H∞ loop shaping method proposed by McFarlaned, cannot improve further the performance of the system. Instead, the resulting controller is unstable, with is not easy to tune on in practice. In the proposed, the system bandwidth is chosen as the performance index for the H∞ optimal control. The robustness of the system is further improved by considering the performance of the system. Furthermore, the controller is stable, i.e., the H∞ strong stabilization problem is resolved. With this design, the control accuracy and the speed of response is improved, and also the controller can be tuned on easily. The proposed work is important for the application of flexible structures in the real world. Keywords Flexible system · H∞ control · Optimal design · Weighting function · Satellite attitude control

G. Q. Zhai (B) · R. Y. K. Zhang · F. W. Meng · Z. Y. Liu · S. Liu · X. R. Yan School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei Province, China e-mail: [email protected] R. Y. K. Zhang e-mail: [email protected] F. W. Meng e-mail: [email protected] Z. Y. Liu e-mail: [email protected] S. Liu e-mail: [email protected] X. R. Yan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_15

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1 Introduction Components with flexible structures are widely used in modern automation devices due to their light weight, high reliability, and good adaptability to tasks. Many of the controlled objects studied in the control design belong to the flexible system, large to spacecraft, small to read-write head in computer hard drive and other control systems. Such as satellites with large space truss structures or spacecraft with attachments [1, 2], such as solar panels [3] or antennas [4]. Another example is a magnetic suspension structure bearing [5] and a drive arm [6, 7] in the hard disk positioning control system with a long rod structure, as well as a flexible Robotic arm for space capture or industrial production [8–11]. Both belong to the flexible system. From the point of view of the controlled object, this paper studies the control problems of these flexible systems, and the applications involved are wide. The resonant mode of a flexible system tends to have weak damping characteristics. Therefore, the vibration of the flexible structure can prolong the response time of the system and even cause instability of the system. The high-order resonant mode may also cause modal overflow problems. Therefore, the design of the control system must suppress the effects of these dynamic characteristics, or at least avoid the effects of exciting these modes at high frequencies, making the control system robust to parameter perturbations or high frequency unmodeled dynamics. The authoritative H∞ loop forming method for flexible systems proposed by McFarlaned also failed to solve these robust control problems of weakly damped flexible systems [12, 13]. In addition, current research on the control of flexible systems, whether based on rigid system design (the flexible mode is not modeled dynamic processing), or some existing design methods considering flexible modes are only calm design, and When you want to increase the bandwidth, the controller is unstable. The unstable control here means that the closed loop system is stable, but the designed H∞ controller is unstable. There is relatively little research on unstable controllers, and the investment of unstable controllers is actually very difficult in fact [5]. The main indicators for measuring the performance of a control system (servo system) are bandwidth and accuracy, where the system bandwidth determined by the frequency response reflects the system’s rapidity. The greater the bandwidth, the better the speed, and the improved response speed makes the flexible system stabilize and reduce fatigue damage as quickly as possible after rapid maneuvering. However, an increase in system bandwidth will include more weakly damped resonant modes resulting in reduced or even unstable stability. For this reason, the optimality of the control design is important, that is, how to find an optimal compromise between robust stability and system bandwidth at design time. How to make the attenuation process fast and stable, that is, whether the system performance (bandwidth) can be done better and ensure that the controller itself is stable is still a subject worth studying.

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2 System Model Reference [12] is a classic work of H∞ loop shaping method, and two examples of the last three application examples in the literature [12] are flexible systems. In this paper, the satellite attitude control with two solar panels in the McFarlaned method is taken as an example to analyze the design problem of the flexible system. The state space model is shown in Eq. (1) [12, 14] x˙ = Ax + Bu y = Cx

(1)

where u is the control torque (N · m), y is the measurable roll angle, and the corresponding matrix is ⎡

0 ⎢0 A=⎢ ⎣0 0

1 0 0 0

⎡ ⎤ ⎤ 0 0 0 −5 ⎥ ⎢ ⎥  0 0 ⎥, B = ⎢ 1.7319 × 10 ⎥, C = 1 0 1 0 ⎣ ⎦ ⎦ 0 0 1 3.7859 × 10−4 −ωn2 −2ζn ωn

In the formula ωn = 1.539 rad/s, ζn = 0.003. Then the transfer function corresponding to Eq. (1) is 1.7319 × 10−5 3.7859 × 10−4 + s2 s 2 + 0.009s + 2.369 −4 2 3.9591 × 10 (s + 0.0004s + 0.1036) = s 2 (s 2 + 0.009s + 2.369)

G(s) =

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It can be seen that the model consists of a primary mode plus a rigid mode. Wherein the primary mode amplitude k1 = 3.7859 × 10−4 significantly larger, the magnitude of k0 = 1.7319×10−5 rigid mode one order of magnitude difference. The characteristics of the system show obvious flexibility, which brings more problems to the design of the system. It can be seen from Eq. (2) that the gain of this object is relatively small, and the gain of the system is generally increased in the control design to suppress various disturbances that may exist. Figure 1 is a Bode diagram of the Eq. (2) multiplied by the gain K = 10,000. It can be seen from Eq. (2) and Fig. 1 that since the rigid body modal component is small, it is reflected in the low frequency band that the characteristic of the system transitions to the first flexible mode when ω is over 0.3. From a design point of view, it is required to ensure the stability of the system in the frequency band where the amplitude-frequency characteristics are drastically reduced. This is also the design difficulty of such flexible systems [14].

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Fig. 1 Bode plot of the flexible system

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3 H∞ Loop Shaping Method Instability Control and Performance Analysis Figure 2 shows the amplitude-frequency characteristics of a nominal mathematical model of a flexible structure in a hard disk drive (Fig. 2 in Ref. [15]). It can be seen that in the amplitude-frequency characteristic of the weakly damped flexible system, the region where the resonant mode is dense and the amplitude changes drastically belongs to the middle frequency band of the system flat 0 dB line. In the example of the flexible system shown in Fig. 1, since the model Eq. (2) only considers the primary mode, the middle frequency band only reflects the situation in which the amplitude changes drastically. The H∞ loop shaping design is precisely the stability Fig. 2 Amplitude-frequency characteristics of lightly damped flexible systems

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problem of this mid-band. It seems that the H∞ loop shaping method proposed by McFarlaned can improve the performance of the system, and the bandwidth of the system can reach the resonant frequency (ω1 = 1.539), but it is not the case. The H∞ loop shaping method proposed by McFarlaned for flexible systems is a well-established robust method, and is also available in the authoritative literature [12]. Subsequent studies have not questioned the method proposed by McFarlaned. However, analytical studies have shown that the McFarlaned H∞ design proposed for weakly damped flexible systems is not as effective as expected, as Ref. [16] shows poor robustness. In addition, the H∞ control design is mainly the selection of structural problems and weight functions. The structural problems include two blocks, four blocks, and µ synthesis, but regardless of the structure, Weak damping flexible systems may produce an unstable H∞ controller [5, 12, 14, 17]. It is illustrated by the design in [12]. The H∞ loop shaping design first selects the appropriate weight function to determine the frequency characteristics of the designed system in advance [14]. The weighting function chosen by the literature [12] for the controlled object [see Eq. (2)] is W (s) = 10,000

s + 0.4 s

(3)

When McFarlaned chooses this weighting function, the design is designed to increase the bandwidth to the primary mode. Therefore, when designing the object after forming, as described above, first multiplying K = 10,000. Second the low frequency part of the controlled object becomes 0.17319 s2 . Then the frequency √ when passing the 0 dB line is 0.17319 ≈ 0.42. In order to increase the bandwidth, W (s) adds a zero point. So that the amplitude-frequency characteristic is raised by 20 dB before crossing the 0 dB line, and when it reaches the first mode, it is further reduced by 20 dB over the 0 dB line. In order to achieve the purpose of improving system performance, the H∞ controller designed for the forming object WG is [15] K ∞ (s) =

2.2713(s 2 + 0.2795s + 0.04545)(s 2 + 0.1797s + 1.041) (s + 4.417)(s + 0.4048)(s 2 − 0.08855s + 0.1365)

(4)

The amplitude-frequency characteristics of the input-end disturbance to the output transfer function G/(1 + K G) of the designed system are shown in Fig. 3. From the Bode diagram of G/(1 + K G), after 0.3219 rad/s (the first zero of the controlled object), the G/(1 + K G) coincides with the controlled object G, so the effective bandwidth of the system is actually only before 0.3219. The bandwidth does not actually increase, and the designed H∞ controller is unstable. Look at the sensitivity characteristic S( jω) of this system, as shown in Fig. 4. As can be seen from Fig. 4, S ≈ 1 after ω = 0.3, there is no ability to disturb the suppression. It is only suppressed at the resonance peak point. In [15], Nie et al. used the H∞ weighting method in the servo control of the data storage system. Although

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Fig. 3 Amplitude-frequency characteristics of controlled plant and disturbance rejection

Fig. 4 The S( jω) of model Eq. (2)

the optimal design was proposed, the final sensitivity characteristic is still the same as that in Fig. 4, only with disturbance at low frequencies. The inhibition ability is shown in Fig. 5 (i.e., Figs. 5 and 9 of [15]). The same problem is explained, and the actual bandwidth of the system has not increased. Next, analyze the cause of the unstable controller. The Nyquist curve of the designed W (s)G(s)K ∞ is shown in Fig. 6. There is a zero point before the resonant mode, then the resonant mode (ω1 = 1.539) appears a large circle after the W (s)G(s)K ∞ is close to the origin (so that it can stay away from −1 point to ensure robustness). However, if the frequency difference between the pole and the zero point is large, the zero point of this example is ω = 0.3219, that is, when ω = 0.3219, the K G( jω) is already close to the origin. In this way, W (s)G(s)K ∞ can only rotate one turn counterclockwise around −1 point and wait for ω1 = 1.539 to approach the

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Fig. 5 The S( jω) and disturbance rejection of Fig. 2

origin, so that the large circle of the resonant mode appears again after passing the origin. This requires the controller to have a pair of unstable poles. If there is no zero point before the resonant mode, then artificially add a notch before the resonant mode, the large circle of the resonant mode enters the right half plane, increasing the robustness [18]. But in general, although the effective bandwidth is just before zero (0.3219), the latter feature does not help the bandwidth increase, the robustness is improved because the W (s)G(s)K ∞ big circle enters the right half plane. The disadvantage is that the controller is not stable. If the bandwidth is limited before the first zero (using gain stabilization), you can avoid unstable controllers. So how wide can bandwidth be in the same robustness?

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Fig. 6 Nyquist plot of system Eq. (2)

4 Optimal Performance Stable Control Design The choice of the weight function is the core issue of the H∞ design method. The design methods of state feedback, output feedback, and loop shaping in H∞ theory all involve the selection of weight functions (or weight coefficients) [19]. In the H∞ design, the disturbance suppression capability and robustness correspond to the low frequency band and high frequency band characteristics of the system respectively. Therefore, the weight function in the H∞ design is generally considered only from the requirements of the low frequency band and the high frequency band, without specifically considering the mid-band of the controlled object. McFarlaned’s loop shaping method is the same when selecting the weight function, which is why it creates problems such as unstable controllers, bandwidth, and robustness. In fact, the mid-band of the weakly damped flexible system contains just a few weakly damped resonant modes that are difficult to control. Therefore, this scheme differs from the conventional design idea in the selection of the weight function, and proposes a weighted selection method as shown in Eq. (5). W (s) = ρ

(s + r1 )a (s + r2 )a

(5)

 where r2 = ω12 /k and r1 = kr2 . Here are three parameters k, a and ρ need to be determined. The first inflection point r2 of the amplitude-frequency characteristic of the weighting function should be after zero point 0.3219, before the first mode ω1 = 1.539. The second turning point r1 should be after 1.539 and should not exceed too much, otherwise it will bring about the effects of high frequency unmodeled dynamics. So you can take k = 10, then r2 = 0.4876, r1 = 4.876

(6)

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where (10)a ρ corresponds to the reciprocal of the controller gain, reflecting the design requirements of the system, that is, increasing the gain of the system to suppress the interference, but the gain of the controller is rapidly attenuated after the primary modal frequency, in order to avoid exciting the high-order resonance mode in the system. When taken a = 5, ρ = 0.023

(7)

The system has the best sensitivity characteristics and bandwidth. The sensitivity is basically the same as that of Fig. 4. Then (10)a ρ = 2300, the open loop gain value in the original McFarlaned method is 4000 [see Eq. (3)]. The loop shaping design is performed according to the weight determined by Eqs. (6), (7), and the obtained H∞ controller is

K ∞ (s) =

4.6442(s + 0.3633)(s + 0.06993) (s 2 + 1.121s + 0.3161)(s 2 + 0.9438s + 0.2322) (s 2 + 0.00923s + 2.369) (s 2 + 1.79s + 0.854)(s 2 + 0.1398s + 0.0927) (s 2 + 0.9367s + 0.5078)(s 2 + 0.001007s + 2.731)

(8)

It can be seen that the design of the McFarlaned method is improved according to the weighted selection method of the Formula (5), the obtained controller is stable, and the sensitivity characteristics and bandwidth are not deteriorated. Figure 7 is a Bode diagram of the H∞ controller obtained by the improved method of the present invention. Figure 7 shows the correction made by the H∞ design for the original shaped W (s)G(s). It can be seen from the figure that the corrections made mainly in the middle frequency band are used to ensure stability and robustness, and the low frequency band and the high frequency band only slightly adjust the gain. Fig. 7 Bode plot of of the H∞ controller

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Figure 8 is a response curve of the control signal of the feedback control system under step disturbance. The response curve indicates that after feedback control, the system has sufficient damping and the steady-state error is zero. This H∞ loop shaping design is also robust to parameter perturbations. It has been verified that when the frequency of the flexible mode is perturbed from 1.539 to 1.7 rad/s, the response under the step disturbance begins to diverge, as shown in Fig. 9. Fig. 8 System response under step disturbance

Fig. 9 Response of system with perturbation

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5 Conclusion (1) The reason why the McFarlaned loop forming method produces an unstable controller is given; (2) The weighting selection in the loop forming design is improved, the system performance (bandwidth) is better under the premise of ensuring the controller is stable, and the problem that the unstable controller is difficult to put into use is avoided. (3) Design to find the best compromise between robust stability and system bandwidth. Try to increase the system bandwidth while making the design results of the flexible system more robust. Acknowledgements Manuscript received April 7, 2018. This work was supported in part by the Doctoral Foundation of Liaoning Province (No. 20170520333), the Fundamental Research Funds for the Central Universities (No. N182304010), the Doctoral Foundation of Hebei Province (No. F2019501012).

References 1. Chen, L., Yan, Y., Mu, C., Sun, C.Y.: Characteristic model-based discrete-time sliding mode control for spacecraft with variable tilt of flexible structures.IEEE/CAA J. Automat. Sin. 3(1), 42 (2016) 2. Zhao, C., Guo, H.W., Deng, Z.Q., et al.: Structure design and performance evaluation of variable configuration truss-type satellite platform. J. Harbin Inst. Technol. 50(1), 11 (2018) 3. Tan, T.L.: State transition control of satellite attitude. Control Theor. Appl. 34(5), 655 (2017) 4. Wu, Y.L., Li, J.J., Zeng, H.B., et al.: Robust H-infinity control design for spacecrafts with large flexible netted antennas. Control Theor. Appl. 30(3), 365 (2013) 5. Balini, H., Scherer, C.W., Witte, J.: Performance enhancement for AMB systems using unstable H∞ controller crossovers. IEEE Trans. Control Syst. Technol. 19(6), 1479 (2011) 6. Cherubini, G., Chung, C.C., Messner, W.C., et al.: Control methods in data-storage systems. IEEE Trans. Control Syst. Technol. 20(2), 296 (2012) 7. Lu, Y.S.: Internal model control of lightly damped systems subject to periodic exogenous signals. IEEE Trans. Control Syst. Technol. 8(3), 699 (2010) 8. Sun, C.Y., He, W., Hong, J.: Neural network control of a flexible robotic manipulator using the lumped spring-mass model. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 1863 (2017) 9. Yang, Y.C., He, W., Li, X.J.: Reinforcement learning control of a single-link flexible robotic manipulator. IET Control Theor. Appl. 11(9), 1426 (2017) 10. Yang, J., Shao, R., Li, B., et al.: Iterative learning observer based robust output feedback tracking control for flexible manipulator. J. Harbin Eng. Univ. 39(2), 1 (2018) 11. Liu, F.C., Gao, J.F., Jia, X.J.: Adaptive network control of flexible-joint space manipulator in task space under gravity effect. J. Astronaut. 36(12), 1391 (2015) 12. McFarlane, D., Glover, K.: Robust controller design using normalized coprime factor plant descriptions. Lecture Notes in Control and Information Sciences. Springer, New York, 138 (1989) 13. Meng, F.W., Lv, X.Y., Liu, Y.Q., et al.: Hydrothermal preparation and microstructure analysis of silver tin oxide contact materials. Control Decis. 33(2), 371 (2018) 14. Meng, F.W., He, Z., Wang, G.X., et al.: Control design of flexible systems and H-infinity loop-shaping method. Control Theor. Appl. 30(8), 1014 (2013)

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15. Nie, J., Conway, R., Horowitz, R.: Optimal H∞ control for linear periodically time-varying systems in hard disk drives. IEEE/ASME Trans. Mechatron. 18(1), 212 (2013) 16. He, Z., Meng, F.W., Liu, W., et al.: Robustness of H∞ loop shaping design. Acta Automatica Sin. 36(6), 890 (2010) 17. He, Z., Jiang, X.M., Meng, F.W., et al.: µ-synthesis in H∞ loop-shaping design. Control Theor. Appl. 29(3), 347 (2012) 18. Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems (Fourth Edition). Pearson Education, Beijing (2003) 19. Meng, F.W., Pang, A.P., Dong, X., et al.: H∞ optimal performance design of an unstable plant under Bode integral constraint. Complexity (Bio-Inspired Learning and Adaptation for Optimization and Control of Complex Systems) (2018)

Eigenvalue Sensitivity Analysis of Aircraft Power System Jianying Liu, Jin Cai, Jiawang Huang and Zhangang Yang

Abstract Many existing literatures are about improving the controller to improve the stability of the power system. However, the discussion of the power system line parameters is little. This paper models the circuit of aircraft power system based on dq transformation method. Based on the stability analysis of the system, the eigenvalue sensitivity of the power system parameters of the power supply system is calculated, and the influence of the parameters of power system on the small disturbance stability of the power supply system is analyzed. Finally, the simulation verified the correctness of the eigenvalue sensitivity analysis. Keywords Aircraft power system · Modeling · Eigenvalue sensitivity · Simulation

1 Introduction In traditional power system small disturbance analysis, modal analysis methods (including participation factors, damping ratios, oscillation frequencies) are widely used to analyze system stability [1]. It is also an effective method that has been used to extract the main modes to analyze the dynamic characteristics [2–4]. However, the modal analysis method can only give the degree of participation of the parameters to the stability of the system, but cannot give the influence of the parameters on the stability. The literature [5] first proposed the concept of parameter sensitivity, and also presented a method for analyzing the sensitivity of large-scale, multi-loop control system parameters using linear first-order differential equations. This parameter sensitivity calculation method makes up for the shortcomings of the modal analysis method and is widely used in the parameter design and optimization of power system stabilizers (PSS). Literature [6] proposes a sensitivity analysis method based on the sensitivity of eigenvalues to PSS transfer function and the sensitivity of damping to PSS amplification. Literature [7] proposed a new sensitivity concept for power J. Liu (B) · J. Cai · J. Huang · Z. Yang College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_16

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systems: eigenvalue operation mode sensitivity. Compared with traditional sensitivity calculation, this sensitivity calculation method is more intuitive, reflecting the influence of eigenvalues on the system operation mode. Literature [8] proposed the concept and method of eigenvalue calculation relative to the sensitivity of a transfer function, The sensitivity of the transfer function can more fully consider the effects of changes in all parameters compared to the sensitivity of the parameter considering only the influence of one parameter change. The above three eigenvalue sensitivity calculation methods belong to the first-order sensitivity calculation method based on steady-state operating point calculation, and are not applicable to complex nonlinear dynamic systems. Literature [9] proposed a second-order sensitivity calculation method. First-order sensitivity calculation is simple, second-order sensitivity is closer to actual trend. Since the structure of the aircraft power system calculated in this paper is relatively simple, the first-order sensitivity calculation is adopted. This paper models the aircraft power supply system based on the dq transformation method. Then using the model to analyze the stability of the system. The main mode of the eigenvalue is analyzed, and the sensitivity of the main modal is calculated. The influence of line parameters on the stability of the system is analyzed. The correctness of the method is verified by simulation. Provide a theoretical basis for the design of the line parameters of the aircraft power system.

2 Modeling and Stability Analysis of Aircraft Power System The aircraft power system circuit studied in this paper is shown as in Fig. 1. The system circuit consists of a three-phase voltage source, a transmission line, a six-pulse transformer rectifier, a DC filter, and an equivalent ideal constant power load. Req , L eq , and C eq are equivalent resistance, inductance, and capacitance on the transmission line, respectively. CPL is the ideal constant power load. r F , L F , and C F are the 6-pulse Diode Rectifier Source Bus

AC Bus

Fig. 1 Aircraft power system circuit diagram

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resistance, inductance, and capacitance of the DC side filter, respectively. E dc and V out represent the output voltage of the rectifier and the output voltage of the DC side filter, respectively. λ is the phase difference between the source bus bar and the ac bus bar. Performing dq equivalent transformation on the system circuit shown in Fig. 1. Then using the first sequence expansion of Taylor’s formula to analyze the system matrix of the equation of state A [10]. ⎡

R

− L eqeq

ω

− L1eq

0

0

0

⎢ R 0 − L1eq 0 0 ⎢ −ω − L eqeq ⎢  √ ⎢ 1 2 3 ⎢ − Ceq 0 0 ω − 23 · πC 0 eq A=⎢ ⎢ 0 − 1 −ω 0 0 0 ⎢ Ceq    √ ⎢ rμ rF 3 2 3 ⎢ 0 0 · 0 − L F + L F − L1F ⎣ 2 πLF PC P L0 1 0 0 0 0 CF C V2 F

out,o

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 6×6

The matrix parameters are shown in Table 1. Basing on the parameters shown in Table 1, the stability calculation is performed in combination with matrix A. The calculation results are shown in Fig. 2. Increasing the value of PCPL in order of calculation, calculating the value of the eigenvalue of the system state matrix A under different conditions. Known by the eigenvalue theory, when all the eigenvalues is in the imaginary axis of the coordinate axis, the system is in a steady state. Conversely, when the eigenvalues is in the real axis, the system is in an unstable state. It can be seen from the calculation results in Fig. 2, when the eigenvalues exceeds 17 KW, the system changes from stable to unstable. And with the increase of PCPL value, the stability of the system is getting worse. In summary, this paper calculates the parameter sensitivity of the aircraft power system at the steady-state operating point of PCPL = 17 kW. Table 1 Aircraft power system parameters

Description

Parameter

Value

Transmission line resistance

Req

0.1 

Transmission line inductance

L eq

24 μH

Transmission line capacitance

C eq

1.5 mF

Phase source voltage

VS

230 V

Source frequency voltage

ω

400 * 2π rad/s

DC link inductor resistance

rF

0.01 

DC link inductor

LF

2 mH

DC link inductor capacitance

CF

500 μF

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Fig. 2 Influence of PCPL on eigenvalues

3 Eigenvalue Sensitivity Analysis Method In the analysis and design of the operation of the power system, generally analyze the influence of certain parameters on system stability, in order to change parameters to improve system stability. The eigenvalue sensitivity analysis method can not only analyze the key parameters of parameters affecting the stability of small disturbances, but also analyze the influence trend of parameters on system stability, which is a common analysis method for power systems. The eigenvalue sensitivity analysis method can be divided into three types: the sensitivity of the eigenvalue to the component parameter, the sensitivity of the eigenvalue to the transfer function, and the sensitivity of the eigenvalue to the operation mode. They all belong to the field of static analysis, but the research objects for sensitivity are different. The eigenvalue sensitivity analysis method is to find a steady-state operating point of the system operation through stability analysis, and analyze the influence of the research object on the eigenvalue based on the steady-state operating point. Since this paper deals with the sensitivity analysis of the parameters, the following are all about the sensitivity calculation of the eigenvalues to the component parameters. The state matrix A of the system is a function of a parameter α in the system, which is called A(α). Therefore, any eigenvalue of A is a function of α. When the parameter α is changed, λi (α) will also change accordingly. This change can also reflect the influence of the change of the parameter α on the stability of the system. Assuming that the parameter α changes from α0 to α0 + α, the corresponding eigenvalue will also change from λi (α0 ) to λi (α0 + α), and λi (α0 + α) will be Taylor-expanded at α0 . ∂λi (α)  α=α0 α ∂α ∂ 2 λi (α)  2 + α=α0 ( α) + · · · ∂α

λi (α0 + α) = λi (α0 ) +

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When  α is small, λi (α0 , α) can be approximated as λi (α0 +α)−λi (α0 ) = α. i is the first-order sensitivity of the eigenvalue λi , which The partial derivative ∂λ ∂α is referred to as the eigenvalue sensitivity. In general, the sensitivity of the calculated parameters to the eigenvalues is calculated using the usual Formula (1). ∂λi (α)  ∂α α=α0

dA dλi = u iT vi dα dα

(1)

The row vector uTi in Eq. (1) is the left eigenvector of the matrix A with respect to the eigenvalue λi Column vector vi is the right eigenvector of matrix A with respect to λi . Left and right feature vectors need to satisfy Eq. (2). u iT vi = 1

(2)

The current sensitivity analysis method is to calculate the sensitivity of each parameter separately for different eigenvalues, and then analyze the main modalities of the parameters affecting the stability of the system, and then perform sensitivity analysis on this main modality. This method is too complicated to calculate the sensitivity process. Therefore, this paper proposes to analyze the main mode first, and then perform sensitivity calculation analysis. The calculation steps are as follows: (1) Calculate the eigenvalues for the system state matrix A. The calculation process is as follows:

det[λI − A] = 0 where A is the state matrix, I is the identity matrix, and λ is the eigenvalue to be solved. (2) Each eigenvalue corresponds to a modal state, and the main modality is analyzed. The real part depicts the damping of the oscillation of the system, and the imaginary part reflects the frequency of the oscillation. The eigenvalue can be expressed as the Formula (3):

λi = −σi ± jβi

(3)

The oscillation frequency and damping ratio in this mode can be expressed as Eqs. (4) and (5): σi ξi =  σi2 + βi2

(4)

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f osi =

|βi | 2π

(5)

The main mode can be analyzed based on the calculated oscillation frequency and damping ratio. (3) The sensitivity of the parameters in the main mode is calculated and analyzed according to Eqs. (1) and (2).

4 Aircraft Power System Sensitivity Analysis Calculate all eigenvalues in combination with the line parameters in Table 1 and the state matrix A of the system. λ1,2 , λ3,4 , λ5,6 are complex eigenvalues corresponding to three oscillating modes. The oscillation frequency and damping can be calculated by the Formulas (3)–(5) as shown in Table 2. The oscillation frequency and damping ratio of the λ1,2 , λ3,4 , λ5,6 modes calculated in Table 2 are known. The oscillation frequency of λ1,2 is the smallest, the damping ratio is the largest, and the mode λ1,2 is the main mode of the system. So in this paper, λ1,2 is taken as an example to calculate the sensitivity of L eq and analyze it. Calculating the sensitivity value of L eq using Formula (1). The calculated parameter sensitivity is complex, and the real part reflects the influence of the parameter change on the oscillation of the oscillation mode, the imaginary part reflects the influence of the change of parameters on the frequency of the oscillation mode. ∂λ/∂ L eq = −2.3968e + 11 + 3.0650e + 10i. The real part is negative, that is, when L eq is decreased, the real part of the dominant eigenvalue will also increase, and the stability of the system will become better. The sample text performs a small range perturbation change for the value of L eq in the case of a given parameter and calculates the eigenvalue. The calculation result is shown in Fig. 3. It can be seen from Fig. 3 that when the value of L eq increases, the eigenvalue of the system will also shift to the left, and the stability of the system is getting better and better. The calculation result is consistent with the sensitivity calculation result. In order to verify the correctness of the parameter sensitivity calculated for the dominant eigenvalues in this paper, the simulation model of the aircraft power supply system circuit diagram shown in Fig. 1 is simulated in the Simulink module in Table 2 Eigenvalue of the power system Serial number

Eigenvalue

ξi

f osi

λ1,2

−2039.2 ± 4.6142e6i

7.3437e+05

4.4194e−04

λ3,4

−2083.2 ± 4.5642e6i

7.2641e+05

4.5642e−04

λ5,6

−4.2976 ± 982.17 i

156.1692

0.0032

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Fig. 3 Influence of L eq on eigenvalues

MATLAB, and the stability of the system is analyzed by observing the output voltage waveform. The calculation results are shown in Fig. 4. In the simulation, the values of L eq are reduced at 0.2, 0.4, 0.6, and 0.8 s, respectively. Observing the output voltage waveform, it is known that as the L eq decreases, the time it takes for the output voltage waveform to converge to stabilize becomes longer and longer. The stability of the power supply is getting worse and worse.

Fig. 4 Influence of L eq on output voltage

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The simulation results are consistent with the sensitivity calculation results, and the effectiveness of the method is verified by numerical study.

5 Conclusion In this paper, the equivalent circuit model of aircraft power supply system based on dq transformation is established. The equation of state of aircraft power system is obtained by this equivalent circuit. The stability of small disturbance of aircraft power system is analyzed by using state equation. The main mode is proposed. The sensitivity analysis method is used to analyze the sensitivity of the line parameters of the aircraft power system, and the influence of the line parameters on the stability of the aircraft power system is obtained. Finally, the simulation of the aircraft power system circuit of Fig. 1 is carried out. The simulation results verify the correctness of the proposed sensitivity analysis method for the main modal calculation. Acknowledgements This work was supported by the Innovation Team Cultivation Plan of Colleges and Universities in Tianjin (TD13-5071), the Fundamental Research Funds for the Central Universities (3122018D005), Aeronautical Science Foundation of China (20170267002).

References 1. Rosero, J.A., Ortega, J.A., Aldabas, E., et al.: Moving towards a more electric aircraft. Aerosp. Electr. Syst. Mag. IEEE 22(3), 3–9 (2007) 2. Ciezki, J.G., Ashton, R.W.: Selection and stability issues associated with a navy shipboard DC zonal electric distribution system. IEEE Trans. Power Delivery 15(2), 665–669 (2000) 3. Zhou, S., Qi, R., Lin, H.: Load stability analysis of multi-electric aircraft power system. Aeronaut. Comput. Technol. 32(4), 93–95 (2002) 4. Lokman, H., Hassan, H., Moghavvemei, M., Haider, A.F., et al.: Optimization of power system stabilizers using participation factor and genetic algorithm. Int. J. Electr. Power Energy Syst. 55(55), 668–679 (2014) 5. Ness, J.E.V., Boyle, J.M., Imad, F.P.: Sensitivities of large, multiple-loop control systems. IEEE Trans. Autom. Control 10(3), 308–315 (1965) 6. Qianru, X.U., Yong, C.U.I.: Power system stabilizer configuration and parameter tuning based on eigenvalue sensitivity. East China Electr. Power 42(10), 2069–2073 (2014) 7. Liu, X., Lu, S., Guo, Q., Xia, D.: Calculation of sensitivity of eigenvalues to operation mode. Autom. Electr. Power Syst. 22(12), 9–12 (1998) 8. Zhou, E.Z.: Functional sensitivity concept and its application to power system damping analysis. IEEE Trans. Power Syst. 9(1), 518–524 (1994) 9. Gibescu, M., Christie, R.D.: Quadratic sensitivities for power system steady-state control. IEE Proceed. Gener. Transm. Distrib. 144(3), 317 (1997) 10. Areerak, K.: Modelling and Stability Analysis of Aircraft Power Systems. University of Nottingham (2009)

Modeling and Simulation of Closed-Loop Control Circuit of Aircraft Fuel Metering Valve Xudong Shi, Shaoshuai Yuan, Yakun Wang and Xu Wang

Abstract The fuel metering valve is an important part of the aircraft fuel system and it controls the supply of metered fuel. In this paper, the closed-loop control principle of fuel metering valve is analyzed and the closed-loop control circuit of certain aero engine fuel metering valve is modeled and simulated by MATLAB/Simulink simulation software. The function of the Engine Electronic Controller (EEC) controls the opening of metering valve is simulated by establishing a model. A new idea is proposed to study the problem of the accessory limit value in the aircraft component maintenance manual through model simulation and the impact of the accessory limit value on the fuel metering valve is obtained. Keywords MATLAB/simulink · Modeling · Simulation · Limit value · Fuel metering valve · Closed-loop control

1 Introduction Aircraft fuel metering unit is the core component of aero-engines, and it provides accurate metering fuel and servo fuel for aero-engines [1]. It is important to study the internal structure of fuel metering unit for aircraft safety [2]. In the aero engine in-field maintenance, the aero engine should be tested according to the test process in the aircraft component maintenance manual. The manual lists a fixed limit value range for each accessory. At present, there are few theoretical studies on its setting basis. It is studied by using software modeling and simulation methods in the paper. At present, many scholars have used different methods to model and simulate fuel metering devices. For example, Zeng Detang of Beihang University used MATLAB software simulation to study the characteristics of different oil return profiles of X. Shi (B) · S. Yuan · Y. Wang College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] X. Wang Aircraft Maintenance and Engineering Corporation, Beijing (AMECO), Beijing 101399, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_17

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metering devices [3], Yu Ling of Nanjing University of Aeronautics and Astronautics used AMESim software to study the modeling of aero-engine fuel metering devices [4]. Based on the experience of the former, the fuel metering component of certain aero engine is used as the research object in this paper. According to the component principle, MATLAB/Simulink software is used to construct the closed-loop control circuit of the EEC to the fuel metering valve, and the accessory limit value problem in the aircraft component maintenance manual by adjusting the coil resistance is studied.

2 Fuel Metering Valve Closed-Loop Control Circuit Principle The closed-loop control circuit of the metering valve in the certain aero-engine fuel metering component is studied in this paper, which is mainly composed of electrohydraulic servo valve, fuel metering valve, displacement sensor. The schematic is shown in Fig. 1. The servo structure for controlling the fuel metering valve is a four-side jet tube type electro-hydraulic servo valve, as shown in Fig. 2. The jet electrohydraulic servo valve is a two-stage valve operated by a torque motor. The first stage is the jet amplifier and the second stage is the spool valve. The spool valve guides the servo pressure to control the opening position of the fuel metering valve [5, 6]. Fig. 1 FMV closed-loop control circuit schematic

FEEDBACK SIGNALS

+ V1 + V2

TM

SPOOL VALVE FMV

SECONDARY COILS LVDT

EEC

PRIMARY COIL + EXCITATION VOLTAGE

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Fig. 2 Jet pipe valve

3 Fuel Metering Valve Closed-Loop Control Circuit Modeling 3.1 Torque Motor The main function of the torque motor (TM) in the servo valve is to convert the electrical signal input from the EEC into the output of the hydraulic servo regulated by the jet pipe spool valve. The structure of the torque motor is shown in Fig. 2. It consists mainly of permanent magnets, armatures, coils, amplifiers and spring tubes [7]. Basic Voltage Equation The basic voltage equation is expressed as: 2K u u g = (Rc + r p )i + 2K b

dθ di + 2L c dt dt

(1)

where K u is the amplifier gain, u g is the voltage signal input to the amplifier, Rc is the resistance of the coil, L c is the self-inductance coefficient of the coil, r p is the internal resistance of the amplifier, i is the input current of the torque motor, K b is the back electromotive force constant of the coil, θ is the armature deflection angle.

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Electromagnetic Moment Equation Since the permanent magnet generates a polarized magnetic flux, the control coil generates a control magnetic flux under the condition of energization, and the electromagnetic moment equation of the armature can be obtained under the joint action of the two magnetic fluxes. Td = K t i + K m θ

(2)

where Td is the Electromagnetic torque, K t is the medium electromagnetic torque coefficient of torque motor, K m is the torque motor neutral spring stiffness, the electromagnetic moment Td obtains the armature motion equation. Td = Ja

d 2θ dθ + Ba + K a θ + (r + b)K f [(r + b)θ + xv ] dt dt

(3)

where Ja is the moment of inertia of the armature assembly, B a is the viscous damping force of the armature assembly, K a is the spring tube stiffness, r is the feedback rod end to the center of rotation, K f is the feedback rod stiffness, xv is the displacement of the jet pipe spool valve. Combining (2) and (3), then the Laplace transform is expressed as: K t i = Ja θ s 2 + Ba θ s + K m f θ + (r + b)K f xv

(4)

In the Formula (4), K m f = K a − K m + (r + b)2 K f . Torque motor models are established by using MATLAB/Simulink software according to the Eqs. (1) and (4), as shown in Fig. 5.

3.2 Jet Amplifier The jet amplifier is composed of a nozzle and a receiving hole. When the jet amplifier is in the null position, the fuel flow on both sides of the spool valve is equal. When the EEC commands the torque motor to change the position of the jet amplifier, the armature of the torque motor will change the position of the armature. The jet nozzle redirects the fuel flow to either side of the spool valve, changing the pressure on both sides of the receiving bore, causing a change in the servo output and driving the displacement of the servo spool valve. In the middle energy conversion, because the energy loss is relatively small, the deflection displacement is also relatively small. The nonlinear factor is ignored in this paper. The mathematical model of the jet amplifier is expressed as [8]: x f = r0 θ

(5)

Q L = K qs x f − K cs p L

(6)

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where x f is the jet pipe deflection displacement, r0 is the jet pipe deflection radius, Q L is the jet pipe output flow rate, K qs is the jet pipe flow rate gain, K cs is the jet pipe flow-pressure coefficient, p L is the jet pipe output pressure.

3.3 Jet Pipe Spool Valve The jet pipe spool valve is the second stage of the electro-hydraulic servo structure of the jet pipe. The main function is to control the pressure on both sides of the fuel metering valve through the displacement of the spool valve to achieve the purpose of controlling the opening of the metering valve. The flow of the spool valve can be calculated by the following equation [8]: Q L = Av

d xv dt

(7)

Ignoring the viscous damping force and the feedback rod spring force of the spool valve movement, only considering the inertial force and the steady-state hydraulic power, the jet pipe spool valve load pressure is: Av p L = m v

d 2 xv d xv + K f xv + K f r θ + 0.43Wv ( ps − pm )xv + Bv dt 2 dt

(8)

where m v is the quality of the spool valve, Av is the spool area of the spool valve, Bv is the viscous damping coefficient of the spool valve, Wv is the overflow area gradient of the spool valve, pm is the load pressure of the metering valve chambers, modeling is shown in Fig. 5.

3.4 Fuel Metering Valve The principle of the fuel metering valve (FMV) is to keep the pressure difference before and after the metering valve constant, and the EEC controls the opening degree of the valve through the electro-hydraulic servo valve. The electro-hydraulic servo valve provides the pressure of the fuel metering valve abdominal cavity, so that the metering valve moves axially in the abdominal cavity. It can be seen from the flow Formula (9) that the pressure difference, fuel density and fuel flow coefficient are constant. It is assumed that the metering valve inlet is an ideal rectangular valve port, and the fuel opening area is linear with the valve. The displacement of the valve is linear with the fuel flow. The displacement curve of the fuel metering valve is directly simulated in this paper to explain the problem of fuel flow. The schematic diagram of the fuel metering valve is shown in Fig. 3.

178 Fig. 3 Schematic diagram of the FMV

X. Shi et al. TO AIRFRAME SHUT-OFF FROM SOLENOID VALVE EHSV

FROM EHSV

P1

EEC FUEL METERING VALVE

METERING VALVE RESOLVERS P2

According to the principle of the metering valve, the flow formula is as follows:  Q mf = μA(L f mv )

2(P1 − P2 ) ρ

(9)

where Q mf is the fuel flow, ρ is the fuel density, μ is the fuel flow coefficient, P1 is the inlet pressure of the metering valve, P2 is the outlet pressure of the metering valve, L f mv is the displacement of the metering valve and A is the flow area of the metering valve. The metering valve is driven by a second stage spool valve of the jet electrohydraulic servo valve. According to the output flow of the spool valve, the output pressure, and the displacement of the spool valve, a mathematical model is established: q L = K q p xv − K cp pm

(10)

The continuity equation of the metering valve is expressed as: qL = A p

dxp vt dpm + dt 4βe dt

(11)

where q L is the jet pipe spool valve output flow, K q p is the jet pipe spool valve flow gain, K cp is the jet pipe spool valve flow-pressure coefficient, A p is the metering valve spool valve area, x p is the metering valve displacement, vt is the total Compressed area, βe is the effective volume elastic modulus. The load force acting on the metering valve generally has inertial force, steady state hydraulic power, and viscous damping force. The force balance of the metering

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valve is calculated by the following equation [9]: A p pm = m t

d2x p dxp + Bp + 0.43W p ps x p 2 dt dt

(12)

where m t is the quality of metering spool valve, B p is the viscous damping coefficient of metering valve, W p is the flow area gradient of metering valve. Laplace transform for Eqs. (10)–(12): The modeling diagram is shown in Fig. 5.

3.5 LVDT Sensor The linear variable differential transformer (LVDT) is a feedback device. The displacement sensor provides an EEC with an electrical feedback signal proportional to the FMV position to achieve closed loop control. The schematic is shown in Fig. 4. The LVDT displacement sensor consists of a primary coil and two secondary coils. The EEC provides the AC excitation voltage for the primary coil and the induced voltages E 21 and E 22 for the secondary coils L 21 and L 22 [10]. Output voltage formula: U0 = E 21 − E 22 = − jw(M1 − M2 )I1 = − jw(M1 − M2 )

U1 R1 + jwL 1

(13)

where M1 and M2 are the mutual inductance between the primary coil and the secondary coil, I1 is the primary coil current, R1 is the primary coil resistance, L 1 is the primary coil inductance, U1 is the primary coil excitation voltage. When the position is not in the middle position, the mutual inductance difference is linear with the core displacement [10]. According to the above analysis, the function relationship between the metering valve displacement and the feedback voltage is as follows: Fig. 4 LVDT equivalent schematic

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Fig. 5 Total modeling of the closed control loop of the fuel metering valve

U0 =

K tr L f mv +1

s Wtr

(14)

where K tr is the gain of displacement sensor and Wtr is the corner frequency of displacement sensor.

3.6 Fuel Metering Valve Closed-Loop Total Modeling The above voltage amplifying structure, torque motor, jet amplifier, spool valve, fuel metering valve, displacement sensor and other modules are connected for total modeling and the total modeling diagram is shown in Fig. 5.

4 Simulation Analysis of Closed Loop Control Circuit of Fuel Metering Valve 4.1 Torque Motor Coil Resistance Simulation There are two coils on the torque motor armature, and the coil directly receives the EEC command to actuate the spool valve. To keep the other parameters constant, the resistance values of the torque motor coils is set to 100, 200, 300 and 400 . The simulation results are shown in Figs. 6 and 7. From the step response curve in Figs. 6 and 7, it can be seen that different resistance values correspond to different metering valve displacements. The curve rises rapidly in the early stage and then gradually slows down, and reaches a stable value after 0.05 s. As the resistance of the coil increases, the step response rises slowly before reaching the stable value. It also can be seen from the figure that the coil resistance

Modeling and Simulation of Closed-Loop Control Circuit … Fig. 6 Effect of T/M on FMV displacement

181

0.01 R=100 Ω R=200 Ω R=300 Ω R=400 Ω

Lfmv/m

0.008

0.006

0.004

0.002

0

0

0.05

0.1

0.15

0.2

t/s

Fig. 7 Effect of the T/M on the jet spool valve

-3

1.5

x 10

R=100 Ω R=200 Ω R=300 Ω R=400 Ω

1

Xv/m

0.5

0

-0.5

-1 0

0.05

0.1

0.15

0.2

t/s

value is less than 300 , and the curve fluctuates greatly. When the coil resistance is greater than 300 , the larger the resistance, the longer the response time, so a reasonable resistance range should be set. If the motor coil fails, the resistance value exceeds the limit value, which will affect the metered fuel flow.

4.2 Displacement Sensor Coil Resistance Simulation The function of the displacement sensor mainly detects the size of the metering valve opening and the sensor converts the metering valve displacement signal into an electrical signal and feeds it back to the EEC. The EEC receives the position feedback signal, and after analyzing and processing this signal, it will sends a new metering valve position command to the torque motor. The metering valve displacement sensor forms a closed loop structure with the electro-hydraulic servo valve and the metering valve.

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There is a primary coil and two secondary coils in the displacement sensor. From Eq. (15), it can be seen that the resistance of the primary coil is inversely proportional to the output voltage. Since the resistance is converted into a corner frequency by the formula during the modeling process, the other parameter values are kept unchanged, and changing the corner frequency is equivalent to changing the resistance of the coil. The input voltage is 3 V. As the resistance of the primary coil increases, the corner frequency becomes smaller. Therefore, the corner frequency is selected as 100 rad/s, 300 rad/s, 500 rad/s and 700 rad/s respectively. The simulation results are shown in Figs. 8 and 9. In Fig. 8, the step response curve shows that as the corner frequency Wtr increases, that is, as the resistance value of the primary coil R1 decreases, the displacement of the metering valve enters the steady state more quickly, and the valve displacement Fig. 8 Effect of LVDT on the FMV

x 10

8

-3

7 6 Wtr=100rad/s Wtr=300rad/s Wtr=500rad/s Wtr=700rad/s

Lfmv/m

5 4 3 2 1 0

0

0.05

0.1

0.15

0.2

t/s

Fig. 9 Effect of LVDT on the jet spool valve

8

x 10

-4

Wtr=100rad/s Wtr=300rad/s Wtr=500rad/s Wtr=700rad/s

Xv/m

6

4

2

0

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remains stable at 0.0065 m. It can also be seen from Figs. 8 and 9 that when Wtr

(15)

is 100 and 300 rad/s, the curve fluctuates greatly, and the stabilization time becomes longer. It can also be seen that the resistance value of the primary coil has a critical value. When the resistance is increased to a certain extent, the fluctuation time will be longer, the measurement valve response is insensitive, and the dynamic response of the fuel metering component is not good.

5 Conclusion MATLAB/Simulink software is used to model and simulate the closed-loop control loop of the fuel metering valve in this paper. The control signal of the EEC to the fuel metering component is simulated by modeling, and the function of the EEC to control the fuel metering valve opening degree is realized. The impact of the accessory limit value on the fuel metering valve is obtained. By setting different torque motor coil resistance values and displacement sensor resistance values, the corresponding curves are simulated. From the curve analysis, as the resistance value of the coil increases or decreases, the displacement curve of the jet spool valve and the displacement curve of the metering valve have changed significantly. It can also be seen in the curve that when the resistance value exceeds a certain range, the amplitude fluctuation of the curve suddenly becomes larger, and the time for the system to reach the steady state becomes longer. So the accessory should be set the appropriate limit value. MATLAB/Simulink modeling method can be used as a basis for judging the limit value of accessory. Acknowledgements The research is supported by the Important and Specific Projects of Civil Aviation Science and Technology Project (Grant No. MHRD20140104). The research is supported by the Innovation Team Cultivation Plan of Colleges and Universities in Tianjin (TD13-5071).

References 1. Yang, Y., Lu, Q.: The research of dynamic modeling and analysis of commercial engine fuelmetering unit. Manuf. Autom. 38(06), 106–110 + 130 (2016) 2. Afiz, I.A., Cunliffe, R., Alukaidey, T.: Mathematical modeling and simulation of a Twin-engine aircraft fuel system using matlab-simulink. Int. J. Control Sci. Eng. 8(1), 1–12 (2018) 3. Zeng, D., Wang, W., Pei, D., Xu, M.: Fuel scavenger contour performance analysis of fuel metering devices. Aero Eng. 36(06), 23–25 + 38 (2010) 4. Yu, L., Zhifeng, Y.E.: AMESim modeling of aero-engine fuel metering device. Mod. Mach. 5, 26–29 (2014) 5. Kang, Y., Zhao, L., Yao, L.: Fault diagnosis and model predictive fault tolerant control for stochastic distribution collaborative systems. IJMIC 30, 30–37 (2018)

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6. Feng, J., Gao, Q., Guan, w., He, Z.: Mathematical modelling and backstepping adaptive sliding mode control for multi-stage hydraulic cylinder. IJMIC 30, 322–332 (2018) 7. Sharan, A.S., Hiremath, S.S., Venkatesha, C.S., Karunanidhi, S.: Investigation on the critical parameters affecting the working design dynamics of a torque motor employed in an electrohydraulic servovalve. Simul. Trans. Soc. Model. Simul. Int. 95(1), 31–49 (2019) 8. Mesropyan, A.V., Sharipov, R.R.: Mathematical modeling of transient processes in the jet pipe servo actuator with a dual-mode controller. Ufa Procedia Eng. 150, 168–172 (2016) 9. Zhang, L., Chen, K., Wu ,W., Zhan, C.: Modeling and dynamic characteristics simulation of three-stage electro-hydraulic servo valve with jet pipe. Hydraul. Pneumatics 6, 66–72 (2018) 10. Ren, H., Li, W., Zhu, T., Wang, Y., Jiang, X.: The simulation modeling research of linear variable differential transformer displacement sensor. J. Astronaut. Metrol. 33(06), 20–25 (2013)

A Static Gesture Recognition Algorithm Based on DAG-SVMs Mengxin Li, Tongwei Jiang, Rui Xu and Baifeng Lin

Abstract In this paper, a static gesture recognition method with Kinect depth sensor to collect various gesture depth images was proposed. Based on the depth probability statistics of the original depth histogram, the neighborhood statistical parameters were added to construct the two-dimensional depth histogram so as to extract gesture images. In addition, the idea of integrating edge feature Hu moment and edge length moment as new features of static gesture is presented, and the improved DAG-SVMs algorithm is used to train gesture recognition so as to improve the recognition rate of the algorithm. Experimental results show that recognition rate of the recognition method achieves 97.96% Keywords Kinect · DAG-SVMs · Feature extraction · Gesture recognition

1 Introduction Human-computer interaction system has become an indispensable link in daily life and industrial production. As a kind of body language, gesture can most intuitively express our emotions or communication intentions, and is the most commonly used form of communication in daily life except language. So gesture are widely used in intelligent interactive technologies. Early gesture recognition was mainly realized based on ordinary color cameras and external wearable devices. Delamare et al. [1], used two ordinary cameras to collect human gesture images to simulate the binocular visual effect of human, and proposed a 3d link model for 3d reconstruction of human hands. But the outline of the fingers and palm of model is rough, and unable to build a complete and clear hand model. Zeller [2] et al., used data gloves as the control device of a virtual environment system . they used the HOG feature recognition algorithm based on

M. Li · T. Jiang (B) · R. Xu · B. Lin School of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110000, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_18

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gesture and achieved good results. However, the gesture recognition method based on wearable devices has not been further developed. The main reason is that it is difficult for data gloves to match the dynamic gestures of each user, and it is difficult to popularize due to its high price. Kinect 2.0 is a depth visual interactive device launched by Microsoft. The appearance of the sensor provides a broader space for gesture interaction. Zhou et al. [3] proposed a gesture recognition method based on Kinect and FEMD (finger-earth move’s distance) algorithm was used to realize gesture recognition with stable effect. But this algorithm required a large amount of data for training. Currently Jin et al. [4] proposed a sign language recognition algorithm, which took a single Hu moment as a gesture feature and used SVM for classification, and successfully identified 5 kinds of sign language. In this paper, Kinect depth sensor is used to collect depth images. Aiming at the noise interference defect of the original depth histogram, one-dimensional depth histogram statistical results are used as the threshold for image segmentation to obtain gesture segmentation images (Sect. 2.1). After the image is preprocessed, extract gesture feature according to the new feature gesture recognition algorithm proposed in this paper (Sect. 2.2), and train static gesture sample with the improved DAG-SVMs (Sect. 2.3). Therefore, the traditional static recognition method and the gesture recognition rate is improved.

2 Static Gesture Recognition with DAG-SVMs 2.1 Two-Dimensional Depth Histogram In this paper, Kinect is used for data collection of gesture image. Microsoft has given different depth levels when the acquisition depth difference is greater than 3–4 mm. The value of image depth reflects the relative distance between the pixel and Kinect sensor. The probability distribution expression of depth histogram is defined as described by the following equation: Pi =

L−1  ni , pi > 0, pi = 1 M×N i=0

(1)

where L is the sum of depth levels in depth histogram.ni is the number of pixels at the ith depth level in the depth histogram. Aiming at the problems of noise and small statistical variance in one-dimensional depth histogram establish by only collecting the depth value of image pixel points. We propose a joint probability statistical algorithm based on references [5]. On the basis of the depth probability statistics of the original depth histogram, the statistical parameters of the neighborhood depth were added. While the probability distribution

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(a). One-dimensional histogram

(b). Two-dimensional histogram

Fig. 1 Comparison of histogram statistics of gesture image

of the depth value of each pixel was statistically analyzed, the probability distribution of the average neighborhood depth of the image was statistically analyzed to construct the two-dimensional depth histogram of “depth value-neighborhood depth value”. The construction formula of the neighborhood depth is shown as follows: g(xi , yi ) =

L−1 1  f (xi , yi ) Ni (x ,y ) i

(2)

i

where Ni denotes the number of pixels in the neighborhood, and the general value range of Ni is 9 pixels of 3 × 3 in the region around the pixel. Based on the statistical results of two-dimensional depth histogram obtained above, Otsu algorithm [6] is adopted to select the optimal threshold and then the binary gesture graph can be obtained. In Fig. 1a, the horizontal axis of the original one-dimensional depth histogram only represents the depth value parameters of the gesture image, while the horizontal axis of the improved two-dimensional depth histogram in Fig. 1b represents the fusion parameters of the depth value of the domain pixel, and the vertical axis of the image represents the frequency of the parameters of pixel points. The two-dimensional depth histogram mainly reflects the spatial position distribution probability of each pixel in the image. Compared with the statistical results of the one-dimensional depth histogram, the noise interference of the gesture target area in the two-dimensional depth histogram is reduced and the frequency crest is obvious.

2.2 Edge Extraction and Feature Extraction Edge extraction Image edge feature can directly reflect the contour feature of an object. In the process of edge detection, the abrupt changes of image edges are mainly

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reflected in the discontinuity of environment depth, the discontinuity of object surface direction, the change of object surface material, and the change of scene illumination. Image edge features exist in the target region and background region of the image. By edge detection of the image, the edge contour of the image can be obtained and the non-target region can be removed [7]. The step change of the gray value in the gray image represent the edge characteristics of the object. But because the first derivative of image edge has strong directional fixity, the detection of edge has obvious limitations. In order to overcome this shortcoming, gradient operator is used to define image gradient vector, and the maximum change rate of gradient vector is used to reflect the step change of edge pixel function. The commonly used edge detection operators include Canny operator, Robert operator, Sobel operator, etc. These three operator were used to carry out image edge detection experiments for static gesture images respectively (see Fig. 2). Because of its good anti-interference ability to filtering noise and adapt ability, the image effect processed by Sobel operator is clearer than other edge detection effects. Besides, we focuses on detecting the edge information of the hand, which requires little detail of the hand texture. Therefore, Sobel operator is taken as the first choice for edge detection in our work. Feature extraction Feature extraction is a key step in gesture recognition. Considering that each gesture image collected has changes in translation, size and rotation [8]. Hu moment is a geometric feature based on image contour. According to the definition, Hu moment has invariance of rotation, scaling and translation, so that can be used to express the characteristics of the image edge contour. By means of the nonlinear combination of central moment characteristics, the following 7 geometric

(a). Original image

(c). Canny operator

(b). Binary image

(d). Robert operator

Fig. 2 The result of image edge detection

(e). Sobel operator

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invariant moments can be constructed (Eq. 3). But In the calculation process of a single Hu moment, noise far away from the center of mass will seriously interfere with the important information in the region around the center of mass and affect the recognition effect. Therefore, it is far from enough to use the 7 Hu invariant moments as feature vectors for recognition. The edge length moment is the perimeter of the contour of the gesture image. That is, the total length of the connected region of the entire image edge obtained after gesture edge detection (Eq. 4). In order to improve gesture recognition rate, we put forward an ideal that combine Hu moment with edge length moment as new features of static gesture. 7 Hu moment and edge length moments are collected as the eigenvectors of gesture recognition. h u1 = η2,0 + η0,2 2  2 h u2 = η2,0 − η0,2 + 4η1,1 2  2  h u3 = η2,0 − η1,2 + η2,0 − 3η1,1 2  2  h u4 = η3,0 − η1,2 + η2,1 + η0,3   2 2    h u5 = η3,0 − 3η2,1 3η1,2 + η2,0 η3,0 + η1,2 − 3 η2,1 + 3η0,3     2  2  + 3η2,1 + η0,3 η2,1 + η0,3 3 η3,0 + η1,2 − η2,1 − η0,3

(3)

  2  2     h u6 = η2,0 + η0,2 η3,0 + η1,2 η2,1 + η0,3 + 4η1,1 η3,0 + η1,2 η2,1 + η0,3   2  2   h u7 = 3η1,2 + η3,0 η2,0 + 3η1,2 η3,0 + η1,2 − η2,1 + η0,3      2  2  3η1,2 − η0,3 η2,1 + η0,3 + 3 η0,3 + η1,2 − η1,2 + η0,3 H = Ne + 2No

(4)

2.3 DAG-SVMs Static Gesture Recognition Algorithm SVM is a binary classification model based on supervised training mode and is used for the recognition of the five types of digital gestures in this paper, so it is necessary to construct a multi-class support vector machine that meets the classification requirements with the help of multiple binary classifiers. We use DAG-SVMs gestures because DAG-SVMs does not need to traverse the entire sample, and construction to recognize hand has the advantages of no overlapping classification and indivisibility of sample [9, 10]. However, there is a challenge to use the methods is that the sequence of DAG -SVMs nodes is random, and different sequence of nodes will generate different paths for sample recognition. So when the

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classification error occurs near the root node, the misjudgment rate accumulates continuously, and finally affects the recognition accuracy of the whole algorithm. Aiming at the defects of random arrangement in the multi-layer structure of DAG-SVMs, multi-layer structure of DAG-SVMs is presented. During the training stage, Above all, five types of standard static gesture images of Numbers 1 to 5 are collected, Set up a five-class classifier and the five gesture categories are abbreviated as: 1, 2, 3, 4, 5. Then, according to the hand characteristic parameters, 10 SVM (1-vs-2, 1-vs-3, 1-vs-4,…, 4-vs-5) can be obtained by machine training. finally, a DAG-SVMs classifier which meets the requirements of five categories is constructed based on the static gesture features by using the multi-layer structure mode. In the test stage, a total of 100 static digital gesture images were collected to extract the gesture features to be tested, and the gesture features were input into 10 SVM binary classifiers that had been constructed for classification and recognition. Taking 1-vs-2 as an example, the binary classifier 1-vs-2 with the largest number of classification votes in the test stage is category 1. If the final result is the same as that of the dag-svms classifier, the binary classifier is set to successfully identify category 1 in the whole recognition process, and is recorded as one successful identification. The percentage of the total number of successful recognition times of 1-vs-2 is recorded as the recognition accuracy of the classifier, and the recognition accuracy is used to invert the size of the classification interval of 1-vs-2 classifier. The greater the recognition accuracy is, the more the classification interval of sample gesture features is difference. Ten reference binary classifiers were constructed in the training stage, and the recognition accuracy results of each algorithm are shown in Table 1 According to the statistical results (Table 1), 1-vs-5 with the highest recognition rate was selected as the root node of the DAG-SVMs classifier, and the rest nodes were sorted and divided from high to low recognition accuracy. The structure of the improved five classifiers, DAG-SVMs, was finally constructed as shown in Fig. 3. Table 1 Recognition experimental result of each SVMs

SVM

Recognition accuracy (%)

1-vs-2

90

1-vs-3

92

1-vs-4

95

1-vs-5

97

2-vs-3

88

2-vs-4

93

2-vs-5

96

3-vs-4

91

3-vs-5

94

4-vs-5

86

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Fig. 3 Improved structure of DAG-SVMs

3 Experiments and Results In the experiment, Kinect was used to collect gesture image data. Set gesture image acquisition conditions: the distance between the operator and Kinect sensor is required to be 1.2–1.4 m, and the elevation degree of Kinect camera is set to be 0. The palm plane and the camera image acquisition direction are at an Angle of 90°. In this paper, a total of five types of static digital gesture depth images are collected from digital gesture 1 to digital gesture 5, and two-dimensional depth histogram of the image is drawn to extract the gesture target area. Then, a total of 500 deep gesture images were collected through Kinect sensor to create a gesture sample. 50 digital gestures images of the five categories were collected as training sample sets. In the training stage, the edge contour features of five types of static gestures were acquired, and machine learning was carried out through the DAG-SVMs classifier constructed by us. Then 250 gesture depth images were randomly collected as the test sample. In Ref. [4], a SVM gesture recognition algorithm based on single Hu moment parameter feature proposed and a improved Hu moment gesture recognition method proposed in reference [11]. According to the methods proposed by Refs. [4, 11], these three algorithms are respectively used to identify the digital gesture samples to be tested in this paper, and the recognition accuracy obtained by the three algorithms is compared with the average rate of gesture recognition by the algorithm. The simulation image of experimental results is shown in Table 2. As can be seen from Table 2, the average recognition rate of the methods that based on Kinect are obviously higher than method that do not use Kinect. Recognition rate of the method proposed in this paper reaches 97.96%, which is 1.78 and 6.62% higher than the methods proposed in two references. Because new characteristic parameters

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Table 2 Experimental results of three methods Methods

Recognition accuracy Gesture 1 (%)

Gesture 2 (%)

Gesture 3 (%)

Gesture 4 (%)

Gesture 5 (%)

Average accuracy (%)

Reference [4]

95.7

93.3

96.7

97.7

96.2

96.18

Reference [11]

93.3

96.7

86.7

86.7

93.3

91.34

This paper

96.5

98.5

98.7

99.0

97.9

97.96

are added, the operating time of the system is extended by 1.3 ms, but the realtime performance of the system is not affected. Therefore, through experiments, it can be proved that the static gesture recognition method proposed in this paper can effectively improve the accuracy of gesture recognition.

4 Conclusion In this paper, we introduce a method for edge feature extraction of static gesture image with the idea of combining depth value and neighborhood depth value. Kinect was used to extract gesture images with depth information to solve the influence of complex background, illumination and other factors, and to find the best range of gesture collection. Then we chose Sobel operator to detect the edge of digital image, and proposed the fusion of Hu moment and edge length moment as the classification features of static gestures used to extract new geometric parameters of edge contour. In addition, in the process of static gesture recognition, we optimize and improve the structure of DAG-SVMs to improve the recognition rate of the algorithm. In the case of small samples, the recognition rate of support vector is high, but the real-time performance is relatively poor. Therefore, the following research will improve the real-time performance on the premise of ensuring the accuracy, so as to further study gesture recognition algorithms with higher recognition rate and realtime performance.

References 1. Delamarre, Q, Faugeras, O.: 3D Articulated models and multi-view tracking with silhouettes. In: The Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, pp. 716–721. IEEE (1999) 2. Sharma, R., Zeller, M., Pavlovic, V.I.: Gesture interface to a visual-computing environment. J. IEEE Comput. Graph. Appl. 20(2), 29–37 (2000) 3. Ren, Z., Meng, J., Yuan, J.: Robust hand gesture recognition with Kinect sensor. In: MM’1 l -Proceedings of the 2011 ACM Multimedia Conference and Co-Located Workshops (2011)

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4. Hong, J., et al.: Research on gesture image recognition based on kinect. Microprocessors 3, 47–53 (2018) 5. Yu, J., Zhao, J., Wang, G.: Depth image segmentation using layered graph cuts. J. CEA 50(22), 183–188 (2014) 6. Jiao, S., Li, X., Lu, X.: An improved Ostu method for image segmentation. In: International Conference on Signal Processing (2007) 7. Saha, S., Ghosh, S., Konar, A., et al.: Gesture recognition from indian classical dance using kinect sensor. In: Fifth International Conference on Computational Intelligence, Communication Systems and Networks, pp. 3–8. IEEE (2013) 8. Dong, L.: Static Gesture Recognition and Application Based on Hu Moments with Support Vector Machines. Wuhan: Wuhan Technology University (2012) 9. Molchanov, P., Gupta, S., Kim, K., et al.: Hand gesture recognition with 3D convolutional neural networks. In: Computer Vision and Pattern Recognition Workshops, pp. 1–7. IEEE (2015) 10. Liu, X., et al.: Gesture recognition based on multi-feature and SVM classification. J. Comput. Eng. Des. 38(4), 953–958 (2017) 11. Huang, G., et al.: Character gesture recognition based on improved Hu moments. J. Chifeng Univ. (Nat. Sci. Ed.), 5, 23–24 (2013)

Professor Li Mengxin’s major research direction is Image Processing. Pattern Recognition, Moving Target Inspection and Tracing. She received her B.Sc. (SJZU), M.Sc. (SJZU) degrees in China, and Ph.D. (Bedfordshire University) degree in UK. She has published more than 100 papers in which 30 are SCI or EI-cited and 6 monographs as a chief editor.

Semiconductor Bonding Equipment Grouping Model Based on Processing Task Matching Zhijun Gao, Wen Si, Zhonghua Han, Jiayu Peng and Hongzhi Zheng

Abstract For the problem that the fixed equipment grouping on the semiconductor packaging line cannot achieve the dynamic matching with the processing capacity of the processing task, this paper applies the graph theory method to the equipment grouping, and uses the topological structure of the graph theory to establish the equipment matrix. Also it uses the adjacency matrix to generate the relationship matrix between devices. And the device is grouped with closed position constraints and matching constraints between device types and processing types. A semiconductor bonding device grouping model based on processing task matching is established. The grouping model is simulated under different processing tasks, and it is verified that the equipment grouping model can realize dynamic grouping. Keywords Semiconductor package line · Graph theory · Association matrix · Device grouping

1 Introduction According to the product model and functional requirements, the semiconductor package is a process of processing a wafer which has passed the test to obtain a Z. Gao · W. Si (B) · Z. Han · J. Peng Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, China e-mail: [email protected] Z. Han Department of Digital Factory, Shenyang Institute of Automation, The Chinese Academy of Sciences (CAS), Shenyang 110016, China Key Laboratory of Network Control System, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China H. Zheng School of Mechanical Engineering, Beijing Institute of Technology Beijing, Beijing 100081, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_19

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separate chip [1]. Due to the large number of devices and large difference in capacity between devices, the bonding process in the package test has become the focus of semiconductor package process management which can improve the utilization rate of the bonding process equipment and the working efficiency of the entire semiconductor package line. Currently, the actual semiconductor package on-line bonding equipment adopts a fixed grouping method according to the sub-type of the device. Such a grouping method cannot match the required capacity of the processing LOT and match the processing task dynamically [2]. With the development of the semiconductor industry to a variety of small batch production models, the traditional large-scale fixed group production mode is no longer applicable, so how to achieve flexible grouping has been widely concerned by many researchers at home and abroad. Wan and Yao [3] used the quantum genetic algorithm to achieve the intelligent body grouping. Rong and Zhang [4] used other two-stage algorithms based on Pareto search and information entropy evaluation to realize flexible grouping. Wang and Dong [5] used the linear weighting method to transform the multi-objective group optimization model into a single-objective group optimization model, and solved the grouping results with a controlled random search algorithm. Krajnovic et al. [6] simulated a variety of marshalling forms through the URANS model. Although the above studies have all implemented variable grouping, they are all concentrated in the field of railway transportation. There are few studies on dynamic grouping in the semiconductor field. Therefore, in view of the current problem that the semiconductor package wire bonding equipment group cannot be dynamically matched with the processing task, this paper proposes a semiconductor bonding equipment grouping model based on processing task matching. The association matrix between the device matrix and the device is established by the graph theory method to realize dynamic grouping between devices.

2 Semiconductor Bonding Equipment Grouping Model Based on Processing Task Matching In actual production, semiconductor production equipment is produced according to a fixed grouping method. Dynamic grouping is not performed according to the matching of demand capacity and capacity supply. Once the actual grouping has been determined, the processing capacity of the group is also fixed. Although it is easy to produce and manage, there are also some problems [7], such as the waste of production capacity of some production equipment and capacity redundancy. Due to the indivisible nature of the wafers, when several devices are grouped together to create a single production unit, only one device can be selected for processing wafers in the group. That way wastes the production capacity of the remaining equipment and results in a great waste of resources in the same processing time. If it can be grouped according to the production capacity of the production task, it will increase

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the utilization rate of the production equipment, thereby improving the efficiency of the entire production line. A directed graph is a graph of many nodes and branches used to describe the structure of the system under study. Each node represents each component of the system, and the branch and its direction represent the causal relationship and direction of action between the components. The distribution and connection shape of the processing equipment in the semiconductor bonding process itself constitutes a network diagram, which combines the concept of a directed graph to establish a semiconductor bonding equipment grouping model based on processing task matching. In the graph theory, the adjacency matrix is usually used to represent the directed graph. If there are n nodes in the graph, it is represented by the matrix M of n ∗ n, which is defined as follows:  1, (ther e is a side f r om node i pointing to node j) Mi, j = (1) 0, (N odes i and j have no edge connections)

2.1 Establishing a Device Marshalling Model Process The process of grouping method of semiconductor bonding equipment based on processing task [8] is shown in Fig. 1. Step 1 Minimum punishment sum of equipment grouping and processing tasks matching is the device grouping optimization goal. The punishment sum of equipment grouping and processing tasks. fo =

PN    α p PC p + β p EC P

(2)

p=1

PC p indicates insufficient capacity provided by the processing task W P matching device group. EC P indicates the processing task matching device group provides the difference in capacity redundancy. α p indicates the penalty for the capacity of the processing task p, β p indicates the redundancy penalty for capacity of the processing task p. Step 2 Simplify each device as a point on a two-dimensional plane [9], and abstract all device points of this process into n rows and m columns of device matrices. Mi, j represents row i and column j. Step 3 Form a network structure with devices as nodes by connecting all devices with wires [10]. Use “0” or “1” to indicate the correlation coefficient between the generated devices. “0” means that two devices are not in one group, and “1” means that two devices are in one group.

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Fig. 1 The flow chart of semiconductor bonding device grouping method based on processing task matching

Step 4 According to the relationship between devices, establish a device marshalling line association matrix LR and column association matrix LC. Use LR and LC to establish temporary equipment group G. Line association matrix LR is shown in Formula (3), L ri, j represents the row correlation coefficient between the devices of the i-th row and the (i + 1)-th row of the j-th column. L ri, j ∈ {0, 1}, i ∈ {1, . . . , n − 1}, j ∈ {1, . . . , m}. If L ri, j equals “1”, it means that adjacent row of devices are in one group. Because of the same principle, column association matrix LC is shown in Formula (4) as L i,c j . If L i,c j equals “1”, it means that adjacent column of devices are in one group.

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L r1,1 ⎢ Lr ⎢ L R = ⎢ 2,1 ⎣ M L rn−1,1 ⎡ L c1,1 ⎢ Lc ⎢ LC = ⎢ 2,1 ⎣ M L cn,1

⎤ L L r1,m L L r2,m ⎥ ⎥ ⎥ L ri, j M ⎦ L L rn−1,m ⎤ L c1,2 L L c1,m−1 L c2,2 L L c2,m−1 ⎥ ⎥ ⎥ M L i,c j M ⎦ L cn,2 L L cn,m−1

L r1,2 L r2,2 M L rn−1,2

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(3)

(4)

Step 5 Correct group association: The equipment grouping temporary coding matrix obtained in step 3 conforming to the grouping rules, but it does not meet the actual grouping situation. Therefore, we need to use the temporary group number gt of each group ID in Step 3. to correct the grouping relationship by using line scan detection and column scan detection. Line detection is to check whether the correlation coefficient of each line is correct from the first line to the n-th line. When the device group number gi, j of the i-th row and the j-th column is equal to the device group number gi, j+1 of the i-th row and the j + 1 th column, L i,c j should equal one. If it equals “0”, we need modify it to “1”. Column detection and row detection are similarly modified column associations. Step 6 Device grouping constraint check. This step includes two parts detection of the device group closed position relationship constraint and the device type and the processing type matching. If any one of the constraint detections is not satisfied, the grouping result is invalid and the process should go back to Step 3 and start over. (1) Constraint of closed positional relationship of equipment grouping It is required that the enclosed area formed by the grouping device either contain devices that do not belong to the device group or can it contain another independent device group. If this marshalling situation exists, the overlapping of the jurisdiction of the two equipment marshalling managers will cause confusion in the production management organization. If it is necessary to determine whether the device is in the closed range of the device group, it needs to group the relationship according to the device group matrix G. After the line detection and column detection, if it is detected that the closed area composed of all the devices in a device group contains devices that not belong to this group, it is considered that the device grouping is unreasonable. Assume the variable gz t,i, j . gz t,i, j equals “1” when the grouping information of the group to which the device of the i-th row and the j-th column belongs is the same as the grouping number of t-th group.  gz t,i, j =

1 gi, j = gt 0 gi, j = gt

i ∈ {n1t , . . . , n2t }, i ∈ {m1t , . . . , m2t }

(5)

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If Ft,i equals “1”, it indicates that the i-th row of the t-th device group contains devices that do not belong to the t-th group. Similarly, Ft, j indicates whether the j-th column of the t-th device group contains devices that do not belong to the tth group.

Ft,i =

⎧ m2   t,i ⎪ ⎪ ⎪ gz t,i, j = m2t,i − m1t,i ⎨1 j=m1t,i

m2   t,i ⎪ ⎪ ⎪ gz t,i, j < m2t,i − m1t,i ⎩0

(6)

j=m1t,i

Ft indicates whether the non-grouped device is included in the enclosed area formed by the t-th device group. If it equals “0”, it indicates that the t-th device grouping includes the presence of non-t-group devices. F indicates that the device grouping result satisfies the device location constraint. When all device groups constitute a closed area, the non-grouped devices are not included, that is, the number of groups satisfying the closed constraint is equal to the number of device groupings, indicating that the grouping result is reasonable. If the device group closed position relationship constraint is not met, return to Step 3 to start over. (2) Whether the device type matches the processing type. The product type k x has a total of kn product types, and the device type K N has a total of KN device types. M K li, j,y indicates the device type and device matching relationship. The device and product type matching relationship matrix Mk is obtained by Mk = M K ∗ K k. For the device group gt , the device set contained in the group is represented by Mgt = Mi, j |gi, j = gt . The device grouping matches the device type and the processed product type matching constraint, when there is Mgt ⊆ Mkx , k x ∈ k for any device marshalling gt and product type k x . Step 7 Match the device grouping with the processing task. Gga indicates device grouping based on product type provides capability matrix. gat,kx is the processing capability of equipment group gt to produce k x type products [11]. ⎤ ga1,k1 ga1,k2 L ga1,kkn ⎢ ga2,k ga1,k L ga2,kkn ⎥ 1 2 ⎥ Gga = ⎢ ⎣ M M gat,kX M ⎦ gaGN,k1 gaGN,k2 L gaGN,kkn ⎡

(7)

for the processing task is GW = The set of capacity required  gw p / p ∈ {1, 2, . . . , P N } . Processing task demand matching  equipment group capability  capability and sequence Gamc = gw p , gma p / p ∈ {1, 2, . . . , P N } , where gma P indicates equipment group capability, gw P indicates processing task demand ability.

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Step 8 Device grouping optimization target is the sum of penalty for device grouping and processing tasks f o . After the device grouping being matched with the processing task, we take the minimum penalty value to get the optimal device grouping result. If the optimization range is satisfied, the temporary grouping result is saved. If it is not satisfied that return to Step 3 until reach the maximum number of iterations. The grouping is stopped and the minimum penalty and the corresponding group are taken as the final grouping result.

2.2 Description of Equipment Grouping Method Based on Processing Task Matching (1) The situation of the fixed grouping of the bonding equipment on the semiconductor package line is changed, and the equipment can be grouped according to the release production dynamics, thereby realizing the dynamic matching of the equipment grouping and processing tasks. During the equipment grouping process, the equipment in the group is in a complete unicom area, which is convenient for the management of the production line staff. (2) According to the type of equipment that can be processed by the equipment type, instead of just grouping by equipment type, the equipment grouping can be performed according to the product types included in the processing task, which shows that the equipment grouping structure is driven by the processing task and the flexibility of equipment grouping is increased. (3) Using the concept of directed graphs in graph theory, it is matrixed to establish a device marshalling model. Through the change of adjacency matrix, the relationship between devices is changed to realize the dynamic grouping of devices.

3 Simulation Verification and Result Analysis 3.1 Simulation Experiment Design Related Information The simulation experiment platform uses MATLAB R2016a, and the hardware parameters are CPU R 2.50 dual core and 4G memory. In the simulation experiment, the equipment is divided into three types: A, B and C. The processing task product types are divided into two types: a and b. Among them, type a products can only be processed by type A and type B equipment, and type b products can only be processed by type B and type C equipment.

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3.2 Analysis of Simulation Experiment Results As shown in Fig. 2, the grouping result with the smallest penalty result obtained by grouping 4 * 5 device scale is taken as an example. The first column shown in Fig. 2 is a type A device, the second column to the fourth column are type B devices, and the fifth column is a type C device. The twenty devices are abstracted into twenty nodes to establish a device matrix. The adjacency matrix is used to generate the association relationship between the devices, indicating the row association or column association between the devices, and then grouping the devices directly related or indirectly related to each other. The temporary device grouping result is generated, and then the closed area constraint detection and the matching constraint detection of the device type and the processed product type are performed, and the device grouping result by the constraint detection is matched with the processing task. As shown in Fig. 3, twenty devices are programmed into five production units. The number of equipment groupings is equal to the number of processing tasks, indicating that the grouping deviation is 0, and all equipment is processed and produced. As can be seen from Fig. 3, this grouping result satisfies the closed constraint condition, the equipment production units do not cross each other, and the A and B type equipment are programmed in one production unit to process the a-type product, and the B and C type equipment are combined in one. The production unit processes the b-type product and conforms to the constraint of the matching relationship between the product type and the device type. Fig. 2 Schematic diagram of the relationship between devices

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Fig. 3 Take the grouping result of 4 * 5 device scale as an example

4 Conclusion In this paper, the fixed equipment grouping on the semiconductor packaging line cannot achieve the dynamic matching of the demanding capacity of the processing task. The method of graph theory is applied to the equipment grouping, and the semiconductor bonding equipment grouping model based on the processing task matching is established. Change the marshalling relationship between devices by changing the matrix of associations between devices. The grouping model is simulated under different processing tasks, and it is verified that the equipment grouping model can realize dynamic grouping. In summary, the device grouping method based on processing task matching realizes flexible matching of equipment grouping and processing tasks, and realizes dynamic grouping.

References 1. Jia, P.D., Wu, Q.D., Li, L.: Objective-driven dynamic dispatching rule for semiconductor wafer fabrication facilities. J. Comput. Integr. Manuf. Syst. 20(11), 2808–2813 (2014) 2. Zhang, G.H., Liu, C., Yao, L.L.: A method of bottleneck detection of semiconductor assembly and test production line. J. Chin. J. Electron Dev. 38(1), 44–48 (2015) 3. Wan, L.J., Yao, P.Y.: Cooperative task allocation methods in multiple groups using DLS-QGA. J. Control Decis. 29(9), 156–158 (2014) 4. Rong, Y.P., Zhang, X.C.: Optimization for train plan of urban rail transit based on hybrid train formation. J. Transport. Syst. Eng. Inf. Technol. 16(5), 117–122 (2016) 5. Wang, K.S., Dong, Q.Z.: An analysis on optimizing part and full routes of urban rail transit under different marshalling plans. J. Railw. Transp. Econ. 40(5), 94–99 + 110 (2018) 6. Liu, T.H., Jiang, Z.H., Krajnovic, S.: Differences in aerodynamic effects when trains with different marshalling forms and lengths enter a tunnel. J. Tunnel. Undergr. Space Technol. Incorporating Trenchless Technol. Res. 84, 70–81 (2019) 7. Min, Y., Wu, N.Q.: Review of operations and control of cluster tools in semiconductor wafer fabrication. J. Ind. Eng. J. 15(02), 1–15 (2012)

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8. Xiao, C.J., Chen, H.: Math model and scheduling method for the semiconductor assembling and testing line. J. Trans. Beijing Ins. Technol. 33(11), 1161–1164 + 1170 (2013) 9. Hu, F.N., Sun, S.J.: Fault location of distribution network by applying matrix algorithm based on graph theory. J. Electr. Power 49(3), 94–98 (2016) 10. Fu, S.P., Li, S.B.: Topological transformation and characteristics analysis of vehicle auto transmission based on graph theory. J. Shanghai Jiao Tong Univ. 52(3), 348–355 (2018) 11. Xue, J., Liu, F., Bai, J., Hou, T.: Modelling of gene signal attribute reduction based on neighbourhood granulation and rough approximation. Int. J. Model. Ident. Control, 31(2), 161–168 (2019)

Research on the Improved Dragonfly Algorithm-Based Flexible Flow-Shop Scheduling Zhonghua Han, Jingyuan Zhang, Shuo Lin and Chunguang Liu

Abstract Compared with the classic flexible flow shop, limited buffer flexible flow shop may have a limited buffer production blockage, which will increase the complexity and uncertainty of the scheduling process. In order to solve the limited-buffer flexible flow-shop scheduling problem (LBFFSP), a mathematical programming model of limited buffer flexible flow shop is established and an Improved Dragonfly Algorithm (IDA) is proposed to solves this problem. Based on the standard Dragonfly Algorithm (DA), the idea of Simulated Anneal (SA) is combined to improve the ability of the algorithm to jump out local extremum and the algorithm combines the standard Dragonfly Algorithm (DA) with the Simulated Anneal (SA) idea to improve the ability to jump out local extremum and improve its persistence. Keywords Flexible flow-shop · Limited buffer · Dragonfly algorithm · Simulating anneal

1 Introduction The flexible flow-shop scheduling problem (FFSP) is an extension of the traditional flow shop scheduling problem, which has been proved to be an NP-hard problem Z. Han · J. Zhang (B) · S. Lin Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, Liaoning, China e-mail: [email protected] Z. Han Department of Digital Factory, Shenyang Institute of Automation, The Chinese Academy of Sciences (CAS), Shenyang 110016, China Key Laboratory of Network Control System, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China C. Liu Editorial Department, Journal of Shenyang Jianzhu University, Shenyang, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_20

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[1–4], and LBFFSP has also received more and more attention in recent years. In the traditional FFSP, the buffer between each process is assumed to be infinite. However, in the actual production process, the buffer capacity is limited by the physical storage space, and the intermediate buffer is usually limited. When the upper limit of the buffer capacity is reached, the finished workpiece is blocked at its current station due to the inability to enter the buffer, causing production blockage, which in turn affects the entire production process. If the problem can be solved well, the production efficiency will be improved and the leverage the potential of existing resources [5]. Therefore, the research on the LBFFSP problem has important theoretical and practical significance. DA is an emerging swarm intelligence algorithm inspired by Mirjalili [6] in 2014. For a problem of optimization, DA can effectively improve the initial random population, exhibits excellent optimization performance and better convergence, and thus has received more and more attention and wide application in recent years. Fu et al. [7] applied DA to transformer fault diagnosis. Hamdy et al. [8] applied DA to solve near-zero energy building design problems. Suresh [9], using DA to generate a combined solar thermal system, proposed a method for solving solar static economic dispatch. Li et al. [10] applied DA to the parameter optimization of PID parameter controller. In these applications, DA exhibits better characteristics in terms of global optimization ability and convergence speed, and has a good optimization effect. At present, as a newly proposed swarm intelligence algorithm, DA is still relatively rare in the field of scheduling optimization. Although DA has certain advantages in many optimization problems, like other majority swarm intelligent algorithms, it still has problems such as slow convergence speed and easy to fall into local extremum in the optimization process. Therefore, this paper combines DA and SA to improve its ability to jump out of local extremum, and apply it to solve LBFFSP.

2 Mathematical Programming Model for LBFFSP 2.1 Problem Description The mathematical model of the limited buffer scheduling problem in the flexible flow shop is described as follows: m workpieces are processed in the first process, and at least one of the n processes has more than one parallel station and the workpiece has the same processing time on the parallel station in the same process. There is a buffer with a limited capacity between every two processes. After the workpiece is processed, it enters the buffer and waits for the next process. When the number of workpieces stored in the buffer reaches the upper limit of the buffer capacity, the workpiece in the previous process cannot enter the buffer and is blocked to the current station, thereby blocking the entire production process until the workpiece of the buffer is removed, and the blocking is blocked. This increases the completion time and extends the uncertainty of the scheduling process. After all the workpieces have been

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processed and produced, the production result includes all the determined working positions of the workpieces in each process, and the start-up time and completion time at the work station. Better scheduling results can be obtained by optimizing the online sequence through the global optimization algorithm.

2.2 Model Parameters m n Ji Bu j O Pj Mj Bj W S j,k Bu j,l Ti, j T Si, j T E i, j T L i, j T Bi, j

Total number of workpieces to be processed. Total number of processing operations. The ith workpiece, i ∈ {1, . . . , n}. The buffer of the stage O P j and the buffer volume is infinite, j ∈ {1, . . . , n}. The jth process. The paralleled workstation number of process O P j . The maximum number of stations in the buffer Bu j .  The kth workstation of the process OP j , k ∈ 1,. . . , M j . the lth Station of the buffer Bu j , l ∈ 1, . . . , B j . The standard time of workpiece Ji in the O P j process. The start time of workpiece Ji in the O P j process. The completion time of workpiece Ji in the O P j process. The time when workpiece Ji leaves the O P j process. The time when workpiece Ji enter the Bu j buffer.

2.3 Limitation Conditions

Assumed Variable ⎧ ⎪ ⎪ ⎨ 1,

the job Ji is distributed to W S j,k wor kstation in O P j stage to be pr ocessed Ai, j,t (t) = ⎪ the job Ji is distributed to W S j,k ⎪ ⎩ 0, wor kstation in O P j stage to be pr ocessed

(1)

Constraint Conditions of LBFFSP Mj  k=1

Ai, j,t (t) = 1

(2)

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T E i, j = T Si, j + Ti, j

(3)

T E i, j−1 ≤ T Si, j

(4)

T E i, j−1 ≤ T Bi, j

(5)

Equation (2) indicates a limitation of the workpiece Ji can be processed in one workstation. Equation (3) indicates the constraint relationship between the start time and the completion time of the workpiece Ji in the O P j process. Equation (4) indicates the former process of the workpiece Ji must be done before the latter one. Equation (5) indicates that due to the possible production blockage of the limited buffer, the time that the workpiece enters the buffer is greater than or equal to the time during which the workpiece was processed in the previous process.

3 Improved Dragonfly Algorithm 3.1 Dragonfly Algorithm The static and dynamic clustering behavior of the dragonflies population is very similar to the two main phases of meta-heuristic optimization: exploration and development. The positional movement of the dragonflies group is determined by the separation, alignment, cohesion, foraging and evading the natural enemies which mathematical models are as follows: Calculated separation Si = −

N 

X − Xj

(6)

j=1

In the Eq. (6), X is the position of the current individual, X j represents the position jth neighboring individual, and N is the number of neighboring individuals. Calculated alignment N Ai =

j=1

Vj

N

In the Eq. (7), V j represents the velocity of jth neighboring individual. Calculated cohesion N j=1 X j Ci = N

(7)

(8)

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In the Eq. (8), X is the position of the current individual, N is the number of neighborhoods, and X i represents the position jth neighboring individual. Calculated the dragonfly individual’s attraction to food sources Fi = X + − X

(9)

In the Eq. (9), X is the position of the current individual, and X + is the position of the food source. Calculate the dragonfly individual’s distraction outwards the enemy Ei = X − − X

(10)

In the Eq. (10), X represents the position of the current individual, and X − represents the position of the enemy. The step vector calculation equation is as follows: X t+1 = (s Si + a Ai + cCi + f Fi + eE i ) + wX i

(11)

In the Eq. (11), s shows the separation weight, a is the alignment weight, c indicates the cohesion weight, f is the food factor, e is the enemy factor, Si is the separation of the ith individual, Ai indicates the alignment of ith individual, Ci is the cohesion of the ith individual, Fi is the food source of the ith individual, E i is the position of enemy of the ith individual, w is the inertia weight, and t is the iteration counter. After calculating the step vector, the position vectors are calculated as follows: X t+1 = X t + X t+1

(12)

X t+1 = X t + Levy(d) ∗ X t

(13)

In the Eqs. (12) and (13), t is the current iteration. When there are other individuals in the vicinity of the current individual, the position is updated according to the Eq. (12); otherwise, according to the Eq. (13), the Lévy flight is performed to perform the position update. The Lévy flight is calculated as follows: Levy(x) = 0.01 ×

r1 × σ 1

|r2 | β

(14)

In the Eq. (14), r1 , r2 are two random numbers which value between 0 and 1, β is a constant which equal to 1.5 in this paper, and the calculation of σ is shown as in Eq. (15).

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⎞ (1 + β) × sin πβ 2 ⎟ ⎜

⎠ σ=⎝  β−1 ×β ×2 2  1+β 2 ⎛

(15)

where (x) = (x − 1)!

3.2 Improved Dragonfly Algorithm Simulating Anneal DA as a global optimization algorithm in the process of updating, the valuable evolutionary information contained in the old individuals is not preserved, which is not conducive to maintaining population diversity. Therefore, in combination with the idea of SA, a selection probability P is calculated according to Eq. (16), and this poor new individual is accepted with probability P. In the equation, Ti expresses the fitness of the current individual.  P=

1,  Ti > Ti+1 Ti −Ti+1 , Ti ≤ Ti+1 exp Ti

(16)

Improved Dragonfly Algorithm Process Introduction Step 1 Initialize the algorithm program, set the population size to N pop , the spatial dimension dim, and the maximum evolution algebra to itermax . Step 2 Randomly initialize the position X of the population and the step vector X . Step 3 Calculate the fitness values of all individuals in the dragonfly population, find the best individuals and the worst individuals, and treat the best individuals as food and the worst individuals as foreign enemies. Step 4 The values of weights w, s, a, c, f, e is updated and calculate the values of S, A, C, F, E by using Eqs. (6)–(10). Step 5 The neighborhood radius and the position of each individual is updated. If there are neighboring individuals around the individual, use the Eqs. (11) and (12) to update the individual’s step size and position; if there is no individual in current individual field, the current individual position is updated using Eq. (13). Step 6 According to the idea of SA, the retention probability is calculated by Eq. (15). The new individual will be retained directly if the fitness value is better than the original individual. Otherwise, the new individual will be retained with a certain probability. Step 7 Determine whether the termination condition is met (reach the maximum number of iterations itermax ). If it is satisfied, go to Step 7. Otherwise, return to Step 3 to continue the iteration. Step 8 Output the optimal dragonfly individual and obtain the global optimal solution.

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4 Simulated Experiments The maximum completion time is taken as the optimization goal to verify the impact of the introduction of SA on the performance optimization of standard DA, and the IDA, DA and Particle Swarm Optimization (PSO) are tested and analyzed. PSO was proposed in 1995 by Kennedy and Eberhart et al. [11, 12]. The algorithm simulation program is written in Python language.

4.1 Algorithm Parameter Setting In order to verify the superiority of IDA algorithm optimization ability, this paper uses DA and PSO for comparison. The maximum evolution algebra is set to 500 generations, and the individual populations is set to 30. The inertia weight w in PSO is 1.2, and the acceleration constants c1 and c2 is 2. Inertia weight w in IDA and DA is 0.7, separation weight s is 0.1, alignment weight is a 0.1, cohesion weight is c 0.7, food impact factor is f 1 and natural enemy impact factor e is 1.

4.2 Optimization Simulation Results and Analysis The DA, PSO and IDA are tested and analyzed by 4 sets of small scale and 4 sets of large-scale FFSP standard examples. The study set is divided into five types, proposed by Carlier and Neron [13]. The average maximum completion time T E max and the average relative error (ARE) of 30 runs are selected as the main evaluation indicators of the small-scale test data and the results are recorded in Table 1, Where LB is the lower limit of the maximum completion time (Lower Bound) which given by Santos D L and Nerson E. The ARE calculation, as shown in Eq. (17), represents the relative deviation of the average maximum completion time from the operation of each algorithm and the theoretical lower limit of the standard example. The results of the large-scale data of the average maximum completion time T E max as the main evaluation index are recorded in Table 2. Table 1 Small-scale data test results Example

LB

PSO

DA

T E max

ARE (%)

T E max

IDA ARE (%)

T E max

ARE (%)

J10c10c3

98

117.33

19.72

117.17

19.56

116.83

19.21

J10c10c4

103

120.17

16.67

119.33

15.85

118.67

15.21

J15c5d3

77

88.17

14.51

87.67

13.86

86.33

12.12

J15c5d4

61

88.83

45.62

88.67

45.36

87.83

43.98

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Table 2 Large-scale data test results

Example

PSO

DA

IDA

J80c8d1

1878.67

1861.33

1847.83

J80c8d2

1876.83

1857.67

1844.67

J120c4d1

2171.67

2163.67

2154.83

J120c4d2

2275.33

2267.33

2259.67

 T E max − L B × 100% ARE = LB 

(17)

According to the table, under the small-scale data test, the results obtained by IDA are better than the other two algorithms. Taking the example J15c15d3 as an example, IDA obtains the solution 86.33, and its ARE value is 12.12%, and its value is significantly smaller than 13.86% obtained by DA and 14.51% obtained by PSO. In the example J15c15d4, the ID value obtained by IDA is 43.98%, which is lower than the 45.36% obtained by DA and 45.62% obtained by PSO. In the large-scale data test, taking the j80c8d class as an example, the average value of IDA optimization results is 1846.25, DA is 1859.50, and PSO is 1877.75. The average value of IDA optimization results for the j120c4d problem is 2207.25, the DA is 2215.50, and the PSO is 2223.50. The J120c4d1 standard example using four processes of 120 workpieces is used as test data. The DA algorithm and the PSO algorithm are selected as comparison objects and compared with the IDA algorithm. The relationship between the maximum completion time T E max value and the number of iterations obtained by optimization is shown in Fig. 1. As can be seen from the figure, although PSO and DA evolve faster than IDA, they are easy to fall into local extremum and stop evolution in the 38th and 18th generations respectively. While IDA evolved stagnation in the

Fig. 1 3 algorithms evolution curve

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Fig. 2 Gantt chart of IDA scheduling results

28th generation, it began the evolution process in the 308th generation, indicating that the algorithm jumped out of the local extremum. Figure 2 is a Gantt chart of the limited buffer flexible flow shop scheduling result optimized by IDA using j15c5d3 as an example. The abscissa is the time axis, and the ordinate indicates the station and buffer station for each process [14]. Three parallel stations are set for each process, and the limited buffer station is set to two. Optimized by DA, PSO and IDA respectively, the maximum and minimum completion times are 90, 93 and 88 respectively. Among them, the DA and PSO optimized production results showed blocking of 1 and 3 respectively, while the IDA optimized production results showed no production blockage, and the overall completion time was reduced. It can be proved that IDA has a good effect on solving LBFFSP. According to the above analysis, IDA has better optimization effect than DA and PSO for solving the optimization problem of different data scales which shows that it overcomes the problem that DA premature convergence has fallen into local extremum to some extent. Compared with DA and PSO, the minimum and maximum completion time obtained by IDA for scheduling optimization is smaller, and there is no production blockage in the production process, indicating that IDA can better solve LBFFSP.

5 Conclusion This paper studies LBFFSP and uses IDA as the global optimization algorithm. In view of the shortcomings of DA easily falling into local extremum, this paper improves it with SA, retains valuable information in the evolution process, and

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enhances the optimization performance of the algorithm. The simulation results show that the idea of adding SA can effectively improve the accuracy of DA search and obtain a better optimization solution for LBFFSP. Acknowledgements This work was supported by Liaoning Provincial Science Foundation (No. 2018106008), Project of Liaoning Province Education Department (LJZ2017015).

References 1. Khamseh, A., Jolai, F., Babaei, M.: Integrating sequence-dependent group scheduling problem and preventive maintenance in flexible flow shops. Int. J. Adv. Manuf. Technol. 77(1–4), 173–185 (2015) 2. Gerstl, E., Mosheiov, G., Sarig, A.: Batch scheduling in a two-stage flexible flow shop problem. J. Found. Comput. Decis. Sci. 39(1), 3–16 (2014) 3. Gupta, J.N.D.: Two-stage, hybrid flow shop scheduling problem. J. Oper. Res. 39(4), 359–364 (1988) 4. Rock, H.: The three-machine no-wait flow-shop problem is NP-complete. J. Assoc. Comput. Mach. 31(2), 336–345 (1984) 5. JIANG, et al.: Improved heuristic algorithm for modern industrial production scheduling. Int. J. Model. Ident. Control (IJMIC), 30(4), 284–292 (2018) 6. Mirjalili, S.: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27(4), 1053–1073 (2016) 7. Fu, et al.: Transformer fault diagnosis based on dragonfly optimization algorithm and support vector machine J. East China Jiaotong Univ. 33(04), 103–112 (2016) 8. Hamdy, M., Nguyen, A.T., Jan, L.M., Hensen, H.: A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems. J. Build. Energy Effi. 44(06), 4 (2016) 9. Suresh, V., Sreejith, S.: Generation dispatch of combined solar thermal systems using dragonfly algorithm. Comput. 99(1), 59–80 (2017) 10. Li, et al.: Parameter optimization of PID controller based on dragonfly algorithm. Mod. Electr. Tech. 41(12), 102–107 (2018) 11. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International, Conference on Neural Networks, Proceedings (1995) 12. Li, et al.: Parameter identification and optimisation for a class of fractional-order chaotic system with time delay. Int. J. Model. Ident. Control. 29(2), 153–162 (2018) 13. Alaykyran, K., Engin, O., Doyen, A.: Using ant colony optimization to solve hybrid flow shop scheduling problems. J. Int. J. Adv. Manuf. Technol. 35(5–6), 541–550 (2007) 14. Zhang, et al.: Job-shop schedule modelling and parents-crossover evolutionary optimisation for integrated production schedules. Int. J. Comput. Appl. Technol. (IJCAT) 58(4), 288–295 (2018)

Modeling and Adaptive Control for Tower Crane Systems with Varying Cable Lengths Menghua Zhang, Yongfeng Zhang, Huimin Ouyang, Changhui Ma and Xingong Cheng

Abstract Tower cranes are highly underactuated nonlinear systems with five degrees-of-freedom (trolley displacement, jib angle, cable length, payload swing angles), and only three control inputs (one for the trolley driving, another for the jib driving, and another for the cable length varying). The three main control objectives of tower crane systems are driving the trolley and the jib to the desired position and desired angle, respectively, hoisting the cable length to the desired length while suppressing and eliminating the payload swing angles. Therefore, the model of tower crane systems with varying cable lengths is established, and on this basis, an adaptive control with payload swing suppression is proposed in this paper. Lyapunov method and LaSalle’s invariance theorem are illustrated to prove the stability of the closed system and the convergence of the system states. Simulation results are provided to validate the superior performance of the proposed control method. Keywords Underactuated system · Tower crane · Modeling · Adaptive control

1 Introduction As powerful transportation tools, tower cranes have been widely used in construction sites. Like other cranes, tower cranes have less control inputs than the degreesof-freedom to be controlled [1, 2]. In other words, they are typical underactuated nonlinear systems whose control problems are challenging and still open. Till now, almost all tower cranes are operated by manual, which has the shortcomings of low working efficiency, poor anti-swing ability, high risk of human injury accidents, long time to train a skilled operation, and so on [3]. Therefore, it is urgent to design automatic control methods for tower crane systems. M. Zhang (B) · Y. Zhang · C. Ma · X. Cheng School of Electrical Engineering, University of Jinan, Jinan 250022, China e-mail: [email protected] H. Ouyang School of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing 211816, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_21

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In recent decades, control problems for tower crane systems have gained wide attention and many effective control methods have been designed. The existing controllers are roughly divided into two categories based on whether they require realtime state feedback or not: open-loop control methods and closed-loop control methods. Two common open-loop controllers are input shaping [4, 5] and optimal velocity control [6], which are simple and hence easy to be implemented in practical applications. However, they are sensitive to external disturbances and parametric uncertainties [7]. Therefore, when disturbances present, the overall control performance of open-loop control methods will be badly attenuated and even lead to instability. In this case, closed-loop control methods including gain scheduling feedback control [8], laser-based path tracking control [9], model predictive control [10], recurrent neural network-based control [11], and energy-based control [12], adaptive SMC method [13], might provide better results. The above mentioned control methods are designed for tower cranes with constant cable length. In many cases, to improve working efficiency, tower cranes lift/lower the payload while the trolley and the jib travel with the cable-suspended payload. Therefore, the dynamic model of the tower crane systems is firstly established by using Lagrangian method. And on this basis, an adaptive control method is proposed for the crane system, which is used to provide adaptive control performance with respect to uncertain/unknown friction-related parameters and parametric uncertainties. Lyapunov method and LaSalle’s invariance theorem are used to prove the stability and convergence. Simulation results show the proposed method achieves superior control performance. The rest of this paper is organized as follows. In Sect. 2, the dynamical equations of tower crane systems with varying cable lengths are derived. The main results including the adaptive control with payload swing suppression design and stability analysis are discussed in Sect. 3. In Sect. 4, simulation results are given to verify the control performance of the designed controller. Section 5 concludes the whole paper.

2 Modeling for Tower Crane Systems with Varying Cable Lengths In this section, the dynamic model of tower crane systems with varying cable lengths is established. Figure 1 shows the schematic diagram of the tower crane systems. In Fig. 1, M t and m stand for the trolley mass and the payload mass, respectively, l denotes the cable length, x and φ represent the trolley translation displacement and the jib slew angle, respectively, θ 1 and θ 2 denotes the payload swing angles. The Lagrange approach [14] is utilized to derive the dynamic equations of tower crane systems with varying cable lengths. As can be seen from Fig. 1, the position vectors of the trolley and the payload are given as follows:

Modeling and Adaptive Control for Tower Crane Systems … Mt

217 Trolley Jib

x(t)

φ(t)

θ2(t) θ1(t)

Z

l

Mast Payload Base

mpg

Fig. 1 Schematic diagram of tower crane systems

 T pM = x 0 0 ,

(1)

pm = [x + l S1 C2 l S2 lC1 C2 ]T ,

(2)

where S 1 , S 2 , C 1 , and C 2 stand for the abbreviations of sin θ 1 , sin θ 2 , cos θ 1 , and cos θ 2 , respectively. The angular velocity vector of the tower crane systems is  T ω = 0 0 φ˙ ,

(3)

The velocity vectors of the trolley and the payload are given by d pM + ω × pM dt  T  T  T = x˙ 0 0 + 0 0 φ˙ × x 0 0  T = x˙ x φ˙ 0 ,

vM =

d pm + ω × pm dt ⎡ ⎤ x˙ + l θ˙1 C1 C2 − l θ˙2 S1 S2 + l˙S1 C2 ⎦ =⎣ l θ˙2 C2 + l˙S2 ˙ 1 C2 −l θ˙1 S1 C2 − l θ˙2 C1 S2 + lC  T + 0 0 φ˙ × [x + l S1 C2 l S2 lC1 C2 ]T

vm =

(4)

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⎡

⎤ ˙ 2 + l˙S1 C2 x˙ + l θ˙1 C1 C2 − l θ˙2 S1 S2 − l φS ⎦. ˙ + l S1 C2 ) + l˙S2 =⎣ l θ˙2 C2 + φ(x ˙ ˙ ˙ −l θ1 S1 C2 − l θ2 C1 S2 + lC1 C2

(5)

The kinematic energy of the tower crane systems is obtained as follows: 1 1 1 Mt vTM v M + mvmT vm + J φ˙ 2 2 2 2 1 1 = (Mt + m)x˙ 2 + (Mt + m)x 2 φ˙ 2 2 2 ⎫ ⎧ ⎪ l 2 θ˙12 C22 + l 2 θ˙22 + l 2 φ˙ 2 S22 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2 ˙2 2 2 2 ˙ ˙ ⎪ ⎪ +l S C + l + 2l x ˙ θ C C φ 1 1 2 ⎪ ⎪ 1 2 ⎪ ⎪ ⎬ 1 ⎨ 1 −2l x˙ θ˙2 S1 S2 − 2l x˙ φ˙ S2 + m + J φ˙ 2 , −2l 2 φ˙ θ˙1 C1 S2 C2 + 2l 2 φ˙ θ˙2 S1 ⎪ 2 ⎪ 2 ⎪ ⎪ ⎪ ⎪ ⎪ ˙ θ˙2 C2 + 2lx φ˙ 2 S1 C2 ⎪ ⎪ ⎪ +2lx φ ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ ˙ S2 +2 x˙ l˙S1 C2 + 2l˙φx

T =

(6)

with J being the moment of inertia of the jib. The potential energy is P = mgl(1 − C1 C2 ),

(7)

with g representing the gravitational acceleration. Define the Lagrangian V as V = T − P.

(8)

From (6)–(8), it can be obtained that ∂V = 0, ∂φ

d dt



∂V ∂ φ˙



∂V = (Mt + m)x 2 φ˙ + J φ˙ ∂ φ˙  2 2  ˙ 12 C22 − l x˙ S2 − l 2 θ˙1 C1 S2 C2 l φ˙ S2 + l 2 φS +m , ˙ S2 +l 2 θ˙2 S1 + lx θ˙2 C2 + 2lx φ˙ S1 C2 + lx

(9)

(10)

    = (Mt + m)x 2 + ml 2 S22 + S12 C22 + 2mlx S1 C2 + J φ¨

− ml x¨ S2 + mx l¨S2 − ml 2 θ¨1 C1 S2 C2 + ml θ¨2 (xC2 + l S1 ) + 2(Mt + m)x x˙ φ˙ + 2mlx φ˙ θ˙1 C1 C2 + 2ml x˙ φ˙ S1 C2 + ml 2 θ˙12 S1 S2 C2 + 2ml 2 θ˙1 θ˙2 C1 S22   − mlx θ˙2 θ˙2 + 2φ˙ S1 S2 + ml 2 φ˙ θ˙1 sin(2θ1 )C22 − ml 2 φ˙ θ˙2 S12 sin(2θ2 ) + m x˙ l˙S2 + mx l˙θ˙2 C2 .

(11)

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By using the Lagrange equations, d dt



∂V ∂ φ˙

 −

∂V = Fφ − F f φ , ∂φ

(12)

where F x is the slew control torque, F fx denotes the friction torque. It can be obtained from (9) to (12) that 

   (Mt + m)x 2 + ml 2 S22 + S12 C22 + 2mlx S1 C2 + J φ¨ − ml x¨ S2 + mx l¨S2 − ml 2 θ¨1 C1 S2 C2 + ml θ¨2 (xC2 + l S1 ) + 2(Mt + m)x x˙ φ˙ + 2mlx φ˙ θ˙1 C1 C2   ˙ 1 S2 + 2ml x˙ φ˙ S1 C2 + ml 2 θ˙12 S1 S2 C2 + 2ml 2 θ˙1 θ˙2 C1 S22 − mlx θ˙2 θ˙2 + 2φS + ml 2 φ˙ θ˙1 sin(2θ1 )S22 − ml 2 φ˙ θ˙2 S12 sin(2θ2 ) + m x˙ l˙S2 + mx l˙θ˙2 C2 = Fφ − F f φ . (13) In a similar way, the following results are obtained as follows: ¨ 2 + (Mt + m)x¨ + m l¨S1 C2 + ml θ¨1 C1 C2 − ml θ¨2 S1 S2 − (Mt + m)x φ˙ 2 − ml φS     − 2ml θ˙1 θ˙2 C1 S2 − mlC2 S1 θ˙12 + θ˙22 + φ˙ 2 + 2φ˙ θ˙2   ˙ 2 − θ˙1 C1 C2 + θ˙2 S1 S2 = Fx − F f x , (14) − m l˙ φS   ¨ S2 + m x¨ S1 C2 − ml θ˙12 C22 − ml θ˙22 − m φ˙ 2 l S22 + l S12 C22 − x S1 C2 m l¨ + m φx   ˙ + 2m φ˙ x˙ S2 + 2ml φ˙ θ˙1 C1 S2 C2 − θ˙2 S1 − mgC1 C2 = Fl − dl l, (15) ˙ 1 C2 ¨ 1 S2 C2 + ml xC ¨ 1 C2 + ml 2 θ¨1 C22 − ml(l S1 C2 + x)φ˙ 2 C1 C2 − m x˙ lC −ml 2 φC   2 ˙ 1 C2 θ˙2 + mgl S1 C2 = 0, −2ml C2 θ˙1 S2 + φC (16)   ˙ 2 + ml S2 x S1 − mlC12 C2 φ˙ 2 ml(l S1 + xC2 )φ¨ − ml x¨ S1 S2 + ml 2 θ¨2 + 2ml x˙ φC   ˙ 2 + mglC1 S2 = 0, (17) + 2ml 2 φ˙ θ˙1 C1 C22 + ml 2 θ˙12 S2 C2 + m l˙ x˙ S1 S2 − φxC

where F x and F l stand for the control forces in directions x and l, respectively, F fx and dl l˙ represent the friction forces in direction in directions x and l. The friction torque F fx and the friction force F fx have the following forms [15]:  F f φ = F f 0φ tanh  F f x = F f 0x tanh

φ˙ εφ x˙ εx



  ˙ + k f φ φ˙ φ,

(18)

+ k f φ |x| ˙ x. ˙

(19)



Without loss of generality, the following assumption is reasonable.

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Assumption 1 For cranes working in practice, the payload is always beneath the trolley and the jib, therefore, the payload swing angles always satisfy [16]: −

π π π π ≤ θ1 ≤ , − ≤ θ2 ≤ . 2 2 2 2

(20)

3 Main Results In this section, an adaptive controller with payload swing reduction is designed for 5 DOF tower crane systems, which achieves simultaneous accurate positioning performance and effective payload swing suppression and elimination.

3.1 Adaptive Controller Development The control objective is to drive the trolley and the jib to desired position pdx and desired angle pdx while changing the cable length from the initial value to the target value pdl . At the same time, the payload swing should be suppressed and eliminated during the transportation, in the sense that lim x(t) = pd x , lim φ(t) = pdφ , lim l(t) = pdl , lim θ1 (t) = 0, lim θ2 (t) = 0.

t→∞

t→∞

t→∞

t→∞

t→∞

(21) The tower crane system energy including the kinematic energy and the potential energy is denoted by VE (t) =

1 T q˙ M(q)q˙ + mgl(1 − C1 C2 ), 2

(22)

where M(q) and q˙ represent the inertia matrix, and the state vector. Detail expressions of the matrix and the vector are given as follows: ⎡

m 11 ⎢ −ml S ⎢ 2 ⎢ M(q) = ⎢ mx S2 ⎢ ⎣ m 13 m 14

−ml S2 Mt + m m S1 C2 mlC1 C2 −ml S1 S2

mx S2 m S1 C2 m 0 0

m 13 mlC1 C2 0 ml 2 C22 0

⎤ m 14 −ml S1 S2 ⎥ ⎥ ⎥ 0 ⎥, q = [φ x l θ1 θ2 ]T , ⎥ ⎦ 0 ml 2

with   m 11  (Mt + m)x 2 + ml 2 S22 + S12 C22 + 2mlx S1 C2 + J,

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m 13  −ml 2 C1 S2 C2 , m 14  ml(xC2 + l S1 ). Taking the time derivative of (22), it can be obtained that 1 T ˙ ˙ − C1 C2 ) − mgl θ˙1 S1 C2 − mgl θ˙2 C1 S2 ¨ q˙ M(q)q˙ + mgl(1 V˙ E (t) = q˙ T M(q) q+ 2       ˙ = Fφ − F f φ φ˙ + Fx − F f x x˙ + Fl − dl l˙ − mg l, (23) ˙ x, ˙ and indicating that the tower crane system with Fφ , Fx , and Fl as the inputs, φ, ˙l as the outputs, is passive. It is shown that the system energy VE (t) can merely be ˙ ˙ x, damped out by the actuated motion φ, ˙ and l. In consideration of (18), (19), (23) can be rewritten as:       ˙ V˙ E (t) = Fφ − ηφT ωφ φ˙ + Fx − η Tx ω x x˙ + Fl − ηlT ωl l,

(24)

where the vectors are defined of the following forms: 



    T  T φ˙   ˙ ˙ ηφ  tanh φ φ , ωφ  F f 0φ (t) k f φ , εφ    T T  x˙ |x| η x  tanh ˙ x˙ , ω x  F f 0x k f x , εx ˙ ω x  dl . ηl  l,

(25) (26) (27)

To facilitate the following analysis and controller development, define the following error signals: eφ = φ − pdφ , ex = x − pd x , el = l − pdl .

(28)

In view of the structure of (24), the adaptive controller is defined as follows: Fφ = −k pφ eφ − kdφ φ˙ + ηφT ωˆ φ ,

(29)

Fx = −k px ex − kd x x˙ + η Tx ωˆ x ,

(30)

Fl = −k pl el − kdl l˙ + mg + ηlT ωˆ l ,

(31)

with k pφ , kdφ , k px , kd x , k pl , and kdl representing the control gains, ωˆ φ , ωˆ x , and ωˆ l being the estimation of ωφ , ω x , and ωl , respectively. The update law for ωˆ φ , ωˆ x , and ωˆ l are defined as ˙ ˙ ω˙ˆ x = −x η Tx x, ˙ ω˙ˆ l = −l ηlT l, ω˙ˆ φ = −φ ηφT φ,

(32)

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where φ ∈ R2×2 , x ∈ R2×2 , l ∈ R2×2 denote positive definite diagonal matrixes. As can be seen from (29) to (31), the payload swing-related information is not included in the control force. To solve this problem, the final controller is proposed as   ˙ Fφ = −k pφ eφ − kdφ φ˙ + ηφT ωˆ φ − kφ θ˙12 + θ˙22 φ,

(33)

  Fx = −k px ex − kd x x˙ + η Tx ωˆ x − k x θ˙12 + θ˙22 x, ˙

(34)

  ˙ Fl = −k pl el − kdl l˙ + mg + ηlT ωˆ l − kl θ˙12 + θ˙22 l.

(35)

3.2 Stability Analysis The proposed adaptive controller (33)–(35), along with the update law (32), can guarantee the trolley and the jib reach their desired position and desired angle, and damp out the payload swing simultaneously, in the sense that  T  T lim φ x θ1 θ2 φ˙ x˙ θ˙1 θ˙2 = pdφ pd x 0 0 0 0 0 0 .

t→∞

(36)

Proof The detailed proof of state convergence is omitted which is also available upon request.

4 Simulation Results In this section, simulation results are provided to verify the effectiveness and correctness of the proposed controller. The tower crane system parameters are set as Mt = 3.5 kg, m p = 1 kg, g = 9.8 m/s2 , F f 0φ = 4.4, k f φ = −0.5, F f 0x = 6.8, k f x = −1.2, respectively. The initial jib slew angle, trolley position, and cable length are φ(0) = 0◦ , x(0) = 0 m, and l(0) = 1.5 m, respectively. The desired jib slew angle, trolley position, and cable length are taken as pdφ = 45◦ , pd x = 1 m, and pdl = 0.5 m, respectively. To verify the superior control performance of the proposed control law, we compare the designed controller with PD controller. The PD controller is of the following form: ˙ Fφ = −k pφ eφ − kdφ φ,

(41)

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Table 1 Control gains Controllers

Control gains

Proposed controller

k pφ = 20, kdφ = 25, k px = 7.7, kd x = 13.2, k pl = 20, kdl = 5, φ = diag(2, 2), x = diag(2, 2), l = 2, kφ = 200, k x = 200, kl = 200

PD controller

k pφ = 15, kdφ = 20, k px = 8, kd x = 10, k pl = 20, kdl = 5

Fx = −k px ex − kd x x, ˙

(42)

Fl = −k pl el − kdl l˙ + m p g.

(43)

where k pφ , kdφ , k px , kd x , k pl , and kdl stand for positive the control gains. After careful tuning, the control gains of the proposed controller and the PD controller are provided in Table 1. The following performance indices are introduced to better exhibit the simulation results. (1) Maximum payload swing amplitudes: θ1max and θ2max , which are defined as θ1max  maxt {|θ1 (t)|}, and θ2max  maxt {|θ2 (t)|}, respectively. (2) Residual payload swing angles: θ1res and θ2res , which are defined as the maximum payload swing amplitudes after the jib, the trolley, and the cable stop, respectively. (3) Maximum control force/torque amplitudes: F φ max , Fx max , and Fl max , which   are defined as the Fφ max  maxt Fφ (t) , Fx max  maxt {|Fx (t)|}, and Fl max  maxt {|Fl (t)|}, respectively. The simulation results are shown in Fig. 2. It is noted that the designed controller shows better payload swing suppression effects and less maximum control force/torque amplitudes compared with the PD controller. More precisely, the payload swing angles are suppressed and eliminated within a smaller range by the proposed adaptive control scheme with payload swing suppression (θ1max : 4.1°, θ2max : 1.9°, θ1res : 0.5°, θ2res : 0.1°) than by the PD controller (θ1max : 10.0°, θ2max : 5.9°, θ1res : 4.5°, θ2res : 5.5°). θ1max and θ2max of the designed controller account for only 41 and 32.2% of those corresponding to the PD controller. In addition to this, the payload keeps swing back and forth after the jib, the trolley, and the cable stop for the PD controller, while the payload is much more steady for the designed controller. Moreover, the maximum control force/torque amplitudes of the proposed control scheme (Fφ max : 11.8 N, Fx max : 13.6 N, Fl max : 19.5 N) are less than those of the PD controller (Fφ max : 15.5 N, Fx max : 14.5 N, Fl max : 19.6 N). These results have evidently proven that the designed controller shows superior control performance.

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x[m]

Φ[deg]

(a) 45 0

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5 Conclusion We establish the dynamic model of tower crane systems, and on this basis propose an adaptive control with payload swing suppression for them. The proposed method needs neither approximations no linearizations to the original tower crane systems. The designed law is composed of three parts: PD part is used to stabilize the controlled system; the adaptive part is utilized to provide adaptive control performance; and the swing-eliminating part is used to suppress and eliminate the payload swing angles. Rigorous mathematical analysis is provided to prove the effectiveness of the proposed control scheme. In our future work, we intend to extend this method by introducing appropriate SMC mechanisms so as to further improve its robustness with respect to unmodeled uncertainties. Acknowledgement This work is supported by the National Key R&D Program of China under Grant No. 2018YFB1305400, the Key Research and Development (Special Public-Funded Projects) of Shandong Province under Grant No. 2019GGX104058, the National Natural Science Foundation for Young Scientists of China under Grant No. 61903155, and the Natural Science Foundation of Shandong Province under Grant No. ZR2019QEE019.

References 1. Zhang, M., Zhang, Y., Cheng, X.: An enhanced coupling PD with sliding mode control method for underactuated double-pendulum overhead crane systems. Int. J. Control Autom. Syst. 17(6), 1579–1588 (2019) 2. Zhang, M.: Finite-time model-free trajectory tracking control for overhead cranes subject to model uncertainties, parameter variations and external disturbances. Trans. Ins. Meas. Control. 41(12), 3516–3525 (2019) 3. Sun, N., Yang, T., Fang, Y., Wu, Y., Chen, H.: Transportation control of double-pendulum cranes with a nonlinear quasi-PID scheme: design and experiments. IEEE Trans. Syst. Man Cyber. Syst. 49(7), 1408–1418 (2019) 4. Vaughan, J., Kim, D., Singhose, W.: Control of tower cranes with double-pendulum payload dynamics. IEEE Trans. Control Syst. Technol. 18(6), 1345–1358 (2010) 5. Vaughan, J., Kim, D., Singhose, W.: Comparison of robust input shapers. J. Sound Vib. 315(4/5), 797–815 (2008) 6. Devesse, W., Ramteen, M., Feng, L., Wikander, J.: A real-time optimal control method for swing-free tower crane motions. In: IEEE International Conference on Automation Science and Engineering, Madison, WI, USA, pp. 336–341 (2013) 7. Ouyang, H., Hu, J., Zhang, G., Mei, L., Deng, X.: Decoupled linear model and s-shaped curve motion trajectory for load sway suppression control in overhead cranes with double-pendulum effect. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. (in press) https://doi.org/10.1177/ 0954406218819029 8. Omar, H.M., Nayfeh, A.H.: Gain scheduling feedback control of tower cranes with friction compensation. J. Vib. Control 10(2), 269–289 (2004) 9. Lee, G., Kim, H.H., Lee, C.J., Ham, S.I., Yun, S.H., Cho, H., Kim, B.K., Kim, G.T., Kim, K.: A laser-technology-based lifting-path tracking system for a robotic tower crane. Autom. Constr. 8(7), 865–874 (2009) 10. Böck, M., Kugi, A.: Real-time nonlinear model predictive path following control of a laboratory tower crane. IEEE Trans. Control Syst. Technol. 22(4), 1461–1473 (2014)

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11. Duong, S.C., Uezato, E., Kinjo, H., Yamamoto, T.: A hybrid evolutionary algorithm for recurrent neural network control of a three-dimensional tower crane. Autom. Constr. 23, 55–63 (2012) 12. Sun, N., Fang, Y., Chen, H., Lu, B., Fu, Y.: Slew/translation positioning and swing suppression for 4-DOF tower cranes with parametric uncertainties: design and hardware experimentation. IEEE Trans. Ind. Electr. 63(10), 6407–6418 (2016) 13. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2002) 14. Zhang, M., Zhang, Y., Chen, H., Cheng, X.: Model-independent PD-SMC method with payload swing suppression for 3D overhead crane systems. Mech. Syst. Sig. Process., 129, 381-393 (2019) 15. Yang, T., Sun, N., Chen, H., Fang, Y.: Neural network-based adaptive antiswing control of an underactuated ship-mounted crane with roll motions and input dead-zones. IEEE Transactions on Neural Networks and Learning Systems, in press. https://doi.org/10.1109/tnnls.2019. 2910580 16. Liu, D., Yi, J., Zhao, D., Wang, W.: Adaptive sliding mode fuzzy control for a two-dimensional overhead crane. Mechatronics 15(5), 505–522 (2005)

EEG Recognition with Adaptive Noise Reduction Based on Convolutional LSTM Network Hengxing Lv, Xuemei Ren and Yongfeng Lv

Abstract In this paper, a new EMD adaptive decomposition algorithm is designed to denoise the original EEG signals, and a deep neural network model ConvLSTM is used to extract the features of the denoised signals. First, EEG signals are collected by a brain equipment. Then we use the proposed method to denoise the collected signals. Finally, the needed features are extracted with the convLSTM. Compared with previous methods, this proposed algorithm can extract the temporal and spatial characteristics of EEG more effectively. The proposed method is implemented on the actual moving EEG dataset, which verifies the validity and practicability of the proposed model. Keywords Electroencephalogram · Empirical mode decomposition · Deep learning · ConvLSTM

1 Introduction The electroencephalogram (EEG) signals are the sum of the electrical activities of a large number of neuronal cells recorded by the epidermis of the brain, which contains a lot of useful information. In recent years, the brain-computer interface (BCI) technology has developed rapidly, and accurate recognition of EEG is the most important component of BCI technology. However, the EEG signal is a nonstationary bioelectrical signal, and its own strength is weak, so it is easy to be polluted by noise in the process of collection, which makes it extremely difficult to extract the characteristics of the signal. In view of the strong background noise of EEG signals, the traditional noise reduction ideas are mostly based on wavelet transform and independent component analysis [1–5]. The wavelet denoising is based on the decomposition and reconstruction of the multi-scale wavelet transform. The wavelet coefficients belonging to the signal are preserved as much as possible, and the wavelet coefficients of the noise are removed. Finally, the inverse wavelet transform is used to reconstruct the H. Lv · X. Ren (B) · Y. Lv School of Automation, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_22

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signal, such that it can achieve the purpose of noise reduction. Wavelet denoising method is simple to calculate, but the decomposition layers and wavelet bases need to be pre-selected before signal processing. In [6], it is shown that different decomposition layers and wavelet bases have great influence on the results. Independent component analysis (ICA) is a common processing method in EEG signal separation, which can separate the original signal from multiple linear mixed signals. The non-Gaussian metrics of the separation results show the mutual independence of the results. When the result value reaches the maximum, it indicates that the separation of the independent components has been completed, but the ICA has the possibility of slow convergence or even no convergence. Empirical mode decomposition (EMD) proposed by Huang is an adaptive signal processing method based on the time scale characteristics of data itself [7]. It can decompose arbitrary signals into finite intrinsic mode functions (IMF) without setting a priori basis function. It is very suitable for processing non-stationary and non-linear signals such as EEG signals. In this paper, an EEG denoising algorithm based on EMD decomposition is constructed. Before the deep learning [8] was proposed, there were three main types of EEG feature extraction methods. The first one is based on simple statistical methods. By statistic the mean, peak value and power spectral density function of EEG signal, which have practical physical significance, as the extracted signal feature [9]. This method extracts few features and relies heavily on human experience. The second type is to extract the wavelet coefficients or energy spectra of the useful frequency bands of the signal by wavelet transform [10] and wavelet packet transform [11]. This method can extract the time-frequency information of the signal sufficiently, but it has no self-adaptability. The third is the Common Spatial Pattern (CSP) [12] method, which is based on the spatial distribution of the brain. This method needs a lot of leads and is complicated to use. In recent years, deep neural networks such as convolutional neural networks (CNN) and long short-term memory (LSTM) networks have been applied to the field of EEG signal recognition [13, 14]. The recognition accuracy has also been greatly improved. However, CNN can’t reflect the timing characteristics of data. LSTM network can’t extract local features between different channels of EEG signals, so they have their own limitations in the field of EEG recognition. Convolutional LSTM (ConvLSTM) was originally proposed to predict precipitation in a short period of time [15]. This network structure combines the advantages of CNN and LSTM. Using this network structure for feature extraction of EEG can fully mine the spatiotemporal characteristics of the signal. In this paper, the original signals are adaptively denoised by the EMD algorithm, and the ConvLSTM is used to extract the characteristics of EEG. Finally, the Softmax classifier is used for classification. The rest of the paper is organized as follows: Sect. 2 introduces the noise reduction principle of the EMD algorithm. Section 3 introduces the ConvLSTM network structure and its use in EEG and Sect. 4 is the model simulation and control experiments. Finally, the conclusions and directions for improvement are discussed in Sect. 5.

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2 EMD Denoising Algorithms The collected EEG signals are very weak and vulnerable to high-frequency noise pollution such as electrooculogram (EOG) and electromyography (EMG). So it is very important to denoise the original signals.

2.1 EMD Decomposition Huang et al. in [7] proposed an EMD algorithm which can decompose arbitrary signals into finite IMF and one residual according to their own time scale features. The model is given as x(t) =

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2.2 EMD Noise Reduction Method for EEG Signals The essence of EMD denoising is to remove IMF components which contain most of the noise signals and reconstruct IMF components which contain most of the original signals. The EMD algorithm can decompose the signal according to the frequency from high to low. The frequency of the EEG signal is mostly concentrated in the low frequency range below 50 Hz, and the noise is mostly concentrated in the high frequency of the signal, corresponding to the low-order part of the IMF. Therefore, the proportion of noise in the low-order IMF needs to be measured to determine the noise reduction boundary of the IMF. Assuming that the fast Fourier transform of the IMF component is F, according to the Parseval theorem, the square of the signal Fourier transform modulus is defined as the energy spectrum. If the energy spectrum is E, then: F = [ f (1), f (2), . . . , f (k), . . . , f (K )]

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3 Feature Extraction and Classification Based on ConvLSTM Network Model With the development of deep learning, deep neural networks have shown strong superiority in the field of pattern recognition. Compared with the traditional machine learning algorithm, the deep neural network can avoid the process of artificial feature extraction, and reduce the impact of human prior experience on the model results. In this section, ConvLSTM network structure, which combines the advantages of CNN and LSTM, is introduced into the field of EEG signal recognition. This network model makes full use of the temporal and spatial characteristics of EEG signals.

3.1 CNN and LSTM Convolution operation in CNN is actually a cross-correlation function. Assuming that the input is I and the convolution core is K, the formula is as follow: S(i, j) = (I ∗ K )i j =

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S is Convolution output. When the result of the convolution is added to the bias term b and then processed by the nonlinear activation function f, the output of the convolutional layer can be obtained.   y = f (I ∗ K )i j + b

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The convolutional neural network has the characteristics of sparse connection and weight sharing, and it has great advantages in local feature extraction of signals. LSTM is a deformed structure of the recurrent neural network (RNN). The memory of current signals and the forgetting of past signals are realized by setting controllable gates. Thus the neural network has real memory. The LSTM cell structure is as follows:     f t = σ W f · h t−1 , xt + b f

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Among them, f t , i t and Ot are forgetting gate, input gate and output gate respectively. xt is the cell input at the current time. Ct is the current cell state, and Ct−1 is the cell state at the last moment.h t is the current output of LSTM cells and h t−1 is the last output of LSTM cells. W f , Wi , Wc , and Wo are parameters that need to be trained. b f , bi , bc , and bo are the bias terms of the model. The parameters are updated using the back propagation through time (BPTT) algorithm. · represents matmul product. ◦ is the hadamard product of two matrices. σ is the activation function of Sigmoid. The function is defined as follow: σ (x) =

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3.2 ConvLSTM Network Structure and Whole Model Design EEG signals are voltage values collected by electrodes covering the brain epidermis. Each channel corresponds to the specific location of the brain, so EEG signals have not

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only temporal characteristics, but also rich spatial location information. ConvLSTM is a network structure that can extract temporal and spatial characteristics. From (9)–(13) we know that W and h t−1 , xt are matmul products, that is, the form of full connections between the former layers and the latter layers of the networks. Referring to Eq. (8), we convert the general product of matrices into convolution, and then Formulas (9)–(12) are transformed as:   f t = σ Wh f ∗ h t−1 + Wx f ∗ xt + b f

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The data preprocessing and the design of the network model are shown in Fig. 2. Firstly, we need to slice the collected EEG signals in the time window. After processing, the EEG dataset format is (num, W L , c), where num is the total number of samples, WL is the time window length of samples, which is also the length of cycles required by ConvLSTM, and c is the number of channels. Since the input of ConvLSTM is a three-dimensional tensor, it is necessary to change the dimensions of the samples and transform the original (num, W L , c) into (num, W L , 1, c, 1). In this way, convolution kernels can be used to extract features from different channels of signals in ConvLSTM cells. We designed three ConvLSTM layers to mine the temporal and spatial characteristics of EEG signals. In addition, three full-connection

Fig. 2 Data preprocessing of a single sample and structural design of the network model

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layers are designed to further extract the characteristics of signals. The outputs of the third layer of ConvLSTM are used as the inputs to the fully connected layer. We add Flatten layer between them to match dimensions.

4 Model Simulation and Control Experiment In this section, we will validate the advancement and rationality of the model by using the actual motion EEG signals collected independently as experimental datasets.

4.1 Datasets Introduction The data were collected from the actual motion signals of the same adult man. The data were divided into five categories: neutral, nodding, shaking head, raising the left hand and raising the right hand. We collected data for each category three times, and each time we collected about one minute, during which we repeated the category action and controlled the time of completing one action within one second. The equipment EMOTIV EPOC+ Neuroheadset was used to collect data. The sampling frequency was 125 Hz. The wearing mode and the position of each electrode are shown in Fig. 3. A total of 15 sets of data were obtained for the test. For each set of data, a time sliding window of length 150 was constructed. Due to the non-stationary nature of the EEG signal, the displacement from the previous time window to the next time window contains only one sample. The experiment collected 720 valid samples and evenly disrupted the data sets. 80% of them were used as training set and 20% as a test set. The data shape of the training set is (576, 14, 150) and that of the test set is (144, 14, 150).

Fig. 3 Equipment usage and electrode placement

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In Fig. 4, the top is the original EEG signals, and the following is the decomposed IMF and the remainder. It can be found that the IMF components of the signals are arranged from high to low frequency. High-frequency noise is mainly distributed in the low-order part of the IMF. It can be seen from Fig. 5 that the high-frequency noise of the EEG signal after denoising is suppressed. The denoised EEG signals are input into the model, and the classification results are shown in Fig. 6. Compared with traditional machine learning algorithms such as Bayes and SVM, the deep neural network model shows great advantages. The classification accuracy of EEG signals after adaptive denoising with EMD is better than that of original signals. The experimental results also show that compared with LSTM, ConvLSTM network structure can extract the temporal and spatial characteristics of EEG more fully. Generally speaking, the model using EMD_ConvLSTM has the highest classification accuracy, and the experiment verifies the practicability and reliability of the model.

5 Conclusion In this paper, a recognition model of original EEG signals based on EMD_ConvLSTM is proposed. An adaptive denoising algorithm based on EMD decomposition is used to process the high-frequency background noise of EEG signals. The denoised signals are extracted by using ConvLSTM, which is an improved structure of LSTM. Finally, the extracted features are classified by using Softmax. The biggest advantage of this model is that it can better extract the temporal and spatial characteristics of the original EEG signals. The feasibility of the algorithm is verified by training the actual motion EEG dataset. Deep neural network has achieved initial results in the field of EEG signals recognition, but how to reduce the size of the network and improve the real-time performance of the model under the premise of ensuring the recognition accuracy is our future work. Acknowledgments The work was supported by National Natural Science Foundation of China (No. 61433003, No.61621063).

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References 1. Hamaneh, M.B., Chitravas, N., Kaiboriboon, K., et al.: Automated removal of EKG artifact from EEG data using independent component analysis and continuous wavelet transformation. J. IEEE Trans. Biomed. Eng. 61, 1634–1641 (2014) 2. Mammone, N., La Foresta, F., Morabito, F.C.: Automatic artifact rejection from multichannel scalp EEG by wavelet ICA. J. IEEE Sens. J. 12, 533–542 (2012) 3. Akhtar, M.T., Mitsuhashi, W., James, C.J.: Employing spatially constrained ICA and wavelet denoising, for automatic removal of artifacts from multichannel EEG data. J. Sig. Process. 92, 401–416 (2012) 4. Geetha, G., Geethalakshmi, S.N.: Artifact removal from EEG using spatially constrained fastica and fuzzy shrink thresholding technique. J. Procedia Eng. 30, 1064–1071 (2012) 5. Babu, P.A., Prasad, K.: Removal of ocular artifacts from EEG signals using adaptive threshold PCA and wavelet transforms. In: 2011 IEEE International Conference on Communication Systems and Network Technologies, pp. 572–575. IEEE Press, Katra (2011) 6. Zhang, L., Bao, P., Wu, X.: Multiscale LMMSE-based image denoising with optimal wavelet selection. J. IEEE Trans. Circ. Syst. Video Technol. 15, 469–481 (2005) 7. Huang, N.E., Shen, Z., Long, S.R., et al.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. J. Proceed. R. Soc. Lond. 454, 903–995 (1998) 8. Hinton, G.E., Osindero, S., The, Y.W.: A fast learning algorithm for deep belief nets. J. Neural Comput. 18, 1527–1554 (2006) 9. Millán, J.D.R.: Adaptive brain interfaces. J. Commun. ACM 46, 219–227 (1999) 10. Hazarika, N., Chen, J.Z., Tsoi, A.C., et al.: Classification of EEG signals using the wavelet transform. J. Sig. Process. 59, 61–72 (1997) 11. Cai, M., Hu, P.: Task classification of right-hand and foot motion imagery based on wavelet packet transform. Chin. J. Med. Ins. 41, 177–180 (2017) 12. Liu, C., Zhao, H.B., Chun-Sheng, L.I., et al.: CSP/SVM-based EEG classification of imagined hand movements. J. Northeast. Univ. 31, 1098–1101 (2010) 13. Mao, Z., Yao, W.X., Huang, Y.: EEG-based biometric identification with deep learning. In: 8th International IEEE/EMBS Conference on Neural Engineering, pp. 609–612. IEEE Press, Shanghai (2011) 14. Ahmedt-Aristizabal, D., Fookes, C., Nguyen, K., et al.: Deep classification of epileptic signals. In: 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 332–335. IEEE Press, Hawaii (2018) 15. Xingjian, S.H.I., Chen, Z., Wang, H., et al.: Convolutional LSTM network: A machine learning approach for precipitation nowcasting. In: 29th Conference on Neural Information Processing Systems, pp. 802–810. Montreal (2015)

Peaking Reduction of CRM-Based Adaptive Control via a Modified Adaptive Law Yafei Liu, Jun Yang, Jing Na, Guanbin Gao, Shubo Wang and Qiang Chen

Abstract To circumvent the oscillations induced by high-gain adaptation in the model reference adaptive control (MRAC), closed-loop reference model (CRM) based MRAC was recently proposed. However, although a fair steady-state performance can be guaranteed, the induced peaking phenomenon in the CRM based adaptive control system may deteriorate the transient tracking response. In this paper, we first analyze the peaking value based on L2 norm and Cauchy-Schwartz inequality. Then according to the analysis, a novel adaptive law containing the parameter estimation error is constructed to alleviate the peaking phenomenon. This proposed method can allow using a fairly large feedback gain in the CRM based MRAC system to achieve better transient performance. Experiment results based on a 3-DOF helicopter show that the modified CRM adaptive control system can alleviate the peaking phenomenon. Keywords Closed-loop reference model · Adaptive control · Peaking phenomenon · Parameter estimation Y. Liu · J. Yang · J. Na (B) · G. Gao Faculty of Mechanical & Electrical Engineering, Kunming University of Science & Technology, Kunming 650500, China e-mail: [email protected] Y. Liu e-mail: [email protected] J. Yang e-mail: [email protected] G. Gao e-mail: [email protected] S. Wang School of Automation, Qingdao University, Qingdao 266071, China e-mail: [email protected] Q. Chen College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_23

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1 Introduction Large learning gain in the adaptive laws can help address the uncertainties in the adaptive control but can also excite high frequency unmolded dynamics [1–3]. Hence, large learning gain is not a preferable choice to achieve fast adaptation in the model reference adaptive control (MRAC) systems. To circumvent the above issue, several solutions have been reported in [4, 5]. A modified MRAC framework that is called CRM based MRAC has recently been proposed in [6], where an error feedback term was incorporated into the reference model. Since the feedback gain can shift the eigenvalues of the system matrix of the tracking error, the convergence of the tracking error can be improved so as to enhance the transient performance of the closed-loop systems [7, 8]. In addition, the introduced feedback coefficient adds another degree of freedom to regulate the system’s performance, such that the conflict between the convergence and the robustness against the uncertainties can be managed. According to these facts, CRM adaptive control has drawn much attention and been applied to some practical applications, e.g., [9, 10]. However, it is worth noticing that since the tracking error is introduced into the reference model as an error feedback term in the CRM-based MRAC framework, the closed-loop reference model will be different from the open-loop reference model (ORM) [11]. For this point, the CRM scheme may suffer a peaking phenomenon when the CRM is adopted in the adaptive control designs [2], which in turn may lead to degraded transient control response. Although some preliminary solutions have been proposed to address this induced peaking phenomenon, e.g., [9, 10], the peaking phenomenon reduction in the CRM based adaptive control is still an open problem to be solved. In this paper, we focus on addressing the peaking phenomenon induced by the closed-loop reference model and improving its transient performance. The key idea is to modify the adaptive law as [12] to alleviate the undesired transient dynamics. For this purpose, we first revisit the CRM based MRAC system in terms of the peaking phenomenon analysis, and then present a novel adaptive law containing the estimation error to guarantee the convergence of both the tracking error and the parameter estimation error. The effectiveness of proposed method is validated through practical experiment results based on a 3-DOF helicopter prototype.

2 Problem Formulations 2.1 CRM Based Adaptive Control System Consider the following system x˙ = Ax + B(θ T φ(x) + u(t))

(1)

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where x = [x1 , x2 · · · xn ]T ∈ R n is the system state; u(t) is the control input; A ∈ R n×n , B ∈ R n×m are the system matrices. The pair (A, B) is controllable and the matrix (B T B) is invertible; θ ∈ R d×m is an unknown constant weight matrix; φ(x) = [φ1 (x) · · · φd (x)]T ∈ R d is a known function vector. The open-loop model reference is designed as x˙r (t) = Ar xr (t) + Br r

(2)

where xr ∈ R n is the state of the reference model; r ∈ R m is the external control command; Ar ∈ R n×n is a Hurwitz matrix and Br ∈ R n×m is the input matrix. Then we can find positive definite matrices P, Q ∈ R n×n satisfying the Lyapunov function ArT P + P Ar = −Q. According to [9, 10] ,the tracking error is incorporated into the reference model through a feedback gain α, such that the closed-loop reference model is given as x˙cr (t) = Ar xcr (t) + Br r + αecr

(3)

where xcr ∈ R n is the state of reference model (3); ecr = x − xcr is the tracking error; α is a positive scalar. In the conventional CRM adaptive control system [9, 10], the control action u is given as u = N x x + Nr r + u a

(4)

with the matched condition Ar = A + B N x , Br = B Nr . Then, the adaptive law is designed as u a = −θˆ T φ(x)

(5)

where θˆ is the estimate of the unknown weight matrix θ , which can be updated by T PB θ˙ˆ = γ φ(x)ecr

(6)

where γ > 0 is the adaptive gain. Substituting (5) and (6) into system (1), then we have x˙ = Ar x + Br r + B θ˜ T φ(x)

(7)

where θ˜ = θ − θˆ is the estimation error. Subtracting (3) from (7), we have the modified tracking error dynamics as e˙cr = (Ar − α I )ecr + B θ˜ T φ(x)

(8)

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where I is an identity matrix. We define Ar = Ar − α I , and then can verify that Ar is also a Hurwitz matrix. For comparison, from (2) and (7), we can get the tracking error of the open-loop reference model based MRAC system as e˙ = Ar e + B θ˜ T φ(x)

(9)

From (8) and (9), we find that there exists another tuning parameter α to regulate the performance of the CRM based adaptive control system. It is clearly showed in (8) that α can shift the eigenvalues of the tacking error convergence matrix Ar − α I and enhance the error convergence. However, the potential peaking phenomenon, as reported in [2], induced by this feedback mechanism is prominent, which could make the transient control performance degraded. Then, a further analysis based on Cauchy-Schwartz inequality is first introduced in next section.

2.2 Peaking Phenomenon of CRM Based Adaptive Control System In this section, we will further illustrate the merit of the CRM-based scheme and analyze the peaking phenomenon from a new perspective. From Eqs. (2) and (3), we can obtain xr and xcr as t xr = e

Ar t

xr (0) +

e Ar (t−τ ) B r (τ )dτ

0

t xcr = e

Ar t

xcr (0) + +

e

Ar (t−τ )

0

t Br (τ )dτ + α

e Ar (t−τ ) ecr (τ )dτ

(10)

0

In this case, the difference between xcr of CRM (3) and xr of standard MRAC (2) is used to measure the peaking phenomenon. To simplify the analysis, we assume that xr (0) = xcr (0). Then we have t xcr − xr = α

e Ar (t−τ ) ecr (τ )dτ

(11)

0

From the above Eq. (11), the error feedback term ecr can cause an difference between xcr and xr , which may lead to a peaking phenomenon in the CRM based adaptive control system. To further reveal the peaking phenomenon, L2 norm and Cauchy-Schwartz inequality are first used.

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Lemma 1 [11] If Ar is Hurwitz matrix, ξ is the maximum real part of the eigenvalues of Ar , i.e., ξ < 0, ξ = max(r eal(λi (Ar ))). For any constant ε > 0 and t ≥ 0, we can get:  A t  e r  ≤ Me ξ2t 3 M = (1 − 4Ar /ξ )n−1 2

(12)

where  • is the induced Euclidean norm. According to Lemma 1, for CRM based adaptive control system (1), (4–6) with the CRM (3), the following inequality can be obtained  ecr (t) 2 ≤ ecr (0)2 M  e

ξt 2

     + M   B 2  θ˜ T (t)  φ(x) 2 / −ξ  2

(13)

By applying the Cauchy-Schwartz inequality, we can get   ξt Mα M M α    xcr − xr  2 ≤ √ ecr (0)2 M  e 2 + √ √   B 2  θ˜ T (t)  φ 2 2 −ξ −ξ −ξ

(14)

  where ξ  = max(r eal(λi (Ar ))) and M  = 3(1 − 4 Ar /ξ  )n−1 /2. From (13), we can clearly find that the bound of the tracking error ecr could be reduced because of the increased eigenvalue ξ  induced by the feedback coefficient α. Thus, the analysis results derived by Cauchy-Schwartz inequality further illustrate the mechanism of CRM control scheme and verify its effectiveness. However, from (14), although the initial tracking error ecr (0) will exponentially decrease due to  the exponential term eξ t/2 , the effects of the parameter estimation error θ˜ cannot be reduced for constant eigenvalues ξ and ξ  , especially the bound of ||xcr − xr || could be increased when a large feedback gain α is used. From the analysis, we can see that the unknown estimation error θ˜ plays a critical role in creating the peaking phenomenon. However, it is also shown that the peaking phenomenon can be alleviated by decreasing the bound of θ˜ , such that a fairly large feedback gain can be used to further reduce the tracking error without triggering a large peaking value.

3 Modified CRM Based Adaptive Control System The inequality (14) shows that the peaking phenomenon can be reduced by decreasing ˜ Inspired by our previous results in [3, 12, 13], a modified the estimation error θ. adaptive law is proposed in this section, which can effectively make the estimation error θ˜ converge to zero quickly. The following filtered variables are defined as [12, 13] based on the available system input and output

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⎧ ⎨ κ x˙ f + x f = x κ u˙ + u f = u ⎩ ˙f κφ f + φ f = φ

(15)

where κ > 0 is a filter parameter. As long as κ is small, we can verify that x f → x, u f → u, φ f → φ. An auxiliary term F ∈ R n is denoted as F = (x − x f )/κ − Ax f − Bu f

(16)

Then, auxiliary matrices W ∈ R d×d and H ∈ R d×m are defined as 

W˙ = −ηW + φ f φ Tf , W (0) = 0 H˙ = −ηH + φ f F T Z , H (0) = 0

(17)

where η > 0 is a design parameter, and Z = B(B T B)−1 ∈ R n×m exists due to det(B T B) = 0. Applying the filter operations on (1), we have Bθ T φ f =

1 (x − x f ) − Ax f − Bu f κ

(18)

Combining (18) with (17), we have H˙ = −ηH + φ f φ Tf θ

(19)

Then the solutions of W˙ and H˙ are obtained as ⎧

t −η(t−τ ) ⎪ ⎪ φ f (τ )φ Tf (τ )dτ ⎨ W = e 0

t ⎪ ⎪ ⎩ H = e−η(t−τ ) φ f (τ )φ Tf (τ )dτ θ

(20)

0

From (20), we can obtain the following relationship between W and H H = Wθ

(21)

From (21) we can see that the auxiliary matrix H contains the unknown parameter θ . Thus, based on the defined matrices W and H, a modified adaptive law is constructed as  T P  B − σ (W θˆ − H ) (22) θ˙ˆ (t) = γ φ(x)ecr

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where P  ,Q are positive definite matrices satisfying the Lyapunov function (Ar )T P  + P  Ar = −Q, and σ is also a positive constant. It can be verified the tracking error of CRM based adaptive control system with (3), (4) and the adaptive law (22) are the same as that given in (8). Hence, we choose  T P ecr + tr (θ˜ T γ −1 θ˜ ). Then, by calculating the the Lyapunov function as V = ecr derivative of V along (8) and (22), we can obtain V˙ ≤ −aV for a being a positive constant. Based on Lyapunov theorem, we can obtain that the tracking error and estimation error are convergent to zero exponentially, e.g., ecr → 0 and θ˜ → 0 as t → ∞. Through the above analysis, the proposed adaptive law can guarantee the bound of the estimation error θ˜ reducing to zero rapidly. Thus, the modified CRM based MRAC method with this proposed adaptive law can significantly alleviate the peaking phenomenon from inequality (14).

4 Experiments In this section, experiment results based on a 3-DOF helicopter as shown in Fig. 1 are provided to verify the effectiveness of the modified methods in alleviating the peaking phenomenon. In this paper, we focus on the control of the elevation axis of the helicopter. Thus, the mathematical model of the elevation axis can be given as 3-DOF Helicopter System

DSP Based Control

Upper Computer

DC Power

CCS PWM

QEP

DSP28335

Host PC

USB

UART

Serial to USB

Fig. 1 Diagram of the 3-DOF helicopter

Encoder

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x˙1 x˙2



01 = 00



  x1 + x2

0 2L a K f Mh L a2 +Mw L 2w

  M h L a g − Mw L w g u− cos(ϕ+ϕ0 ) La K f (23)

where L a = 0.545 m, L w = 0.444 m, K f = 0.85 N/V, Mh = 1.87 kg, Mw = 2.21 kg, g = 9.8 m/s−2 and ϕ0 = −23 is the initial bias of the elevation. In the T  experiments, the regressor vector is chosen as φ(x) = u cos(x1 + θ0 ) and θ1 =   2L a K f /(Mh L a2 + Mw L 2w ), θ2 = 2(Mh L a g − Mw L w g)/ Mh L a2 + Mw L 2w are the parameters to be estimated. The closed-loop reference model is designed as

x˙cr 1 x˙cr 2



0 1 = −1 −1.414



  

0 ecr 1 xcr 1 + rd + α xcr 2 ecr 2 1

(24)

Consequently, the nominal control can be designed as N x = [ −1 −1.414] , Nr = 1, The filter parameters are chosen as κ = 2. The external command rd is a square signal with period 30 s and the amplitude 10 rads. Two cases of experiment results are provided: Case 1: The traditional CRM based MRAC system with adaptive law (6) and adaptive learning gain γ = diag([ 10 10 ]) and different α = 5, 10. Case 2: The modified CRM based MRAC system with adaptive law (22) and adaptive learning gain γ = diag([ 10 10 ]) and different α = 5, 10. Experiment results are provided in Figs. 2, 3, 4. According to the experiment results of the traditional CRM based MRAC system given in Fig. 2, we can see that a larger feedback gain α can lead to significant peaking phenomenon in the CRM based adaptive control system, which is consistent with the theoretical analyses. Comparing Fig. 2 with Fig. 3 of the modified CRM based MRAC system, it is obvious that the modified CRM based control system can reduce the peaking phenomenon even for a large feedback gain α = 10.

a. Traditional CRM control system with α = 5

b. Traditional CRM control system with α = 10

Fig. 2 Tracking performance of traditional CRM control system with γ = diag([10 10])

Peaking Reduction of CRM-Based Adaptive Control …

a. Modified CRM control system with α = 5

247

b. Modified CRM control system with α = 10

Fig. 3 Tracking performance of modified CRM control system with γ = diag([10 10])

θˆ1

θˆ1

θˆ2

θˆ2

a. Estimated parameters of traditional CRM control system α = 5 γ = diag ([10 10])

b. Estimated parameters of modified CRM control system α = 5 γ = diag ([10 10])

θˆ1

θˆ1

θˆ2

θˆ2

c. Estimated parameters of traditional CRM control system α = 10 γ = diag ([10 10])

d. Estimated parameters of modified CRM control system α = 10 γ = diag ([10 10])

Fig. 4 Parameter estimation results

The above performance improve can be attributed to the adopted modification on the adaptive law, which leads to better parameter estimation convergence. Comparing the parameter estimation results given in Fig. 4, we can see that the modified CRM control system can achieve better results of parameter estimation, showing the effectiveness of the proposed adaptive law.

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5 Summary Peaking phenomenon may be a problematic in the CRM based adaptive control system. In this paper, we first analyze the peaking phenomenon from a new perspective, which shows that the parameter estimation convergence can be beneficial for reducing the peaking phenomenon. Hence, we propose a new adaptive law to achieve guaranteed parameter estimation convergence and then to reduce the peaking phenomenon in the CRM based MRAC systems. Experiment results show that the proposed method can effectively reduce the peaking phenomenon and retain satisfactory transient control response. Acknowledgements This work was supported by the National Natural Science Foundation of China (grant 61573174 and 61922037).

References 1. Yucelen, T., Calise, A.J.: Kalman filter modification in adaptive control. J. Guid. Control Dyn. 33, 426–439 (2010) 2. Gibson, T.E., Annaswamy, A.M., Lavretsky, E.: On adaptive control with closed-loop reference models: transients, oscillations, and peaking. IEEE Access 1, 703–717 (2013) 3. Na, J., Herrmann, G., Zhang, K.: Improving transient performance of adaptive control via a modified reference model and novel adaptation. Int. J. Robust Nonlinear Control 27, 1351–1372 (2017) 4. Yang, J., Liu, Y., Na, J., Gao, G.: Improving transient performance of modified model reference adaptive control. In: Innovative Techniques and Applications of Modelling, Identification and Control, pp. 331–343 (2018) 5. Xiao, L., Liu, F., Xue, L., Yu, G.: Parameter identification and optimisation for a class of fractional-order chaotic system with time delay. Int. J. Model. Ident. Control 29, 1–12 (2018) 6. Lee, T.G., Huh, U.Y.: An error feedback model based adaptive controller for nonlinear systems. In: IEEE International Symposium on Industrial Electronics, pp. 1095–1100 (1997) 7. Stepanyan, V., Krishnakumar, K.: M-MRAC for nonlinear systems with bounded disturbances. In: Decision and Control and European Control Conference, Orlando, FL, USA, pp. 5419–5424 (2011) 8. Lavretsky, E.: Combined/composite model reference adaptive control. IEEE Trans. Autom. Control 54, 2692–2697 (2009) 9. Lavretsky, E.: Reference dynamics modification in adaptive controllers for improved transient performance. In: AIAA Guidance, Navigation, and Control Conference, Portland, Oregon (2006) 10. Stepanyan, V., Krishnakumar, K.: MRAC revisited: guaranteed performance with reference model modification. In: American Control Conference, Marriott Waterfront, Baltimore, MD, USA, pp. 93–98 (2010) 11. Narendra, K.S., Annaswamy, A.M.: Stable Adaptive Systems. Prentice-Hall (1989) 12. Na, J., Mahyuddin, M.N., Herrmann, G., Ren, X.: Robust adaptive finite-time parameter estimation and control for robotic systems. Int. J. Robust Nonlinear Control 25, 3045–3071 (2015) 13. Yang, J., Na, J., Gao, G.: Robust adaptive control with a modified controller for transient response improvement. In: 2017 9th International Conference on Modelling, Identification and Control, Kunming, China, pp. 929–934 (2017)

Unbalance Suppression for Active Magnetic Bearing Rotor System Based on Disturbance Observer Zhuangzhuang Yue, Huimin Ouyang, Guangming Zhang, Lei Mei and Xin Deng

Abstract Aiming at the problem of co-frequency disturbance caused by mass imbalance in the AMB system, a dynamics model is established firstly, and then a composite controller based on the model is proposed, which combines a proportional differential (PD) and a disturbance observer (DOB). Finally, the simulation verified that the proposed method can have good robust control performance under the conditions of constant speed. Keywords Active magnetic bearing · Disturbance observer · Unbalance suppression

1 Introduction In active magnetic bearing rotor systems, factors such as gyroscopic effects, parameter coupling, and imbalance can cause vibrations in the system. The most important factor is the co-channel disturbance caused by the mass imbalance. Unlike conventional mechanical bearings, AMB uses electromagnetic force to suspend the rotor. So they have the characteristics of high speed, low noise, and no lubrication [1, 2]. Therefore, the vibration caused by the mass imbalance of the rotor can be achieved by controlling the external electromagnetic force. The suppression of unbalanced vibration has pro-posed many control strategies. The main idea of vibration suppression is based on the same frequency disturbance signal plus controller to compensate. The main purpose is to generate electromagnetic forces of opposite magnitude and opposite directions to counteract the vibrational force. Many researchers have proposed a variety of control strategies. Schuhmann [3] proposed a method based on Kalman filter, however, the center frequency of the rotational speed is preset, and the robustness to the variable rotational speed is lowered.

Z. Yue · H. Ouyang (B) · G. Zhang · L. Mei · X. Deng School College of Electrical Engineering and Control Science, Nanjing 211816, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_24

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Yoon [4] utilizes input delay to improve output to compensate for rotor imbalance. Zhu [5–7] proposed a method based on variable step size iterative search to eliminate unbalanced disturbances. Fang [8] proposed a perturbation observer-based method to suppress disturbances. Fekry [9] proposed a Robust Q-parametrisation method to eliminate the imbalance. Chen [10] proposed a method based on adaptive frequency estimation to eliminate the imbalance. Zheng [11] put forward a way based on synchronous rotating coordinate system to suppress unbalanced disturbance. Gao et al. [12] raised a method of output displacement compensation to suppress co-channel interference caused by mass imbalance. He [13] suggests an iterative learning control method to suppress co-channel perturbations. In the existing literature, although the rapid suppression of rotor disturbance can be realized, the control algorithm is relatively complicated and the calculation is cumbersome. Therefore, this paper mainly focuses on the problem of disturbance suppression of the AMB rotor system in the fixed speed range. A composite controller consisting of a proportional differential controller (PD) and a disturbance observer (DOB). Finally, the numerical simulation results show that the proposed method has outstanding control performance and robustness.

2 AMB Rotor System Modeling Generally, the rotor system can be divided into five degrees of freedom. Since the coupling of four degrees of freedom in the radial direction and one degree of freedom in the axial direction is negligible, the modeling is as shown in Fig. 1. Therefore, the axial and degree of freedom of the rotor are usually designed and analyzed separately [14].

y ys1

θy

y1

y2

ys 2

z o1 xs1

o2

o

o3

ω x2

x1

x θx l p Fig. 1 Schematic diagram of the motion of the rotor

n q

o4 xs2

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According to Newton’s law and the law of rotor kinematics: m x¨ = f L x + f Rx + f ex

(1)

m y¨ = f L y + f Ry + f ey

(2)

Jx (−θ¨x ) + Jz ωθ˙y = l f L y − n f Ry + Tεx

(3)

Jy (−θ¨y ) − Jz ω(−θ˙x ) = l f L x − n f Rx + Tεy

(4)

In the above formula, m represents the mass of the rotor; Jx , Jy is expressed as the equatorial moment of inertia in the x, y directions; Jz represents the moment of inertia of the polar axis; f L x , f Rx : f L y , f Ry indicate the electromagnetic force of the left and right bearings in the radial direction, respectively; f ex , f ey ; Tεx , Tεy represent the unbalanced forces and moments of the rotor. Equations (1–4) can be organized into a matrix form as follows: M q¨c + G q˙c = TL Fc + Runb ⎡ ⎤ 0 1 1 0 0 ⎢0 ⎢0 0 1 1 ⎥ ⎢ ⎥ TL = ⎢ ⎣ 0 0 l −n ⎦, G = ⎣ 0 0 l −n 0 0 T   qc = x y −θx θ y Fc = f L x ⎡

M = diag[ m m Jx Jy ] Runb =



0 0 0 0 0 0 0 −Jz ω f Rx f L y

(5) ⎤ 0 0 ⎥ ⎥ Jz ω ⎦ 0 T f Ry

f ex f ey Tex Tey

T

Due to the limitations of conventional processes or the unevenness of material density, the rotor usually has a mass imbalance [15]. The influence of mass imbalance on the rotor mainly includes static unbalance disturbance and dynamic unbalance disturbance, that is, e is eccentricity and ε is inclination angle in the shaft and the equilibrium position when the rotor rotates, and θ is a static and dynamic unbalanced phase angle. Therefore, meω2 cos(ωt + θ ) = f ex

(6)

meω2 sin(ωt + θ ) = f ey

(7)

(Jx − Jz )εω2 cos(ωt + θ ) = Tεx

(8)

(Jy − Jz )εω2 sin(ωt + θ ) = Tεy

(9)

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On the other hand, linearizing the electromagnetic force at the equilibrium point gives [16]: Fc = ki i − ks ql

(10)

ki is the magnetic bearing current stiffness, ks is the magnetic bearing displacement stiffness. The above model will be used for the design of the controller.

3 Controller and Disturbance Observer Design In this paper, we mainly aim at the same-frequency disturbance caused by rotor imbalance. Then we design the disturbance observer shown in Fig. 2. The main composition is to make the difference between the actual input u of the system and the inverse model G −1 n (s) of the rotor system as low-pass. The input of filter Q(s) is then passed through a low pass filter to obtain the compensation value Runb for ˆ disturbance A. According to the block diagram, the following mathematical relationship can be obtained: ˆ u(s) = i(s) − A(s)

(11)

A(s) = G −1 n (s)ql (s) − u(s)

(12)

ql (s) = G iql i(s) + G dql Runb (s)

(13)

Runb

qd

e

Gc ( s )

i

u

GP ( s )

 Gn 1 ( s )

Q(s)

Fig. 2 Rotor control system diagram

A

DOB

ql

Unbalance Suppression for Active Magnetic Bearing Rotor System …

ˆ A(s) = [(u + Runb )G p (s)G −1 n (s) − u]Q(s)

253

(14)

At the same time, we can get the transfer function of G cql (s), G Runb ql (s) as follows: G p (s)G −1 ql (s) n (s) = −1 i(s) G n (s) + Q(s)(G p (s) − G −1 n (s))

(15)

G p (s)G −1 ql (s) n (s)(1 − Q(s)) = −1 Runb (s) G n (s) + Q(s)(G p (s) − G −1 n (s))

(16)

G cql (s) = G dql (s) =

In the frequency domain |Q( jw)| ≈ 1, s = jw, Eqs. (13), (15), (16) becomes: G cql ( jw) ≈ G −1 n ( jw), G Runb ql ( jw) ≈ 0

(17)

ql ( jw) = G −1 n ( jw)i( jw)

(18)

According to Fig. 2, the modulus of the product of the actual model and the



nominal model is 1, which is G p (s)G −1 n (s) = 1, also know |Q( jw)| ≈ 1. Substitute (14) shows:



ˆ A(s) = [(u(s) + Runb (s)) G p (s)G −1 n (s) − u(s)]|Q( jw)| = [(u(s) + Runb (s)) − u(s)]|Q( jw)| ≈ Runb (s)

(19)

For the design of the disturbance observer in this section, the controller is designed for four radial degrees of freedom in the AMB rotor system-rotor system in Fig. 2. The transfer function G c (s) of the designed PD controller is as follows: G c (s) = k P + k D s

(20)

where k P is the proportionality factor and k D is the differential coefficient. According to the Hurwitz theorem, if the system is to be stabilized, the real part of all poles of the closed-loop eigen-root trajectory can be located in the left half-plane of the complex plane in Fig. 3.

4 Simulation and Analysis This chapter will verify the validity of the proposed method. First, set the initial  T position and target position of the rotor to be ql = 0.1 0.1 −0.1 −0.1 mm  T and qd = 0 0 0 0 mm, respectively. In addition, system parameters and control parameters are shown in Tables 1 and 2.

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Fig. 3 System pole-zero diagram

Table 1 Parameter of rotor system Parameter

Value

Parameter

Value

m

6.539 kg

p

0.10671 m

Jx

0.083 kg m2

q

0.21728 m

Jz

0.006 kg m2

e

0.00001 m

l

0.11678 m

θ

0.0005 rad

n

0.06921 m

Jy

0.083 kg m2

Table 2 Parameter of controller Parameter

Value

Parameter

Value

k p1

15

k p2

30

k p3

11.6

k p4

22.5

kd1

240.2

kd2

230.4

kd3

169.5

kd4

191.4

w1

100,000 Hz

w2

100,000 Hz

w3

434,000 Hz

w4

434,000 Hz

Verify the effectiveness of the method at the rated speed of the rotor ω = 12,000 rpm. Figure 3 shows the disturbance estimation in the x and y direction (ω = 12,000 rpm), in which the solid red line represents real disturbance, and the solid blue line represents estimated disturbance. Figure 4 shows the displacement response curve of the bearing in the x and y direction (ω = 12,000 rpm), in which the solid red line represents the PD controller, and the solid blue line represents the PD-DOB controller (Fig. 5).

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Fig. 4 Disturbance estimation map

Similarly, Figs. 6 and 7 respectively shows the disturbance estimation map and displacement response curve of the bearing in the x and y direction (ω = 15,000 rpm). Meanwhile, it can be seen from Figs. 8 and 9 that the co-frequency disturbance force becomes larger in (ω = 18,000 rpm). Under the proportional differential control, the rotor displacement overshoot also becomes larger, and the stability of the system becomes worse. The disturbance is estimated after adding the disturbance observer. There is basically no deviation from the actual disturbance, and the suppression of the disturbance is realized, which greatly improves the stability of the system. It can be clearly obtained from Tables 3, 4, and 5. As the rotation speed increases, the same frequency disturbance power gradually increases, and it can be seen that the suppression effect after the observer is increased. More obvious. Further, the rotor vibration generated by the co-frequency disturbance can be reduced by about 90%, and at the same time, Conventional PD controllers have difficulty suppressing this vibration.

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Fig. 5 Response trajectory of bearing displacement

5 Conclusion Co-channel interference is the main factor affecting the stable operation of the bearing-rotor system. Based on the establishment of the dynamics model, the corresponding controllers and observers are designed. Finally, compared with the traditional PD controller, it both shows that the method can reduce the rotor vibration by about 85% when the rotor speed is constant (ω = 12,000, 15,000, 18,000 rpm).

Unbalance Suppression for Active Magnetic Bearing Rotor System …

Fig. 6 Disturbance estimation map

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Fig. 7 Response trajectory of bearing displacement

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Fig. 8 Disturbance estimation map

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Fig. 9 Response trajectory of bearing displacement Table 3 Comparisons for disturbance rejection performance (ω = 12,000 rpm) Maximum amplitude (m)

xl

xr 10−4

PD

0.7 ×

PD-DOB

1.1 × 10−6

yl

0.65 ×

10−4

1.5 × 10−6

yr 10−4

0.6 × 10−4

1.55 × 10−6

2.3 × 10−6

0.9 ×

Table 4 Comparisons for Disturbance Rejection Performance (ω = 15,000 rpm) Maximum amplitude (m) PD PD-DOB

xl

xr

0.8 ×

10−4

1.2 ×

10−6

yl

0.85 ×

10−4

1.95 ×

10−6

yr

0.95 ×

10−4

0.7 × 10−4

1.6 ×

10−6

2.4 × 10−6

Table 5 Comparisons for disturbance rejection performance (ω = 18,000 rpm) Maximum amplitude (m) PD PD-DOB

xl

xr

1×

10−4

1×

10−6

yl

1.1 ×

10−4

2×

10−6

yr

1.2 ×

10−4

0.9 × 10−4

1.5 ×

10−6

2.2 × 10−6

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Acknowledgements Project Supported by the Key Research and Development Project of Jiangsu Province (BE2017164).

References 1. Schweitzer, G., Maslen, E.H.: Magnetic Bearings: Theory, Design, and Application to Rotating Machinery. Springer, New York, NY, USA (2009) 2. Abrahamson, J., Hedlund, M., Kamf, T., Bernhoff, H.: High-speed kinetic energy buffer: optimization of composite shell and magnetic bearings. IEEE Trans. Industr. Electron. 61(6), 3012–3021 (2014) 3. Schuhmann, T., Hofmann, W., Werner, R.: Improving Operational performance of active magnetic bearings using Kalman filter and state feedback control. IEEE Trans. Industr. Electron. 59(2), 821–829 (2012) 4. Yoon, S.Y., Di, L., Lin, Z.L.: Unbalance compensation for AMB systems with input delay: an output regulation approach. Control Eng. Pract. 46, 166–175 (2016) 5. Mao, C., Zhu, C.: Vibration control for active magnetic bearing rotor system of high-speed flywheel energy storage system in a wide range of speed. In: 2016 IEEE Vehicle Power and Propulsion Conference (VPPC), Hangzhou, pp. 1–6 (2016) 6. Kejian, J., Changsheng, Z., Liangliang, C.: Unbalance compensation by recursive seeking unbalance mass position in active magnetic bearing-rotor system. IEEE Trans. Industr. Electron. 62(9), 5655–5664 (2015) 7. Chuan, M., Changsheng, Z.: Unbalance compensation for active magnetic bearing rotor system using a variable step size real-time iterative seeking algorithm. IEEE Trans. Industr. Electron. 65(5), 4177–4186 (2018) 8. Peng, C., Fang, J., Xu, X.: Mismatched disturbance rejection control for voltage-controlled active magnetic bearing via state-space disturbance observer. IEEE Trans. Power Electron. 30(5), 2753–2762 (2015) 9. Fekry, M., Mohamed, A.M., Fanni, M.: Robust Q-parametrisation control for nonlinear magnetic bearing systems with imbalance based on TSK fuzzy model. IJMIC 29(3), 195–208 (2018) 10. Chen, Q., Liu, G., Han, B.: Suppression of imbalance vibration in AMB-rotor systems using adaptive frequency estimator. IEEE Trans. Industr. Electron. 62(12), 7696–7705 (2015) 11. Zheng, S., Han, B., Feng, R., Jiang, Y.: Vibration suppression control for AMB-supported motor driveline system using synchronous rotating frame transformation. IEEE Trans. Industr. Electron. 62(9), 5700–5708 (2015) 12. Gao, H., Xu, L., Zhu, Y.: Unbalance vibratory displacement compensation for active magnetic bearings. Chin. J. Mech. Eng. 26(1), 95–103 (2013) 13. He, Y., Shi, L., Shi, Z., Sun, Z.: Unbalance compensation of a full-scale test rig designed for HTR-10GT: a frequency-domain approach based on iterative learning control. Sci. Technol. Nucl. Install. 2017 (2017 Jan) 14. Husain, A.R., Ahmad, M.N., Yatim, A.H.M.: Modeling of a horizontal active magnetic bearing system with uncertainties in deterministic form. In: First Asia International Conference on Modelling & Simulation (AMS’07), Phuket, pp. 42–47 (2007) 15. Chen, S., Lin, S.: Imbalance compensation for an AMB system with adaptive immersion & invariance control. In: The 27th Chinese Control and Decision Conference (2015 CCDC), Qingdao, pp. 1530–1534 (2015) 16. Huo, X., Feng, S., Liu, X., Zhao, Q.: Modelling of aerodynamic interference of three-DOF Gyro Wheel rotor. IJMIC 29(1) 29(1), 53–63 (2018)

Investigation of Pilot Flight Technology Based on Exploratory Factor Analysis Peipei Zeng, Zhonghua Li and Yan Chen

Abstract The development of flight technology is accompanied by the synchronous evolution of aircraft technology. The mode of flight operation has changed from traditional “operation” to “monitoring, decision-making and control”. Understanding the elements of pilot flight technology can improve the effectiveness and pertinence of pilot training and safety management. This paper summarizes the literature on pilots’ flight technology from different scholars in three stages of flight development, and obtains 16 elements of pilots’ flight technology according to relevant laws and regulations. Through questionnaires of first-line pilots and quantitative analysis of pilots’ flight skills based on exploratory factor analysis, four aspects of pilots’ flight technology are obtained, flight control, information decision-making, flight monitoring and crew resource management. It provides theoretical support for improving the flight technology of civil aviation pilots and has important guiding significance for flight safety management. Keywords Flight technology · Flight control · Information decision-making · Flight monitoring · Crew resource management

1 Introduction Pilot is the implementer of the flight, the last defense to ensure the safe aircraft operation, and the most important gateway of flight safety. The safety of civil aviation pilots directly affects the safety and performance of airlines. Therefore, a continuous improvement of pilot competency is an important safeguard of flight safety. In other words, pilot competency is a determinant of flight safety. The development of pilot technology has simultaneously accompanied with the evolution of aircraft technologies. Traditional flight technology put emphasis on the development of the technical capabilities of individual pilots. In the past, most pilots P. Zeng (B) · Z. Li · Y. Chen Engineering Technology Training Center, Civil Aviation University of China, Tianjin 300300, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_25

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held an opinion that the mastery of the “stick and rudder” technology would make a pilot fully qualified to operate an aircraft meanwhile ensuring the flight safety [1]. This opinion focused on technical knowledge and operational skills, with emphasis on the performance of pilot individuals. With the development of aviation technologies, aircrafts have become more automatic, and the flight mode is converted from “operation” into “monitoring, decision-making and control”. An accident analysis by the US Transportation Safety Board showed that a captain would violate operations than a deputy captain did, indicating that a higher technical level is not equal to a higher flight safety. Some scholars have made statistical analysis of aviation accidents and unsafe incidents in the past 10 years. It shows that about 70–80% of aviation accidents and unsafe incidents involve the causes of human errors of flight crew, that is, human errors which are exactly the concerns in the crew resource management [2]. All of these imply that the flight mode has shifted its emphasis from “operation” to “management”. At present, in the process of civil aviation transportation, pilots adopt the multiunit model. In recent years, International Civil Aviation Organization (ICAO) has introduced a Multi-crew pilot licence, mainly for the training of Multi-crew pilot flight technology. In China, a series of regulations of Civil Aviation Administration of China put forward requirements for pilots’ flight technology, mainly for pilots to obtain flight licences. Although different regulations have made relevant requirements for pilots to obtain licenses, there is still no clear definition of the connotation of current pilots’ flight technology. As a result, Airlines lack pertinence and effectiveness in pilots’ training and safety management. What has followed these different focuses is the difference in training requirements, which would be eventually reflected in the difference of the pilot technology. However, the definition of the compositional elements of pilot technology is still unclear. As a result, it is impossible to assess the effect of each element on flight safety. Consequently, the pilot training and safety management of a airline are not specifically targeted and not very effective. So, making clear of the compositional elements of pilot technology is of great importance to make pilot behaviors safe. Based on the above situation, this paper will do a systematic analysis of the pilot technology and define the compositional elements as well, with an intention to provide a reference for constructing the indexes of the pilot performance assessment as well as for completing the performance assessment program.

2 Research of Compositional Elements of Pilot Technology As recorded in researches, pilot technology has gone through the following three stages: perceptual operation, decision-making on information and crew resource management. In early days, pilot technology refers to technical skills required for fulfilling a flight task. The skills include the controls of height, course, and velocity and state of an aircraft. Researches in that period put emphasis on maneuverability, stability and some special controls of aircraft, such as inclination, lift, yaw, balance,

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velocity, flight environment (e.g., weather, visibility and turbulence) and pressure. Many scholars have studied flight technology from three aspects: maneuverability, stability and special flight control. Hunter P. A. points out that the main components of flight technology are longitudinal stability, control of control surface, direction stability, up-and-down effect, pitch moment and stall warning [3]. Barber M. R., Jones, C. K., Sisk, T. R. point out that the characteristics of static, control, dynamic stability and control are the key points of flight technology [4]. With the development of high-speed aircraft and the use of the highly complex navigation and flight management system, traditional pilot technology has changed so significantly that it focuses more on the capacity of collecting and processing information; meanwhile, the role of pilot has also changed: a pilot is also a decision maker [5]. Since then, the pilot entered decision-making stage. In this period, a pilot must have the ability to quickly and accurately process the received information and, based on which, make crucial decisions. As a decision maker, a pilot has to implement the flight activities. A major objective of the research in this stage was to study whether information process had significant effect on pilot technology or not [6]. Researchers began to study the ability of a pilot to process information as well as to monitor the aircraft. Sumwalt R. L., Thomas R. J., Dismukes K. studied flight monitoring. It was pointed out that altitude deviation, course deviation, required velocity deviation, flight terrain control deviation, damage or shutdown of aircraft equipment system, intrusion, stall or warning out of control, deviation from runway or taxiway would affect pilots’ flight technology [7]. Fleishman E. A. pointed out that information input, information processing and information output had a significant impact on flight technology, summarized necessary skills and tasks of a pilot and built a model of the decision-making concept that must be focused on [8]. In 1981, the first crew recourse management (CRM) (a set of training procedures) was applied by United Airlines to improve the effectiveness of cooperation and management of the crews. These training procedures were designed to correct human errors, such as the assertive behaviors of a dictatorial captain [6]. Research at that time believed that the CRM was not to train individuals but to train the entire crew and teach them how to communicate [7]. At present, researchers and the aviation industry generally believe that while paying attention to the technical knowledge and control skills of pilots, the training of crew resource management should be strengthened so as to enhance the working skills of crew. Byrnes R. E., Black R. proposed that team building, concise strategy, situational awareness and stress management are important factors affecting flight technology in the research phase of unit resource management [9]. Du Hongbing and Deng Lijuan pointed out that in order to improve flight technology, attention must be paid to the cooperation and communication of pilots, situational awareness, threat, error management and decision-making, and workload management [10]. In addition to the research on pilots’ flight technology in the above-mentioned documents, the laws and regulations of the Civil Aviation Administration have put forward relevant requirements for pilots’ flight technology in all aspects of flight activities.

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The ICAO International Civil Aviation Convention Annex 1 Personnel License states that pilots should use good judgment and skilled knowledge, skills and attitudes to achieve flight objectives in the course of flight activities [11]. An airline pilot can operate the aircraft manually smoothly and accurately in all stages of the flight and within the limits of the aircraft, can operate the aircraft in automation mode to maintain the awareness of automation mode, can accurately complete normal and abnormal emergency procedures, can use good judgment and flight technology, including orderly decision-making and alert to events, and effective communication with other crew members, including the assignment of pilot tasks, crew cooperation, standard operating procedures. At the same time, it is pointed out in Unit Resource Management Training that the overview of Unit Resource Management, Threat and Error Management, Culture, Standard Operating Procedures and Unit Resource Management, Personal Factors Affecting Team Performance, Unit Communication, Situational Awareness, Workload Management, Flight Decision-making, Leadership and Cooperation, Automation Management are all the training contents of Airline Flight Pilots [12]. Through literature research and analysis of relevant regulations, we get the elements of civil aviation pilots’ flight technology, which are detailed in Table 1. They mainly include pitch control, balance control, complex weather control, complex terrain control, stall control, information acquisition, information processing, information execution, Handbook execution, monitoring and cooperation ability, emergency awareness ability, communication ability, workload management ability, leadership and cooperation ability, situational awareness, automation management. Table 1 Compositional elements of the pilot technology Variables

Compositional elements

Variables

Compositional elements

Variables

Compositional elements

X1

Pitch control

X7

Information processing

X13

Workload management ability

X2

Balance control

X8

Information execution

X14

Leadership and cooperation ability

X3

Complex weather control

X9

Handbook execution

X15

Situational awareness

X4

Complex terrain control

X10

Monitoring and cooperation ability

X16

Automation management

X5

Altitude control

X11

Emergency awareness ability

X6

Information acquisition

X12

Communication ability

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3 Methodology A questionnaire was used in this study. The data collected from the questionnaire together with the factor analysis approach are used to investigate the expertly modified compositional elements of the pilot technology, so as to verify the rationality and scientificity of compositional elements from a quantitative calculation perspective.

3.1 Compilation of Questionnaire We compile the questionnaire based on the previous collected compositional elements of the pilot technology. The Likert7 point scale is used to design the questionnaire, in which there are seven options representing: 1 strongly disagree, 2 disagree, 3 weakly disagree, 4 uncertain, 5 weakly agree, 6 agree and 7 strongly agree. The questionnaire consists of three parts. The first part is a cover letter written to introduce the objective, value and content of our research. The second part is an instruction telling the respondents how to correctly fill out the questionnaire and explaining some special issues. The third part is questions and answers, which is the principal part of this questionnaire.

3.2 Sample Statistics In this research, a total of 200 questionnaires were distributed to pilots and managers from Shenyang branch of China Southern Airlines, Xiamen Airlines, Chengdu Airlines, Qingdao Airlines and Kunming Airlines, and of the collected questionnaires, 167 were valid, with the rate reaching to 83.5%, which meets the requirement of the sampling statistics. The statistical analysis of the sample information in the collected questionnaires is made to ensure the uniformity and generality of our research as well as to ensure that the samples meet the normal distribution. This analysis takes into account age, education, work experience and duty. Only male is optional for gender because of the particularity of the job of pilot. Please see Table 2 for specific statistical information.

4 Processing the Questionnaire Data 4.1 Analysis of Reliability and Validity The questions were randomly distributed with questionnaires, make sure that the collected data are valid and, therefore, avoid system errors. First of all, the reliability

268 Table 2 Distribution of the sample information

P. Zeng et al. Items

Category

Percentage

Age

50 Education

3

College degree and below

37

Bachelor degree

58

Master’s degree and above Work experience

Duty

Table 3 Result of the reliability analysis

5

15 years

20

Copilot

35

Pilot

42

Instructor

12

Airline manager

11

Reliability coefficient Cronbach Alpha = 0.8475

Number of questions = 16

of the data is analyzed. The coefficient of Cronbach Alpha is used to represent the degree of reliability, and the software SPSS20.0 is used to make the reliability analysis of 20 questions. The result shows that the value of Cronbach Alpha is 0.8475, which proves that the questionnaire is reliable, as shown in Table 3.

4.2 Analysis of Exploratory Factors of the Questionnaire It is necessary to make KMO (Kaiser-Meyer-Olkin) and Bartlett sphericity test for the 16 compositional elements before making the factor analysis of the data. It is generally accepted that if the KMO measure is larger than 0.7 and if it is closer to 1, then the partial correlation of the variables is stronger and the factor analysis will be better. The Bartlett sphericity test is used to determine weather the correlation matrix is a unit matrix or not. As can be seen from the Bartlett test, the significance level is smaller than 0.05. So the hypothesis—variables are independent of each other—is not invalid. In other words, the variables are strongly correlated. For our questionnaire, the KMO value is 0.760 and the statistic of the Bartlett sphericity test χ 2 is 1674.528, reaching the significance level of 0.001, as shown in Table 4. Therefore, it is reasonable to make the factor analysis.

Investigation of Pilot Flight Technology … Table 4 KMO and Bartlett sphericity test (16 elements)

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KMO measure of sampling adequacy Bartlett’s test of sphericity Sig

χ2

0.760 1674.528 0.000

Varimax rotation is used to make the analysis. The results show that the cumulative sum of the eigenvalues of the first five factor variables accounts for 86.131%. In other words, the contribution rate of the cumulative variances for the five factors extracted out of the 20 elements is 86.131%, which indicates that the questionnaire is of good construct validity. After the rotation, the variance contribution rates of the five factors are changed and become closer to each other. As a result, the variable information contents are reallocated, but the contribution rate is still 86.131%, as shown in Table 5. To rotate the factors is to make a mathematical transformation, after which, the factors are clearly distinguished and have specific meanings. In the new coordinates, the factor loadings are reallocated, which facilitate us to name and explain the factors. From the rotation results we see that the variables are divided into four groups: Fac1, Fac2, Fac3, Fac4, and the factor loading of each variable is greater than 0.7, which indicates that the factor can reflect 70% of the information, as shown in Table 6.

4.3 Naming the Factors The group Fac1 includes variables X1, X2, X3, X4 and X5, which are related to operationality and stability of the flight. So, Fac1 is named as the factor of flight control. The group Fac2 includes variables X6, X7 and X8, which are related to decisionmaking on information. So Fac2 is named as the factor of decision-making on information. The group Fac3 includes variables X9, X10 and X11, which are related to fight monitoring. So Fac3 is named as the factor of fight monitoring. The group Fac4 includes variables X12, X13, X14, X15 and X16, which are related to CRM. So Fac4 is named as the factor of CRM.

5 Conclusions From the perspective of different development stages of the pilot technology, with consideration of both relevant researches and regulations, this paper has worked out the compositional elements of the pilot technology, which are: pitch control, balance control, complex weather control, complex terrain control, stall control, information acquisition, information processing, information execution, Handbook execution, monitoring and cooperation ability, emergency awareness ability, communication

4.725

3.257

2.516

2.005

1.278

0.615

0.471

0.319

0.248

0.182

0.106

0.085

0.068

0.051

0.042

0.032

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0.200

0.263

0.319

0.425

0.531

0.663

1.138

1.550

1.994

2.943

3.843

7.988

12.531

15.725

20.356

29.531

100.000

99.800

99.537

99.218

98.793

98.262

97.599

96.461

94.911

92.917

89.974

86.131

78.143

65.612

49.887

29.531

1.278

2.005

2.516

3.257

4.725

7.988

12.531

15.725

20.356

29.531

86.131

78.143

65.612

49.887

29.531

Sum (%)

Total

Variance (%)

Extraction of sum of squares input Sum (%)

Total

Variance (%)

Initial Eigenvalues

1

Components

Table 5 Accumulative explanation variable coefficient

1.292

1.396

2.073

3.834

5.186

Total

8.075

8.725

12.956

23.962

32.413

Variance (%)

86.131

78.056

69.331

56.375

32.413

Sum (%)

Rotation of sum of squares input

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Table 6 Factor loading matrix after rotation Item

Components Fac1

X1 pitch control

Fac2

Fac3

0.816

X2 balance control

0.763

X3 complex weather control

0.825

X4 Complex terrain control

0.831

X5 altitude control

0.784

X6 information acquisition

0.861

X7 information processing

0.793

X8 information execution

0.742

X9 Handbook execution

0.758

X10 monitoring and cooperation ability

0.819

X11 emergency awareness ability

0.806

X12 communication ability

Fac4

0.827

X13 workload management ability

0.809

X14 Leadership and cooperation ability

0.794

X15 situational awareness

0.781

X16 automation management

0.804

and communication ability, workload management ability, leadership and cooperation ability, situational awareness, automation management. The exploratory factor analysis, a statistical approach, is used to investigate the data collected from the questionnaire of the compositional elements of the pilot technology, and four dimensions of flight controls, decision-making on information, flight monitoring and CRM. Acknowledgements Supported by the National Natural Science Foundation of China (Grant No. U1733119); Basic Scientific Research Projects in Universities (Grant No. 3122017018); Basic Scientific Research Projects in Universities (Grant No. 3122017015); Basic Scientific Research Projects in Universities (Grant No. 3122015D008).

References 1. Mu, H.: Enhancing monitoring skill for flight crew to ensure flight safety. China Saf. Sci. J. (2003) 2. Smode, A.F., Hall, E.R., Meyer, D.E.: An assessment of research relevant to pilot training (vol. II). Tech. Rep. No. AMRL-TR-66-196. Aerospace Medical Research Laboratory, Wright Patterson Air Force Base, OH (1966) 3. Blake, R.R., Mouton, J.S.: The new managerial grid: strategic new insights into a proven system for increasing organization productivity and individual effectiveness, plus a revealing

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4. 5. 6. 7.

8. 9. 10. 11. 12.

P. Zeng et al. examination of how your managerial style can affect your mental and physical health. Gulf Pub. Co. (1964) Orlady, H.W, Foushee, H.C.: Cockpit resource management training. In: Cockpit Resource Management Training Workshop (1987) Hunter, P.A.: Flight measurements of the flying qualities of five light airplanes (1948) Barber, M.R., Jones, C.K., Sisk, T.R., et al.: An evaluation of the handling qualities of seven general aviation aircraft. National Aeronautics and Space Administration (1966) Sumwalt, R.L., Thomas, R.J., Dismukes, K.: Enhancing flight-crew monitoring skills can increase flight safety. In: Annual International Air Safety Seminar. Flight Safety Foundation (1998, 2002), vol. 55, pp. 175–206 Fleishman, E.A.: Performance assessment based on an empirically derived task taxonomy. Hum. Factors J. Hum. Factors Ergon. Soc. 9(4), 349–366 (1967) Byrnes, R.E., Black, R.: Developing and implementing CRM programs: The Delta experience. Cockpit Resour. Manag., 421–443 (1993) Hongbing, Du, Lijuan, Deng: Research on evaluation model of CRM training effectiveness. J. Civ. Aviat. Flight Univ. China 5, 17–20 (2014) Annex, I.: 1-Personnel Licensing. ICAO, Montreal (2006) Civil Aviation Administration of China. Crew resource management training. Beijing, Department of Flight Standard, Civil Aviation Administration of China (2011)

Study on Crack Propagation of Rivet Stiffened Plate Containing MSD Structure in Corrosive Environment Yuan Zhao and Jinfang Zhao

Abstract Rivet stiffened plate containing MSD (Multiple-Site Damage) structure is very common problems in engineering. The test specimen is aluminum alloy rivet stiffened plate containing multiple hole-edge cracks in this paper. Crack propagation tests were carried out in laboratory air and 3.5% NaCl solution. Comparing the crack propagation in non-corrosive environment with the one in corrosive environment, the paper studied the interference effect between the MSD cracks in two environments. The test result shows that the crack propagation rate of rivet stiffened plate containing multiple hole-edge cracks in corrosive environment is much faster than the one in non-corrosive environment. This phenomenon is especially obvious in the later stage of the crack propagation. Keywords Multiple-site damage · Rivet stiffened plate · Corrosive environment · Crack propagation

1 Introduction Multiple-Site Damage (MSD) is a typical problem in aging aircraft structures. It often occurs in the overlap panel (shell) structure such as wing panel, aircraft skin and so on. Interaction between cracks in MSD structure will aggravate crack propagation and crack coalescence, resulting in the reduction of structural residual strength, which will pose a great threat to the structural safety of the aircraft. Therefore, MSD problem has attracted widespread attention from academia and engineering circles in recent years [1–4]. As an air transport tool, aircraft needs to work in various external environments and corrosion is inevitable. There will be a certain gap between the aircraft skin and rivet head around the rivet, the invasion of moisture and dirt will lead to the cracking or peeling of the paint layer and come to be a corrosion source. This is a typical case where corrosion occurs simultaneously with MSD structure. At present, the Y. Zhao · J. Zhao (B) College of Mechanical and Vehicle Engineering, Shenyang Institute of Technology, Fushun 113122, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_26

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influence of MSD on structural strength in corrosive environment is not very clear, so the problem needs to be solved urgently [5–7]. In this paper, crack propagation tests of riveted stiffened aluminium alloy plates with MSD structure were carried out in laboratory air and 3.5% NaCl solution respectively. Through the analysis of test data, the crack propagation law of MSD structure in two environments is studied.

2 Test Process 2.1 Specimen The material of the specimens plate is 2024-T62 aluminum alloy, the thickness is 2 mm, the tensile strength σ b = 455 MPa, the yield strength σ p0.2 = 414 MPa, the elastic modulus E = 71.4 GPa. The material of the angle stringer is TC4 aluminum alloy, the elastic modulus E = 73 GPa. Typical riveted panel structure (stiffened plate with three symmetry hole-edge crack structure) is chosen as the test specimen. The central hole of the panel have 2 mm length prefabricated incisions on both sides, and the other holes have 1 mm length prefabricated incisions on both sides. The structure and the specific dimensions of the specimen are shown in Fig. 1. Fig. 1 Structure and concrete measurement of test specimen

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Four specimens were selected for the test, including pre-corrosion, fatigue initiation and crack propagation tests. Two specimens were tested in laboratory air and other two specimens were tested in 3.5% NaCl solution. The grouping of the specimens is shown in Table 1.

2.2 Test Scheme MTS-500kN fatigue testing machine was used to carry out the fatigue crack initiation test and crack propagation test. The loading level in the test is shown in Table 2. Make sure the static load error is less than 1% and the dynamic load error is less than 3%. The specimens were clamped by special fixture and the test data were recorded by wide-range microscope. Notice that the test carried out in 3.5% NaCl solution must use corrosion circulating device and leak-proof tray. The test steps are as follows: (1) Fix the specimen, for specimens in corrosive environment, corrosion cycle and protection devices should be fixed. (2) Fatigue initiation test was carried out according to the load level in Table 2. The crack initiation at the hole edge is observed every 5000 times. When the average length of crack initiation at the edge of the central hole is about 2 mm and the average length of crack initiation at the edge of the other holes is about 1 mm, the crack propagation test will be carried out. (3) Crack propagation tests were carried out according to the load level in Table 2. When the average crack propagation was about 0.5 mm, the crack propagation data of the hole edge were recorded by a wide-range microscope. (4) The test is stopped until the crack is close to coalescence, i.e. when the distance between the crack tips is 4–8 mm.

Table 1 grouping of the specimens

Table 2 Loading level in the test

Specimen number

Test environment

SYK-1 SYK-2

Laboratory air

SYF-1 SYF-2

3.5% NaCl solution

Specimen number

Test environment

Fatigue crack initiation

F max = 46kN; σ max = 70 MPa

Fatigue crack propagation

F max = 40kN; σ max = 60.6 MPa

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3 Test Results Ignoring the cyclic loading number of fatigue crack initiation, the a-N curve (crack propagation curve) of specimens in laboratory air and NaCl solution are obtained, shown in Figs. 2, 3, 4 and 5. N is the cyclic loading number of fatigue crack propagation. a is the crack length, which is the distance from crack tip to hole edge. The hole number is 1–3 from left to right. For the specimens in laboratory air (SYK-1 and SYK-2), when the cyclic loading number goes to 67,850 and 68,000 times, the cracks near the hole edge are close to coalescence. For the specimens in NaCl solution (SYF-1 and SYF-2), when the cyclic loading number goes to 51,700 and 49,700 times, the cracks near the hole edge are close to coalescence. The following conclusions can be obtained from the test results: (1) According to Figs. 2, 3, 4 and 5, in the initial stage of crack propagation, there is little difference between non-corrosive environment and corrosive environment. In the later stage of crack propagation, the crack propagation speed in corrosive environment is accelerated. In the stage of near-coalescence of cracks, the cyclic loading number in corrosive environment is obviously less than that in noncorrosive environment, and the difference between them is about 17,000 times. It shows that corrosion environment accelerates the crack propagation of MSD cracks. (2) According to Figs. 2 and 3, for the two specimens in non-corrosive environment, the four cracks of Hole 1 and 3 and the two cracks of Hole 2 have almost the same crack propagation characteristics at the initial stage of crack propagation.

Fig. 2 Crack propagation data of SYK-1

Study on Crack Propagation of Rivet Stiffened Plate …

Fig. 3 Crack propagation data of SYK-2

Fig. 4 Crack propagation data of SYF-1

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Fig. 5 Crack propagation data of SYF-2

At this time, the main influence of crack propagation comes from the initiation hole itself. The same initiation hole structure and crack distribution lead to this phenomenon. As the main crack, Hole 2 has a longer prefabricated notch, the difference between the two cracks in Hole 2 and the other four cracks is reflected in the initial stage of crack propagation. For the two specimens in corrosive environment, the same conclusion can be obtained, as shown in Figs. 4 and 5. (3) According to Figs. 2 and 3, for the two specimens in non-corrosive environment, the six cracks show differences characteristics with the crack propagation. The crack propagation rate of the two sides of Hole 2 is faster than that of the other side cracks. Because at this stage, the effect of crack propagation comes not only from the initiation hole, but also from other holes and the boundary of the finite plate. The specific sources and sizes of the crack propagation are different, and it is obvious that the cracks on both sides of hole 2 are the most affected. For the two specimens in corrosive environment, the same conclusion can be obtained, as shown in Figs. 4 and 5. (4) According to Figs. 2, 3, 4 and 5, whether the specimens is in non-corrosive environment or in corrosive environment, the effect of adjacent holes (or finite plate boundary) on cracks increases with the crack propagation. When this effect becomes leading factor, the crack propagation rate at the edge of the hole is obviously accelerated. When the crack extends to a certain extent, the coalescence between cracks will occur, resulting in structural failure.

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4 Conclusion In this paper, crack propagation tests of riveted stiffened aluminium alloy plates with MSD structure were carried out in laboratory air and 3.5% NaCl solution respectively. By comparing the crack propagation process of MSD cracks in two experimental environments, it can be seen that the corrosion environment accelerates the crack propagation of MSD structure, especially in the later stage of crack propagation. Through the analysis of the crack propagation of MSD crack in the same experimental environment, it can be seen that the stress concentration of the hole itself is one of the factors affecting the crack propagation and fatigue life of MSD structure. This factor mainly affects the initial stage of the crack propagation at the edge of the hole. It is not the unique characteristic of MSD crack, but the common characteristic of any crack at the edge of the hole. The interference between cracks is another factor affecting the crack propagation and fatigue life of MSD structure. The factors of propagation and fatigue life mainly affect the middle and late stage of the hole edge crack propagation, which can truly reflect the characteristics of MSD crack. When the hole edge crack and adjacent crack (or boundary) begin to interfere seriously, it will cause structural failure and will lead to extremely dangerous consequences. Acknowledgements Financial support from Liaoning Province Doctoral Research Initiation Fund Guidance Project (20170520125) is gratefully acknowledged for this investigation.

References 1. Schijve, J.: Fatigue of aircraft materials and structures. J. Int J Fatigue, 21–32 (1994) 2. Goranson, U.G.: Elements of structural integrity assurance. J. Int J Fatigue, 43–65 (1994) 3. Yu, D., Chen, Y., Yu, Z., Duan, C.: Finite element analysis of SIF of flat MSD panels with a number of collinear holes. J. Nav. Aeronaut. Eng. Inst., 561–565 (2006) 4. Zhao, J., Zhao, Q.: Testing research and analysis on fatigue life of MSD structure. J. Modul. Mach. Tool Autom. Manuf. Tech., 42–44 (2015) 5. Labeas, G.: Assessment of widespread fatigue damage in the presence of corrosive mechanics. J. Autom. Control Robot., 689–706 (2003) 6. Zambe, J.E., Hillberry, B.: Probabilistic approach to predicting fatigue lives of corroded 2024T3. J. AIAA J., 1311–1317 (1999) 7. Pantelakis, S.P., Vassilas, N.: Effects of corrosive environment on the mechanical behavior of the advanced Al-Li alloys 2091 and 8090 and the conventional aerospace alloy 2024. J. Metall., 135–141 (1993)

H ∞ Phase Control for Flexible Systems Junfeng Yang, Muzhou Yu, Yanjie Niu, Wenjie Zhang and Fanwei Meng

Abstract A new weighted H ∞ optimization method is proposed to design a robust controller for the flexible system, it solves the problem that the controller is unstable and poor robustness which using H ∞ loop shaping method design. The idea of phase control is realized by the configuration of the closed-loop poles which corresponding to the flexible modes, and the closed-loop poles of the high-frequency parts are allowed to differ from the expected poles and weakening the strict positive real constraints. Combined with the phase control and H ∞ optimization, the desired closed-loop poles can be realized by the controller. The new method has the advantage of flexibility, and a clear physical meaning in the design process. The feasibility of the proposed method is verified by two simulation examples. Keywords Flexible systems · Phase control · H ∞ optimization · Robustness · Local positivity

J. Yang (B) · M. Yu · W. Zhang · F. Meng School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei, China e-mail: [email protected] M. Yu e-mail: [email protected] W. Zhang e-mail: [email protected] F. Meng e-mail: [email protected] Y. Niu PLA Navy 92012 Troops, Zhoushan, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_27

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1 Introduction The system with flexible structure is widely used in automatic control. From large spacecraft to small read-write heads in computer hard drives, they are flexible. For example, satellites with large space truss structure [1], spacecraft with solar panels or antennas [2, 3] bearings with magnetic levitation structure [4], drive arms with read and write heads in hard disk [5, 6], and flexible manipulators for space capture or industrial production [7] are all flexible systems. The control design of flexible systems needs to solve robust stability problems including parameter perturbation and unmodeled dynamics. McFarlane first proposed the H ∞ loop shaping method based on coprime decomposition, and wrote literature [8], which became the classic work of H ∞ loop shaping method. Two of McFarlane’s last three examples in document [8] are flexible systems. Therefore, the H ∞ loop shaping method is often used in the design of flexible systems nowadays, and it has been widely used in practical systems [9]. The description of uncertainty in H ∞ loop shaping method is based on the mutual prime factor perturbation. When introducing the perturbation of reciprocal factors in common literature, the advantages of this kind of perturbation are generally illustrated by one or two simple flexible examples of lower order, with particular emphasis on perturbations that can be used to describe weakly damped modes [10, 11]. From the relevant literature, no further discussion has been made on the interaction factor perturbation, which has been accepted as the basis of H ∞ loop shaping method. However, in recent years, with the improvement of control technology requirements, the flexible system gradually embodies the weak damping characteristics. From the perspective of frequency characteristics, the weak damping characteristics refer to that the open-loop transfer function of the controlled object traverses the 0 dB line many times, that is to say, the Nyquist curve of the open-loop object surrounds the critical stability point more complex. In reference [12], the H ∞ loop shaping design of weakly damped flexible systems is studied. It is pointed out that weakly damped systems increase the perturbation norm of reciprocal factors, thus greatly reducing the allowable actual perturbation range of systems. It is also pointed out that the H ∞ loop shaping design system does not necessarily have robustness. For this reason, the paper [13] proposes to combine H ∞ loop shaping and Mu synthesis to solve the robust design problem under parameter perturbation. In reference [14], an example shows that the combination of the two methods has not achieved the desired results. The addition of Mu synthesis in the design of circuit forming only affects the value of stability margin, and does not improve the permissible range of perturbation. Therefore, weak damping is the difficulty in the design of flexible systems using H ∞ . Reference [15] gives a comprehensive analysis of H ∞ loop shaping method combined with flexible system, and gives a new understanding of H ∞ norm, performance and robustness in H ∞ loop shaping design. When the weakly damped flexible system is designed by H ∞ loop shaping method, besides the robustness difference mentioned above, there is also the problem of unstable controller. H ∞ control design is mainly about the structure problem and

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the selection of weight function. Its structural problems include two-block, fourblock and mu-synthesis. However, no matter what the structure is, an unstable H ∞ controller [4, 8, 13, 15] will be generated for a weakly damped flexible system. This means that the closed-loop system is stable, but the H ∞ controller designed is unstable. There are relatively few studies on unstable controllers. In fact, the input of unstable controllers is very difficult [4]. As shown in Formula (1) of the H ∞ controller in reference [15], the high frequency components are omitted. The H ∞ controller shown in Formula (1) is an unstable controller. K ∞ (s) =

2.2713(s 2 + 0.2795s + 0.04545)(s 2 + 0.1797s + 1.041) (s + 4.417)(s + 0.4048)(s 2 − 0.08855s + 0.1365)

(1)

In this paper, the unstable controllers and poor robustness of the above flexible systems using H ∞ are studied. See Sect. 3 for the principle of the method used.

2 Mathematical Model of Flexible System The mathematical model of a flexible system can be expressed by the infinite dimensional transfer function shown in Eq. (2) [16]. ∞  i=0

ci s 2 + 2ζi ωi s + ωi2

(2)

where, the first corresponding term in Eq. (2) is the rigid body model, followed by the flexible modes of each order. Generally speaking, the amplitude of flexible modes with low frequency is larger, so the previous modes are often used to approximate a flexible system in control design. In this paper, the flexible arm model in reference [17] is studied. Its transfer function is shown in Eq. (3). G(s) =

3 3 2.5527 1.26 + 2 + 2 (3) − 2 2 s s + 0.713s + 27.9 s + 0.4s + 100 s + 0.8s + 400

The corresponding Bode diagram is shown in Fig. 1. As can be seen from Formula (3) and Fig. 1, the flexible arm has a weak damping mode with ζ = 0.02. Although the modes in the transfer function are additive, they do not overlap in frequency characteristics and can be clearly distinguished in Fig. 1. This frequency characteristic provides a new design idea for robust control of flexible systems, that is, multiple flexible modes can be designed separately.

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Fig. 1 Bode plot of controlled plant

3 Phase Control Principle The uncertainties considered in H ∞ design are norm-bounded transfer functions, so the corresponding method is small gain method. H ∞ robust control is mostly studied in this direction. Therefore, the importance of phase information in the system is neglected. In the design of circuit forming, the Nyquist diagram is never concerned when drawing Bode diagram only considering the amplitude-frequency characteristics. Drawing the open-loop Nyquist diagram of McFarlane method with reference to reference [15], it will be found that the unstable controller ensures the closed-loop stability of the system by winding (−1, j0) counter-clockwise. When the resonant frequency is slightly perturbed, the circle surrounding (−1, j0) will move up or down until it is not surrounded, which makes the closed-loop system unstable. Therefore, the robust of the weakly damped flexible system using H ∞ loop shaping method of McFarlane is poor and the permissible parameter perturbation range is small. The phase control in this paper is the H ∞ design research aiming at changing the phase frequency characteristics of the system. Phase control is a new design idea for flexible systems in recent years. Taking a system with a flexible mode as an example, in the Bode diagram of the system, the amplitude-frequency characteristics of the flexible system change dramatically due to the existence of weak damping, and can cross the 0 dB line many times, as shown in Fig. 1. Reflected on the Nyquist curve, the weak damping mode is a large circle. When the parameters are perturbed, it is easy to change the circumference of point

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(−1, j0) of a large circle. Phase control requires that the vertices of the Nyquist curve corresponding to the weakly damped modes all fall on the positive real axis, so the system with parameter perturbation has better robustness [18]. Its principle is shown in Fig. 2, which is called strict positive real design [5]. The simplicity and effectiveness of the control idea have been well used in hard disk storage system [5]. The idea of phase control is essentially consistent with the idea of early positive position feedback control (design of positive position filter). This design idea is embodied in document [19], which combines this phase control idea with H ∞ design. However, the positive and real requirements shown in Fig. 2 are too conservative for

Fig. 2 Bode and Nyquist plot when strict positive

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Fig. 3 Nyquist plot when local positive

the stability requirements of the system, and the H design requirements used need rich H ∞ design experience, and the designed controller has a high order. Therefore, this requirement is relaxed in the design, as long as the vertex of the Nyquist line of the weakly damped mode (see the location of * in Fig. 3) is located in the right half plane. The vertex of the circle corresponding to the weak damping in Fig. 3 is in the right half plane, but not on the positive real axis. Even if the parameters (ζi , ωi ) of the model are changed, the open-loop characteristic will not cross the critical point and cause instability (see Fig. 5). We call it local positive real design. In this paper, the Nyquist diagram is shown in Fig. 3 by pole placement and H ∞ weighted optimization design. Compared with reference [19], the H ∞ weighted optimization design method here is more direct and systematic, with clear physical concepts and low order controllers.

4 H ∞ Weighted Optimal Design Method Assuming that the transfer function of the object is G(s) = n g (s)/dg (s), the general order of dg (s) is higher than that of n g (s). Represent G(s) with a coprime factor. G(s) =

N g (s) n g (s)/d f (s) = Dg (s) dg (s)/d f (s)

(4)

where, N g (s) and Dg (s) are stable rational functions, polynomial d f (s) is related to the characteristic equation of the system, and the coefficient of the first term s n

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is 1 [12]. Notice here that rational functions are represented by capital letters and polynomials by lowercase letters. Similarly, controller K (s) can also be written as a representation of coprime decomposition K (s) =

n k (s)/dc (s) Nk (s) = Dk (s) dk (s)/dc (s)

(5)

where, the coefficient of the first term s n of dc (s) is 1, and dc (s) is also related to the characteristic equation of the system. According to G(s) and K (s), the closed-loop transfer function T (s) is T (s) =

N g (s)Nk (s) Dg (s)Dk (s) + N g (s)Nk (s)

(6)

Let P(s) represent the denominator part of T (s) P(s) = Dg (s)Dk (s) + N g (s)Nk (s) =

dg (s)dk (s) + n g (s)n k (s) d f (s)dc (s)

(7)

In Eq. (7), the molecular polynomial is the closed-loop characteristic equation of the system, and denominator d f (s)dc (s) is introduced in the coprime decomposition, representing the desired characteristic equation. If P(s) = 1 can be guaranteed in the design, the characteristic equation of the closed-loop system can be equal to the expected d f (s)dc (s). If the expected poles are specified in Eq. (7), then the controller K (s) = n k (s)/dk (s) can be solved according to the requirement of P(s) = 1, but it is impossible to achieve P( jω) ≈ 1 in the whole frequency band. So the weighted method is used to solve the following H ∞ optimization problems. minW (s)(1 − P(s))∞ K (s)

(8)

where, W (s) is a weight function and has low-pass property. In this case, it can be taken as W (s) =

1 (10s + 1)2

(9)

Under this weight function, the optimization problem of Formula (8) can be solved in the frequency band of the dominant pole so that P( jω) → 1. That is to say, the dominant poles corresponding to the low-order modes are consistent with the expected values, while the closed-loop poles corresponding to the high-frequency flexible modes are different from the expected values. This design is more flexible than the general pole configuration. In the strict positive real design shown in Fig. 2, the positive real lemma [19] is used. In the local positive real design of this paper, the optimization problem of

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Formula (8) can be solved by the bounded real lemma in H ∞ control theory. The set W (s)(1 − P(s)) state space is implemented as [Awp , Bwp , Cwp , 0]. Then bounded real lemma explains, the important condition of W (s)(1 − P(s))∞ ≤ γ is the existence of X = X T > 0 to make the following matrix inequalities valid, which is proved by lemma 5.3 in reference [20]. That is to say, ⎡

⎤ T ATwp X + X Awp X Bwp Cwp ⎢ ⎥ T Bwp X −γ I 0 ⎦ < 0 ⎣ Cwp 0 γ

(10)

Formula (10) is a linear matrix inequality. Because by expanding the state space implementation of W (s)(1 − P(s)), we can see that the coefficients of controller n k (s) and dk (s) only appear in matrix Cwp and are linear. min γ K (s)

(11)

The optimal solution of Formulas (10) and (11) can be solved by existing functions in MATLAB. The above design idea is mainly aimed at the flexible modes with weak damping, requiring that the poles corresponding to the closed-loop are located in the left halfplane and have a certain damping ratio. The use of weighted H ∞ optimization can relax some restrictions on the design of high-frequency poles, so it is convenient for design. In addition to the flexible mode, the other pole assignment principle of closedloop system is to make the Nyquist curve phase lag as far as possible after crossing the 0 dB line, that is, after entering the unit circle, so that it can be transferred to the right half plane as soon as possible, so that the local positive real problem mentioned above can be solved. Firstly, the expected pole, the root of d f (s)dc (s) = 0, is determined. Where d f (s) denotes the closed loop poles formed by feedback of the poles of the controlled object. Formula (3) the first term is double integral, which forms the dominant pole of the system after closed-loop. The remaining three flexible modes affect the stability of the system, so the damping ratio of the dominant pole is (s + 1)2 . The remaining three modes of the controlled object are weakly damped, and the corresponding poles are located near the imaginary axis, so they can not enter the right half plane after closed-loop. According to the common knowledge of feedback design, if they are pulled to the far left, the control input will be too large. To sum up, choose d f (s) as follows: dc (s) = (s 2 + 9s + 36)(s + 2.5)

(12)

It can be seen from Formulas (12) and (3) that the closed-loop poles increase the damping ratio. In Formula (7), dc (s) is the closed-loop pole brought by the controller, and the order of dc (s) is determined by the controller. By summing up the general components

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of Eq. (3), it is found that there is a pair of non-minimum phase zeros (s 2 − 7.932s + 36.54) in the object. Non-minimum phase zeros are helpful to the positive real design, because non-minimum phase can delay the phase angle and facilitate the Nyquist curve to enter the right half plane. Zero (s 2 + 9.038s + 36.64) in Formula (3) is disadvantageous to positive and real design, and can be cancelled by the poles of the controller. Stable zero-pole cancellation does not affect the performance of the system. Whether it is strict cancellation or approximate cancellation, there will be poles close to (s 2 +9.038s +36.64) in the closed-loop system, so dc (s) can be chosen as dc (s) = (s 2 + 9s + 36)(s + 2.5)

(13)

where, (s + 2.5) in formula is also set in order to lag the phase angle of Nyquist line. From this formula, it is also known that the designed controller is of third order. After determining d f (s) and dc (s), (10) and (9) optimization problems can be solved. The obtained controller is K (s) =

3.7145(s + 0.3753)(s 2 + 0.6289s + 46.39) (s + 5.652)(s 2 + 8.821s + 36.17)

(14)

It can be seen from (14) that the controller is stable. It is shown that the design solves the problem of instability controller in back-to-back forming design.

5 Performance Indicators of Control Systems The performance of control system should be expressed by sensitivity function. There is a feedback system shown in Fig. 4, in which K is the controller and G is the control object. If the closed-loop transfer function of the system is T, then T =

KG 1 + KG

(15)

Define the sensitivity S of the system as e

r

+

-

Fig. 4 Feedback control system

K

u

G

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dT T d ln T S= = d ln G dG G

(16)

Formula (16) shows that the sensitivity of the system quantitatively represents the sensitivity of closed-loop T to the change of object parameters. If the sensitivity of the system is low, it shows that the design is robust to modeling errors. If G is taken as a variable and T is taken as its function, the sensitivity expression can be obtained by deriving Formula (15) and substituting Formula (16). S=

1 GdT = T dG 1 + KG

(17)

In addition to the robustness expressed in Eq. (17), the sensitivity function also reflects other important characteristics of the system. Figure 5 shows the Nyquist line K (s)G(s) of a system. P in graph shows the minimum distance between KG and point −1. According to the geometric relationship in the graph, it can be seen that p = min|1 + K G|

(18)

If the maximum peak value of sensitivity is expressed in M s , then there is Ms = max|S( jω)| =

1 p

(19)

The larger M s is, the closer the open-loop characteristic distance is to −1 point. At this time, if the parameters of the controlled object G are perturbed, it will easily lead to instability of the system. Therefore, the peak M s of sensitivity function is often regarded as an index of robustness of closed-loop system. The sensitivity is related to the stability margin in classical theory, as shown in Fig. 6. According to Fig. 6, the relationship between sensitivity on unit circle and phase margin γ can be written as follows. Fig. 5 Nyquist curve of system

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Fig. 6 Classification of the gas-lubricated bearing







1

= |1 + K G| = 2

sin γ



S( jω)

2

(20)

So it’s visible from the graph.

γ



p ≤ 2 sin

2

(21)

This shows that phase margin γ can only give the upper limit of p, but not the real value of M s , which represents robustness. In fact, the system with good phase margin and amplitude margin, M s may be very large without robustness, so the maximum sensitivity M s truly reflects the stability of the system, M s is the real stability margin. This peak is usually considered to be appropriate between 1.2 and 2.0 if the designed system with M s = 3, it’s hard to control. In Formula (17), the formula of S gives a method of measuring sensitivity: Fig. 7 is the system block diagram when disturbance d exists, and S is regarded as a transfer function. The transfer function from d to y is S. S means that the output is insensitive to disturbance, which is that feedback weakens the influence of disturbance, so sensitivity is also an important characteristic of feedback control system. Of course, if S > 1, the system will magnify the disturbance instead. d

+ e

r

+

K

-

Fig. 7 Restrainment of output disturbance d

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Fig. 8 Amplitude-frequency characteristic curve of sensitivity function

In Fig. 7, the transfer function from reference input r to error signal e is also equal to sensitivity, namely, E(s) 1 = =S R(s) 1 + KG

(22)

So the sensitivity also indicates the performance of tracking input signal, and the smaller the S, the smaller the tracking error. It can be seen that the sensitivity represents the performance of the system under the action of r and d, and its peak value also indicates the influence of parameter changes on the stability of the system. Therefore, the performance of feedback system is generally expressed by sensitivity function, and its sensitivity should be kept as low as possible in design. By introducing the control object G(s) (Eq. 3) and controller K(s) (Eq. 14) into the sensitivity function (Eq. 17), and combining with the simulation tool of MATLAB, we can get the amplitude-frequency characteristic curve of the sensitivity function of the system (Fig. 8). It can be seen from the figure that the control system has lower sensitivity. It can be seen that the control system has good feedback performance and robustness.

6 Simulation Analysis and Verification The transfer function of the closed-loop system consisting of the controlled object (3) and the controller (14) is

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T (s) =

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17.6124(s + 0.3753)(s 2 + 9.038s + 36.64)(s 2 − 7.932s + 36.54) (s 2 + 0.6289s + 46.39)(s 2 + 0.4288s + 223.1) (s + 2.467)(s + 1.02)(s + 0.9823)(s 2 + 8.707s + 35.24) (s 2 + 1.109s + 407.8)(s 2 + 0.8979s + 101.4)(s 2 + 1.203s + 25.43) (23)

It can be seen from Formula (23) that the closed-loop poles do not exactly coincide with expected d f (s)dc (s), and this difference is introduced by weight function W (s). This reflects the flexibility of the method proposed in this paper. Figure 9 shows the open-loop characteristics of the designed system. It can be seen from the figure that the vertices of three flexible modes corresponding to three circles are all in the right half plane, which satisfies the design requirements of local positive reality after weakening. The curve corresponding to the flexible mode in Fig. 9 does not enter the left side of M = 0 dB of the closed-loop amplitude M-circle graph. The frequency characteristics of the closed-loop transfer function can also be plotted. It can be found that the corresponding amplitudes of the flexible modes are also less than 0 dB. It also shows that the local positive real requirement is the same as the limited peak value, so the pole placement after the closed-loop of weakly damped flexible modes can be used to deal with the local positive real problem. Next, try the robustness of the closed-loop system. The damping and frequency of the controlled object are changed by 10% respectively. In Fig. 10a, the solid line corresponds to the controlled object (3), +line corresponds to the increase of 10% for each modal damping perturbation and the dotted line corresponds to the decrease

Fig. 9 Nyquist plot of the system

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(a) Damped perturbation

(b)

Frequency perturbation

Fig. 10 Nyquist plot for various parameters

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of 10% for each modal damping perturbation. It can be seen that the circular distribution of each modal in the open-loop characteristic after the perturbation remains unchanged, but only the size changes. The frequency perturbation curve is shown in Fig. 10b, which shows that the open-loop characteristic is still far from the critical stability point (−1, j0) after the perturbation. It can be seen that the design method proposed in this paper has certain robustness. Taking the satellite attitude control system with flexible structure as an example in reference [12], when using loop shaping method, the unstable controller which is difficult to put into operation is obtained, and the allowable parameter perturbation range is only 3.5%. The controller obtained by this method is a stable controller as shown in Formula (24). K 1 (s) =

230089(s + 0.3242)(s 2 + 0.1153s + 0.7518) (s + 36.14)(s 2 + 115.5s + 3575)

(24)

Compared with the simulation of Fig. 9 in reference [12], the step response curve of the system after perturbation is drawn. The results show that the system is still stable after 100% frequency perturbation. In summary, the proposed H ∞ optimal design method under pole assignment guarantees robustness and achieves a stable controller.

7 Conclusion H ∞ design has always been based on gain control. In H ∞ design, phase condition is used to ensure the stability and control performance of closed-loop system. Aiming at the problem of how to design positive-real phase control using H ∞ theory, an H ∞ optimization method of pole placement and weighting function is presented, which relaxes the strict requirement of positive-real and makes use of the advantage of non-minimum phase zero to make the design more flexible. The design results show that the controller is stable and the robustness of the closed-loop system is obviously better than that of H ∞ loop shaping method. Acknowledgements Manuscript received April 7, 2018. This work was supported in part by the Doctoral Foundation of Liaoning Province (No. 20170520333), the Fundamental Research Funds for the Central Universities(No. N182304010), the Doctoral Foundation of Hebei Province (No. F2019501012).

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References 1. Ding, S.H., Zheng, W.X.: Nonsmooth attitude stabilization of a flexible spacecraft. IEEE Trans. Aerosp. Electron. Syst. 50(2), 1163–1181 (2014) 2. Si, Z., Liu, Y.: High accuracy and high stability attitude control of a satellite with a rotating solar array. J. Astronaut. 31(12), 2697–2073 (2010) 3. Wu, Y., Li, J., Zeng, H., Duan, G.: Robust H-infinity control design for spacecrafts with large flexible netted antennas. Control Theory Appl. 30(3), 365–371 (2013) 4. Balini, H., Scherer, C.W., Witte, J.: Performance enhancement for AMB systems using unstable H∞ controller crossovers. IEEE Trans. Control Syst. Technol. 19(6), 1479–1492 (2011) 5. Cherubini, G., Chung, C.C., Messner, W.C., et al.: Control methods in data-storage systems. IEEE Trans. Control Syst. Technol. 20(2), 296–322 (2012) 6. Lu, Y.S.: Internal model control of lightly damped systems subject to periodic exogenous signals. IEEE Trans. Control Syst. Technol. 8(3), 699–704 (2010) 7. Pradhan, S.K., Subudhi, B.: Nonlinear adaptive model predictive controller for a flexible manipulator: an experimental study. IEEE Trans. Control Syst. Technol. 22(5), 1754–1768 (2014) 8. McFarlaned, D., Glover, K.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Information Sciences, 138. Springer, New York (1989) 9. Sun, X., Yang, X., Geng, Y., Yang, D.: H∞ loop-shaping attitude stabilization control fora large flexible satellite platform. Syst. Eng. Electron. 27(3), 490–493 (2005) 10. McFarlane, D.C., Glover, K.: A loop shaping design procedure using H∞ synthesis. IEEE Trans. Autom. Control 37(6), 759–769 (1992) 11. Glover, K., McFarlane, D.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Information Sciences, vol. 138. Springer, New York (1990) 12. He, Z., Meng, M., Liu, W., Wang, G.: Robustness of H∞ loop shaping design. Acta Autom. Sin. 36(6), 890–893 (2010) 13. Lanzon, A., Tsiotras, P.: A combined application of H∞ loop shaping and µ-synthesis to control high-speed flywheels. IEEE Control Syst. Technol. 13(5), 766–777 (2005) 14. He, Z., Jiang, X., Meng, F.-W., Wang, G.: µ-synthesis in H-infinity loop-shaping design. Control Theory Appl. 29(3), 347–352 (2012) 15. Meng, F.-W., He, Z., Wang, G., Zhou, D.: Control design of flexible systems and H-infinity loop-shaping method. Control Theory Appl. 30(8), 1014–1020 (2013) 16. Franklin, G.F., Powell, J.D., Abbas, E.N.: Feedback Control of Dynamic Systems (4th edn). Pearson Education, Beijing (2003) 17. Doyle, J.C., Francis, B.A., Tannenbaum, A.R.: Feedback Control Theory, 208–213. Tsinghua University Press, Beijing (1993) 18. Mahmoodi, S.N., Ahmadian, M., Inman, D.J.: Adaptive modified positive position feedback for active vibration control of structures. J. Intell. Mater. Syst. Struct. 21(4), 571–580 (2010) 19. Coustal, P., Michelin, J.M.: Industrial application of an H-infinity design method for flexible structures. IEEE Control Syst. 14(4), 49–54 (1994) 20. Guangxiong, W.A.N.G., Zhen, H.E.: Applied H∞ Control. Harbin Institute of Technology Press, Harbin (2010)

Mixed Sensitivity Design of Magnetic Suspension System Muzhou Yu, Junfeng Yang, Fanwei Meng and Yanjie Niu

Abstract When the mixed sensitivity method is applied to the system design, the model of the augmented plant is often not satisfied with the standard H∞ control problem. Because of the rank D12 assumption, the design problem cannot be solved. In order to solve this problem, the augmented model of the system is established, and the selection of a decimal number is analyzed. The principle of selecting decimals in full rank D12 design is given, and the simulation of magnetic suspension system is carried out, which shows that the wrong design results can be easily obtained if the decimals are not properly chosen. This paper also points out that the Bode integral constraint should be taken into account in the design, based on which the weight function can be selected reasonably to achieve a better performance. The analysis method given in this paper is generally applicable to controlled plants whose direct transfer coefficient matrix is equal to zero. Keywords Mixed sensitivity · Weight function · Bode integral · Magnetic suspension system

1 Introduction Whatever design method is adopted in the design of control system, it can not avoid a constraint that exists in the system itself: Bode integral constraint [1]. This constraint should be taken into account first before the design, and more attention should be paid M. Yu (B) · J. Yang · F. Meng School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei, China e-mail: [email protected] J. Yang e-mail: [email protected] F. Meng e-mail: [email protected] Y. Niu PLA Navy 92012 Troops, Zhoushan, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_28

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to this point for unstable controlled objects [2]. Therefore, the emphasis and difficulty of the design lies in choosing reasonable weight parameters or functions to make the system achieve the best performance under the consideration of Bode integral constraints [3]. The H∞ design can often be transformed into a mixed sensitivity problem. However, in solving the mixed sensitivity problem, simply selecting the weight function and taking out the state of the column after selecting the weight function can not satisfy the standard H∞ control problem about the assumed condition of rank D12 [4]. That is to say, the choice and treatment of the weight function is not only constrained by the Bode integral, but also restricted by the rank D12 . In combination with the mixed sensitivity design of the magnetic suspension system, the following is an analysis of a choice of decimals full rank method, and then select a reasonable weight function to make the system achieve better performance.

2 Description of the System Figure 1 is a schematic diagram of the magnetically levitated train model [5], the mass of suspending magnets in the diagram is m = 15 kg, the effective pole area is am = 1.024 × 10−2 m2 , the turn number of coils on electromagnet is N = 280, the coil resistance is Rm = 1.1 , the work point is z 0 = 4.0×10−3 m, and the operating point current is i 0 = 3.054 A. The linearized equation without disturbance is [6]: x˙ = Ax + Bu ⎡ ⎤ ⎡ ⎤ 0 1 0 0 =⎣ 4900 0 −6.4184 ⎦ x + ⎣ 0 ⎦u 0 763.45 −8.7228 7.9298 y = C x + D u = [ 1 0 0 ]x

(1)

Fig. 1 Model of the electromagnetic levitation system

Track

F(i,z) i(t) u(t)

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mg

z

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where x˙ = [x1 x2 x3 ]T , x1 = z is the gap between electromagnet and track, x2 = z˙ and x3 = i is the current in coil, and u is the voltage acting on the coil.

3 Mixed Sensitivity Design H∞ design can often be transformed into a mixed sensitivity problem, and its design block diagram is shown in Fig. 2. In this way, the design is transformed into constructing a controller K which can satisfy Eq. (2).    W1 S    ≤1 min K stabili zing  W3 T  ∞

(2)

where W1 (s) and W3 (s) are corresponding weight functions, S is sensitivity function, T is complementary sensitivity function. W1 (s) is usually a low-pass form in order to meet the performance requirements of low frequency sensitivity. W3 (s) is a high-pass form to restrict the high-frequency characteristics of closed-loop transfer function. Such as limit the bandwidth of the system or ensure the robust stability and so on. The specific selection requirements can be seen in the literature [7]. The transfer function W1 (s) can be expressed by state equation as follows: x˙ W 1 = AW 1 x W 1 + B W 1 y z 1 = C W 1 x W 1 + D W 1 y

(3)

The transfer function W3 (s) can be expressed by state equation as follows: x˙ W 3 = AW 3 x W 3 + B W 3 y z3 = C W 3 x W 3 + D W 3 y

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(4)

W3 ( s )

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⎡

⎤ x The augmented state is x = ⎣ x W 1 ⎦, and notice that y  = y+w, so the augmented xW3 equation of state is ⎡

⎤ ⎡ 0 0 0 ⎣ ⎦ ⎣ x˙ = B W 1 C AW 1 0 x + BW1 B W 3 C 0 AW 3 0 ⎡ ⎤ ⎡ DW 1 C C W 1 0 DW 1 Y = ⎣ DW 3 C 0 C W 3 ⎦x + ⎣ 0 C 0 0 I A

⎤  w BW1 D ⎦ u BW3 D ⎤ D W 1 D  w DW 3 D ⎦ u D B

(5)

⎤ z1 where Y = ⎣ z 3 ⎦. In theory, a reasonable choice of W1 (s) and W3 (s) can satisfy the y design requirements. However, when dealing with practical problems, there is often a problem that can not meet the assumed condition of rank D12 in the standard H∞ control problem. For example, the object

given in

Eq. (1) has D = 0. This makes the 0 DW 1 D = augmented object has D12 = . And this also makes it impossible DW 3 D 0 to solve. So full rank D12 becomes the key to solve the standard H∞ control problem. A common way to do this is to artificially introduce a decimal, such as we take D W 3 D as a decimal ε so that D12 is a column full rank. In this way, the system in which the decimal is introduced is changed from Fig. 2 to the form of Fig. 3. That is to say, we draw a gain from controlled quantity u to directly add to z 3 . In many books and references, the method of selecting the decimal number is given, but the criterion of selecting the decimal number is not explained. When using MATLAB to solve the solution, because the accuracy of its calculation is generally 1/100,000, then the general designers often choose this decimal number randomly as 1/100,000 or 1/10,000, and some even specify it as 1/1000. Combining Eq. (1), the magnetic levitation system can show that such a selection method will generally lead to wrong design results. At the same time, it can be shown that the selection ⎡

+

ε K

−

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+

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z3

W1 ( s )

z1

w Fig. 3 Another design block diagram of a mixed sensitivity problem

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of this decimal number is not only related to the controlled object, but also directly related to the selection of the weight function W3 (s). The transfer function corresponding to the controlled object Eq. (1) is as follows: g(s) =

−50.9 s 3 + 8.723s 2 + 0.02748s − 42,740

(6)

Considering the constraint of Bode integral, the ideal performance should be approximated to a rectangle [2]. The performance weights selected according to this principle are no longer like the usual integral form of −20 dB/dec. But is a curve of a similar rectangle that is approximately symmetrical with respect to the frequency axis to the best performance characteristics. The weight functions selected are as follows: 0.65 +1  s 2  1 s+1 92 1000  1  1 W3 (s) =  1 s + 1 1600 s + 1 2000 s+1 1500 W1 (s) =

1 s 180

(7)

(8)

4 Selection Analysis of Decimal It is easy to notice that the open loop gain from controlled quantity u to z 3 approximately is 10–6 . However, when ε is bigger than this open loop gain, such as ε = 10−5 , the minimum of γ is 1.1140 by applying hinfsyne command [8]. The system has allpass characteristic. The design results are shown in Figs. 4 and 5. It can see from Fig. 4 that the adding introduction ε becomes the leading factor from controlled quantity to. Therefore, the result is that in all-pass characteristic, although W3 (s)T is not high-pass, ε can be the replenishment. As we can see from Fig. 5, the performance of the designed system is 4.68 dB which is bigger than 3.76 dB. This design result can not satisfy the condition S∞ ≤ W1 ∞ , which means the design is not successful. While it has ε = 10−10 , the minimum of γ is 1.0006 by applying hinfsyne command. The system also has all-pass characteristics. The design results at this point are shown in Figs. 6 and 7. As can see in Fig. 6, the selected parameter ε doesn’t work anymore in the useful frequency area. The all-pass characteristic of system is almost decided by W1 S and W3 T . And it can see from Fig. 7, the performance of the designed system is 3.73 dB which is smaller than 3.76 dB. It indicates that the design meets the requirements of the indicators. It can be seen that experience the same weight function and the same calculation process, but the results are very different from the above two decimals of different orders of magnitude. So in the actual design process, the decimal ε can not be selected

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Fig. 4 All-pass characteristic when ε = 10−5

Fig. 5 Sensitivity function characteristic when ε = 10−5

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Fig. 6 All-pass characteristic when ε = 10−10

Fig. 7 Sensitivity function characteristic when ε = 10−10

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randomly to make the full rank D12 . Selection should be compared with the original system which can be approximately ignored. In this way, the design can be effective. Although the actual character of Fig. 7 is not an ideal rectangle, the character of Fig. 7 can also be equivalent to a rectangle. The rectangular height can be taken as M S = 1.53 = 3.69 dB. At the same time, according to Eq. (6), the unstable pole of the controlled object is 32.28. We can obtain the equivalent bandwidth is according to Bode integral constraint. When there is M S = 1.53 = 3.69 dB, the peak value of sensitivity can reach the minimum value.

5 Conclusion For a general control object, since the denominator order of the transfer function is higher than the molecular order, the usual solution to the question S/T can not satisfy the requirement of rank, so it is necessary to change the feature of object to satisfy the requirement of rank. The idea of choosing decimal numbers instead of zeros is feasible, but it cannot affect the characteristics of the system itself, otherwise it may not be able to obtain the required performance. It can be proved when there is ε = 10−5 . For unstable controlled plant, according to Bode integral theorem, the best performance index can be predicted before the design. So, when select the performance weight function W1 (s), a different principal of selection should be considered to obtain the character which is approximately similar to the character of rectangle. This way can make the peak value of sensitivity to be minimum. Acknowledgements Manuscript received April 7, 2018. This work was supported in part by the Doctoral Foundation of Liaoning Province (No. 20170520333), the Fundamental Research Funds for the Central Universities (No. N182304010), the Doctoral Foundation of Hebei Province (No. F2019501012).

References 1. Wang, G., He, Z.: Control System Design. Tsinghua University Press, Beijing (2008) 2. He, Z., Wang, Y., Meng, F., et al.: Magnetic Levitation System: an application of the Bode’s theorem. Electr. Mach. Control 11(3), 253–256 (2007) 3. Meng, F., He, Z., Wang, Y.: H∞ state feedback design of Maglev system. J. Electr. Mach. Control 12(1), 89–92 (2008) 4. Wang, G., Yuan, X.: H∞ control: 2-block or 3-block problem. Electr. Mach. Control 5(2), 81–83 (2005) 5. Sinha, P.K., Pechev, A.N.: Nonlinear H ∞ controllers for electromagnetic suspension systems. IEEE Trans. Autom. Control 49(4), 563–568 (2004) 6. Meng, F., He, Z., Wang, Y., et al.: Linearization of a nonlinear system. Electr. Mach. Control 12(1), 89–92 (2007) 7. Wu, X., Xie, X.: H∞ robust control. J. Tsinghua Univ. 37(1), 27–30 (1997) 8. Xue, D.: Computer Aided Design of Control System. Tsinghua University Press, Beijing (2005)

Unmanned Autonomous Helicopter Integral Sliding Mode Control and Its Stability Analysis Haojia Zhang, Aijun Li and Yu Wang

Abstract Aiming at the coupling problem of the unmanned autonomous helicopter (UAH) which is a fairly complex aerodynamic system with special flight characteristics, this paper analyses the changing of eigenvalues considering the influence of rotor flapping in different flight modes. Through this, the natural characteristics of helicopter are reflected in valid, and it is also conducive to further design of flight control systems. Based on the analysis, designing an integral sliding mode controller and then comparing with the conventional sliding mode controller, the simulation results show that the former can not only achieve better tracking performance but also eliminate the static error. To the author’s best knowledge, there is few application of integral sliding mode control which is suitable for different state points in the field of helicopter flight control and the controller parameters are easy to adjust. This method has perfect applicability to underactuated helicopter system and engineering application. Keywords Helicopter dynamics · Stability analysis · Integral sliding mode control

1 Introduction It is known that unmanned autonomous helicopters (UAH) are different from fixedwing aircraft due to its special flight characteristics since helicopters have better lowspeed maneuverability. These features make it widely used in military missions such as aerial reconnaissance and combat, as well as for civil applications such as rescue after disaster, aerial photography and so on. However UAH is an open-loop unstable, highly coupled, time-varying parameters and high-order nonlinear underactuated H. Zhang (B) · A. Li · Y. Wang College of Automation, Northwestern Polytechnical University, Beilin District, Xi’an Shaanxi 710072, P.R. China e-mail: [email protected] A. Li e-mail: [email protected] Y. Wang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_29

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aerodynamic system. Hence whatever modeling or designing a controller are difficult for unmanned autonomous helicopter. Modeling is the first step for flight control design. The general modeling method is mechanism modeling method which combines with the aerodynamic model of the main rotor, tail rotor, fuselage, vertical fin and horizontal tail. And then analyzing the changing of UAH eigenvalues in open-loop state is prerequisite for autonomous flight control. The universal stability analysis method is analyzing the dominant eigenvector of the eigenvalues. Thomas F analyzed the stability of the body frame using participation factor method [1]. Xu et al. explained the state of the body frame and didn’t consider the influence of rotor flapping when they analyzed the stability of helicopter [2]. Based on an accurate model and stability analysis, controller can be designed. Sliding mode control as a modern control method with strong applicability to highly coupled MIMO system so that it can be perfectly applied to helicopter systems. Although the sliding mode is completely robust to the uncertainty and the external disturbance, the inherent chattering problem limits its application range in practice [3]. Slotine et al. introduced the boundary layer in the design of sliding mode control which makes the system state reach a small area around zero instead of directly reaching zero. This method opened the way for the application in engineering which can reduce the chatter from controller effectively [4]. However, the boundary layer method will lead to large steady-state errors in the presence of system uncertainty and external disturbances. Then C, hern first introduced the integral term to suppress the steady-state error and enhanced the robustness in the design of the sliding surface [5]. This integral sliding surface was applied into the speed control of PM synchronous motor by Baik [6]. Binglong Cong et al. used adaptive integral sliding mode control for attitude tracking in spacecraft [7]. In this paper, the nonlinear helicopter aerodynamic model is established with a single-rotor and tail rotor using mechanism modeling method considering the flapping dynamics of the rotor which reflects the dynamic characteristics of UAH more complete and more accurate. Then the natural response characteristics of UAH are analyzed in detail which can provide reference for the design of control law. On the basis of the above research, the integral sliding mode control method is applied to the MIMO underactuated unmanned helicopter system and then compared the simulation results with the conventional sliding mode control method.

2 Model and Trim Method of UAH 2.1 Dynamic Equations of Motion According to the model of a helicopter, the translational equations of motion and the rotational equations of motion as well as the Euler angles to describe the relative motion of helicopter to the ground are given as follows,

Unmanned Autonomous Helicopter Integral Sliding Mode Control …

F V˙ + ω×U = m

(1)

I ω˙ + ω×(Iω)=τ

(2)

˙ = R1 ω Ω

(3)

⎤ Ix 0 −Ix z I = ⎣ 0 I y 0 ⎦, −Ix z 0 Iz ⎡

307

⎡

⎤ 1 sinφtanθ cosφtanθ ⎦ R1 = ⎣ 0 cosφ −sinφ   0 sinφ cosθ cosφ cosθ

(4)

 T where m denotes the mass of the fuselage, V = u v w denote the forward veloc T ity, lateral velocity and the vertical velocity; ω = p q r denote the roll rate,  T pitch rate and yaw rate, Ω = φ θ ψ denote the angle of roll, pitch and yaw. T  F= Fx , Fy , Fz and τ =[L , M, N ]T are the projection of the external forces and torques on the body axis, which are generated by the main rotor, tail rotor, flat tail, vertical tail and fuselage. Ix , I y , Iz , Ix z denote the moments of inertia.

2.2 Dynamics Equation of Rotor In this paper, a model with higher precision and more comprehensive dynamic characteristics is established by taking into account the second-order flapping dynamics of rotor of unmanned helicopter. The second-order differential equation of the flapping motion of the rotor blade which affects the forces and moments of the fuselage of the unmanned helicopter is expressed as follows: Define a = [a0 , a1 , b1 ]T , then a¨ + D a˙ +K a=F

(5)

where a0 , a1 and b1 denote blade coning angle, the longitudinal flapping angle and lateral flapping angle; D,K ,F are defined in the reference [8], and the coefficient matrixes D is the damping matrix, K is spring matrix, F is External excitation matrix which is a function of inflow ratio λ, blade root collective pitch

θ0 , lateral cyclic pitch A1c , longitudinal cyclic pitch B1c , where λ = λcmr −CT 2 μ2 + λ2 ,   λcmr = wh (R), where C T is rotor thrust coefficient, C T = Tmr πρ2 R 4 , where Tmr is rotor thrust which is a function of θ0 , B1c , λ, a, a˙ , a¨ [9]. Thus the equation needs to be solved by Newton-Raphson method in combination with the equation of main rotor tension and the rotor inflow ratio. Then the nonlinear unmanned helicopter model is established with assuming that the rotor rotates at constant velocity, the function as follows:

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x˙ = f (x,δ u , t)

(6)

 T where the x = u, v, w, p, q, r, φ, θ, ψ, a0 , a1 , b1 , a˙ 0 , a˙ 1 , b˙1 denote the system T  state, δ u = δa , δe , δc , δ p denote the control input. Thus the 9-DOF helicopter model is established [10].

2.3 Trimming Method Trimming is the prerequisite to obtain a linear model. The equilibrium state of UAH is described as f (xe , u e ) = 0, which means when the control input and the states at the equilibrium point, Formula (6) is zero. Then the trimming problem is converted into optimization searching, which is expressed as follows:

· 2

2

˙ 22 + Ω + a˙ 22 minJ = V˙ 2 + ω 2  V 2 ≥0 s.t. u i min ≤ u i ≤ u imax i = 1, 2, 3, 4

(7)

3 Stability Analysis 3.1 Linearization Linearization is a necessary condition for stability analysis. By using the small perturbation theory [11], Formula (6) is linearized approximation as follows: 

 x˙ 1 = A11 x 1 + A12 x 2 + B 1 δ u  x˙ 2 = A21 x 1 + A22 x 2 + B 2 δ u

(8)

where x 1 =[u, v, w, p, q, r, φ, θ, ψ]T , x 2 = [a0 , a1 , b1 , a˙ 0 , a˙ 1 , b˙1 ]T . It is known that the natural frequencies of rotor flapping dynamics is usually higher than those of the rigid body dynamics of helicopter fuselage. Therefore, this paper command  x˙ 2 =0 in order to simplify the 15-order 9-DOF unmanned helicopter model, write as:  x˙ 1 = A1 x 1 + B 1 δ u

(9)

 where A1 B1 is A11 − A12 A−1 is (B1 − A12 A−1 22 A21 , 22 B2 ), T  δ u = δa , δe , δc , δ p , x 1 =[u, v, w, p, q, r, φ, θ, ψ].

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Pole position map

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1.5 5knots/s 20knots/s 140knots/s

Im

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-8

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-0.2

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Re Fig. 1 Distribution of eigenvalues in different velocity

3.2 Stability Analysis The characteristics of mode which can reflect the motion law of the unmanned helicopter are generally analyzed through the eigenvalues in the open loop state [12]. This paper selects three states containing hovering, medium velocity and high velocity. The eigenvalues obtained by Eq. (9) are as follows: Figure 1 reflects the variation tendency of eigenvalues in different velocities, analyzing the pole distribution can be seen that the advancing flap substantially unchanged. The rotation flap mode is gradually moving closer to the rigid body, while the coupling between regressing flap and roll angle mode decreases with velocity increasing. The stability of pitch angle mode increased gradually. Yaw angular rate mode and the vertical velocity mode are stable which characteristics of unmanned helicopter are similar to the fixed wing by degrees and yaw angular rate mode is adjusted downward slightly for seeing directly while the vertical velocity mode upward. Next with the increase of velocity, the stability of Dutch roll mode strengthened on account of the vertical tail aerodynamic, and the dynamic pressure enhanced leads to the frequency of Dutch roll increases accordingly. The phugoid mode which lying in the right hand side indicating instability, while the stability of this mode is gradually enhancing attributed to the instability of the attack angle weakened by the aerodynamic effect of flat tail, but as it increases further, the stability of the attack angle of rotor worsened again gives the rise to the mode back to the right.

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4 Integral Sliding Mode Control Define the tracking error of the system state e x1 = x d − x 1 and x d is the command for Eq. (10). Define sig(x) = sign(x)|x|a , a > 0. To achieve the control goal that the e1 converge to zero, an integral sliding mode surface is developed as Eq. (10) t s = C e x1 + C 1

sig(ex1 )dt

(10)

0

where C = diag(c1 · · · c9 ) and C 1 = diag(c11 · · · c19 ) ∈ R n×n . By using the integral sliding mode surface, a robust controller is designed as  −1 C 1 sig(e x1 ) + ka s + kb sign(s) δ u = B −1 1 − A1 x 1 + C

(11)

where C and C 1 ∈ R n×n , ka = diag(ka1 · · · ka9 ), kb = diag(kb1 · · · kb9 ), k a > 0, k b > 0. Considering the system Eq. (9), if the sliding mode surface and the control law are chosen as Eqs. (10) and (11), the following conclusions can be deduced: (1) The closed-loop system is asymptotic stable. (2) The sliding mode surface s and the tracking error e x1 are ultimately bounded. Proof In order to prove the stability of s, the Lyapunov function is selected as: V =

1 T s s 2

(12)

The time derivative of the Lyapunov function V along sliding mode surface s can be obtained. And substitute control law (11) into Formula (12), the results as follows: V˙ = sT s˙   = sT C e˙ x1 + C 1 sig(ex1 )   = sT −C( A1 x 1 + B 1 δ u ) + C 1 sig(ex1 )     (− A1 x 1 +C −1 C 1 sig(ex1 ) A1 x 1 + B 1 B −1 T 1 = s −C +C 1 sig(e x1 ) + ka s+kb sign(s)) = − ka s2 − kb |s| ≤ 0

(13)

Obviously, V˙ ≤ 0 means V is bounded. Thus, it can be concluded that s is bounded. Define e x1 = [ex11 · · · ex19 ]T . Once conclusion (1) stands, we have s = 0, s˙ = 0. then

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e˙x1i = −Ci−1 C1i sig(ex1i ), i=1, 2 · · · 9

(14)

9 2 Lyapunov function is designed as V = 21 i=1 ex1i . Take the derivation of equation above yields:   V˙ = ex1i e˙x1i = ex1i −Ci−1 C1i sig(ex1i ) = −Ci−1 C1i |ex1i |1+a ≤ 0

(15)

According to Lyapunov theory, conclusion (1) and (2) is valid. Remark 1 In order to eliminate chattering in sliding mode, the symbolic function is replaced by the saturation function referring to reference [6].  sat =

 s    0 0 i f Sk−1 + s(r (k)) < 0

(16)

In which, Sk stands for the maximum likelihood cumulative sum, the value of Sk will gradually increase with the occurrence of failure. Therefore, the fault detection logic can be expressed as:  d=

n Sk ≥ J 0 Sk < J

(17)

In which, J stands for the warning threshold, d = n stands for the warning, if the current sensor of phase a has fault, the value of n is 2, if the current sensor of phase b has fault, the value of n is 3, if the current sensor of phase c has fault, the value of n is 4, if the current sensor of position has fault, the value of n is 5.

3 The Fault Diagnosis of the Motor 3.1 The Mathematical Model of the Motor The most commonly used model of motor is the dq axis mathematical model of the motor. Therefore, the state equation of the motor is as below:

Fault Diagnosis of the Motor of Electro-Mechanical Transmission …

⎡ · ⎤ x1 ⎢ · ⎥ ⎢ ⎢ x2 ⎥ ⎢ ⎢ · ⎥=⎢ ⎣ x3 ⎦ ⎣ · x4 ⎡

⎤ ⎡ 1 L − LRds + L qd Pωm i q 0 Ld ψf ⎢ ⎥ Rs Ld 1 − L q i q − L q Pωm i d − L q Pωm ⎥ ⎢ 0 Lq +     ⎢ ⎥ 1 [P ψ f i q + L d − L q i d i q − TL − Rω ωm ] ⎦ ⎣ 0 0 Jm 0 0 Pωm

365

⎤ ⎥  ⎥ ud ⎥ ⎦ uq (18)

In which, Rs stands for the phase resistance of three phase symmetrical winding, L d and L q stand for the inductance of stator winding of d axis and q axis, respectively. ψ f stands for the flux linkage produced by permanent magnet, P stands for the magnetic pole logarithm, Jm stands for the moment of inertia after conversion between rotor inertia and mechanical load. The state values are the current of d axis i d , the current of q axis i q , the angular velocity of the motor ωm and the rotor position θ. The input values are the voltage of d axis u d , the voltage of q axis u q . The measurements are three-phase current i a , i b and i c and rotor position θ. ⎤ ⎡ −sin θ  0 ia cos θ  ⎢ i b ⎥ ⎢ cos θ − 2 π − sin θ − 2 π 0 3  3  ⎢ ⎥=⎢   ⎣ i c ⎦ ⎣ cos θ + 2 π − sin θ + 2 π 0 3 3 θ 0 0 0 ⎡

⎤⎡ ⎤ 0 id ⎢ ⎥ 0⎥ ⎥⎢ i q ⎥ ⎣ ⎦ ωm ⎦ 0 θ 1

(19)

3.2 Fault Impact Analysis of the Current Sensors and the Position Sensor of the Motor The motor is the actuator of the system, therefore, if the current sensors and position sensor break down, the electro-mechanical transmission will not work as expected. Figure 2 show the output torque of the motor and the output speed of the transmission when one of the current sensors has fault and the position sensor has fault.

Fig. 2 a The current sensor has fault, b The position sensor has fault

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From Fig. 2, when one of the current sensor has fault, the fault will cause small range fluctuation of motor output torque. The rotor position sensor fault of the motor will cause the output torque of the motor to fluctuate sharply. Therefore, fault diagnosis is very necessary.

3.3 The Specific Method of the Fault Diagnosis of the Motor Sensor fault diagnosis of motor is usually accomplished by motor controller, so only three-phase permanent magnet synchronous motor drive system is considered. The sensor faults considered in this paper are mainly three-phase current sensor faults and rotor position sensor faults. Since the motor control system has strong nonlinear characteristics, considering the real-time and computational complexity, the fault detection and isolation strategy based on UKF observers is adopted in this paper. Since there are four measurements, three observers are designed to diagnose and locate the fault, all the observers have the inputs of u d u q , and for the first observer, the inputs are i a i b and θ, the inputs of observer are i a i c and θ, the inputs of the last observers are i b i c and θ (Fig. 3). According to Fig. 1, the residual error has two levels, for the first level, the equation is shown below:

abc dq

Input

Controller

PMSM

FDI UKF Fault diagnosis and locaƟon

Residual analysis

UKF

UKF

Fig. 3 The specific method of the fault diagnosis of the motor

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Table 1 Response of the fault of the first level residual Observer 1 (1)

Observer 2 (1)

(1)

(2)

Observer 3 (2)

(2)

(3)

(3)

(3)

ria

rib

riθ

ria

ric

riθ

rib

ric

riθ

f ia

1

1

1

1

1

1

0

0

0

f ib

1

1

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0

0

1

1

1

f ic

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1

1

1

1

1

1

f iθ

1

1

1

1

1

1

1

1

1

r x( j) = yx − yˆ x

(20)

( j)

r x stands for the residual signal, and (j) stands for the observer number. Only one failure is considered here. In the first stage, each UKF corresponds to three residuals. The response of each residual signal to different faults is shown in Table 1, where ‘1’ indicates that the sensor has faults and the corresponding residuals will react. In order to analyze the response of residual signals to sensor more conveniently, the second residual is introduced as shown below [2]: R ( j) = α

3 

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(21)

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In which, α is a constant. According to Table 2, “1” means that when a fault occurs in the table, the corresponding level 2 residual will respond. For example, when the sensor for measuring A-phase current fails, R1 and R2 will respond. In order to reduce the rate of the false alarm and missing alarm caused by system noise and model error, the residual evaluation method used is CUSUM. Its fault detection and alarm can be expressed as Eq. (17). Table 2 Response of the fault of the second level residual f ia

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Fig. 4 The residual of R1, R2 and R3

Fig. 5 The CUSUM result of R1, R2, R3 and warning

3.4 The Simulation Analysis of Fault Detection and Separation In order to reduce the false alarm rate, the threshold value is usually selected to be slightly larger than the CUSUM test result Sk without fault. Finally, the threshold J is 2500. This section gives the fault detection and isolation of current sensors and position sensor. Under normal conditions, only one sensor has fault, so in this paper, only the position sensor has fault, or only one of the current sensors has fault. The A phase current sensor is set to have gain fault at time 10 s, like Eq. (3), so the residual error of the three observers are shown in Fig. 4. In order to avoid false alarm and missing alarm, use the CUSUM method to analyze the residuals. According to the figures of CUSUM (Fig. 5), the CUSUM of

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Fig. 6 The residual of R1, R2 and R3

Fig. 7 The CUSUM result of R1, R2, R3 and warning

R1 and R2 increase sharply at time 10 s, and exceed the threshold at about 10.02 s, the CUSUM of R3 fluctuates far below the threshold. So we can judge that the A phase current sensor has fault, the warning is shown in Fig. 5. Because the fault sensor is a phase current sensor, the alarm is 2, the time of a phase current sensor has fault is at 10 s, and the time that the fault is diagnosed is near 10 s. Thus the fault diagnosis is timely and effective. The rotor position sensor is set to have gain fault at time 10 s, like Eq. (3), so the residual error of the three observers are shown in Fig. 6. In order to avoid false alarm and missing alarm, use the CUSUM method to analyze the residuals. According to the figures of CUSUM (Fig. 7), the CUSUM of R1, R2 and R3 increase sharply at time 10 s, and exceed the threshold at about

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10.05 s. So we can judge that the rotor position sensor has fault, the warning is shown in Fig. 7. Because the fault sensor is rotor position sensor, the alarm is 5, the time of rotor position sensor has fault is at 10 s, and the time that the fault is diagnosed is near 10 s. Thus the fault diagnosis is timely and effective.

4 Conclusions The aim of the paper is to diagnose the fault of the current sensors and the rotor position sensor of motor of EMT, the work is shown below: First, the model-based fault diagnosis method is used, the UKF is used to design the observer, and the CUSUM method is used to analyze the residual to avoid the fault alarm or missed alarm. Second, the impacts of the fault of current sensors and position sensor of the motor of EMT are analyzed. Moreover, the specific method of the fault diagnosis of the current sensors and the position sensor are analyzed, and the simulation results show the accuracy and timeliness of the method. The fault of the motor of EMT is diagnosed. When the motor has fault, the transmission may not work as usual, therefore, the tolerant control will be used to make the transmission work as usual. Next, the tolerant control will be used when the motor of the system has fault [14].

References 1. Kalinin, D.V.: Multithreaded continuously variable transmission synthesis for next-generation helicopters. In: 29th Congress of the International Council of the Aeronautical Sciences, 7–12 (2014) 2. Liu, Z.: Model-Based Fault Diagnosis of Electrified Driver Powertrain in Pure Electric Vehicles. Beijing Institute of Technology, Beijing (2016) 3. Berriri, H., Naouar, M.W., Slama-Belkhodja, I.: Easy and fast sensor fault detection and isolation algorithm for electrical drives. IEEE Trans. Power Electron. 27(2), 490–499 (2012) 4. Zhou, Z.J., Hu, C.H., Xu, D.L., et al.: A model for real-time failure prognosis based on hidden Markov model and belief rule base. Eur. J. Oper. Res. 207(1), 269–283 (2010) 5. Tony, B., Liang M.: Monitoring data-based automatic fault diagnosis for the brake pipe of high-speed train. Int. J. Comput. Appl. Technol. (IJCAT) 25(6), 2102–2124 (2011) 6. Xie, G., Ye, M.: On-line fault diagnosis of hydraulic systems using Unscented Kalman Filter. Int. J. Control Autom. Syst. 57(3) (2018) 7. Huang, S., Tan, K.K., Tong, H.L.: Fault diagnosis and fault-tolerant control in linear drives using the Kalman filter. IEEE Trans. Ind. Electron. 59(11), 4285–4292 (2012) 8. Mirzaee, A., Salahshoor, K.: Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive unscented Kalman filter and switched MPC and H-infinity loopshaping controller. J. Process Control 22(3), 626–634 (2012) 9. Izadian, K.: Application of Kalman filters in model-based fault diagnosis of a DC-DC boost converter. In: Conference of the IEEE Industrial Electronics Society. IEEE, New York (2010) 10. Liu, H., Liu, D., Lu, C., et al.: Fault diagnosis of hydraulic servo system using the unscented Kalman filter. Asian J. Control 16(6), 1713–1725 (2014)

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11. Wang, D.: Study on Schemes of Fault Detection and Diagnosis & Fault Tolerant Control. Jilin University (2004) 12. Venkatesh Kumar, P., Rajeswari, R.: A recursive discrete Kalman filter for the generation of reference signal to UPQC with unbalanced and distorted supply conditions. Int. J. Model. Ident. Control (IJMIC) 31(1) (2019) 13. Rizzoni, G.: Statistical inference methods for residual analysis and change detection. The Ohio State University Lecture in Fault Diagnosis in Dynamic Systems 14. Yao, L., Wang, H.: Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model. Int. J. Model. Ident. Control (IJMIC) 29(1), 22–30 (2018)

Backstepping Sliding Mode Control for the Displacement Tracking of Permanent Magnet Linear Synchronous Motor Based on Nonlinear Disturbance Observer Hong-jiao Song, Le Liu, Man-jun Cai and Nuan Shao Abstract For the problem that the displacement tracking control accuracy of permanent magnet linear synchronous motor (PMLSM) is prone to be affected by the uncertain factors such as parameter perturbation, and load disturbance, a backstepping sliding mode control method is proposed based on the nonlinear disturbance observer in this paper. Firstly, the nonlinear disturbance observer is developed to observe the uncertainty dynamically, so as to improve the displacement tracking accuracy of the system. Secondly, the displacement tracking controllers of PMLSM are presented by combining the backstepping sliding mode control with the command filter, which enhance the anti-jamming capability of the system, and solve the “explosion of complexity” problem during using the conventional backstepping control. Theoretical analysis shows that all the signals of the resulting closed-loop system are uniformly ultimately bounded. Finally, the proposed control method in this paper is compared with the backstepping control method, and the simulation results verify the effectiveness of the proposed control method. Keywords Permanent magnet linear synchronous motor · Nonlinear disturbance observer · Backstepping sliding mode control · Command filter

1 Introduction In recent years, with the development of modern industrial technology, the traditional rotary motors have difficult to be applied to some industrial fields due to the problems of long response time and large loss [1]. While the permanent magnet linear synchronous motor (PMLSM) has the characteristics of quick response, low loss, precise positioning, etc, and it has been widely used in microelectronics production, H. Song · L. Liu (B) · M. Cai College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China e-mail: [email protected] N. Shao Hebei University of Environmental Engineering, Qinhuangdao 066102, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_35

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industrial robots, aerospace, and other fields [2]. Compared with the traditional rotary motors, the PMLSM eliminates the mechanical transformation between the load and the motor, which can directly generate large electromagnetic thrust, decrease the mechanical losses, improve the rigidity of the traditional system, reduce the elastic deformation and mechanical friction of the mechanical structure during motor starting and braking. However, the PMLSM is prone to be affected by the uncertain factors such as parameter perturbation, load disturbance, which may further affect the stable operation and control accuracy of the system [3]. In view of the above problems, Kim et al. [4] proposed a sensorless speed control strategy for a permanent magnet synchronous motor based on sliding mode observer, and the observer had simple structure and strong robustness, while it is sensitive to measurement noise. Zhang et al. [5] designed a self-adaptive fuzzy control method based on RBF neural network, and the node parameters of the neural network hidden layer in the controller design method were determined based on the empirical method, but it is not conducive to enhance the system tracking control accuracy. Sun et al. [6] used an adaptive global sliding mode control method to improve the robust stability of the system, which eliminated the arrival stage in the ordinary sliding mode variable structure control and got good results. Wei et al. [7] proposed a backstepping sliding mode control method based on neural network, while the controller design method needs repeat differential on the virtual control inputs during the derivation process, which appears “differential explosion” phenomenon. He et al. [8] proposed a dynamic surface adaptive integral terminal sliding mode control method, which solved the “explosion of complexity” problem during using the backstepping control, while it is easy to cause the noise amplification problem. The command filter [9] can also be used to solve the “explosion of complexity” problem during using the backstepping control, and it takes the virtual control variable as the input signal, and obtains the filtered signal’s numerical solution and derivative value through the integration process; moreover, by reasonably designing the cut-off frequency and bandwidth of the filter, the noise influences can be effectively reduced. Furthermore, for the system uncertainty, nonlinear disturbance observer [10] can be adopted to conduct estimate and compensation, which is useful to enhance the tracking control accuracy of the system. Based on the above analysis, for the displacement tracking control of permanent magnet linear synchronous motor (PMLSM) with uncertainty, a backstepping sliding mode control method is proposed based on the nonlinear disturbance observer in this paper. Firstly, the nonlinear disturbance observer is developed to observe the uncertainty dynamically. Secondly, the backstepping sliding mode control method is employed for the displacement tracking of the permanent magnet linear synchronous motor. Moreover, the command filters can be used to solve the “explosion of complexity” problem during using the conventional backstepping control. Finally, comparing the proposed control method with the backstepping control method, and simulation results show that the proposed control method can achieve effective displacement tracking control of the PMLSM, and has fast dynamic response and strong antijamming capability.

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2 The System Model of PMLSM Considering the influence of uncertain factors such as parameter perturbation and load disturbance of the system, The mathematical model of the PMLSM in d-q axis is shown as follows [11]: ⎧ d˙ = v ⎪ ⎪ ⎪ ⎨ v˙ = − B v+ K f i − 1 F + D M M q M ˙q = 1 u q − R i q − πv i d − πψ f v i ⎪ ⎪ L L p pL ⎪ ⎩ i˙ = 1 u − R i + πv i d L d L d p q

(1)

where d is the mover displacement; v is the mover velocity; M is the total mass of the mover; K f is the thrust force constant; B is the viscous friction coefficient; F is the load, which mainly including the end-effecting force Fe f and the friction force F f ric ; u d , u q and i q , i d denote the voltages and currents of d-axis and qaxis, respectively; L is the winding inductance; p denotes the pole pitch; R denotes the winding resistance; ψ f is the permanent magnet flux linkage; D denotes the uncertainty (including parameter perturbation and load disturbance).

3 Design of Nonlinear Disturbance Observer for the Uncertainty Considering the uncertainty D in the system model (1) is complex and unknown, thus in order to increase the displacement tracking control accuracy of the system, we adopt the nonlinear disturbance observer [10] to conduct dynamic observation for the uncertainty D in this section. The nonlinear disturbance observer can be designed as ⎧ Kf B 1 ˙ ⎪ ⎪ ⎨ vˆ = − M v+2 M i q − M F + z (2) z = −λ1 sig 3 (ˆv − v) + Dˆ ⎪ 1 ⎪ ⎩ ˙ˆ D = −λ sig 2 ( Dˆ − z) 2

where vˆ and Dˆ are the estimated values of v and D, respectively; z is the intermediate state; λ1 , λ2 > 0 are the observer gains. Define the observation errors of the nonlinear disturbance observer as  v˜ = v − vˆ (3) D˜ = D − Dˆ And take the time derivative of Eq. (3) yields

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⎧ 2 2 ⎨˙ v˜ = v˙ − v˙ˆ = D − z = D + λ1 sig 3 (ˆv − v) + Dˆ = D˜ − λ1 sig 3 (˜v ) ⎩ D˙˜ = D˙ − D˙ˆ = D˙ + λ sig 21 ( Dˆ − z) = D˙ − λ sig 21 ( D˜ − v˙˜ ) 2 2

(4)

where D˙ˆ = λ2 sig 2 (λ1 sig 3 (˜v )). There exists λ1 , λ2 ∈ R+ , which makes the observer convergent finitely, that is, there exists a moment T ∗ , when t ∈ [0 , T ∗ ], then v˜ and D˜ are all bounded; when t > T ∗ , then v˜ = 0, D˜ = 0. The proof process of the convergence of the observer is detailed in [10]. 1

2

4 Designs of Controllers for the PMLSM In this section, the backstepping sliding mode controllers for the PMLSM will be designed, and in order to avoid the “explosion of complexity” problem in the conventional backstepping procedure, we can let the nominal virtual control input ∂¯d pass the following command filter [9], and then obtain the virtual control input ∂d and its first time derivative signal ∂˙d . The command filter is defined as  ϕ˙1 = ϕ2 (5) ϕ2 = −2ξ W ϕ2 − W 2 (ϕ1 − ∂¯d ) where ∂d = ϕ1 , ∂˙d = ϕ2 ; 0 < ξ < 1 and W > 0 are the damping and bandwidth of the command filter, respectively; ∂¯d is the nominal virtual control input. Moreover, ˙ when the input ∂¯d is bounded, then the outputs ∂d and  ∂d arebounded and continuous, and by choosing the right ξ and W , we can make ∂d − ∂¯d  is small enough. We here adopt the field-oriented vector control strategy for the PMLSM, that is, d-axis expected current value i d∗ = 0, and define the error variables as ⎧ e1 ⎪ ⎪ ⎨ e2 ⎪ e ⎪ ⎩ q ed

= d − d∗ = v − vd = i q − i qd = i d − i d∗

(6)

where d ∗ is the given value of the PMLSM, vd and i qd are the virtual control inputs. Furthermore, define the compensation error variables as 

where ε1 and ε2 are variables.

z 1 = e1 − ε1 z 2 = e2 − ε2

(7)

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Step 1: Define the variable ε1 as

ε˙ 1 = −k1 ε1 + (vd − v¯ d )

(8)

where v¯ d is the nominal virtual control input, k1 ∈ R+ is the control parameter. Take the time derivative of z 1 yields z˙ 1 = e˙1 − ε˙ 1 = v − d˙ ∗ + k1 ε1 − vd + v¯ d = e2 − d˙ ∗ + k1 ε1 + v¯ d

(9)

By Eq. (9), the first nominal virtual control input v¯ d can be chosen as v¯ d = −k1 e1 + d˙ ∗ − ε2

(10)

Substituting Eq. (10) into Eq. (9), and we have z˙ 1 = z 2 − k1 z 1

(11)

Step 2: Define the variable ε2 as

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Kf  i qd − i¯qd M

(12)

where i¯qd is the nominal virtual control input, k2 ∈ R+ is the control parameter. Take the time derivative of z 2 yields z˙ 2 = e˙2 − ε˙ 2 =

Kf Kf ¯ 1 B eq − v − F + D + k2 ε2 − v˙ d + i qd M M M M

(13)

By Eq. (13), the second nominal virtual control input i¯qd can be chosen as

 Kf 1 M B v˙ d − eq + v+ F − Dˆ − k2 e2 − z 1 i¯qd = Kf M M M

(14)

Substituting Eq. (14) into Eq. (13), and we have z˙ 2 = −k2 z 2 − z 1 + D˜

(15)

Step 3: Take the time derivatives of eq and ed yields

i − e˙q = i˙q − i˙qd = L1 u q − RL i q − πv p d 1 R πv ∗ ˙ ˙ e˙d = i d − i d = L u d − L i d + p i q

πψ f v pL

− i˙qd

(16)

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In order to improve the robust stability of the system, the global sliding mode surfaces are selected as follows:  Sq = β1 z 1 + β2 z 2 + eq − β1 e−η1 t z 1 (0) − β2 e−η2 t z 2 (0) − e−η3 t eq (0) (17) Sd = ed − e−η4 t ed (0) where e−η1 t z 1 (0), e−η2 t z 2 (0), e−η3 t eq (0) and e−η4 t ed (0) are the global sliding factors, which can eliminate the arrival stage in the sliding mode variable structure control; ηi (i = 1, 2, 3, 4), β1 , β2 ∈ R + are the sliding surface parameters. Take the time derivative of Eq. (17) based on Eqs. (1) and (16), and we can get ⎧ πψ f v 1 R πv ⎪ ⎨ S˙q = L u q − L i q − p i d − pL − i˙qd + β1 z˙ 1 + β2 z˙ 2 +β1 η1 e−η1 t z 1 (0) + β2 η2 e−η2 t z 2 (0) + η3 e−η3 t eq (0) ⎪ ⎩ S˙ = 1 u − R i + πv i + η e−η4 t e (0) d 4 d L d L d p q

(18)

Then the backstepping sliding mode controllers for the PMLSM can be designed as

⎧ πψ f v R πv −η1 t ˙ ⎪ z 1 (0) ⎪ ⎨ u q = L L i q + p i d + pL + i qd − β1 z˙ 1 − β2 z˙ 2 − β1 η1 e −η2 t −η3 t − β2 η2 e z 2 (0) − η3 e eq (0) − k3 Sq  ⎪ ⎪ ⎩ u d = L R i d − πv i q − η4 e−η4 t ed (0) − k4 Sd L

(19)

p

where k3 , k4 ∈ R+ are the control parameters.

5 Stability Analysis Choose the Lyapunov function candidate as V1 =

 1 2 z 1 + z 22 + Sq2 + Sd2 + D˜ 2 2

(20)

Take the time derivative of Eq. (20) yields

 V˙1 = z 1 (z 2 − k1 z 1 ) + z 2 −k2 z 2 − z 1 + D˜ − k3 Sq2 − k4 Sd2 + D˜ D˙˜ = −k1 z 12 − k2 z 22 − k3 Sq2 − k4 Sd2 + z 2 D˜ + D˜ D˙˜

(21)

Based on the inequality 2x y ≤ x 2 + y 2 , we can get 1 1 1 1 V˙1 ≤ −k1 z 12 − k2 z 22 − k3 Sq2 − k4 Sd2 + z 22 + D˜ 2 + D˜ 2 + D˙˜ 2 2 2 2 2

(22)

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Then 1 1 V˙1 ≤ −k1 z 12 − (k2 − )z 22 − k3 Sq2 − k4 Sd2 + D˜ 2 + D˜˙ 2 ≤ σ1 V1 + θ1 2 2

(23)

  where σ1 = 2min k1 , k2 − 21 , k3 , k4 , −1 , θ1 = 21 D˙˜ 2 . Multiply both sides of Eq. (23) to get eσ1 t (V˙1 + σ1 V1 ) ≤ eσ1 t θ1

(24)

Further, we can get 0 ≤ V1 ≤

 θ1 θ1 −σ1 t V1 (0) − e σ1 σ1

(25)

Then, we can obtain that the system is uniformly ultimately bounded, and the displacement error can be arbitrarily small by changing the parameters of k1 , k2 , k3 , k4 , and so on.

6 Simulation Research In this section, the simulation research is carried out on the PMLSM system, and through comparing the proposed control method with the backstepping control method to prove the availability of the proposed control method. The main parameters of the PMLSM in the simulation are chosen as ψ f = 0.09 Wb, B = 1.2 N s/m, K f = 50.7 N/A, p = 36 mm, L = 41.4 mH, M = 8 kg, R = 2.1 . For the load F in the system model  (1), we assume that the expression of = 5 cos(2π d p); the expression of the friction force the end-effecting force is F e f   −(v/ 0.01)2 sign(v). is F f ric = 1 + 2e The main parameters of the proposed control method are chosen as λ2 = 200, k1 = 160; k2 = 0.01, k3 = 120, k4 = 120, β1 = 100; β2 = 1, η1 = 500, η2 = 1000, η3 = 1000, η4 = 500. In addition, for the uncertainty D in the system model (1), it is assumed that the PMLSM exists the parameter perturbations and the load disturbance in the actual operation, that is, B changes into 1.1B, K f changes into 1.1K f , and the load disturbance is 0.1F sin(2π t). The displacement signal is given as a sinusoidal signal, and its period is 2 s and the amplitude is 1 mm. The displacement and displacement error response curves are shown as Fig. 1. It can be seen that the PMLSM has faster dynamic response and smaller tracking error based on the proposed control method.

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0.1 0

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Observation curve of the nonlinear disturbance observer is shown as Fig. 2. We can see that the designed nonlinear disturbance observer realizes effectively dynamic observation for the uncertainty D, which can weaken the influence of the system interference. Input-output curves of the command filters are shown as Fig. 3. It can be shown that the command filters realize approximations for the derivative of the virtual control variables, which can avoid the increasing complexity in calculating the analytic derivatives of the virtual control in the conventional backstepping method and facilitate the designed system controllers.

7 Conclusions The displacement tracking control problem of the PMLSM has been investigated in this paper. Firstly, the nonlinear disturbance observer was developed to observe the uncertainty dynamically, which increased the displacement tracking accuracy

vd vd

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of the system. Secondly, the backstepping sliding mode controllers were designed, which enhanced the robustness of the system. Moreover, the command filters were introduced to solve the “explosion of complexity” problem during using the conventional backstepping control, which facilitated the design of the controllers. Theoretical analysis showed that all the signals of the resulting closed-loop system were uniformly ultimately bounded. Finally, through comparing with the backstepping control method, simulation results illustrated that the permanent magnet linear synchronous motor based on the proposed control method has higher tracking control accuracy, better robust stability and faster dynamic response than the traditional backstepping control method. Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant 61803327, the Science and Technology Research Project in Colleges and Universities of Hebei Province under Grant Z2017041, the Key Research and Development Project of Hebei Province under Grant 18212109, the Research Foundation of Hebei University of Environmental Engineering under Grant BJ201604, and the Basic Research Specific Subject of Yanshan University under Grant 16LGA005.

References 1. Yahiaoui, M., Kechich, A., Bouserhane, I.K.: Design and development of permanent magnet linear synchronous motor. Indian J. Sci. Technol. 10(27), 1–4 (2017) 2. Ting, C.S., Liu, J.F., Liu, C.S., et al.: An adaptive FNN control design of PMLSM in stationary reference frame. J. Control Autom. Electr. Syst. 27(4), 391–405 (2016) 3. Cho, K., Kim, J., Choi, S.B., et al.: A high-precision motion control based on a periodic adaptive disturbance observer in a PMLSM. Trans. Mechatron. 20(5), 2158–2167 (2015) 4. Kim, H., Son, J., Lee, J.: A high-speed sliding-mode observer for the sensorless speed control of a PMSM. IEEE Trans. Industr. Electron. 58(9), 4069–4077 (2011) 5. Zhang, R.C., Zhao, H.C., Yu, J.Y.: A three dimensional self-adaptive region fuzzy guidance law based on RBF neural networks. Int. J. Model. Ident. Control 8(3), 184–190 (2009)

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6. Sun, N., Fang, Y.C., Chen H: Global sliding mode control of underactuated inertia wheel pendulum systems. Control Theory Appl. 33(5), 653–661 (2016) 7. Wei, Q.T., Chen, M., Wu, Q.X., et al.: Backstepping based attitude control for a quadrotor UAV with input saturation and attitude constraints. Control Theory Appl. 32(10), 1361–1369 (2015) 8. He, Z.X., Liu, C.T., Zhang, Z.L.: Dynamic Surface adaptive integral terminal sliding mode control for theodolite rotating systems. Int. J. Model. Ident. Control 23(3), 222–229 (2015) 9. Han, Y.X., Yu, J.P., Liu, Z.: Command filter based adaptive neural control for permanent magnet synchronous motor stochastic nonlinear systems with input saturation. Int. J. Model. Ident. Control 30(1), 38–47 (2018) 10. Bu, W.X., Wu, X.Y., Chen, Y.X., et al.: Nonlinear disturbance observer sliding mode backstepping control of hypersonic vehicles. Control Theory Appl. 31(11), 1473–1479 (2014) 11. Chen, C.S., Lin, W.S.: Self-adaptive interval Type-2 neural fuzzy network control for PMLSM drives. Expert Syst. Appl. 38(12), 14679–14689 (2011)

An Edge Extraction Method Based on Gray Lever-Gradient Two-Dimensional Maximum Entropy Threshold Method for Footprint Inspection Mengxin Li, Wenlong Pei, Meiling Li and Rui Xu Abstract The extraction of the edge of the footprint image is the basis of measuring various features, which is used to identify various shapes and analyze various features. In this paper, a gray-scale-gradient two-dimensional threshold method is applied to extract the footprint profile. Firstly, the gray-gradient co-occurrence matrix model is established, and the two-dimensional threshold of gray level and gradient is obtained with the principle of maximum entropy. Then the footprint image is binarized by the two-dimensional threshold vector to accurately segment the blurred edge pixels of the image and extract the edges. Experimental results show that this edge extraction method presented has strong anti-noise ability, which can deal with the edge fuzzy pixels accurately, improve the quality of image segmentation, and further improve the precision of edge extraction. Keywords Gray lever-gradient co-occurrence matrix · Maximum entropy principle · Footprint edge extraction

1 Introduction Digital image processing refers to the process of converting image signal into digital signal by using computer algorithms to perform image processing. The image processing system includes treating the image as a two-dimensional signal and applying the set signal processing method to it. Image segmentation is the process of dividing digital image into segments or parts (sets of pixels) [1]. The goal is to simplify the representation of images into images that are easier to understand and analyze. This is used to locate objects and boundaries such as lines, curves, etc. in the image [2]. Footprints can reflect many of the information related to human characteristics. By analyzing this information, it is possible to correctly judge the physical characteristics such as height, weight, age, etc., and even his occupation. Footprint analysis plays an M. Li · W. Pei (B) · M. Li · R. Xu School of Information and Control Engineering, Shenyang Jianzhu University, 110000 Shenyang, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_36

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important role in the detection of criminal cases. When using computer intelligence to extract footprint features, it is found that measuring various features, identifying footprint shapes, and analyzing their characteristics are based on the extraction of footprint profiles. The accuracy of the extracted footprint edge directly affects the test results [3]. The methods for segmenting footprint images are now varied, among which the threshold method [4] is the most commonly and widely. At present, there are many threshold methods such as the Otsu’s method [5], histogram method, etc. Maximum entropy method can produce better image segmentation effect for different SNR and different size targets, and it is a threshold selection method with high practical value. The gray-lever gradient co-occurrence matrix can reflect the relationship between the gray level and the gradient of each pixel in the image. The gray-lever and gradient distribution rules in the graph can be clearly given. The selected threshold precision is high, so the gray-gradient based co-occurrence matrix is a two-dimensional maximum entropy threshold method for the model to extract the footprint edge [6]. Threshold segmentation algorithm suffers from long computing time and large memory problems. For example, Kapur et al. [7] adopted the earliest image threshold segmentation using one-dimension maximum entropy, but the algorithm could not overcome the effects of imaging noise efficiently. Brink et al. [8] utilized image gray level information and local spatial information to propose a two-dimensional entropy threshold segmentation. The imaging result is good, but the process takes longer. According to the characteristics of the footprint image and the accuracy of the extraction, this paper uses the gray-gradient two-dimensional threshold to extract the edge of the footprint. It has strong anti-noise ability and can correctly segment the blurred edge pixels, thus improving the image segmentation quality. In addition, the etching operation is carried out on the segmented binary image, which not only smoothes the image edge, but also maintains the shape of the edge, thus improving the precision of edge extraction.

2 Proposed Method 2.1 Gray-Gradient Co-occurrence Matrix The gray lever-gradient co-occurrence matrix model describes the two most basic elements in the image, in which the gray-level of each pixel constitutes the basis of the image and reflects the internal information of the image: while the gradient constitutes the elements of the image edge and gives the external information of the image [9].

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2.1.1

385

Calculation of Gradient Matrix

Suppose there is an m × n grayscale image of f (x, y), x = 1, 2, … m, y = 1, 2, … n. The gradient value at the gray image f (x, y) is calculated by using the Sobel operator of window 3 × 3:  (1) g(x, y) = gx2 + g 2y Among them: gx = f (x − 1, y − 1) + 2 f (x − 1, y) + f (x − 1, y + 1) − f (x + 1, y − 1) − 2 f (x + 1, y) − f (x + 1, y + 1)

(2)

g y = f (x − 1, y − 1) + 2 f (x, y − 1) + f (x + 1, y − 1) − f (x − 1, y + 1) − 2 f (x, y + 1) − f (x + 1, y + 1)

(3)

In the formula: x = 1, 2, . . . m, y = 1, 2, . . . n.

2.1.2

Regularization of Gray Scale and Gradient

The purpose of normalization is to reduce the amount of calculation and improve the efficiency of calculation by making appropriate transformation of the image’s gray level and gradient level without affecting the image features. First, the gray matrix is normalized. F(x, y) = INT( f (x, y) × l f / f max )

(4)

where, INT means an integer for the calculation result, l f is defined as the maximum grayscale appearing in the matrix, and f max is the maximum grayscale appearing in image f (x, y). In this paper, l f is 255. Second, the gradient matrix is normalized. gmax is the maximum gradient value appearing in the image, and lg is the gradient value after normalization. In this paper, lg is 255, the normalized gradient matrix is: G(x, y) = INT(g(x, y) × l g /gmax )

(5)

Finally, two normalized matrices F(x, y) and G(x, y) are obtained, which will provide the basis for the co-occurrence matrix.

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Generation of Gray Lever-Gradient Symbiosis Matrix

The value of element H i j in row i and column j of the grey lever-gradient cooccurrence matrix H refers to the number of pixels of the gray image F(x, y) = i and gradient image G(x, y) = j after the normalization process. The probability of the gray-gradient co-occurrence matrix at the point (i, j) is: H (i, j) pi j = l f lg i=1

j=1

(6) Hi j

2.2 Maximum Entropy for Gray-Gradient Two-Dimensional Threshold Value According to the previous introduction, we concluded that the co-occurrence matrix of the footprint image is l f × lg dimensional matrix. If the threshold is set at point (p, q) then the target gray value of the footprint image is low, and the background gray value is high. As a result, the co-occurrence matrix will be divided into four quadrants A, B, C and D, as shown in Fig. 1. The uniform distribution of the background and the target area of the footprint image result in small or even zero gradient value. Therefore, it can be concluded that A represents the target region and C represents the background region. As the q value increases, the probability that the pixel in the image becoming an edge increases. The element H i j in the region of the co-occurrence matrix B is the number of transitions where the gray scale belongs to the target region and the gradient belongs to the edge. The element H i j in region D is gray and belongs to the background region but the gradient is the transfer number of edges. The sum of elements belonging to four quadrants is: Fig. 1 Four-quadrant diagram of the co-occurrence matrix

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pA =

p q  

387

pi j

(7)

i=1 j=1

pB =

lg p  

pi j

(8)

pi j

(9)

i=1 j=q+1 lf q  

pC =

i= p+1 j=1 lg lf  

pD =

pi j

(10)

i= p+1 j=q+1

The normalization treatment of pi j is as follows: piAj

l f lg Hi j / i=1 Pi j j=1 Hi j  = =   lg  l p q f PA i=1 j=1 Hi j i=1 j=1 Hi j / ⎛ ⎞ q p   = Hi j /⎝ Hi j ⎠, 1 ≤ i ≤ p, 1 ≤ j ≤ q.

(11)

i=1 j=1

Similarly, the following expression can be obtained: ⎛ ⎞ lg p   P ij piBj = = Hi j /⎝ Hi j ⎠, 1 ≤ i ≤ p, q + 1 ≤ j ≤ l g . PB i=1 j=q+1

⎞ ⎛ lf q   P i j = Hi j /⎝ Hi j ⎠, piCj = PC i= p+1 j=1

⎛ ⎞ lg lf   P ij = Hi j /⎝ Hi j ⎠, piDj = PD i= p+1 j=q+1

p + 1 ≤ i ≤ l f , 1 ≤ j ≤ q.

(12)

(13)

p + 1 ≤ i ≤ l f, q + 1 ≤ j ≤ l g . (14)

The above Eqs. (13) and (14) respectively indicate the probability from target to edge and from background to edge. The conditional entropy of image definition is: ⎛ H ( p, q) = −⎝ 

∗

p ,q

∗



= arg

lg p  

piBj log2 piBj +

i=0 j=q+1

max

1≤ p≤l f, 1≤q≤l g

H ( p, q)



lf lg   i= p+1 j=q+1

⎞ piDj log2 piDj ⎠/2

(15)

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= arg

⎧ ⎨

⎛ ⎛

⎝−⎝ max ⎩1≤ p≤l f, 1≤q≤lg

lg p   i=0 j=q+1

piBj log2 piBj +

lf lg   i= p+1 j=q+1

⎞ ⎞⎫ ⎬ piDj log2 piDj ⎠/2⎠ ⎭ (16)

According to the maximum entropy principle, the maximum (p*, q*) obtained by Formula (15) is the optimal gray scale and gradient threshold, namely:

2.3 Two-Dimensional Threshold Image Segmentation and Edge Extraction (p*, q*) is the two-dimensional threshold vector obtained, where p* represents gray threshold and q* represents gradient threshold. The footprint image is segmented according to the following principles. Based on the image threshold segmentation principle, all pixel points with threshold less than p* belong to the target set, that is: E 1 = {(x, y) |F(x, y) ≤ p ∗



(17)

The gray value of the pixel points of the fuzzy edge of the footprint image is greater than p*. The segmentation of the footprint image using only a single threshold p* will take the edge pixel points as loss of background information. Since the pixel points of the fuzzy edge have a large gradient value, the two-dimensional threshold (p*, q*) is used to restrict this part of pixel, then the set of this part is: E 2 = {(x, y) |F(x, y) > p ∗ ∩ G(x, y) > q ∗



(18)

This set is also the target set. Then the target set after image segmentation is: E = E1 ∪ E2

  = {(x, y) |F(x, y) ≤ p ∗ ∪ {(x, y) |F(x, y) > p ∗ ∩ G(x, y) > q ∗

(19)

Let the binary image after segmentation be BW, then:

BW =

1, (x, y) ∈ E. 0, (x, y) ∈ other wise.

(20)

The edge is extracted from the acquired BW, so as to extract and analyze the feature points.

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3 Experiment and Result Analysis The original image of the footprint was collected by the footprint acquisition instrument. Simulation experiments were conducted on Inter Core i5 and 2 GB memory microprocessors in the environment of Matlab2014b. A lot of experimental good results on segmentation of footprint images have been accomplished. From the experimental results, it is clear that gray lever-gradient two-dimensional maximum entropy threshold method for footprint inspection proves to be efficient. This edge extraction method has strong anti-noise ability, can accurately segment the edge fuzzy pixels. Only one single image outline segmentation is presented here since space is limited. In this paper, B-spline function based extraction algorithm is used to smooth the surface of binary image edges. The edge detection of spline function is utilized to fit the binar image and to detect the edge of the surface. When the image edge is extracted using the algorithm proposed in this paper, the image noise essentially disappears. Not only the edge of the extracted image is smooth, the shape of the boundary has high similarity with the original image as well. Compared with the algorithm in this paper, there are more footprints edge breakpoints extracted by morphological operator. Canny operator was used to extract the edge to produce false edge, and the image noise was not suppressed well. The footprint boundary extracted by operator produces many breakpoints and the location of the edge is not accurate. The edge location extracted by the method in this section is accurate, and is obviously superior to the edge extracted by other methods (Fig. 2).

4 Conclusion In this paper, the edge of the footprint image is extracted with gray level-gradient co-occurrence matrix, which can accurately locate the edge points. Both improvement of the quality of image segmentation and the precision of edge extraction have been successfully achieved. Through the comparison of different footprint image algorithms, it is obvious that the footprint segmentation algorithm proposed in this paper can accurately extract the boundary of the footprint image, which provides a good basis for the analysis of footprint characteristics.

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Fig. 2 Segmentation of the footprint image

(a) Original image

(b) Proposed method

(d) Canny method

(c) LoG method

(e) Prewiet method

References 1. Ambeth, Kumar, V.D., Ramakrishnan, M.: A comparative study of fuzzy evolutionary techniques for footprint recognition and performance improvement using wavelet-based fuzzy neural network. Int. J. Comput. Appl. Technol. 48(2), 95–105 (2013) 2. Zhang, Y.L.: Image Segmentation. Science Press, Beijing (2001) 3. Yang, S.: Research and Implementation of Barefoot Footprint Recognition Algorithm. Northeastern University, Shenyang (2005) 4. Elaziz, M.A., Oliva, D., Ewees, A.A., Xiong, S.: Multi-level thresholding-based grey scale image segmentation using multi-objective multi-verse optimizer. Expert Syst. Appl. 125 (2019) 5. Wang, L.F.: Research on threshold segmentation algorithm based on OTSU and maximum entropy. Harbin University of Science and Technology (2018) 6. Li, F., Kan, J.X.: Image fast two-dimensional maximum entropy threshold segmentation algorithm based on Sobel operator. Comput. Sci. 42(S1) (2015)

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7. Kapur, J.N., Sahoo, P.K., Wong, A.K.C.: A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 29(3), 273–285 (1985) 8. Brink, A.D.: Thresholding of digital images using two-dimensional entropies. Pattern Recogn. 25(8), 803–808 (1992) 9. Feng, B., Li, Z.T., Hua, G.L.: Image spam recognition method based on gray lever-gradient co-occurrence matrix. Commun. J. 34(02), 001-04 (2013)

Target Feature Extraction and Recognition of SAR Images Based on PCANet Pucheng Li, Junchen Li, Wen Yin and Lei Yang

Abstract In recent years, followed by the development of synthetic aperture radar imagery, target feature extraction and detection becomes a research hotspot. To facilitate SAR target recognition, a simple but powerful method, named by principal component analysis net (PCANet), is introduced for an accurate target feature extraction. Compared with conventional methods, shorter training time and fewer training samples are required in the proposed method. Experiment conducted on the canonical moving and stationary target acquisition and recognition (MSTAR) database is executed to examine the proposed method after the relevant features are extracted by the PCANet. Finally, support vector machine is adopted for the target recognition. It can be noted from the experimental results, the highest accuracy of the recognition can achieve 99.8% when using half of the training samples, which can validate the effectiveness of our proposed method. Keywords Synthetic aperture radar (SAR) · SAR image feature extraction · Target recognition · Principal component analysis net (PCANet)

1 Introduction Synthetic aperture radar (SAR) is an active and coherent microwave imaging sensor, and has been extensively used in civil and military fields because it can resist weather disturbance and work all the time. In recent years, SAR image target feature extraction and recognition have been greatly developed in SAR community [1–4]. With the development of deep learning, more and more researchers focus on the combination of convolutional deep neural network (ConvNet) and SAR target recognition [5, 6]. Compared with traditional feature extraction algorithms, the net methods is capable of utilizing the feature information in the SAR image in a better way. Because the net structure of traditional ConvNet is extremely complex, and its training time is longer, moreover, due to the sensitivity of SAR image field, it P. Li (B) · J. Li · W. Yin · L. Yang Tianjin Key Laboratory of Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_37

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Trainig SAR Images

2 Stages PCANet feature ExtracƟon

Training SVM classifier

Test SAR Images

Preprocessing

ClassificaƟon

Output

Fig. 1 PCANet flowchart

is difficult to have a relatively large data set. These are difficulties to SAR image feature extraction and recognition [7–9]. For the sake of extracting target features more effectively, we studied principal component analysis net (PCANet) and used it for SAR image target extraction and recognition. A PCANet and a traditional Convnet are roughly similar in structure which consist of multiple trainable stages [10]. In PCANet, a data-adapting convolution filter bank is selected as the basic PCA filter, and the nonlinear layer and the block-wise histograms of the binary codes are respectively choose as the feature pooling layer and the final output features of the network. The features of an input SAR image target can be extracted by 2-stage PCANet algorithm, as shown in Fig. 1. In the experiment, we employed moving and stationary target acquisition and recognition (MSTAR) image data set. Through feature extraction of MSTAR image with PCANet and recognition (classification) with support vector machine (SVM), the accuracy reached 99.8%, from which the validity of the proposed method is verified.

2 PCANet Model PCANet is a network designed for target classification and recognition. It has two obvious advantages: Firstly, PCANet has a simple network structure, which means it is easy to train for different deep learning tasks. Secondly, PCANet can overcome the speckle noise which commonly seen in SAR images. Therefore, PCANet is the preferred image classification mechanism we choose in this paper. As is shown in Fig. 1. The common PCANet structure usually consists of two stages which are basically similar in framework. The output of the network is the block-wise histogram with which we can realize the classification of SAR images. Suppose the size of input SAR images are m × n, and we have N input images N . The patch (kernel) size we choosed is k × k at both two stages. Under the [Si ]i=1 above conditions, we can briefly explain the PCANet model as follows.

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2.1 The First Stage For each input SAR image, the patch just like a sliding window. After each feature of SAR image is extracted by the sliding window, we can get all patches of the ith k×k , where each pi, j presents the jth vectorized image, i.e., pi,1 , pi,2 , . . . , pm, ˙ n˙ ∈ R patch in Si , and m˙ = m − [k/2], n˙ = n − [k/2]. When both the patches are meanremoved, the  feature extraction operation for a single picture is completed. We can get P¯i = p¯ i,1 , p¯ i,2 , . . . , p¯ m, ˙ n˙ . After repeating the above operations for all input images, all the quantized patches can be connected together, and we have P = [ p¯ 1 , p¯ 2 . . . , p¯ N ] ∈ R k

2

×N m˙ n˙

(1)

The number of filters in layer i is labelled Ci , we begin to compute the eigenvectors of PPT , and PCA filters Wc1 can be determined by C1 principle eigenvectors. Wc1 = matk,k (qc (PPT )) ∈ R k×k , c = 1, 2, . . . , C1

(2)

  where matk,k (v) is a function that maps v ∈ R k×k to a matrix W ∈ R k×k and qc P P T represents the cth principal eigenvector of P P T . The main information of variable correlation in training patches can be obtained by principal eigenvector. Just like a regular CNN network, we get the cth filter output of the first stage as Sic = Si ∗ Wc1 , i = 1, 2, . . . , N

(3)

where ∗ denotes two dimensional convolution. In order to make Sic have the same size as Si , the boundary of Si is zero-padded before convolving with Wc1 .

2.2 The Second Stage Similar to the first stage, in the second stage  we subtract the mean 2of the image from each filtered output and Q c = Q c = Q¯ c1 , Q¯ c2 , . . . , Q¯ Cc 2 ∈ R k ×N m˙ n˙ can be calculated from all the cth filtered outputs. Next, Q c can be combined together as   2 Q c = Q 1 , Q 2 , . . . , Q C1 ∈ R k ×C1 N m˙ n˙

(4)

It can be noted from (4) that the eigenvectors of Q Q T is computed and PCA filters in second stage can be determined by C2 principle eigenvectors. For each input Sic of the second stage, we will have C2 outputs, each convolves Sic with Wc2 , c = 1, 2, . . . , C2 , The number of outputs of the second stage is C1 C2 . Once the output of the filter is obtained, the second stage is completed.

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In the last stage, the output of the second stage is binarized Sic ∗Wc2 , i = 1, 2 . . . N ; C   c = 1, 2 . . . C2 by using the Heavisid step (like) function H Sic ∗ Wc2 c 2 , c = 1, 2 . . . C2 whose value is one indicating a positive term, otherwise it is zero. Around each pixel, we convert the vector of C2 binary bits into a decimal integer. c In this way, we get an  image of an integer value Ti in which each pixel value is  can C2 in the range 0, 2 − 1 .  C2 c−1  c We transform image Tic = H Si ∗ Wc2 into a histogram c=1 2   cfurther hist Ti . The feature of the input image Sic is defined as follows:

f i = hist (Tic ), . . . , hist (TiC1 )

(5)

The above is the process of PCANet. PCANet not only does not reduce the dimension, but upgrades the dimension, and the output data reaches several hundred thousand dimensions. That is to say, the simplest SVM classifier can achieve better results. This is why it’s so powerful in SAR image classification. The features computed from PCANet are performed in a linear SVM for training a model. It is worth noting that the model parameters are mainly consists of filter numbers C1 , C2 and patch size k × k. It has been proved that two-stage PCANet can perform very well. Therefore, in our experiment, the stage number is set to 2. Moreover, we observed that the detection results are affected by the size of patch. Parameter analysis will be described in detail in Sect. 3.

3 Experiment Analysis In this section, we employed PCANet for feature extraction and linear SVM for recognition, and recognition accuracy was used to evaluate the experimental results. In order to highlight the role of PCANet parameters, we also compared the results of different parameter settings. The experimental data are MSTAR SAR image database published on the internet and the size of each image is 256 × 256. There are ten kinds of ground targets in the MSTAR dataset, the optical images and SAR images of three of them are shown in Fig. 2. We select seven types of SAR target image in Table 1, 1622 of which were as training samples from 17° and 1365 as testing samples from 15°.

3.1 Impact of the Patch Size and Feature Numbers Considering the size of sliding block which also is known as patch size and the number of features are both important factors for recognition rate in a PCANet. We compare the recognition accuracy using SVM method among nine different feature number (14, 49, 105, 210, 315, 490, 1050, 1400, 1622) and six diverse patch size (3,

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Fig. 2 PCANet flowchart (Three of target and SAR images in MSTAR dataset)

Table 1 MSTAR database numbers

Target

Training set

Testing set

Label

BMP2-SN-9563

233

195

1

BMP2-SN-9566

232

196

2

BMP2-SN-C21

233

196

3

BTR-70-SN-C71

233

196

4

T72-SN-132

232

196

5

T72-SN-812

231

195

6

T72-SN-S7

228

191

7

1622

1365

All

None

5, 7, 9, 11, 13,15) in the experimentation simultaneously. And the result can be seen in Table 2. Table 2 presents the recognition rate of different features of radar target based on different patch size. With the increase of the patch size, the recognition rate of MSTAR dataset increase. We can also capture the increase of recognition rate while the number of features raise. Among all the experimentation data, the best recognition performances of PCANet can be achieved at the patch size of 11 and the number of feature of 1050, which is 99.9% and is sufficient enough to meet the actual requirements of radar target recognition task. When the patch size and the feature number increase further, although we have the possibility of obtaining higher recognition rate, but it also means a large amount of training time and computational resources consumption.

26.9

29.2

29.1

26.7

13

15

22.6

7

11

24.2

9

18

5

14

Feature

3

Patch size

Table 2 Recognition rate (%)

78

76.3

75.4

68.3

55.5

41.6

18.5

49

93.1

92.1

88.7

85.3

72.8

51.8

22.3

105

99.4

98.5

97.5

95.6

88.9

65.8

24.7

210

99.6

99.7

99.2

98.1

94.3

75.8

26.7

315

99.9

99.9

99.8

99.6

96.8

82.3

26.8

490

99.9

99.7

99.9

99.5

98

84.7

27

1050

99.6

99.9

99.9

99.4

98

85.1

24.2

1400

99.8

99.8

99.8

99.5

98.1

85.1

26.8

1622

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Fig. 3 Adaptability to training samples

3.2 Adaptability to Training Samples In this experiments, in order to verify whether PCANet can adapt to less data, we let patch size takes 11 and randomly selected 2, 7, 15, 30, 45, 70 and 150 samples from each training set for training, keeps all the extracted features. Then we tested all the test sets and draws a curve drew a curve, as shown in Fig. 3. As can be seen from Fig. 3, when the number of training samples for each type of data is less than 70, the growth curve of recognition rate is very steep, and when the number of training samples is greater than 70, the recognition rate has reached 96.5%. The effect of increasing the number of training samples on the improvement of recognition rate is not obvious, which indicates that PCANet has a good adaptability to a small number of data.

4 Conclusion In this paper, we used a simple and powerful PCANet to extract the features of MSTAR image targets. Through the first experiment, patchsize matching with MSTAR data is selected and ideal accuracy can be achieved under the condition of few features being extracted. It proves that PCANet has a good dimensionality reduction effect. The second experiment shows that PCANet still has a good adaptability to less data, so PCANet has a promising application prospect in SAR recognition field without training samples.

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References 1. Solberg, A.H.S., Jain, A.K., Taxt, T.: Multisource classification of remotely sensed data: fusion of LANDSAT TM and SAR images. J. IEEE Trans. Geosci. Remote Sens. 32, 768–778 (1994) 2. Zhao, Q., Principe, J.C.: Support vector machines for SAR automatic target recognition. J. IEEE Trans. Aerosp. Electron. Syst. 37, 643–654 (2001) 3. Han, P., Wu, J.X., Wu, R.B.: SAR target feature extraction and recognition based on 2D-DLPP. J. Phys. Procedia 24, 1431–1436 (2012) 4. Wang, D.G., Yang, Z.L., Chang, S.: SAR image recognition combined bidirectional 2DPCA with PCA. J. Adv. Mater. Res. 756–759, 4041–4044 (2013) 5. Gao, F., Dong, J.Y., Li, B., et al.: Automatic change detection in synthetic aperture radar images based on PCANet. J. IEEE Geosci. Remote Sens. Lett. 13, 1792–1796 (2016) 6. Li, M., Li, M., Zhang, P., et al.: SAR image change detection using PCANet guided by saliency detection. J. IEEE Geosci. Remote Sens. Lett. 16, 402–406 (2019) 7. Luu, H., Pham, M.V., Man, C. D., et al.: Comparison of various image fusion methods for impervious surface classification from VNREDSat-1. Int. J. Adv. Cult. Technol. (2018) 8. Xie, Q.L., Chen, Z., Chen, H., et al.: Nonrigid registration of cardiac DSCT images by integrating intensity and point features. J. Biomed. Signal Process. Control 47, 224–230 (2019) 9. Yue, X., Kiely, J., McLeod, C.: Analyses of parasitic capacitance effects and flicker noise of the DAC capacitor array for high resolution SAR ADCs. Int. J. Comput. Appl. Technol. 58, 259–266 (2018) 10. Chan, T.H., Jia, K., Gao, S., et al.: PCANet: a simple deep learning baseline for image classification? J. IEEE Trans. Image Process. 24, 5017–5032 (2014)

Evaluation on Symbiotic Performance of Regional Technological Entrepreneurship Ecosystem Chunxiao Sun, Chunyan Li and Jianhua Zhang

Abstract This paper analyzes the components of the regional technological entrepreneurship ecosystem which include the entrepreneurial ecological population and supporting environment from the perspective of ecological theory, and further builds the evaluation index system of population and environment symbiotic performance in the ecosystem. By using the entropy weight coefficient model and the gray system evaluation model, collecting data through questionnaire survey from the characteristic town of technological industry of Hangzhou in China, this paper evaluates population and environment symbiotic performance of the technological entrepreneurship ecosystem and illustrates the final correlation degree is 0.783, indicating that the overall construction and operation situation of the entrepreneurial ecosystem is acceptable. Except for the scientific and technological environment, cultural environment, natural environment and government services, there is a gap with the ideal situation at the correlation degree of market environment, technological intermediaries, science, education and technological start-ups. Keywords Symbiotic performance · Entrepreneurship ecosystem · Ecological population · Gray system evaluation

1 Introduction As technological entrepreneurship increasingly optimizes regional economic structure and promotes economic growth, practitioners are committed to strengthening technological entrepreneurship capabilities and accelerating the industrialization of scientific and technological achievements in many regions [1]. Scholars gradually focus on research of regional technology entrepreneurship ecosystems [2, 3]. C. Sun (B) · C. Li Zhijiang College, Zhejiang University of Technology, 312030 Shaoxing, China e-mail: [email protected] J. Zhang School of Electrical Engineering, Hebei University of Science and Technology, 050018 Shijiazhuang, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_38

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The regional technological entrepreneurship ecosystem is a composite system composed of various resource elements in a certain social environment [4]. Because technological entrepreneurship has highly similar input and output characteristics, growth, competitiveness, environmental adaptability, and periodicity, the technological entrepreneurship system can be regarded as a special type of ecological environment [5]. The main task of ecology is to systematically study the relationship between living things and between living things and living environment. The ecosystem theory of ecological research has important reference and guiding significance for the research of regional technological entrepreneurial ecosystem. In entrepreneurship ecosystem research, scholars focus on identifying the core attributes of existing ecosystems [6–8]. And the studies have separated key components of several highly regarded ecosystems, but it is increasingly clear that to understand entrepreneurship ecosystem and how it is generated, it is necessary to go beyond the list of generated attributes [9]. In fact, the scholars believe that a key constraint on current entrepreneurship ecosystem research is that it focuses on system components, but there is little understanding of the interdependencies between components and how to evaluate the results of the interdependencies [10]. For nearly two decades, entrepreneurship ecosystems have been the research goal of academy and industry; however, due to the lack of attention to the complex interactions between agents, organizations and sociocultural forces, we have little knowledge of how ecosystems emerge and evolve [9]. Attempts have been made to explain the emergence of based on entrepreneurial and corporate dimensions; however, no specific theory has been proposed to evaluate the complexity the symbiosis results of these agents, organizations and sociocultural forces in entrepreneurship ecosystems. Based on the previous researches on the components of the entrepreneurial ecosystem, this paper combines the entropy weight coefficient method and the gray relational analysis to analyze and evaluate the results of the symbiosis of the ecological population of the technological entrepreneurship ecosystem [11]. The structure of this paper is as follows: First, the theory and method of ecology are extended to the research of technological entrepreneurship, and the system of technological entrepreneurship is systematically constructed. Secondly, the Symbiotic Performance of the regional technological entrepreneurial ecosystem and its evaluation index system are designed. Thirdly, the symbiotic performance evaluation model of the regional technological enterprise entrepreneurial ecosystem is proposed. The fourth is to evaluate the entrepreneurial ecosystem of Hangzhou science and technological enterprises in China.

2 System Construction From the perspective of ecosystem theory, in a certain region, like a creature, technological entrepreneurs cannot live alone for a long time, and it will inevitably depend directly or indirectly on other companies or organizations exists and forms

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a regular economic community. In this community, compared with every technological start-ups, the other affiliated enterprises or organizations around it, together with the social and economic environment, constitute the external conditions for their survival. The entrepreneurial enterprise exchanges material, energy and information with its external organization and environment. They form a community of mutual influence, mutual dependence and common development together. Therefore, this community is actually a technological entrepreneurship ecosystem. According to the theory of ecosystem theory, in this paper we believes that the technological entrepreneurship ecosystem is a holistic social system formed by the interaction between the nodes in the technological entrepreneurship system and interaction between the entrepreneurial system and its ecological environment. Similar to the biological individual in the natural ecosystem, the operation law of the technological entrepreneurial ecosystem is similar in many aspects to the laws in the biological ecology field. The social system formed by the interaction between enterprises, organizations and institutions and the interaction is regarded as the technological entrepreneurship ecosystem. The structure of the regional technological entrepreneurship ecosystem refers to the way in which the various elements of the entrepreneurial system are organized and the ways or sequences in which they interact or influence in space or time [12]. Different interactions between the components of the ecosystem can produce different results. To understand the results of the technological entrepreneurial ecosystem, this paper selects the ecosystem represented by Hangzhou’s emerging industrial characteristic towns in China to conduct an empirical investigation to prove its ecological population symbiotic performance. The regional technological entrepreneurial ecosystem consists of two parts: the entrepreneurial ecological population and the support environment. According to the existing research, by organizing and reviewing the literature, this paper illustrates the regional technological entrepreneurial ecosystem evaluation index system shown in Table 1 [13, 14]. The regional social support environment includes four first-level indicators of economic environment (X1 ), scientific and technological environment (X2 ), cultural environment (X3 ) and natural environment (X4 ), and 16 secondary indicators attached to them (from X11 to X44 ); The regional technological entrepreneurial ecological population includes six types of populations, including governments service (X5 ), educational and research institutions (X6 ), investment and financing institutions (X7 ), science and technological intermediary service institutions (X8 ), market environment (X9 ), and technological start-up enterprises (X10 ), and 24 secondary indicators attached to them which undertake different functions in the technological entrepreneurship ecosystem (from X51 to X104 ). Due to the length limit of the paper, the interpretation factors of the secondary indicator are omitted in the text.

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Table 1 Regional technological entrepreneurship ecosystem evaluation index system Factors

First level indicator

Subjects being evaluated

Regional society external support environment (Y1 )

Economic Environment (X1 )

Society environment

Technological Environment (X2 ) Cultural Environment (X3 ) Natural Environment (X4 )

Regional technological entrepreneurship ecological population (Y2 )

Government Services (X5 )

Government support

Science and Education (X6 )

Universities & research institution

Financial Services (X7 )

Investment & financing institution

Technology Intermediary Service (X8 )

technological intermediary

Market Situation (X9 )

Affiliate

Technological Start-ups (X10 )

Technological start-up

3 System Evaluation Model 3.1 Evaluation Index System Establishing a evaluation index system on regional technological entrepreneurship ecosystem needs to follow certain principles, including demand orientation principles, the evaluation indicators should be set according to the needs or satisfaction of technological entrepreneurs; systematic principles, the integrity and dynamics of the system should be fully considered, the comprehensiveness of the system reflecting the information; operational principle, the indicators should be designed to select some representative and typical indicators, and the criteria for selecting the indicators should be both to reduce the evaluation workload and to facilitate the fuller [15]. The situation reflects the reality of the regional technological entrepreneurship ecosystem. Then, according to the existed literature on composition of the regional technological entrepreneurial ecosystem, the evaluation index system consists of two parts, which are the regional social support environment and ecological population in the regional technological entrepreneurial [16]. Among them, the regional social support environment includes four first-level indicators of economic environment, scientific and technological environment, cultural environment and natural environment, and 16 secondary indicators attached to them; regional technological entrepreneurial ecological population includes government service, financial service, science and education, market environment, the technological intermediary service and the technological start-up enterprise have six first-level indicators and 24 secondary indicators attached to them.

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3.2 Evaluation Model 3.2.1

Entropy Weight Coefficient Model

When a system is likely to be in multiple states, and the probability of occurrence of each state is expressed in terms of pi , (i = 1, 2, …, m), the entropy of the system is calculated as: E =−

m 

pi ln pi

(1)

i=1

Obviously, when the probability of each state is equal, i.e. pi = 1/m, (i = 1, 2, …, m), the entropy value of the system is the largest, and its calculation formula is: E max = ln m

(2)

Assuming that there are m states in the system and there are n evaluation indicators, the original indicator matrix can be expressed as R = (rij )m*n . The formula for calculating the information entropy of a certain indicator of the system is: Ei = −

m 

pi j ln pi j

(3)

i=1

In the formula, p is the probability that the state j of the indicator i appears. It can be seen that the smaller the information entropy value of an indicator, the greater the degree of variation of the index value, the richer the information that can be provided, and the greater the influence exerted in the evaluation, so the weight of the indicator is greater. Conversely, the larger the information entropy value of an indicator, the smaller the degree of variation of the indicator value, the less information that can be provided, and the smaller the effect of the evaluation, the smaller the weight of the indicator. Therefore, the weight of each evaluation index can be calculated according to the degree of variation reflected by the information entropy value of each indicator.

3.2.2

Gray System Evaluation Model

Many and complicated factors affect the start-up of technological companies. We don’t know all the influencing factors and can only choose some main indicators when evaluating. In addition, the original data of the evaluation index is subjective and has incomplete information or “gray” characteristics. Therefore, the evaluation of regional technological entrepreneurial ecosystem is a typical gray system evaluation problem, which is more suitable for evaluation using gray system theory. The gray relational analysis is based on the original sample data of each indicator, and the gray correlation degree is used to describe the relationship, strength and order

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of the relationship between the factors [15, 17]. If the original sample data reflects that the changes in the size, speed, and direction of the two factors are basically the same, it means that the degree of correlation between them is large; on the contrary, it indicates that the degree of association is small. In general, the steps of gray correlation analysis: the survey value of each target of the evaluated object constitutes a comparison sequence Xi , and the ideal value of each index constitutes a reference sequence X0, X 0 = (x0 (1), x0 (2), . . . , x 0 (n)) Xi = (xi (1), xi (2), . . . , xi (n)) (i = 1, 2, . . . , m) Using the initial value method, the normalized formula is: X i (k) = X i (k)/ X 0 (k) (i = 1, 2, . . . , m; k = 1, 2, . . . , n)

(4)

where Xi (k) indicates the survey value of each indicator of the object to be evaluated, X i (k) represents the normalized index values, X0 (k) indicates the ideal value for each indicator. Then, we calculate the difference sequence, the minimum difference and the maximum difference, and calculate the absolute difference between the comparison sequence x i and the reference sequence x 0 corresponding index.   0i (k) =  X i (k) − X 0 (k) (i = 1, 2, . . . , m; k = 1, 2, . . . , n)

(5)

Among the absolute differences, the maximum and minimum are the maximum difference (max) and minimum difference (min). Calculate the correlation coefficient, the formula is: ξ0i (k) =

(min) + ρ(max) 0i (k) + ρ(max)

(6)

The value of the resolution coefficient ρ is in the range of (0, 1), generally in the range of 0.1–0.5. The smaller the resolution coefficient, the more the difference between the correlation coefficients can be increased. Correlation coefficient ξ0i (k) is a positive number not greater than 1. The degree of association between the reference sequence X0 and the comparison sequence Xi is generally reflected by n correlation coefficients. γ0i =

n 

ωk ξ0i (k) (i = 1, 2, . . . , m)

(7)

k=1

Let Wx be a vector consisting of the weights of the first-level indicators. Wxi is a vector consisting of the weights of the secondary indicators, and the final relevance of the multilevel evaluation system is calculated. The correlation degree of the secondary indicators is calculated:

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Rxi = Wxi [ξ0i (1), ξ0i (2), . . . , ξ0i (k)]T (c = 1, 2, . . . , p)

407

(8)

The correlation degree calculation of the first level indicator is:  T RY = Wx Rx1 , Rx2 , . . . , Rx p

(9)

4 Symbiotic Performance Evaluation 4.1 Questionnaire Survey The survey sample selected in this paper covers the fields of bio-electronic information, electronic computer and office equipment manufacturing, and new materials in Hangzhou’s emerging industrial towns. The companies surveyed were established for a short time and belonged to technological companies. The target company’s environmental requirements for entrepreneurship are often more demanding. A total of 260 questionnaires were sent out in this survey, and 197 were recovered. The receiving rate was 75.8%, of which 176 were valid questionnaires, and the effective receiving rate was 89.3%. Each indicator in the questionnaire contains two judgments: one is to require the respondent to judge the importance of each indicator; the other is to ask the respondent to judge the status of the indicator in Hangzhou. Each item is measured by the Likert Scale with 5-point, and the attitude or opinion of the phenomenon in the investigation is judged according to the score of each item. The higher the score, the more the respondent agrees with this statement.

4.2 Evaluation Process The comprehensive evaluation of the technological entrepreneurial ecosystem in Hangzhou, China was carried out by using the entropy weight coefficient model and the gray system evaluation model. The first model is used to determine the weight of each indicator; the second is used for comprehensive evaluation.

4.2.1

Weight of Each Indicator

The entropy weight coefficient model is used to comprehensively analyze the firstlevel and the second-level indicators of the technological entrepreneurial ecosystem to determine their respective weights. The data is classified, and the selection frequency of each option in each indicator is counted as xij and a 10 × 5 matrix will be

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Table 2 Entropy (Ej ) and weight coefficient (wj ) of the primary indicator

Indicator name

Entropy

Value weight

Economic Environment (X1)

0.954

0.096

Technological Environment (X2)

1.035

0.087

Cultural Environment (X3)

1.136

0.074

Natural Environment (X4)

1.106

0.075

Government Services (X5)

0.871

0.113

Science and Education (X6)

0.962

0.095

Financial Services (X7)

0.881

0.107

Technological Intermediary Service (X8)

0.886

0.106

Market Situation (X9)

0.921

0.105

Technological Start-ups (X10)

0.675

0.138

obtained. We calculate the proportion of the i-th option belonging to the j-th indicator to the index based on the matrix pij and calculate the entropy value Ej of the j-th indicator in each matrix. The weight wj of the j-th indicator based on the entropy value will be calculated, which is: (1 − e j ) 1 (e j = E j ) w j = 10 ln j=1 (1 − e j )

(10)

It can be seen that if the difference of the j-th indicator is larger, the smaller the ej is, the greater its weight wj will be, indicating that the impact of the indicator on the regional technological entrepreneurial ecosystem will be greater. The entropy values of each indicator are calculated by Eq. (10), and the weight coefficients of each level indicator are calculated. Due to the length of the paper, the table of secondary weights is omitted from this paper (Table 2).

4.2.2

Comprehensive Evaluation

The comparison sequence is the evaluation index value of the technological Entrepreneurship Ecosystem of Hangzhou. Each secondary indicator value is the data obtained from the survey, and its score is converted on a 5-point scale. The positive indicator is generally the higher the score, the closer to the ideal state, the reverse index is the opposite. In the forward indicator reference sequence (ideal sequence), the index value is optimally 5, and the reverse index is 1 being optimal. Using the initial value method, the initial data is normalized. We use Formulas (5) and (6) to calculate the correlation coefficient between each secondary index and the corresponding ideal value (kij ) in the reference sequence.

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(max) = 0.791, (min) = 0.075, the resolution factor is 0.1, then ξ0i (k) =

(min) + ρ(max) 0.075 + 0.1 × 0.791 = = 0.283 0i (k) + ρ(max) 0.465 + 0.1 × 0.791

(11)

And so on, the correlation coefficient between each secondary indicator and the corresponding ideal value can be obtained. Due to the length of the paper, the relevance of the secondary indicators is omitted. Using Formula (8), the degree of correlation RXi of the first-order indicator sequence and the corresponding ideal sequence is obtained, and the correlation degree between the economic environment and the ideal environment is calculated as an example. The specific calculation is as follows: Rx1 = Wx1 [ξ01 (1), ξ01 (2), . . . , ξ01 (k)]T = 0.712

(12)

By analogy, the correlation between the first-level indicator and the corresponding ideal environment can be obtained. The results are shown in Table 3. The relevance of the final evaluation index is calculate using Formula (9), Ry =0.783.

5 Conclusion The final correlation degree is 0.783, which indicates that the overall situation of the technological entrepreneurship ecosystem in Hangzhou is acceptable. From the evaluation of the correlation degree of the first-level indicators, it is concluded that the scientific and technological environment, cultural environment, natural environment and government services in the ecosystem are highly correlated and perform well. The market environment, technological intermediaries, science and education and their ideal environment still have a certain gap. In particular, technological start-ups have the lowest correlation, reaching only 0.538. This paper puts forward five suggestions: First, improve the entrepreneurial policies and regulations, establish a policy support system; second, keep the government’s service level, strengthen technological entrepreneurship services and guidance; third, accelerate the cultivation of venture capital and establish diversified financing channels; The fourth is to focus on the needs of technological entrepreneurship and strengthen the construction of innovation and entrepreneurship platforms; the fifth is to increase the intensity of talent introduction and training, and enhance the ability of innovation and entrepreneurship. Due to limited time, this paper only conducts an empirical analysis of technological Entrepreneurship Ecosystem in Hangzhou City. The survey data collection is limited to this region. If there is more general guiding significance for the regional technological entrepreneurship environment optimization, it is necessary to further expand the scope of empirical research. A more in-depth comparative analysis of technological entrepreneurial ecosystems at different levels and scales is needed.

Rx2

0.865

Rx1

0.712

0.829

Rx3 0.916

Rx4 0.879

Rx5 0.654

Rx6 0.785

Rx7

0.645

Rx8

0.663

Rx9

Table 3 Relevance (coefficient) of the first-level indicators of the technological entrepreneurship ecosystem in Hangzhou, China 0.538

Rx10

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Acknowledgements This study was financially supported by National Social Science Fund Project (Evolution Mechanism and Symbiotic Performance of Entrepreneurial Ecosystem from the Perspective of Regional Characteristic Towns, Project No. 17YBJ036).

References 1. Stam, E., Spigel, B.: Entrepreneurial ecosystems. In: Blackburn, R., De Clercq, D., Heinonen, J., Wang, Z. (eds.) Sage Handbook for Entrepreneurship and Small Business (2017, in press) 2. Cumming, D.J., Johan, S.: Technology parks and entrepreneurial outcomes around the world. Int. J. Manag. Financ. 9, 279–293 (2013) 3. Dong, L.J., Yan, H., Feng, L.J., Tan, Q.F.: Modelling and performance analysis of designed energy-efficient EHA under gravity loads. Int. J. Model. Ident. Control 30(4), 253–260 (2018) 4. Acs, Z.J., Autio, E., Szerb, L.: National systems of entrepreneurship: measurement issues and policy implications. Res. Policy 43(3), 476–494 (2014) 5. Sun, H.Ch.: Construction, evaluation and secondary entrepreneurship of innovation ecosystem in development zones. Doctoral Dissertation. Tianjin University (2007) 6. Spigel, B.: The relational organization of entrepreneurial ecosystems. Entrep. Theory Pract. 41, 49–72 (2017) 7. Isenberg, D.: How to start an entrepreneurial revolution. Harv. Bus. Rev. 88(6), 40–50 (2010) 8. Isenberg, D.: The entrepreneurship ecosystem strategy as a new paradigm for economic policy: principles for cultivating entrepreneurship, invited presentation at the Institute of International and European Affairs, Dublin, Ireland, May 12(2011) 9. Auerswald, P.E.: Enabling entrepreneurial ecosystems: insights from ecology to inform effective entrepreneurship policy. Kauffman Foundation Research Series on City, Metro, and Regional Entrepreneurship (2015) 10. Mack, E., Mayer, H.: The evolutionary dynamics of entrepreneurial ecosystems. Urban Stud. 53, 2118–2133 (2016) 11. Srimanti, R., Anish, D.: Identification of multi-delay systems using orthogonal hybrid functions in state space environment. Int. J. Model. Ident. Control 30(2), 93–104 (2018) 12. Yang, J., Yang, F., Wang, S.H.: Research on operation mechanism of regional innovation system based on system dynamics. Sci. Manag. Res. 4, 1–6 (2010) 13. Theodoraki, C., Messeghem, K.: Exploring the entrepreneurial ecosystem in the field of entrepreneurial support: a multi-level approach. Int. J. Entrep. Small Bus. 31, 47–65 (2017) 14. Auerswald, P.E., Dani, L.: The adaptive life cycle of entrepreneurial ecosystems: the biotechnology cluster. Small Bus. Econ. 49, 97–117 (2017) 15. Kpoor, R., Agarwal, S.: Sustaining superior performance in business ecosystems: evidence from application software developers in the iOS and Android smartphone ecosystems. Organ. Sci. 28(3), 531–551 (2017) 16. Rampersad, G.C.: Entrepreneurial ecosystems: A governance perspective. J. Res. Bus. Econ. Manag. 7(3), 1122–1134 (2016) 17. Cumming, D. Werth, J., Zhang, Y.: Governance in entrepreneurial ecosystems: venture capitalists vs. technology parks. In: Small Business Economics Special Issue Development Conference: The Governance of Entrepreneurial Ecosystems. Catania, Italy, 29–39 Sept (2016)

Fixed-Time Terminal Sliding Mode Control for Quadrotor Aircraft Jie Wang, Xiao Ma, Gaowei Zhang, Yan Zhang and Qing Miao

Abstract The fixed-time trajectory tracking problem of a quadrotor with six degrees of freedom (6-DOF) under bounded disturbances is investigated in this paper. The split-loop design method which divides the quadrotor into position subsystem and attitude subsystem is adopted. Next, the nonsingular fixed-time controllers are developed and both the inner and outer loop can track the expected trajectory within fixed-time. The settling time depends only on the selected control parameters and is independent of the system’s initial state. The stability of the entire system is proved. Finally, the simulation studies based on the quadrotor model illustrate the robustness of the designed fixed-time controller. Keywords Fixed-time · Terminal sliding mode control (TSMC) · Quadrotor · Trajectory tracking

1 Introduction The quadrotor aircraft has received extensive attention from researchers due to the excellent performance in surveillance, data acquisition, reconnaissance mission, traffic monitoring, and rescue [1–4]. However, as is well known, the quadrotor system has under-actuated, strong coupling and nonlinear characteristics which increase the difficulty of controller design [5]. Recently, many control algorithms have been developed to implement the control problem of a quadrotor. In [6], A novel nonlinear PID nonlinear controller is proposed to regulate the posture of the quadrotor. In [7], a backstepping control strategy is presented having in mind that the quadrotor consists of under-actuated subsystem, fully-actuated subsystem and propeller subsystem. In [8], a feedback linearization technology is applied to realize tracking objective of a quadrotor with rotor failure. Sliding mode control (SMC) is a conventional means in quadrotor control because it J. Wang (B) · X. Ma · G. Zhang · Y. Zhang · Q. Miao School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_39

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has strong robustness against disturbances [9]. In [10], an adaptive SMC controller for quadrotor is designed without the knowledge of uncertainties and perturbations bound. However, the results mentioned above can only guarantee the asymptotic convergence of the quadrotor system. For achieving better dynamic property, nonsingular terminal SMC (NTSMC) is investigated [11–14]. However, the system’s initial state affects the finite time convergence which leads to limitations in practical applications. In a fixed-time control strategy, the resolution time is not affected by the initial state. In [15], a fixed-time TSMC technique is applied to implement tracking problem of the quadrotor. However, the form of the sliding mode surface is complicated, and there are many design parameters involved, which is difficult to apply in practice. In [16], a new fixed-time SMC is applied to guarantee fixed-time convergence for reusable launch vehicles. Inspired by all the studies mentioned above, a fixed-time control strategy is presented with a fixed-time sliding mode surface. Due to the nonlinear, under-actuated and coupling characteristics of the quadrotor, it is very difficult to design the controller directly. Therefore, the split-loop design method which divides the multiple UAVs system into position subsystem and attitude subsystem is adopted. An NTSMC controller is applied to achieve fixed-time stability of the quadrotor systems, while ensuring that the tracking errors approach zero within fixed-time.

2 Problem Statement 2.1 Control-Oriented Model of Quadrotors The dynamical model of the quadrotor is described in details by Liu [17]. Consider the quadrotor translational dynamic described by equations ⎧ ⎨ x¨ = u1 (cos φ sin θ cos ψ + sin φ sin ψ) − K1 x˙ /m + d1 y¨ = u1 (sin φ sin θ cos ψ − cos φ sin ψ) − K2 y˙ /m + d2 (1) ⎩ z¨ = u1 cos φ cos ψ − g − K3 z˙ /m + d3 where p = [x, y, z]T and v = [˙x, y˙ , z˙ ]T = [vx , vy , vz ]T denote position and velocity vectors in the inertial frame, m represents the quality of the aircraft, Ki , i = 1, 2, 3. denote the drag coefficients, dp = [d1 , d2 , d3 ]T is external bounded disturbances. The rotational dynamic equations can be derived as ⎧ ˙ 1 + d4 ⎨ θ¨ = u2 − lK4 θ/I ˙ 2 + d5 (2) ψ¨ = u3 − lK5 ψ/I ⎩¨ ˙ φ = u4 − lK6 φ/I3 + d6 ˙ ψ, ˙ φ] ˙ T = [ωθ , ωψ , ωφ ]T indicate the Euler angles where Θ = [θ, ψ, φ]T and ω = [θ, and angular rates. l is the radius of the quadrotors aircraft, which is the distance from

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each end of the rotor to the aircraft mass center, Ii , i = 1, 2, 3. are inertias of the body due to rotations around, g represents the gravity acceleration, dΘ = [d4 , d5 , d6 ]T is external bounded disturbances. In addition, the relationship between intermediate controls input signals ui , i = 2, 3, 4 and propeller forces F = [F1 , F2 , F3 , F4 ]T can be expressed as Based on the translational dynamic system (1), define the following equation ⎧ ⎨ u1x = u1 (cos φ sin θ cos ψ + sin φ sin ψ) u1y = u1 (sin φ sin θ cos ψ − cos φ sin ψ) ⎩ u1z = u1 cos φ cos ψ

(3)

T  Define up = u1x , u1y , u1z as the new control, and fp = −[0 0 g]T − diag([− Km1 , − Km2 , − Km3 ])v. The position subsystem can be derived as 

p˙ = v v˙ = up + fp + dp

(4)

Denote uΘ = [u2 , u3 , u4 ]T and fΘ = [−lK4 /I1 , −lK5 /I2 , −lK6 /I3 ]ω, the attitude subsystem (2) can be described as 

Θ˙ = ω ω˙ = uΘ + fΘ + dΘ

(5)

Assumption 1 There is a constant λ satisfying max(|di |) ≤ λ, i = 1, ..., 6.

2.2 Control Objective Propose a control scheme such that the position outputs p = [x, y, z]T track the expected trajectory pd = [xd , yd , zd ]T in a fixed-time. The attitude of roll angle φ tracks its reference command φd and the attitude angles θd , ψd which are solved as follows remain steady and bounded within fixed-time. The solution process is the same as [17], the reference yaw angle command of the quadrotor is ψd = arctan((sin φd cos φd · u11 − cos2 φd · u12 )/u13 )

(6)

and the reference roll angle command is ⎧ ⎨ π/2, θd = arcsin(X ), ⎩ −π/2,

X >1 |X | ≤ 1 X < −1

(7)

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where X = (cos φd (cos φd · u11 + sin φd · u12 ))/u13

(8)

3 Controller Design Lemma 1 [16] Consider a system with zero equilibrium x˙ = f (x, t), x(0) = x0 , if there is a Lyapunov function V (x) satisfying V (x) = 0, x → 0 and V˙ ≤ −(aV p + bV q )k , ∀x(t) for a, b, p, q, k > 0, pk < 1, qk > 1, then the state converges to equilibrium in fixed-time T (x0 ) T (x0 ) ≤

1 1 + , ∀x0 ∈ Rn ak (1 − pk) bk (qk − 1)

(9)

The position subsystem (4) and attitude subsystem (5) can be rewritten as a secondorder integral form as follows  i x˙ 1 = x2i , i = 1, ..., 6 (10) x˙ 2i = ui + f i + di where [pT , Θ T ]T = [x11 , x12 , x13 , x14 , x15 , x16 ]T , [fpT , fΘT ]T = [f 1 , f 2 , f 3 , f 4 , f 5 , f 6 ]T , [upT , T T ] = [u1 , u2 , u3 , u4 , u5 , u6 ]T . By defining the desired trajectory [pdT , ΘdT ]T = uΘ 1 [xd , xd2 , xd3 , xd4 , xd5 , xd6 ]T , the control objective of the work can be converted to x1i → xdi in fixed-time. The tracking error is defined as ei = x1i − xdi . The NFTSM [16] is defined as p1i i

p2i i

p3i i

si = (˙ei ) q1 + ai (ei ) q2 + bi (ei ) q3

(11)

where ai > 0, bi > 0, and pki , qki , k = 1, 2, 3 are positive odd integers satisfying 1 < p2i /q2i < p1i /q1i < p3i /q3i < 2 and (q1i )2 p3i /((p1i )2 q3i ) < 1, i = 1, ..., 6. Then the fixed-time controller for error system is selected as

ui =

p1i

2− i qi − p1i (˙ei ) q1 1 p1i



p2i

i −1 pi ai q2i (ei ) q2 e˙ i 2 p1i

1− i i −1 qi − p1i μi ((˙ei ) q1 )((˙ei ) q1 1

+ p2i q2i

p3i

i −1 pi bi q3i (ei ) q3 3 p3i q3i

)(ai si + bi si )

q1i p1i

(12)

− (f i − x¨ di + ksgn(si ))

where k = 2λ. There exists a constant τ > 0, satisfying if |x| ≤ τ , μi (x) = sin( π2 τx 2 ), otherwise, μi (x) = 1. 2

Theorem 1 Considering the system of (10), when the NFTSM is selected as (11) and the controller is designed as (12), then the tracking errors converge to zero in

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fixed-time under Assumption 1, such that the position and attitude angle track the desired value in fixed-time T < Tmax = 2T1i + T2i

(13)

where 1

T1i =

1

+

q1i p1i

ai (1 −

p2i q1i ) q2i p1i

bi

(14)

pi qi ( q3i p1i 3 1

− 1)

4τ (1/(p1 /q1 −1)) k i

T2i =

q1i p1i

i

(15)

Proof The derivation of the NFTSM (11) is

s˙i = =

p1i

i −1 p1i (˙ei ) q1 e¨ i q1i p1i

p2i i

pi

+ ai q2i (ei ) q2

−1

2

i −1 p1i (˙ei ) q1 (ui q1i

p3i i

pi

e˙ i + bi q3i (ei ) q3 3

+ f + di − i

x¨ di )

+

−1

e˙ i

p2i

i −1 pi ai q2i (ei ) q2 e˙ i 2

+

p3i

i −1 pi bi q3i (ei ) q3 e˙ i 3

(16)

Replacing the control law ui with (12) results in s˙i = −μi ((˙e ) i

p1i q1i

−1

p2i q2i

p3i q3i

q1i i

pi

)(ai si + bi si ) p1 −

p1i i q1i −1 (˙e ) 1 (ksgn(si ) − di ) q1i

(17)

Consider Lyapunov function Vi = |si | , i = 1, ..., 6, and its time derivation is V˙i = sgn(si )˙si = −μi ((˙e ) i

p1i q1i

−1

With the facts (˙e ) i

p2i q2i

p3i q3i

)sgn(si )(ai si + bi si ) p1i q1i

−1

q1i p1i

+

p1i

i −1 p1i (˙ei ) q1 (di sgn(si ) q1i

− k)

(18)

≥ 0, max(|di |) ≤ λ, Eq. (18) can be further expressed as

V˙i ≤ −μi ((˙ei ) = −μi ((˙e ) i

= −μi ((˙ei )

p1i q1i

p1i q1i p1i q1i

−1

−1 −1

p2i q2i

p3i q3i

q1i i

)sgn(si )(ai si + bi si ) p1

)(ai |si | )(ai Vi

p2i q2i

p2i q2i

p3i q3i

+ bi |si | ) p3i q3i

+ bi Vi )

q1i p1i

q1i p1i

(19)

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pi /qi −1

If (˙ei ) 1 1 > τ , we have μi = 1, therefore V˙i ≤ −(ai Vi

p2i q2i

p3i q3i

q1i i

+ bi Vi ) p1

(20)

Since p2i q1i /q2i p1i < 1, p3i q1i /q3i p1i > 1, applying Lemma 1 Vi will converge to zero

pi /qi −1

or enter (˙ei ) 1 1 ≤ τ in fixed-time T1i .



pi /qi −1

In the region (˙ei ) 1 1 ≤ τ , based on the controller (12), we have  pi pi pi e¨ i = di − ksgn(si ) − q1i p1i

− μi ((˙ei )

p1i q1i

−1

1

2− i q1i (˙ei ) q1 p1i

)((˙ei )

pi 1− 1i q1

2 i

pi

ai q2i (ei ) q2

−1

2

p2i q2i

p3i q3i

)(ai si + bi si )

pi

3 i

e˙ i + bi q3i (ei ) q3 3

q1i p1i

−1

(21)

When ei → 0, we have e¨ i → di − ksgn(si ). For a small τ , we have e¨ i = di − 2λ ≤

pi /qi −1

−λ for si > 0 and e¨ i = di + 2λ ≥ λ for si < 0. Thus Vi will leave (˙ei ) 1 1 ≤ τ in fixed-time T2i . So Vi will converge to zero in fixed-time T1i + T2i . Setting si = 0, we can obtain e˙ = −(ai (e ) i

i

p2i q2i

p3i q3i

+ bi (e ) ) i

q1i p1i

(22)

According to Lemma 1, the tracking errors ei , i = 1, ..., 6 converge to zero within fixed-time T1i . Such that the position and attitude angle follow the desired command in fixed-time T .

4 Simulation In order to verify the effectiveness of the controller designed previously, the quadrotor model parameters in [17] are used: m = 2 kg, d =0.2 m, g = 9.8 m/s2 , K1 = K2 = K3 = 0.01, K4 = K5 = K6 = 0.012, I1 = I2 = 1.25, I3 = 2.5. In the simulation, the desired yaw angle is selected as φd = π/3 and a position trajectory is defined Pd = [0.5cos(0.5t), 0.5sin(0.5t), 0.1t]T . The control parameters are given as: p1i = 5, p2i = 7, p3i = 9, q1i = 3, q2i = 5, q3i = 5, i = 1, ...6; ai = 5, bi = 1, i = 1, 2, 3; ai = 15, bi = 10, i = 4, 5, 6; τ = 0.4; k = 1. So the attitude system settling time solved from (15) is bounded by Tin = 9.7535 s and the position system is Tout = 30.7711 s. The numerical simulation results of the designed fixed-time controllers are shown in Figs. 2, 3, 4, 5 and 6. Figure 1 depicts position 3D tracking performance. The tracking error curves for position and angles are presented in Figs. 2 and 3, which depict the position error and the attitude angle error converge to zero at 5s and 0.5s,

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Fig. 1 Position tracking 3D effects 3

z(m)

2 1 0 1

Real trajectory Desired trajectory 0 −0.5

0

y(m) Fig. 2 Position tracking errors

−1

0.5

x(m)

−1

0.5

e

x

e

y

ez

0

−0.5

0

5

20

15

10

30

25

Time(s) Fig. 3 Attitude tracking errors

0.5

e

φ

0 −0.5 −1 −1.5

2

eθ

0

eψ

−2 0 0

5

1

0.5 10

15

20

25

30

Time(s) Fig. 4 attitude tracking of θ d , ψd

0.2 θ (degree) d

0 −0.2

θ (degree) 0

5

10

15 Time(s)

20

25

30

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0 −0.1

ψ (degree) 0

5

10

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20

25

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u1

20 15 10

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5

10

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Time(s) Fig. 6 Control inputs of attitude subsystem

150

u2 u3 u4

100 50 0 −50

0

5

10

15

20

25

30

Time(s)

respectively. Therefore, all states can track the desired trajectory within 5s, and the upper bound value of the convergence time given in Theorem 1 is verified. The attitude angles θd , ψd obtained from (6) and (7) are shown in Fig. 4. Control inputs are presented in Figs. 5 and 6.

5 Conclusion The problem of fixed-time control for quadrotor system under bounded disturbance is addressed in this paper. The split-loop design method which divides the UAVs system into position subsystem and attitude subsystem is adopted. An NTSMC approach is employed to suppress disturbance. In the system, the robustness is guaranteed. Finally, detailed simulation results are presented to certify the developed theories. Acknowledgements This work is supposed by the National Natural Science Foundation of China under Grants 61703134, 61703135, 61773151, 61803143 and 61871173, the Natural Science Foundation of Tianjin under Grant 17JCQNJC04400, the Natural Science Foundation of Hebei Province under Grants F2019202369, F2018202279, and No. F2019202363), Youth Foundation of Hebei Educational Committee under (No. QN2018140), Graduate Innovation Foundation of Hebei Province under Grant 220056.

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References 1. Tayebi, A., McGilvray, S.: Attitude stabilization of a VTOL quadrotor aircraft. IEEE Trans. Control Syst. Technol. 14(3), 562–571 (2006) 2. Zhu, W., Du, H., Cheng, Y.: Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn. 238(7), 111–125 (2013) 3. Wang, T., Wang, L., Liang, J.: Autonomous control and trajectory tracking of quadrotor helicopter. Comput. Mod. 3, 251–255 (2012) 4. Matouk, D., Gherouat, O., Abdessemed, F., et al.: Quadrotor position and attitude control via backstepping approach. In: International Conference on Modelling (2016) 5. Kondak, K., Bernard, M., Meyer, N.: Autonomously flying VTOL-robots: Modeling and control. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 736–741. IEEE. New York (2007) 6. Gonzlezvzquez, S., Morenovalenzuela, J.: A new nonlinear PI/PID controller for quadrotor posture regulation. In: Electronics, Robotics Automotive Mechanics Conference (2010) 7. Madani, T., Benallegue, A.: Backstepping Control for a Quadrotor Helicopter (2006) 8. Freddi, A., Lanzon, A., Longhi, S.: A feedback linearization approach to fault tolerance in quadrotor vehicles. IFAC Proc. Vol. 44(1), 5413–5418 (2011) 9. Xu, R., Zhang, X., Guo, H., Zhou, M.: Sliding mode tracking control with perturbation estimation for hysteresis nonlinearity of piezo-actuated stages. IEEE Access. 6, 1–13 (2018) 10. Li, S., Li, B., Geng, Q.: Adaptive sliding mode control for quadrotor helicopters. In: Chinese Control Conference. IEEE, New York (2014) 11. Jia, P., Zhang, J., Yang, L.: Adaptive non-singular terminal sliding mode control for structural damaged aircraft. In: Control Conference (2015) 12. Yali, M.A., Zong, Q., Dong, Q., et al.: Fast terminal sliding mode control for quadrotor unmanned aerial vehicle with actuator saturation. Inf. Control (2017) 13. Du, H., Zhang, J., Zhu, W., et al.: Finite-time consensus control for a group of quadrotor aircraft. In: 2017 Chinese Automation Congress (CAC). IEEE, New York (2017) 14. Tian, B., Lu, H., Zuo, Z., et al.: Multivariable finite-time output feedback trajectory tracking control of quadrotor helicopters. Int. J. Robust Nonlinear Control (2017) 15. Yun, H., Zongyu, Z., Zhiguang, S.: Fixed-time terminal sliding mode trajectory tracking control of quadrotor helicopter. In: 2015 34th Chinese Control Conference (CCC). IEEE, New York (2015) 16. You, M., Zong, Q., Tian, B., et al.: Comprehensive design of uniform robust exact disturbance observer and fixed-time controller for reusable launch vehicles. IET Control Theory Appl. 12(5), 638–648 (2018) 17. Liu, J.K.: Sliding Mode Control Design and MATLAB Simulation, 3rd edn. Tsinghua University Press, Beijing (2015)

Nonlinear Observer Based Fault Diagnosis for an Innovative Intensified Heat-Exchanger/Reactor Xue Han, Zetao Li, Boutaib Dahhou, Michel Cabassud and Menglin He

Abstract This paper describes an application of a fault detection and isolation (FDI) scheme for an intensified Heat-exchanger (HEX)/Reactor, where the exothermic chemical reaction of sodium thiosulfate oxidation by hydrogen peroxide is performed. To achieve this, precise estimation of all states of HEX/Reactor, including temperatures and concentrations of different reactants, as well as process fault detection and isolation is completed by a high gain observer. Then, process fault identification is achieved by several banks of interval filters. Finally, an intensified HEX/reactor is used to validate the effectiveness of the proposed strategy. Simulation results are shown to illustrate the performance of the algorithm presented. Keywords Fault diagnosis · Fault identification · High gain observer · Parameter interval filter · HEX/reactor

1 Introduction Due to the increasing demand for higher safety and reliability of the dynamic system, fault detection and isolation (FDI) is becoming an effective method to avoid breakdowns and disasters of major systems. In chemical engineering field, an intensified continuous HEX/reactor [1] is a multifunctional device which combines heat exchanger and reactor together. It is much safer according to its outstanding mixing performance and remarkable heat transfer capacity [2]. However, undesirable failures such as thermal runaway still pose a great threat to such intensified process. Therefore, process monitoring provided by fault detection and diagnosis (FDD) method is necessary to improve its performance. X. Han · Z. Li (B) · M. He Electrical Engineering College, Guizhou University, Guiyang 550025, China e-mail: [email protected] X. Han · B. Dahhou · M. He LAAS-CNRS, Université de Toulouse, CNRS, INSA, UPS, Toulouse 31400, France M. Cabassud Laboratoire de Génie Chimique, Université de Toulouse, CNRS/INPT/UPS, Toulouse 31432, France © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_40

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Extensive review of existing FDD approaches can be found in [3–5]. They are roughly divided into data-based methods and model-based methods. Data-based methods [6–8] only rely on a database of historical data collected under normal operating conditions. While model-based methods require an exact model to estimate process variables. By comparing the measured and corresponding estimated values, a set of deviations (residuals) are generated. After residual evaluation, faults can be isolated and identified. Observer-based approaches, which contribute a lot to model-based methods, are applied to various chemical reactors [9–13]. In addition, the authors of [14, 15], propose a new FDI method based on parameter intervals. The practical domain of the value of each parameter is divided into several intervals, which provides an ideal FDI speed. Since the HEX/Reactor is often connected with field devices (i.e. actuator), [16] focus on the fault diagnosis of such interconnected systems by using invertibility. However, most of previous model-based FDD approaches focus on either heat exchangers [17, 18], or chemical reactors [10, 19]. Moreover, the referred reactor is a stirred tank with poor heat removal capacity, which increases the risk of out of control and reduction of productivity. The multifunctional HEX/Reactor guarantees a proper temperature for chemical reactions by its excellent capacity of heat exchange. In [10, 13], model-based FDD approaches are proposed for fault diagnosis. Nevertheless, chemical reaction, which affects the temperature in turn, is not considered. This paper is aimed at proposing an observer-based FDD strategy to solve the fault diagnosis problem on the studied HEX/Reactor. Firstly, an appropriate model of the studied HEX/Reactor is constructed, where both heat exchange and chemical reaction are taken into consideration. Moreover, an observer-based FDD approach is applied to detect and isolate process faults (i.e. fouling within both channels) by only one temperature output. In addition, the output is used to feed a bank of interval filters to provide fault identification. The rest of this paper is as follows. Firstly, the mathematical model of HEX/Reactor with an exothermic reaction taken place in is presented. Then, the applied FDI method is described in Sect. 3, high gain observer and interval filters are designed to estimate internal states and faulty parameters. Thereafter, Sect. 4 shows the simulation results of the applied FDI scheme. Finally, the conclusion is presented in Sect. 5.

2 Modelling of the Intensified HEX/Reactor 2.1 Physical Structure of the Intensified HEX/Reactor The intensified HEX/Reactor considered in this paper is assembled by three process plates and four utility plates, which are both engraved into 2 mm square cross-section channels (shown in Fig. 1). Steel between channels, which acts as the heat exchange media, are called plate wall. The cell-based structure and flow configuration are

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Fig. 1 a Process channel; b utility channel; c the physical HEX/Reactor [20]

Fig. 2 Description of cells diving and flow configuration

shown in Fig. 2. The process flow Fp_in, which is combined by two (or several) feeding lines (reactant R1 and reactant R2 in Fig. 2), circulates in a single channel, within which the reaction is taken place. The utility fluid Fu_in (water in most cases) flows in parallel zigzag type channels so as to take reaction heat away. The temperature of each cell is influenced by the former and latter cell connected. Note that conductive heat exchange is only considered in horizontal direction.

2.2 Mathematical Modelling The modelling of each cell is based on the expression of mass and energy balance. Each cell is assumed homogenous and no back mixing. In addition, the exothermic reaction of sodium thiosulfate oxidation by hydrogen peroxide is conducted in the pilot. The reaction equation is: 2Na2 S2 O3 + 4H2 O2 → Na2 S3 O6 + Na2 SO4 + 4H2 O

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The concentration of reactants plays an important role in heat generation during the reaction process, and will further result in temperature change. They are also considered as internal states. To sum up, the dynamic of the pilot can be expressed as follows:   h p Ap  F1 + F2  T p_in − T p + Tw − T p T˙ p = Vp ρ p Vp C p p   E aj Hr j 0  C1 C2 k exp −  + ρpC pp j R T p + 273.15  h u Au Fu  Tu_in − Tu + T˙u = (Tw − Tu ) Vu ρu Vu C pu  h p Ap  h u Au T˙w = T p − Tw + (Tu − Tw ) ρ p Vp C p p ρu Vu C pu   a E   + F F j 1 2  C1 C2 C1_in − C1 − 2k 0j exp −  C˙ 1 = Vp R T p + 273.15   E aj   + F F 1 2 0  C1 C2 C2_in − C2 − 4k j exp −  C˙ 2 = Vp R T p + 273.15

(1)

 T where state vector is x = T p Tu Tw C1 C2 . T, C represent temperature (°C) and concentration (mol m−3 ). The index p, u, w represent process plate, utility plate and plate wall. The initial temperature T p_in , Tu_in and Tw are 17.6, 39.7 and 25 °C. Inlet concentrations of reactants C1_in and C2_in are both set at 9% in mass. 1 and 2 represent the reactants Na2 S2 O3 and H2 O2 respectively. The input T  vector u = F1 F2 Fu , stands for volumic flow-rate (m3 s−1 ) of the reactants and T  utility fluid. Input vector is fix at 2.5833 × 10−6 , 1.3056 × 104 , 3.1389 × 10−5 . Output y = T pk is the outlet temperature. ρ (kg m−3 ), V (m3 ), A (m2 ) and Cp (J kg−1 K−1 ) are density, volume, heat exchange area and specific heat of material respectively. The index j stands for reaction j. Hr (J mol−1 ) is the heat generated. k 0 (mol m−3 s−1 ) is pre-exponential factor. E a (J mol−1 ) is activation energy. R (J mol−1 K−1 ) is perfect gas constant. For the reaction concerned, Hr = 5.86 × 105 , k 0 = 8.13 × 108 , E a = 7.6123 × 104 , R = 8.314. For the given HEX/Reactor, heat transfer process is divided in two parts: one is the convective heat exchange between process channel and plate wall, the other is between utility channel and plate wall. The nominal values of heat transfer coefficients (J m−2  T  T K−1 s−1 ) are h p h u = 1.0636 × 104 , 1.1426 × 103 .

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3 Fault Detection and Diagnosis Scheme 3.1 Description of the Proposed FDI Method For the intensified HEX/Reactor, a bank of observers is constructed to generate a bank of residuals. One of the observers serves as the detection and isolation observer. Once the residual exceeds to threshold, the procedure of fault identification is triggered by an alarm of fault. Then, other q observers, corresponding to q different fault types and values, act as interval filters to generate several residuals aiming at identifying the fault.

3.2 High Gain Observer Design The model proposed in Eq. (1) is shortly express as: x˙ = f (x, θ ) + g(x)u y = h(x, θ )

(2)

 T where θ = h kp h ku is the parameter vector. f (·), g(·) and h(·) are smooth vector fields, their first partial derivatives on x and θ are continuous, bounded, Lipschitz in x and θ . In order to estimate all of the states in the presented model (2), a high gain observer presented in [21] is designed as follows:         ˆ θ 0b θ K 0 yˆ − y x˙ˆ = f x, ˆ θ 0b + g xˆ u − Φ ∗−1 x,   yˆ = h x, ˆ θ 0b

(3)

where y is the output vector of the system (2), yˆ is the output vector of the observer. xˆ is the observer state vector, θ 0b is the observer parameter vector, Φ ∗−1 xˆ is the inversion of the Jacobian matrix of the nonlinear change of coordinates T  Φ(x(t)) = h(x(t)) L f h(x(t)) . . . L n−1 . L f h(x) is the Lie derivative f h(x(t))   of h(·) along f (·). θ = diag θ θ 2 . . . θ n , θ is an arbitrary positive constant. T  is the observer gain. It is calculated by K 0 = S −1 C0T , K 0 = k1 k2 k3 k4 k5 where S is a symmetric positive definite matrix which satisfies the  algebraic Lya  I 0 punov equation A0T S+S A0 +S−C0T C0 = 0, with A0 = 4×1 4×4 , C0 = 101×4 , 01×1 01×4 I represents identity matrix. The estimation error ex = xˆ − x of the observer (3) is globally uniformly convergent to zero when t → ∞ in the absence of uncertainties. Furthermore, the convergence is exponential. Define that:

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e y = yˆ − y d yˆ − y d e y = r y (t) = dt dt

(4) (5)

As long as the norm of the residual vector r y (t) exceeds the suitable threshold supr y (t), a fault is detected. According to the different performance of r y (t), the fault is isolated.

3.3 Fault Identification When a fault is detected and isolated, a procedure of fault identification is triggered. The practical domain of the value of each system parameter is partitioned into several intervals as in [14]. For instance, parameter θ j is divided into q intervals, where the value of the faulty parameter is contained in one of the intervals, their bounds q are presented by: θ 0j , θ 1j , . . . , θ ij , . . . , θ j . The boundaries of the ith interval are θ i−1 j bi and θ ij , which is also denoted by θ ai j and θ j . In this paper, the boundary of each interval is calculated by the percentage changes of the nominal value, rather than an accurate value of the parameter. To verify if the faulty parameter is contained in an interval, a parameter interval filter, which is consisted of two observers corresponding to upper and lower bounds, is built for this interval. Each observer serves two neighboring intervals. To illustrate this procedure, the ith interval of parameter Considering the model (2), the parameter filter for the ith interval θ j is discussed. bi θ ai of parameter θ j is given as follows: j , θj

      ai oba   ∗−1 ai + g xˆ ai xˆ j , θ oba θ K 0 yˆ j − y x˙ˆ ai j = f xˆ j , θ j j u−Φ j  ai oba  yˆ ai j = h xˆ j , θ j

(6)

        + g xˆ bij u − Φ ∗−1 xˆ bij , θ obb θ K 0 yˆ j − y j x˙ˆ bij = f xˆ bij , θ obb j j   yˆ bij = h xˆ bij , θ obb j

(7)



θ 0j , t < t f , fault occurs at t = t f . θ bj , t > t f     Define the identification index of this parameter filter: vij (t) = sgn εaij sgn εbij ,

where θ oba = j

θ 0j , t < t f , θ obb = j θ aj , t > t f

bi where εaij = yˆ ai ˆ bij − y. When the fault occurs, if the value of faulty j − y, ε j = y bi i , θ parameter is contained in θ ai j j , v j (t) should equal to −1 after a short transient

time, and fault signature sends 1. Oppositely, if vij (t) remains 1, the faulty parameter is not contained in this interval, and the corresponding fault signature sends 0. If the

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fault lies in the ith interval, the value of the estimated faulty parameter is obtained by: θˆ j =

 1  ai θ j + θ bi j 2

(8)

4 Simulation Results and Discussion To validate the effectiveness of the proposed approach, a case study is developed in this paper. All related experimental data is given in [20], and the normal values of the operating conditions used in simulation are presented in Table 1 and Sect. 2. In this study, two kinds of process faults are considered, the deviation of h p or h u from their nominal values. Temperature of the outlet process fluid is assumed to be the only available measurement and the only criteria of fault diagnosis. As shown in Table 2, the dividing rule of an interval is according to the percentage variation of the nominal value. The limited range of interval for heat transfer coefficient is [100%, 20%], i.e., the value of the faulty parameter decreases from the nominal value to 20% of the nominal value. Since it takes about 230 s for the HEX/Reactor to achieve its thermal equilibrium, the fault is introduced at t = 250 s. The heat transfer coefficient decreases to 70% of the nominal value. Residuals generated by detection observers are shown in Fig. 3. For the studied model, the reduction Table 1 Physical data of the pilot Constant

Description

Value

Units

Volume of process plate

2.68 × 10−5

m3

ρ p , ρu

Density of process/utility plate

103

kg m−3

C p p , C pu

Specific heat of process/utility plate

4.186 × 103

J kg−1 K−1

Heat exchange area of process plate

2.68 × 10−2

m2

Vu

Volume of utility plate

1.141 × 10−4

m3

Au

Heat exchange area of utility plate

4.564 × 10−1

m2

Volume of plate wall

1.355 × 10−3

m3

ρw

Density of plate wall

8 × 103

kg m−3

C pw

Specific heat of plate wall

5 × 102

J kg−1 K−1

Vp

Ap

Vw

Table 2 Interval bounds for heat transfer coefficients No. of interval

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Fig. 3 Isolation residual for heat transfer coefficient h u (left) and h p (right)

of h p has an influence on heat exchange between process plate and plate wall, which affects the temperature of process fluid directly. The decrease of h u influences the heat exchange between utility plate and plate wall, and further affects process fluid temperature indirectly by heat exchange procedure, i.e., output temperature changes slightly as a fault occurs on h u , while it changes greatly as a fault occurs on h p . Therefore, the residual vector r y (t) in Eq. (5) performs differently. Then, the thresholds vary according to the type of fault. In the studied case, when the faulty parameter is h p , the threshold is much bigger than that of a fault occurs of h u . When a fault happens, residual goes over the corresponding threshold, and the fault is detected. Moreover, the fault is isolated by the performance of residual vector r y (t). Once the fault is detected and isolated, a bank of parameter interval filters begins to work to identify the exact value of the faulty parameter. When h u changes, the corresponding estimation error filter is shown in Fig. 4. It is  3parameter   2of each 2 sgn εhu = −1, i.e. faulty parameter stays in obviously that vhu (t) = sgn εhu interval 2. The performances of fault signatures are shown in Fig. 5. Since both the faulty parameters are defined as 70% of their nominal value, the fault signature 1 is sent by interval 2 at about t = 251 s, whose bounds are 80% of nominal value and 60% of nominal value. Other fault signatures stay at 0, which means the faulty parameter is not contained in these intervals. Then, the value of faulty parameter is identified by the upper and lower bounds of interval 2: hˆ u = 21 (80% + 60%) × h u , hˆ p = 21 (80% + 60%) × h p . Even though there exists estimation errors, they can be narrowed by diving in more intervals. Fig. 4 Estimation error of each parameter filter when h u is faulty

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Fig. 5 Fault signatures sent by parameter filters of h u (left) and h p (right)

5 Conclusion In this paper, a model-based FDI approach is applied to an intensified HEX/Reactor with an exothermic reaction taken place in. High gain observer is constructed to serve as detection and isolation observer for process fault detection and isolation. When a fault is detected, identification procedures are triggered. A bank of intervals is divided according to the value of the process parameters. And interval filters are designed to provide fault identification. Then, the presented FDI method is applied to an intensified HEX/Reactor. The effectiveness of the proposed approach is confirmed by the simulation results. Moreover, the ideal isolation speed and the estimation value of the faulty parameter provide support for the following controller reconfiguration in fault tolerant control system. Acknowledgements This work was supported by China Scholarship Council (CSC); the National Nature Science Foundation of China under Grant 61963009; the Department of Science and Technology of Guizhou (grand numbers [2015]4014, [2015]11, [2016]2302, [2019]2154); and the Department of Education of Guizhou (grand numbers ZDXK [2015]8).

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References 1. Anxionnaz, Z., Cabassud, M., Gourdon, C., Tochon, P.: Heat exchanger/reactors (HEX reactors): concepts, technologies: state-of-the-art. J. Chem. Eng. Process Process Intensif. 47(12), 2029–2050 (2008) 2. Benaïssa, W., Gabas, N., Cabassud, M., Carson, D., Elgue, S., Demissy, M.: Evaluation of an intensified continuous heat-exchanger reactor for inherently safer characteristics. J. Loss Prev. Process Ind. 21(5), 528–536 (2008) 3. Gertler, J.J.: Survey of model-based failure detection and isolation in complex plants. J. IEEE Control Syst. Mag. (1988) 4. Frank, P.M.: Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy a survey and some new results. J. Autom. 26(3), 459–474 (1990) 5. Frank, P.M.: Analytical and qualitative model-based fault diagnosis—a survey and some new results. Eur. J. Control. 2, 6–28 (1996) 6. Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault diagnosis in chemical processes using fisher discriminant analysis, discriminant partial least squares, and principal component analysis. 243–252 (2000) 7. Qin, S.J., Zheng,Y.: Quality-relevant and process-relevant fault monitoring with concurrent projection to latent structures. 59(2), 496–504 (2013) 8. Himmelblau, M.D.: Applications of artificial neural networks in chemical engineering. 17(4), 373–392 (2000) 9. Li, Z., Dahhou, B., Zhang, B., Cabassud, M.: Actuator gain fault diagnosis for heatexchanger/reactor. In: Chinese Automation Congress 2019 (CAC). pp. 940–945 (2015) 10. Caccavale, F., Pierri, F., Iamarino, M., Tufano, V.: An integrated approach to fault diagnosis for a class of chemical batch processes. J. Process Control. 19(5), 827–841 (2009) 11. Escobar, R.F., Astorga-Zaragoza, C.M., Tllez-Anguiano, A.C., Jurez-Romero, D., Hernndez, J.A., Guerrero-Ramrez, G.V.: Sensor fault detection and isolation via high-gain observers: application to a double-pipe heat exchanger. ISA Trans. 50(3), 480–486 (2011) 12. Zhang, M., Li, Z., Cabassud, M., Dahhou, B.: An integrated FDD approach for an intensified HEX/Reactor. J. Control Sci. Eng. 2018 (2018) 13. Shoja-Majidabad, S., Zafari, Y.: Robust flux observer and robust block controller design for interior permanent magnet synchronous motor under demagnetisation fault. Int. J. Model. Identif. Control. 30(3), 206–218 (2018) 14. Li, Z., Dahhou, B.: A new fault isolation and identification method for nonlinear dynamic systems: application to a fermentation process. Appl. Math. Model. 32(12), 2806–2830 (2008) 15. Li, Z., Dahhou, B.: Parameter intervals used for fault isolation in non-linear dynamic systems. Int. J. Model. Identif. Control. 1(3), 215–229 (2006) 16. Zhang, M.: Root cause analysis of actuator fault based on invertibility of interconnected system. Int. J. Model. Identif. Control. 27(4), 256–270 (2017) 17. Zavala-Río, A., Santiesteban-Cos, R.: Reliable compartmental models for double-pipe heat exchangers: an analytical study. J. Appl. Math. Model. 31(9), 1739–1752 (2007) 18. Weyer, E., Szederkényi, G., Hangos, K.: Grey box fault detection of heat exchangers. J. Control Eng. Pract. 8(2), 121–131 (2000) 19. Pierri, F., Paviglianiti, G., Caccavale, F., Mattei, M.: Observer-based sensor fault detection and isolation for chemical batch reactors. 21, 1204–1216 (2008) 20. Théron, F., Anxionnaz-Minvielle, Z., Cabassud, M., Gourdon, C., Tochon, P.: Characterization of the performances of an innovative heat-exchanger/reactor. J. Chem. Eng. Process. Process Intensif. 82, 30–41 (2014) 21. Deza, F., Busvelle, E., Gauthier, J.P., Rakotopara, D.: High gain estimation for nonlinear systems. J. Syst. Control Lett. 18(4), 295–299 (1992)

Research on Rudder Roll Stabilization Motion Control Based on Adaptive LQR Yanwen Liu, Changsheng Zhou, Yinlin Liu and Guangqing Zhai

Abstract When a ship sails on the surface of the sea, it will inevitably be disturbed by the waves. The wave interference will not only lead to the ship’s heading posture, but also affect the safety of the occupants and increase the navigation resistance to aggravate energy consumption. The most effective way to solve this problem is to control rolling motion directly. Firstly, the mathematical models of four degrees of freedom Motion model, rudder control and wave interference of ship motion are established. The simulation environment is built by Matlab/Simulink. The Q matrix and the R matrix in the controller design are determined by reducing the roll as a performance indicator. The rudder anti-rolling controller is designed by linear quadratic optimal control theory, and combined with adaptive control and parameter adjustment. The simulation results show that under different sea conditions, significant reduction rate is achieved, and good heading control accuracy can be guaranteed. Keywords Rudder reduction · LQR control · Optimal control · Adaptive control

1 Introduction For all types of ships, it is necessary to establish a stable system. It is used to increase the comfort of passengers on ferries or passenger ships. It is used to prevent cargo damage and safe landing of helicopters on merchant ships or military ships. Compared with other anti-rolling devices, the rudder anti-rolling technology has many advantages such as low production cost, small space occupation and convenient repair. Therefore, it has extremely wide application in various military and civilian ships. Rudder roll stabilization refers to the use of rudder only as an actuator to maintain the course of the autopilot and reduce the roll angle of the ship when turning. As long as the rudder is properly controlled, the rudder can be used to realize the ship’s Y. Liu · C. Zhou (B) · Y. Liu College of Automation, Harbin Engineering University, Harbin 150001, China e-mail: [email protected] G. Zhai Department of Automation and Electrical Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_41

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course control and roll reduction control. Because of the strong coupling between ship roll and yaw, it is necessary to seek multi-input multi-output (MIMO) method to control ship motion. The main methods of ship control are PID control, robust control and fuzzy control. However, in the field of MIMO control, the above methods have general control effects and complicated algorithms. However, the LQR control method has achieved good compatibility in the field of MIMO control in the rudder anti-rolling system, which opens up a new way of thinking. LQR (Linear Quadratic Regulator) is a linear quadratic regulator. The control object is a linear system in the form of state space, while the objective function is a quadratic function of the object state and control input. The optimal solution of LQR has a standard analytic formula, which can form a simple linear state feedback control law. It is easy to form an optimal feedback control. It takes into account the robustness, stability and rapidity of the system and is easy to realize in engineering. Taking Naval Vessel as the research object, based on the mathematical model of Hull, the perturbation force and moment of random wave, this paper proposes an adaptive optimal control method which can be realized by physics, and overcomes the influence of ship model uncertainty on the effect of roll reduction. By constructing the simulation environment, the effect of rocking reduction is verified under different sea conditions.

2 Paper Preparation The principle block diagram of the entire rudder anti-rolling system is shown in Fig. 1. Under the control of the rolling and yaw two rudders, the rudder instruction can be decomposed into: δg = δr oll + δ yaw .Where: δr oll used to control the rolling movement, δ yaw used to maintain the course.

2.1 Mathematical Model of Ship Motion In order to better analyze the movement state of ships in the ocean, it is necessary to establish a coordinate system to describe the movement of ships. Due to the complex motion characteristics of the ship’s three-dimensional space, the ship will generate Fig. 1 Structure of lateral motion control system for ships

r

+ r

+ -

Roll controller Yaw controller The ship lateral motion controller

roll

+ +

yaw

Rudder

Ship

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six degrees of freedom of movement during the voyage, including independent linear motion and rotational motion. The six-degree-of-freedom non-linear motion equation of a ship is expressed by matrix method as follows: M R B v˙ + C R B (v)v = τ

(1)

where: M R B denotes the mass and inertia matrix of the rigid body, and C R B (v) is the composite centripetal force (Coriolis force) and moment. ν = [u, v, w, p, q, r ]T , τ = [X, Y, Z , K , M, N ]T . To facilitate the design of the controller, the model of Formula (1) should be linearized and simplified. It can be reduced to the following four degrees of freedom equation: ⎧ m(u˙ − vr − x G r 2 + z G pr ) = X ⎪ ⎪ ⎨ ˙ =Y m(˙v + ur + x G r˙ − z G p) ⎪ Iz r˙ + mx G (˙v + ur ) = N ⎪ ⎩ Iz p˙ − mx G (˙v + ur ) = K − ρg∇G Mϕ

(2)

where: u˙ is longitudinal acceleration, u˙ is transverse acceleration, r˙ is bow acceleration, p˙ is rolling angular acceleration, g, ρ respectively represents gravity acceleration and water density, ∇ indicates the displacement of the ship, G M sin φ ≈ G Mφ represents the restoring arm, where: G M is the distance from the center of gravity G to M, φ is the roll angle, and X, Y, N , and K is the hydrodynamic force and the hydrodynamic force moment, respectively.

2.2 Ship Hydrodynamics and Hydrodynamic Torque Hydrodynamics are usually represented by hydrodynamic derivatives, The hydrodynamic derivative is derived from the Taylor series and can be expressed as follows: F = f (u, v, p, r, u, ˙ v˙ , p, ˙ r˙ . . .) In order to simplify the calculation, the expansion method using the third derivative is sufficient. The following is the hydrodynamic expansion of the four-degree-offreedom equation:

436

⎧ X hyd ⎪ ⎪ ⎪ ⎪ ⎪ Yhyd ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨K hyd ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Nhyd ⎪ ⎪ ⎩

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= X u˙ u˙ + X u|u| u|u| + X vr vr = Yv˙ v˙ + Yr˙ r˙ + Y p˙ p˙ + Y|u|v |u|v + Yur ur + Yv|v| v|v| + Yv|r | v|r | + Yr |v| r |v| + Yφ|uv| φ|uv| + Yφ|ur | φ|ur | + Yφuu φuu = K v˙ v˙ + K p˙ p˙ + K |u|v |u|v + K ur ur + K v|v| v|v| + K v|r | v|r | + K r |v|r |v| + K φ|uv| φ|uv| + K φ|ur | φ|ur | + K φuu φuu + K |u| p |u| p + K | p| p | p| p + K p p + K φφφ φφφ − ρg∇G Z (φ) = Nv˙ v˙ + Nr˙ r˙ + N|u|v |u|v + N|u|r |u|r + Nr |r |r |r | + Nr |v| r |v| + Nφ|uv| φ|uv| + Nφu|r | φu|r | + N| p| p | p| p + N p p + N|u| p |u| p + Nφu|u| φu|u| (3)

Equation φ = p, ψ˙ = r/ cos φ ≈ r can be obtained from hydrodynamics and other related knowledge, so the state variable x can be defined as x = [v u r p ϕ ψ]T

(4)

2.3 Steering Gear Model The steering gear is an actuator whose purpose is to make the actual steering angle δ equal to the desired steering angle command δg from the autopilot or steering officer. The most widely used mathematical model of the rudder in autopilot design and computer simulation is a simplified model proposed by Van Amerongen, as shown in Fig. 2. The simplified model block diagram contains two limiters, one for the rudder angle limit and the other for the rudder speed limit. The maximum rudder speed depends on the opening of the servo valve and the flow rate of the hydraulic pump. From the relevant standards, it is normally required that the steering gear can be moved from the port side of 35° to the starboard side of 35° in 30 s, and the maximum rudder speed is not less than 2.5◦ every second. Previous

Fig. 2 The simplified model of the steering mechanism

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studies have shown that the rudder anti-rolling system requires a high rudder speed, and the higher the rudder speed, the better the anti-rolling effect. Set to δ˙max = 20◦ /s here. The rudder angle limit can be changed by the autopilot and set to δmax = 35◦ .

2.4 Wave Disturbance Modeling This paper selects the P-M wave spectrum to simulate the wave state, which is defined as follows:   A B (5) Sς (ω) = 5 exp − 4 ω ω where: Sς (ω) is the ordinate, the wave amplitude spectrum in m2 s, and ω is the 2 , g represents the acceleration of frequency in rad/s. A = 0.0081g2 , B = 3.12/H1/3 gravity, and H1/3 represents the sense wave height. Since the wave is a waveform that is irregularly and changing randomly, and its propagation direction changes with the change of the wind direction. Therefore, the impact of the waves on the ship is quite complicated, and it is the main source of disturbance for the ship to roll. In order to better study the motion of ships in computer simulations, it is important to study the wave interference forces and moments to obtain their parameters. Here is the cosine weight coefficient method to study the interference force and moment generated by the waves.

2.5 Ship Model and Parameters The model used in the design of the rudder roll stabilization controller is a standard model ship model with rated speed u = 11 m/s and direct flight status. The hydrodynamic coefficient of the ship has been obtained through experiments and online identification. The detailed Parameters the ship and the hydrodynamic derivatives are given by Blanke and Christensen in literature [10].

3 Design of LQR Controller The core of the LQR controller is to find the optimal control u(t), so that the performance index function J obtains the optimal solution. The performance indicator function is a system that controls the integral and state variables of the quadratic function of the variable. The LQR controller is mainly the rolling moment and the rocking moment that the steering gear generates to act on the ship. The equation of state for this system is:

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x˙ = Ax + Bu y = Cx

(6)

In order to constrain the control vector u well, we must find a control vector with the smallest error e, assuming: e = yˆ − y

(7)

where: yˆ is the expected output vector. Linear quadratic performance indicators are as follows: 1 e(t f )T p(t f )e(t f ) 2 T 1 + (e(t)T Q(t)e(t) + u(t)T R(t)u(t))dt 2

J (u) =

(8)

0

where: p(t f ) is a symmetric constant matrix and is semi-definite. Q(t) is a semidefinite weighting matrix, which is corresponding to the state vector. R(t) is a positive definite weighting matrix, which is corresponding to the control vector. In order to achieve the optimal performance index J, the Lagrange multiplier is introduced to obtain the following optimal feedback control law when the regular equations, governing equations, initial state and cross-section conditions are satisfied: u(t) = −R −1 (t)B T (t) p(t)x(t) = −K (t)x(t)

(9)

where: K (t) is the optimal feedback gain matrix, and P(t) is the solution of the following Riccati equation. P A + A T P − P B R −1 B T P + Q = 0

(10)

The purpose of rudder roll reduction is to reduce the roll while controlling the heading. In order to make the system have a good rate of roll reduction, matrixes R and Q should be selected before designing the LQR controller. Generally speaking, if a certain weighting coefficient in Q is increased, the corresponding R will converge more quickly, and if a certain weighting coefficient in R is increased, the corresponding Q will be smaller. According to Bryson’s selection method, it is assumed that each control vector and state vector correspond one-to-one with the expected maximum quantities u i max and xi max . Q ii =

1 xi2max

Rii =

1 u i2max

(11)

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4 Simulation Environment The four-degree-of-freedom ship mathematical model, wave interference model and the steering gear model is used in the following simulation. Applying the LQR control method of the above design to the rudder roll stabilization system, the simulation model of the rudder roll stabilization adaptive LQR control system is established by Matlab/Simulink software, and the simulation and verification anti-rolling effect is carried out under two different sea conditions. Simulation environment 1: Under the sea state 4, the initial heading is 0◦ , the speed is 7 m/s, the wave height is h 1/3 = 2 m, the frequency period is T = 5.1 s, the wave encounter angle is μ = 90◦ , the rudder speed limit is δ˙ ≤ 20◦ /s, and the rudder angle is limited to −35◦ ≤ δ ≤ 35◦ . In this environment, the resulting simulation curves are shown in Fig. 3. Simulation environment 2: Under the sea state 5, the initial heading is 0◦ , the speed is 7 m/s, the wave height is h 1/3 = 4 m, the frequency period is T = 7 s, the wave encounter angle is μ = 90◦ , the rudder speed is limited δ˙ ≤ 20◦ /s, and the rudder angle is limited to −35◦ ≤ δ ≤ 35◦ . In this environment, the resulting simulation curve is shown in Fig. 4. In order to judge the effectiveness of the controller, the following roll reduction rate (RRR) is adopted: RRR =

SD − SDRD × 100% SD

(12)

where: SD is the standard deviation of the roll when no controller is added, and SDRD is the standard deviation of the roll when the controller is added. It can be seen from Table 1, for the sea state 4, the roll reduction rate after adding the LQR controller is 33.56%, the yaw angle also fluctuates between 0.8° and is well controlled. The actual output steering angle of the steering gear also fluctuates within 15°. For the sea state 5, the roll reduction rate is 41.75% after adding the LQR controller, the yaw angle also fluctuates between 1.5°, and the actual output steering angle of the steering gear also fluctuates within 24°. The rudder angle is significantly larger than that of the level 4 sea state. From the above data, it can be concluded that when the significant wave height and frequency are increased, the roll reduction rate of rudder anti-rolling system will increase significantly, and the roll speed, yaw angular velocity and roll angular velocity will also increase. It is shown that by using the LQR controller, the motion becomes smooth and a good control effect is obtained.

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(a) Simulation curve of roll angle

(b) Simulation curve of the yaw angle

(c) Simulation curve of the rudder angle Fig. 3 Simulation curves with LQR controller

5 Conclusions In this paper, the linear quadratic optimal control theory is applied to design the LQR rudder anti-rolling controller, which solves the multivariable coupling problem very well, the simulation is carried out under different sea conditions and compared with the open loop control. The results verify the effectiveness and superiority of the LQR controller. The roll reduction rate of LQR control method reached 33.56% and 41.75% respectively. The results show that with the increase of the sense wave height and frequency, the sway speed, yaw angular velocity and yaw angular velocity

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(a) Simulation curve of roll control

(b) Simulation curve of the yaw angle

(c) Steering gear actual output rudder angle simulation curve Fig. 4 Simulation curve with LQR controller Table 1 Statistics of control effect of rudder roll reduction and roll reduction Sea state

Open loop standard deviation (°)

With LQR controller

Roll standard deviation

Roll reduction rate (%)

Roll standard deviation

Sea state 4

4.9098

33.56

3.4076

Sea state 5

9.2905

41.75

5.4113

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will increase. The rudder anti-rolling controller designed in this paper combines the adaptive control and parameter adjustment aspects to make the performance index of the LQR controller reach the optimal.

References 1. Santoso, M.Y., Su, S.F., Aisjah, A.S.: Nonlinear rudder roll stabilization using fuzzy gain scheduling—PID controller for naval vessel. In: International Conference on Fuzzy Theory and Its Applications. IEEE, New York (2014) 2. Wang, Y., Chai, S., Khan, F., et al.: Unscented Kalman filter trained neural networks based rudder roll stabilization system for ship in waves. Appl. Ocean Res. 68, 26–38 (2017) 3. Liang, L., Wen, Y.: Feed-forward disturbance compensation model predictive control for rudder roll stabilization. In: 2017 36th Chinese Control Conference (CCC) (2017) 4. Haro, M., Ferreiro, R., Velasco, F.J.: Ship’s roll stabilization by anti-roll active tanks. In: Oceans. IEEE, New York (2011) 5. Qin, H., Ge, P.: Design of golden-section adaptive control for ship course-based mathematical modeling. In: 2016 2nd International Conference on Education Technology, Management and Humanities Science (2016) 6. Bae, S.B., Shin, D.H., Kwon, S.T., et al.: An LQR controller for autonomous underwater vehicle. J. Ins. Control. 20(2) (2014) 7. Lindiya, S.A., Vijayarekha, K., Palani, S.: Deterministic LQR controller for dc-dc buck converter. In: Biennial International Conference on Power & Energy Systems: Towards Sustainable Energy. IEEE, New York (2016) 8. Baelemans, J.A.J., Blanke, M., Galeazzi, R., et al.: Ship autopilot and rudder roll damping using L1 adaptive control. (2012) 9. Jin, H., Pan, L., Wang, L.: Modified variable structure control in rudder roll damping of submarine near free—surface. J. Harbin Ins. Technol. 42(9), 1462–1466 (2010) 10. Blanke, M., Christensen, A.: Rudder-roll damping autopilot robustness to sway-yaw-roll couplings. In: The 10th Ship Control Systems Symposium, Ottawa, Canada (1993)

Study on Non-local Cubic Spline Function Based on Peridynamics Jincai Chang, Jiecheng Wang, Dan Jian, Zhuo Wang and Jianhua Zhang

Abstract Cubic spline function is popular in modeling field because of its excellent properties, but it is difficult to solve because the derivative does not exist in discontinuity of displacement. And when the interpolation point is sparse, the interpolation curve isn’t good. Peridynamic is well in the problem of discontinuity. Therefore, the non-local operator is introduced by peridynamics and non-local calculus theory, and the interpolation method with first-order smoothness is provided. Then the concept of non-local mapping is introduced to the cubic spline interpolation function with second-order smoothness, and non-local cubic spline function and its numerical computational method are definited. This method not only preserves the smoothness of the spline function, but also achieves the good property of the non-local interpolation. It is more accurate and can better show the trend of the data points than the traditional cubic spline interpolation when the interpolation point is sparse. Keywords Non-local calculus theory · Peridynamics · Spline function · Non-local operator · Numerical computational method

J. Chang · J. Wang (B) · D. Jian · Z. Wang College of Sciences, North China University of Science and Technology, Tangshan 063210, China e-mail: [email protected] J. Chang e-mail: [email protected] D. Jian e-mail: [email protected] Z. Wang e-mail: [email protected] J. Zhang School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_42

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1 Introduction Since American mathematician Schoenberg proposed spline function [1] in 1946, spline function is widely used and is a important construction method of the curves and surfaces because of its convenience and good mechanical background. The cubic spline function of spline function is the important method because of its minimum mode property, optimal approximation property and strong convergence [2], and is applied to construct interpolation curves and surfaces [3]. However, When the continuous medium mechanics encounters discontinuous displacement field (such as cracked material) and strain field discontinuity (such as the interface in composites), derivative is difficult to solve in the discontinuous place. Peridynamics (PD) is a relatively new example of non-local [4] mechanical models in the problem of discontinuity. It was proposed by Silling [5] in 2000, and then further popularized, obtained more theoretical basis of constitutive such as elastoplastic, viscoelastic and so on [6]. In recent years, the PD model has been paid attention to by many scholars, and is applied to the static and dynamic simulation of different materials and structures, as well as fracture, failure and failure analysis [7–10], and the plane problem model of linear elastic PD materials has also been deduced by Le [11]. PD is constantly being improved. As a kind of mainstream method to overcome the theoretical defects of the bond-based PD, the theory of the state-based PD has been greatly developed, and the limitation of the Poisson ratio of the bond-based PD theory mainly originates from the interaction of potential, Hu [12] breakthrough the limit of Poisson’s ratio by introducing the shear effect of the bonds. Du [13] introduces a weighted non-local operator to approach to the traditional differential operator defined on the vector field. Through Fourier analysis, Ciarlet [14] shows that by selecting the appropriate kernel function, the non-local operator can correspond to the classical gradient and dispersion operators, so that PD is more closely related to the traditional methods. The integral equation form can provide theoretical methods in the modeling process and provide guidance methods for numerical simulation as the basis for verification and confirmation. The study of PD model inspires the development [15] of non-local model mathematical theory, and the development of mathematical theory around PD helps to solve various problems in other related fields, such as non-local diffusion and stochastic jumping processes. Therefore, to extend the property of spline function, under the framework of PD and non-local calculus theory, we propose non-local spline function and its numerical simulation by combining with the traditional cubic spline function.

2 Non-local Interpolation Spline function is widely used in the field of industrial design because of its good smoothness. However, when cubic spline interpolation is applied to some sparse data points which have an obvious trend [16], the traditional cubic spline interpolation

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functions do not respond well to the overall trend of data points. The interpolation function has points with negative derivative. The traditional cubic spline functions does not guarantee the overall property of some data points [17]. So we define nonlocal interpolation by interpolation method with first-order smoothness.

2.1 Cubic Hermit Interpolation n Let {xi }i=1 be a division on the interval [x1 , xn ], x1 < x2 < · · · < xn . Let { f i } be the corresponding data point, where f i = f (xi ), xi+1/2 = xi+1 − xi . The slope of piecewise linear interpolation between data points is Si+1/2 =  f i+1/2 /xi+1/2 . If (P f )(x) and the derivative less or equal to the K order are continuous, then the interpolation function Pf is C k class. Interpolation formula. Given data points { f i }, and the approximate value of the slope at point xi is f˙i , 1 ≤ i ≤ n. Then the cubic Hermite interpolation function is defined as follows:

P(x) = c1 + (x − xi )c2 + (x − xi )2 c3 + (x − xi )3 c4

(1)

where, 1 ≤ i < n, xi ≤ x ≤ xi+1 , c1 = f i , c2 = f˙i , 3S − f˙i+1 −2 f˙i c3 = i+1/2xi+1/2 , c4 = −

2Si+1/2 − f˙i+1 − f˙i 2 xi+1/2

.

The interpolation function (1) has a continuous first-order derivative, P(x) ∈ C 1 . The continuity of second-order derivative and accuracy of interpolation depend on the calculation method of { f˙i } [18]. We introduce a linear algorithm of { f˙i }: xi−1/2 Si+1/2 + xi+1/2 Si−1/2 f˙i = xi+1 − xi−1

(2)

Define non-local operator N as follows: Nf =

2 Si+1/2

(2 + θ )Si+1/2 Si−1/2 f 2 + Si−1/2 + θ Si+1/2 Si−1/2

To act the non-local operator N on { f˙i }:

(3)

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f˙i =

2 Si+1/2

xi−1/2 Si+1/2 + xi+1/2 Si−1/2 (2 + θ )Si+1/2 Si−1/2 2 xi+1/2 − xi−1/2 + Si−1/2 + θ Si+1/2 Si−1/2 x

(4)

x

The equation is second-order, when −2 < θ ≤ 1 + 3min( xi+1/2 , xi−1/2 ). i−1/2 i+1/2 On the boundary, we adopt a second-order non-central differential approximation method: (2xi+1/2 + xi+3/2 )Si+1/2 − xi+1/2 Si+3/2 f˙i = xi+1/2 + xi+3/2 Or (2xi−1/2 + xi−3/2 )Si−1/2 − xi−1/2 Si−3/2 f˙i = xi−1/2 + xi−3/2

2.2 Numerical Computational Cases Figure 1 shows the interpolation curves of cubic spline and non-local interpolation, where the given data points are in Table 1. In Fig. 1, the curves of non-local interpolation are monotonous, while the cubic spline interpolation curves are not monotonous. In some cases, the method of using non-local interpolation is more advantageous. For example, when the data points come from a state equation of density and pressure, then if the traditional cubic spline interpolation method is used, negative derivatives will be generated, which is inconsistent with the actual situation, and such errors will affect the correctness of all calculation based on these interpolation points. Therefore, it is necessary to ensure monotonicity or concave and convex nature in the interpolation process to accurately represent some physical phenomena.

(a) Cubic spline interpolation

Fig. 1 Interpolation curves of two methods

(b) Non-local interpolation

Study on Non-local Cubic Spline Function Based on Peridynamics Table 1 Original data

x

F

7.99

0

8.09

2.76429 × 10−5

8.19

4.37498 × 10−2

8.7

0.169183

9.2

0.469428

10

0.943740

12

0.998636

15

0.999919

20

0.999994

447

3 Non-local Cubic Spline Interpolation We have introduced non-local operators to Cubic Hermite interpolation and obtained some good properties. However, the piecewise cubic Hermite interpolation has only first-order smoothness at the interpolation node, it can’t meet the engineering needs. The spline curve has continuous second-order derivative at the connection point. So we construct a non-local spline function, so that it not only has the advantage of non-local interpolation, but also retains the good smoothness of the spline function.

3.1 Non-local Mapping If Si−1/2 Si+1/2 > 0, the original data at xi is partially monotonous. If (P f )(x) is monotonous between f i and f i+1 , the interpolation function is piecewise monotonous. Even if { f˙i } is defined, but it need some additional limitations, because Formula (1) does not necessarily generate an interpolation function that responds well to the overall trend of the data point for certain data. If 0 ≤ f˙j ≤ 3min(S j−1/2 , S j+1/2 )

(5)

j = i or i + 1. Then the resulting interpolation function is monotonous on the interval [xi , xi+1 ]. If the interpolation function is Class C 2 , it does not necessarily satisfy Formula (5). For some monotonous data points, they do not have the segmented cubic Hermite interpolation on C 2 . When the data is monotonically incremented or decreasing, limit f˙i to the range of Formula (5), as shown in Formula (6). After calculating the exact numerical approximation, remapping f˙i to the allowed monotone interval, depending on:

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  ⎧ ⎨ min max 0, f˙i ← max min 0, ⎩ 0

  i f˙i  , 3Smin  i f˙i , 3Smax

i , 0 < Smin i , 0 > Smax , 0 ≥ Si−1/2 Si+1/2

(6)

where i i = min(Si−1/2 , Si+1/2 ), Smax = max(Si−1/2 , Si+1/2 ). Smin Near the border, let S−1/2 = S1/2 , Sn−1/2 = Sn+1/2 When spline interpolation occurs, if there is a very large change between the data points, it is inevitable that f˙i will fall outside the range of Formula (5). In this case, if f˙i is reset by Formula (6), the second derivative of the interpolation function will cause f˙i to be discontinuous at the reset point. If the original function is strictly monotonous and sufficiently smooth, and f˙i is an exact approximation of the derivative at point xi , then as the interpolation point spacing continues to refine, the interpolation function will eventually satisfy Formula (5) because: df |x=xi = f˙i + O(x) = Si+1/2 + O(x) = Si−1/2 + O(x) dx

(7)

Therefore, a non-local mapping is required only if the interpolation function requires a large spacing between interpolation points and does not need to ensure the high asymptotic accuracy of f˙i . If the data is not monotonous, then the interpolation function must have an extreme point. To preserve the monotony of a segment, we need to make f˙i = 0. However, for the interval pairs on both sides of the extremum point, the segmented non-local constraints can be weakened, resulting in a better interpolation curve on the whole. If we want to impose a new constraint on the extreme point, then such a small change will result in a very large change in the interpolation curve, we need to discuss the reliability of the new algorithm. If all constraints are relaxed near non-monotonic data and other data points are still mapped through Formula (6), the resulting interpolation function is unreliable. For Formula (5), we make f˙i and the first calculated f˙i of the mapped have the same symbol, and: f˙i ≤ 3min( Si−1/2 , Si+1/2 )

(8)

The final non-local mapping is: f˙i ←



min[max(0, f˙i ), 3min( S i−1/2 , S i+1/2 )], σ >0 max[min(0, f˙i ), −3min( Si−1/2 , Si+1/2 )], σ < 0

where σ = sign( f˙i ). Symbolic functions:

(9)

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sign(S) =

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1, S ≥ 0 −1, S < 0

(10)

In general, the monotonicity of the derivative of the interpolation function is a very important property for the interpolation function. If the data is convex, then a good non-local interpolation function should retain this convex. However, not all data points have the cubic Hermite interpolation function on C 1 that retains convex. For example, when function f = x + |x|, and x = 0 is a data point, the convex interpolation function on C 1 does not exist. If the constraint condition C 1 is relaxed, non-local constraints can retain this convex. Definition (non-local cubic spline interpolation function) Given node a = x1 < x2 < · · · < xn = b, S(x) is a cubic function on each sub-interval [xi , xi+1 ], Si (x) = Ai + Bi x + Ci x 2 + Di x 3 , i = 1, 2, 3, · · · , n − 1, with a total of 4n − 4 unknown. By spline interpolation condition: ⎧ ⎪ S j (x j ) = f (x j ) ⎪ ⎪ ⎨ S (x ) = f (x ) j j+1 j+1   (x ) = S S ⎪ j+1 j j+1 (x j+1 ) ⎪ ⎪ ⎩ S  (x ) = S  (x ) j+1 j+1 j j

j j j j

= 1, · · · = 1, · · · = 1, · · · = 1, · · ·

,n − 1 ,n − 1 ,n − 2 ,n − 2

(11)

Add non-local boundary conditions:

S1 (x2 ) = S2 (x2 )   (xn−1 ) = Sn−1 (xn−1 ) Sn−2

(12)

A total of 4n − 4 conditions, we can find each paragraph of Si (x), and get the first derivative { f˙i }, i = 1, 2, . . . , n at each node. To map { f˙i } by non-local f˙i ←



min[max(0, f˙i ), 3min( S i−1/2 , S i+1/2 )], σ >0 max[min(0, f˙i ), −3min( Si−1/2 , Si+1/2 )], σ < 0

(13)

Get the new { f˙i }, bring in: Ni S(x) = c1 + (x − xi )c2 + (x − xi )2 c3 + (x − xi )3 c4

(14)

Composed of Ni S(x), the first derivative is continuous, and the second derivative has only a finite number of solitary discontinuous function N S(x) is called a non-local cubic spline interpolation function for a given node a = x1 < x2 < · · · < xn = b. Note

 S1 (x2 ) = S2 (x2 ) is a non-local boundary condition. The boundary ➀   (xn−1 ) = Sn−1 (xn−1 ) Sn−2 condition means that S1 (x) and S2 (x), Sn−2 (x) and Sn−1 (x) are equal in the derivative of any order at point x2 and xn−1 , so S1 (x) = S2 (x), Sn−2 (x) = Sn−1 (x). x2 and

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xn−1 will no longer be nodes of piecewise functions, and the interval is extended to [x1 , x3 ] and [xn−2 , xn ], so the boundary condition is called non-local boundary condition. ➁ Non-local mapping can reflect the overall trend of data points and achieve nonlocalization. The { f˙i } is non-local, because the value of f˙i is related to all xi and f˙i . For spline functions, if xi+1/2 (1 ≤ i < n) is not equal, f˙i is O(x 3 ); If xi+1/2 (1 ≤ i < n) is equal, f˙i is O(x 4 ) at the point away from the boundary. The interpolation function has a continuous second derivative on the interpolation point. The spline function interpolation on C 2 may doesn’t content Formula (5) for monotonous data points. By allowing a finite number of discontinuous isolated points in the second-order derivative, we can construct a non-local cubic spline interpolation function. We map the { f˙i } of the spline on C 2 by a non-local mapping of Formula (9) to obtain a new { f˙i }. The spline function obtained by the non-local mapping of Formula (9) is a non-local spline function. For the algorithm of non-local cubic spline, if we want to control the number of jump points of the second derivative as little as possible, it will involve the { f˙i } that the spline function calculates for the first time on interval [x1 , xn ]. If the interpolation function is not monotonous, then navigate to point x j of the corresponding f˙j that is furthest from the non-monotone range. We obtain the new f˙j by non-local mapping of Formula (9). In [x1 , x j ] and [x j , xn ], the cubic spline interpolation of f j and f˙j is boundary conditions. Then the second derivative of interpolation function is discontinuous only at x j . After the above steps, we get the new spline interpolation function { f˙i }. If the f˙i can’t content Formula (9), divide [x1 , x j ] and [x j , xn ] into smaller sub-regions, continue to repeat the above process. If boundary f˙1 and f˙n content Formula (9), the algorithm will stop at a limited number of times.

3.2 Numerical Computational Cases We select several points on function f (x) = e−x , x ∈ [−1.7, 1.9]. The selection method is: x = 3.6/(n − 1). Because the selected data point isn’t symmetric about x = 0. When n = 5, the interpolation curves of cubic spline interpolation and non-local cubic spline interpolation are shown in Fig. 2. Figure 2 directly from the geometric intuitive can be seen, non-local cubic spline 2 interpolation function closer to function f (x) = e−x , better than the traditional cubic spline interpolation. In order to more accurately reflect the accuracy of the interpolation of the two spline methods, we will further refine the spacing of the interpolation points, that is, increase N, the final error results are shown in Table 2. 1.9 1 2 In which, L 2 = ( −1.7 [(P f )(x) − e−x ]2 ) 2 . As can be seen from Table 2, when the value of n is small and the mesh is rough, the non-local spline is more accurate than 2

Study on Non-local Cubic Spline Function Based on Peridynamics

(a) Cubic spline

(b) Non-local cubic spline

Fig. 2 Curves and interpolation curves for f (x) = e−x

451

(c) Curve of f ( x)

e

x2

2

Table 2 Comparison of two kinds of spline interpolation Method

L2 n=5

n=9

n = 17

n = 33

Traditional cubic spline

3.5 × 10−2

2.0 × 10−3

4.0 × 10−5

1.8 × 10−6

Non-local cubic spline

1.7 × 10−2

2.0 × 10−3

1.9 × 10−5

1.8 × 10−6

the traditional spline. With the continuous refinement of the grid, the interpolation results of the two methods tend to converge gradually.

4 Conclusion In view of the discontinuity of displacement field and the discontinuity of strain field in the mechanical background of spline function, it is difficult to solve the problem because the derivative does not exist in the discontinuous place. And when cubic spline interpolation is applied to some sparse data points which have an obvious trend on the whole, the final cubic spline interpolation function does not respond well to the overall trend of such data points. Therefore, according to the theory of PD and non-local calculus, the non-local operator is constructed, the non-local operator N with derivative approximation is introduced to cubic Hermite interpolation, obtaining the non-local interpolation method, and the numerical test verifies that the non-local interpolation method can better maintain the non-local properties of the interpolation point. As data points are constantly changing, the algorithm can significantly reduce the amount of computation, such as interactive graphical programs, each time the data will change a number of points, which greatly reduces the amount of computation of the interpolation function per recalculation. Then in order to improve the smoothness of the interpolation curve, the traditional cubic spline with second-order smoothness is mapped non-locally, and the non-local boundary conditions are given, so that the non-local cubic spline function is defined, the non-local cubic spline has the excellent smoothness of spline function, and the good property of non-local interpolation is achieved. Numerical experimental results and theoretical analysis show that the non-local cubic spline interpolation is more accurate than the

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traditional spline interpolation when the interpolation point is sparse, and can better show the overall trend of the data points (compared with the traditional cubic spline interpolated values). The robustness of the algorithm is further verified. In this paper, we only study the non-local cubic spline function, whether the non-local idea can be introduced into the traditional B-spline and the multivariate spline, introduce the corresponding non-local operator, and obtain some good properties, which need to be further studied. Acknowledgements This work was supported by the National Science Foundation of China (51674121,61702184), the Returned Overseas Scholar Funding of Hebei Province (C2015005014), the Hebei Key Laboratory of Science and Applications, and Tangshan Innovation Team Project (18130209B).

References 1. Schoenberg, J.: Contributions to the problem of approximation of equidistant data by analytic functions. Q. Appl. Math. 4, 45–99 (1946) 2. Farin, G.: Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, pp. 181–192. Elsevier, Amsterdam (2014) 3. Zhang, K., Qiao, S., Gao, K.: Surface reconstruction algorithm based on local data features. Int. J. Model. Ident. Control 30, 197–205 (2018) 4. Wang, J., Yu, C., Guo, Y.: Solvability for nonlinear fractional q-difference equations with nonlocal conditions. Int. J. Model. Ident. Control 30, 303–309 (2018) 5. Silling, S.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000) 6. Silling, S., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. J. Elast. 88, 151–184 (2007) 7. Askari, E., Bobaru, F., Lehoucq, R., Parks, M., Silling, S., Weckner, O.: Peridynamics for multiscale materials modeling. J. Phys: Conf. Ser. 125, 12–78 (2008) 8. Kilic, B., Madenci, E.: Coupling of peridynamic theory and the finite element method. J. Mech. Mater. Struct. 5, 707–733 (2010) 9. Silling, S., Weckner, O., Askari, E., Bobaru, F.: Crack nucleation in a peridynamic solid. Int. J. Fract. 162, 219–227 (2010) 10. Silling, S., Askari, E.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83, 1526–1535 (2005) 11. Le, Q., Chan, W., Schwartz, J.: A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int. J. Numer. Meth. Eng. 98, 1885–1891 (2011) 12. Hu, Y., Madenci, E.: Bond-based peridynamics with an arbitrary Poisson’s ratio. In: 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, pp. 1–15. American Institute of Aeronautics and Astronautics, San Diego (2016) 13. Du, Q., Gunzburger, M., Lehoucq, R., Zhou, K.: A nonlocal vector calculus, nonlocal volumeconstrained problems, and nonlocal balance laws. Math. Models Methods Appl. Sci. 23, 493–540 (2013) 14. Ciarlet, P.: Cubic-Dimensional Elasticity. Elsevier, Amsterdam, vol. 1, pp. 15–18 (1988) 15. Du, Q., Lipton, R.: Peridynamics, fracture, and nonlocal continuum models. SIAM News 47, 20–32 (2014) 16. Chen, Z., Chen, Q., Tao, M., He, X.: Attitude tracking control of rigid spacecraft with disturbance compensation. Int. J. Model. Ident. Control 31, 62–71 (2019)

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17. Cao, D., Wang, H.: Numerical stability of interpolation functions of cubic spline. J. Chin. Univ. Min. Technol. 2, 105–108 (2001) 18. Han, X., Guo, X.: Cubic Hermite interpolation with minimal derivative oscillation. J. Comput. Appl. Math. 331, 82–87 (2018)

Weakly Supervised Semantic Segmentation Based on Deep Learning Binxiu Liang, Yan Liu, Linxi He and Jiangyun Li

Abstract Weakly supervised semantic segmentation has important significance and research value in computer vision. Although the traditional semantic segmentation based on fully supervised learning has achieved great success, the training network needs to rely on a large number of pixel-level labeled data. It is difficult and timeconsuming to obtain such high-quality annotation. In order to alleviate the huge burden of pixel-level labels, many weakly supervised semantic segmentation methods have emerged in recent years. This paper reviews the research progress of weakly supervised semantic segmentation. Firstly, we introduce the existing weakly supervised methods, highlighting their respective contributions and positive impact in this field. Then, datasets and metrics are described. Moreover, the results are analyzed and discussed. Finally, this work summarizes the difficulties of weakly supervised semantic segmentation and further explores the development direction of weakly supervised semantic segmentation in the future. Keywords Weakly supervised learning · Semantic segmentation · Deep learning

1 Introduction Since the advent of deep learning technology, a series of deep convolution neural network models have greatly improved the accuracy of semantic segmentation. The task of semantic segmentation is to distribute semantic tags to each pixel in the image, not only the semantic information in the image can be found, but also the position of the semantic information in the image can be precisely located. Recently, semantic segmentation has been widely applied to autopilot, remote sensing, and medical image analysis. In the field of automatic driving, pedestrians and vehicles can be B. Liang · Y. Liu · L. He · J. Li (B) School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China e-mail: [email protected] Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_43

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avoided by semantically segmenting road scenes [1, 2]. In the field of remote sensing, vegetation, architecture, water, and road can be distinguished well by semantic segmentation [3, 4]. In the medical field, the pathological tissues of patients can be quickly detected by semantic segmentation [5]. Initially, semantic segmentation tasks were studied as strongly supervised learning. Each pixel of image data was marked with a unique category. Such data annotation is very difficult. So, there are obvious limitations in data quantity and diversity. Research based on deep learning relies on a large number of strongly supervised training data to achieve satisfactory results [6]. However, such data is very limited. Considering that there are a large quantity of images with the image-level semantic label on the Internet, the robustness of the network model will be greatly improved if these data can be utilized. Therefore, some researchers began to consider semantic segmentation learning from the object level, which resulted in weakly supervised learning. Recently, weakly supervised semantic segmentation has become a new research direction. It can not only train the network through low-cost data but also make rational use of existing data, thus reducing the waste of data resources. Weakly supervised semantic segmentation is to segment different objects by learning the image through easier annotation. It is different from the dependence of fully supervised semantic segmentation on the pixel-level label. Figure 1 shows the annotation information of fully supervised and weakly supervised semantic segmentation. Compared with using pixel-level class labels to learn network parameters, weak labels are more difficult to learn. With the reduction of labeling information level, accurate image segmentation becomes a huge challenge.

Fig. 1 The annotated map of the semantic segmentation of fully supervised and weakly supervised

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2 Methods Weakly supervised semantic segmentation achieves object segmentation by classifying pixels with weak labels. Figure 2 shows the process of weakly supervised semantic segmentation. Firstly, the weak label is generated into pixel-level pseudo-label by the weakly supervised algorithm. Then the image is trained by deep convolution neural network. Finally, the output result and pseudo-label improve the performance of the model by back propagation minimizing loss function. These weak labels mentioned in this paper include the image-level label, point label, scribble label and bounding box label. As shown in Fig. 3, these weak labels are easier to obtain than pixel-level labels.

2.1 Image-Level Label The image-level label only gives what kind of image exists, and does not give the location and shape information of the object, which makes it very difficult for the

Fig. 2 The pipeline of weakly supervised semantic segmentation. BP means back propagation

Fig. 3 Illustrations of various weak annotations. a Image-level label. b Point label. c Scribble label. d Bounding box label

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image-level label to train the segmentation network. Image-level annotation is the simplest form of weak annotation. Large-scale datasets, for example, ImageNet and PASCAL VOC have a lot of image-level labeled images, which are easier to obtain, so many researchers began to consider the construction of image-level labels and pixel correlation. In [7], Pathak et al. used training data with the image-level label for weakly supervised learning and proposed a constrained convolutional neural network (CCNN). At the same time, a novel multi-class semantic segmentation method based on multiinstance learning (MIL) is proposed in [8]. Vezhnevets et al. [9] proposed a multiimage model (MIM) to restore the pixel labels of images. Pinheiro et al. [10] proposed a model based on convolution neural network, which only considers the minimum priority of image segmentation task to infer the segmentation object. Papandreou et al. [11] proposed an expectation-maximization algorithm (EM) for training data of image-level annotation to estimate unmarked pixel categories and CNN parameters. Qi et al. [12] proposed a two-branch framework for joint learning of semantic segmentation and object location. Saleh et al. [13] employed foreground/background mask extracted directly from the network to complete the segmentation task and achieved good results. Wei et al. have made great contributions to weakly supervised semantic segmentation based on the image-level label. In [14], a method based on candidate regions is proposed. The category information of candidate boxes is judged by the neural network, and candidate boxes with high confidence are screened out. Then a semantic segmentation network is trained by using the target location map as supervisory information. Literature [15] adopts a similar method and explores two kinds of network training strategies. For the first strategy, a new multi-label cross-entropy loss method is proposed. For the second strategy, the network is optimized according to the cross-entropy loss of single label. In [16], simple to complex (STC) framework is proposed, the result of the former CNN is used in the next CNN, which improves the ability of semantic segmentation. Literature [17] proposes to mine and expand the target area continuously by means of adversarial-erase to generate supervisory information for training segmentation model, and the prohibitive segmentation learning (PSL) method is proposed to train the semantic segmentation network, which can provide more accurate supervisory information. Shimoda et al. [18] proposed a new method based on CNN class-specific saliency map and fully connected conditional random field. Kolesnikov et al. [19] adopted class activation maps (CAM) [20] to locate the segmented object, then expanded the region according to the seed, and finally obtained the segmented result using conditional random field and boundary constraint. Zhang et al. [21] proposed a decoupled spatial neural network for generating pseudo-annotations. Li et al. [22] proposed a deep neural network framework, which directs weakly supervised learning by generated attention, to teach the network to generate more accurate and complete segmentation result. Lee et al. [23] proposed FickleNet framework, which discovers the relationship between object locations by dropout method and expands the activation area by the classifier, and introduces a method of extending feature graph to make the algorithm faster.

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2.2 Point Label The point label roughly provides the location of the object through a small point. Point labels provide location information, but the amount of information is extremely sparse, which is the simplest form of tagging to provide the position of the object. In order to get better results, prior knowledge is usually introduced to improve performance. Point label is a more powerful annotation than the image-level label to strengthen the supervision of semantic segmentation. Point label provides the location information of the object compared with the image-level label. Bearman et al. [24] proposed the joint loss function of image-level supervision and pixel-level supervision as the loss function of point supervision. However, it is not easy to deduce the object’s whole range from a given point, the experimental results are not satisfactory. Compared with image-level supervision, it can improve the accuracy by about 5.3%, and provide prior knowledge of the object to estimate the foreground area can further improve the accuracy by 7.6%. Compared with other weakly supervised semantic segmentation methods, point supervised method complete the best balance between labeling time and segmentation accuracy.

2.3 Scribble Label Scribble label is a kind of labeling method between point label and bounding box label, which provides sparse information about the location and scope of the target object. Compared with the image-level label, scribble label provides some location information of pixels, which can bring better results. Compared with the bounding box label, scribble label lacks deterministic object boundaries. Scribble label as an extension of point label further provides the range information of the object. It can complete a picture labeling through a few curves. Lin et al. [25] adopted a graphical model to propagate the scribble label to unmarked pixels. The labeling of training pictures was automatically completed by the energy optimization algorithm, and then the optimal values of pixel markers and model parameters are obtained alternately to complete the training.

2.4 Bounding Box Label The bounding box label covers the entire object area by a rectangular box. which provides more information, but there is still a gap compared with the pixel-level label.

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Bounding box labeling is more difficult than the three weak labeling mentioned above, but the segmentation effect is relatively good. Xu et al. [26] proposed maximum margin clustering (MMC) to complete the segmentation task based on optimizing the objective function and under the restriction of the border. Dai et al. [27] proposed the BoxSup method. The foreground region is obtained by the multi-scale compromise grouping (MCG) and the boundary information of the target object. Then the network parameters are adjusted based on the fully convolutional networks framework to improve the segmentation accuracy. Papandreou et al. [11] filled all the pixels in the border label into the label of the object. If they belong to multiple borders at the same time, they chose the label of the small border to fill in. Then they used conditional random field to subdivide the picture. Finally, the output picture was fed to the deep convolution network as a pseudo-label at the pixel level. Khoreva et al. [28] proposed using DenseCRF to filter the output of the network to get a better target object boundary, and then using the GrabCut algorithm to perform weakly supervised semantic segmentation task. Bounding box supervision is a relatively strong weak supervision. At the same time, it is difficult to get the bounding box label.

3 Experimental Result 3.1 Datasets The rapid development of computer vision is inseparable from large-scale public datasets, mainly including ImageNet, PASCALVOC2012, and MSCOCO. This section introduces the number of categories and pictures contained in these datasets. As shown in Table 1. ImageNet dataset plays an important role in the development of deep learning. Most of the research work on image classification, target detection, and semantic segmentation is based on this dataset. The ImageNet dataset contains more than 14 million images and has more than 20,000 categories. More than one million of them have clear category labeling and object position labeling. PASCAL VOC2012 dataset is expanded in the PASCAL VOC2007 dataset. There are 20 categories of objects to be identified, including human, animal, transport, Table 1 Comparison of classical open source datasets Dataset

Proposed years

Number of classes

Number of pictures

Contributor

ImageNet

2009

20K+

14,000K+

Deng et al.

PASCAL VOC2012

2012

21

2913

Everingham et al.

MS COCO

2014

91

123,287

Lin et al.

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indoor. With background classes, there are 21 classes. PASCAL VOC2012 dataset has good image quality, perfect annotation, very suitable for performance testing algorithm. The MS COCO dataset is mainly designed for scene understanding. It is constructed by collecting images of complex scenes, which contain common objects in natural scenes. The dataset contains 91 object categories. There are 2.5 millions tagged objects in 123,287 images. There were 82,783 training sets and 40,504 validation sets. The MS COCO dataset contains many categories, which are very challenging for various tasks.

3.2 Evaluation Criterion To measure the quality of the segmentation model, its performance needs to be strictly evaluated. In the field of computer vision image segmentation, mIoU is an important index to measure the accuracy of image segmentation. The full name of mIoU is mean intersection over union, which represents the proportion of intersection and union of ground truth and prediction. mIoU is defined as follows: pi j 1    k + 1 i=0 kj=0 pi j + kj=0 p ji − pii k

mI oU =

(1)

where k +1 is the number of classes, pi j indicates the number of pixels that belong to class i and are predicted to be class j, p ji indicates the number of pixels that belong to class j and are predicted to be class i, pii denotes the correct number of predictions.

3.3 Result Analysis This section analyses the results of the existing weakly supervised semantic segmentation methods described in Sect. 2. PASCAL VOC 2012 dataset is often used to evaluate the performance of algorithms and models. This paper presents the results of weakly supervised semantic segmentation based on PASCAL VOC 2012 dataset. The mIoU of validation set and test set for various weakly supervised semantic segmentation methods on PASCAL VOC 2012 datasets are summarized in Table 2. Provide new help in this area [29]. Although the performance of the weakly supervised semantic segmentation method is constantly improving, the mIoU index of the fully supervised semantic segmentation method has reached 89%. Comparatively, the results of weakly supervised semantic segmentation method are still poor. In addition, it is obvious from Table 2 that using the simplest image-level labeling results in poor segmentation results. On the one hand, image-level label information is difficult to relate to pixel-level information. On the other hand, some objects often

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Table 2 Weakly supervised semantic segmentation results on PASCAL VOC 2012 dataset Weak supervision

Method

mIoU (val) (%)

mIoU (test) (%)

Image-level label

MIL-FCN [8]

25.1

25.7

CCNN [7]

35.3

35.6

MIL + Seg [10]

36.6

–

WSSL [11]

38.2

39.6

SN [15]

41.9

–

DCSM [18]

44.1

45.1

STC [16]

49.8

51.2

WSSS [9]

50.2

–

AF-MCG [12]

50.4

–

SEC [19]

50.7

51.7

BF-BP [13]

51.5

–

GAIN [22]

54.8

–

AE-PSL [17]

55.7

56.7

DSNA [21]

58.2

–

DCSP [18]

60.8

–

FickleNet [23]

61.2

61.9

Point label

WTP [24]

42.7

–

Scribble label

Scribble Sup [25]

63.1

–

Bounding box label

WSSL [11]

60.6

62.2

BoxSup [27]

62.0

64.6

SDI [28]

65.7

67.5

appear with corresponding scenes, it is difficult to distinguish the foreground from the background, such as ships and water. When more supervisory information is provided, the segmentation effect will be improved. For example, the bounding box label in the weakly supervised method has the best segmentation effect, because the bounding box label provides information about the position and range of objects, which plays an important role in improving the accuracy of semantic segmentation.

4 Conclusion This paper summarizes the weakly supervised learning of semantic segmentation. A large number of existing algorithms are introduced, but their performance is still poor compared with the fully supervised algorithm. Weak label information is difficult to correlate with pixel-level semantic information, which is a huge challenge for weakly supervised semantic segmentation. In the future, we can consider combining a small number of pixel-level labels to further improve the segmentation effect,

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and make up for the gap between weakly supervised learning and fully supervised learning. Furthermore, we can consider designing new algorithms to ameliorate the performance of semantic segmentation. Acknowledgements This work was supported by National Science Foundation of China (No. 4182038, No. 61671054).

References 1. Barnes, D., Maddern, W., Posner, I.: Find your own way: weakly-supervised segmentation of path proposals for urban autonomy. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 203–210 (2017) 2. Beddad, B., Hachemi, K., Vaidyanathan, S.: Development and optimisation of image segmentation algorithm on an embedded DSP-platform. Int. J. Comput. Appl. Technol. 58, 250–258 (2018) 3. Liu, Y., Ren, Q., Geng, J., Ding, M., Li, J.: Efficient patch-wise semantic segmentation for large-scale remote sensing images. Sensors 18, 3232 (2018) 4. Wang, Y., Liang, B., Ding, M., Li, J.: Dense semantic labeling with atrous spatial pyramid pooling and decoder for high-resolution remote sensing imagery. Remote Sens. 11, 20 (2019) 5. Jia, Z., Huang, X., Eric, I., Chang, C., Xu, Y.: Constrained deep weak supervision for histopathology image segmentation. IEEE Trans. Med. Imag. 36, 2376–2388 (2017) 6. Han, Y., Shao, C., Yang, S., Deng, W.: MLNMF: multi-label learning based on non-negative matrix factorisation. Int. J. Model. Ident. Control 30, 1–8 (2018) 7. Pathak, D., Krahenbuhl, P., Darrell, T.: Constrained convolutional neural networks for weakly supervised segmentation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1796–1804 (2015) 8. Pathak, D., Shelhamer, E., Long, J., Darrell, T.: Fully convolutional multi-class multiple instance learning. arXiv preprint arXiv:1412.7144. (2014) 9. Vezhnevets, A., Ferrari, V., Buhmann, J.M.: Weakly supervised semantic segmentation with a multi-image model. In: IEEE International Conference on Computer Vision (ICCV), pp. 643–650 (2011) 10. Pinheiro, P.O., Collobert, R.: From image-level to pixel-level labeling with convolutional networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1713–1721 (2015) 11. Papandreou, G., Chen, L.C., Murphy, K., Yuille, A.L.: Weakly-and semi-supervised learning of a DCNN for semantic image segmentation. URL http://arxiv.org/abs/. 1502, 2734 (2015) 12. Qi, X., Liu, Z., Shi, J., Zhao, H., Jia, J.: Augmented feedback in semantic segmentation under image level supervision. In: European Conference on Computer Vision, pp. 90–105 (2016) 13. Saleh, F., Aliakbarian, M.S., Salzmann, M., Petersson, L., Gould, S., Alvarez, J.M.: Builtin foreground/background prior for weakly-supervised semantic segmentation. In: European Conference on Computer Vision, pp. 413–432 (2016) 14. Wei, Y., Xia, W., Lin, M., Huang, J., Ni, B., Dong, J., Yan, S.: HCP: a flexible CNN framework for multi-label image classification. IEEE Trans. Pattern Anal. Mach. Intell. 38, 1901–1907 (2016) 15. Wei, Y., Liang, X., Chen, Y., Jie, Z., Xiao, Y., Zhao, Y., Yan, S.: Learning to segment with image-level annotations. Pattern Recogn. 59, 234–244 (2016) 16. Wei, Y., Liang, X., Chen, Y., Shen, X., Cheng, M.M., Feng, J., Yan, S.: Stc: a simple to complex framework for weakly-supervised semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39, 2314–2320 (2017)

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17. Wei, Y., Feng, J., Liang, X., Cheng, M.M., Zhao, Y., Yan, S.: Object region mining with adversarial erasing: a simple classification to semantic segmentation approach. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1568–1576 (2017) 18. Shimoda, W., Yanai, K.: Distinct class-specific saliency maps for weakly supervised semantic segmentation. In: European Conference on Computer Vision, pp. 218–234 (2016) 19. Kolesnikov, A., Lampert, C.H.: Seed, expand and constrain: three principles for weaklysupervised image segmentation. In: European Conference on Computer Vision, pp. 695–711 (2016) 20. Zhou, B., Khosla, A., Lapedriza, A., Oliva, A., Torralba, A.: Learning deep features for discriminative localization. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2921–2929 (2016) 21. Zhang, T., Lin, G., Cai, J., Shen, T., Shen, C., Kot, A.C.: Decoupled spatial neural attention for weakly supervised semantic segmentation. arXiv preprint arXiv:1803.02563 (2018) 22. Li, K., Wu, Z., Peng, K.C., Ernst, J., Fu, Y.: Tell me where to look: guided attention inference network. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9215–9223 (2018) 23. Lee, J., Kim, E., Lee, S., Lee, J., Yoon, S.: FickleNet: Weakly and Semi-supervised Semantic Image Segmentation Using Stochastic Inference. arXiv preprint arXiv:1902.10421 (2019) 24. Bearman, A., Russakovsky, O., Ferrari, V., Fei-Fei, L.: What’s the point: semantic segmentation with point supervision. In: European Conference on Computer Vision, pp. 549–565 (2016) 25. Lin, D., Dai, J., Jia, J., He, K., Sun, J.: Scribblesup: scribble-supervised convolutional networks for semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3159–3167 (2016) 26. Xu, J., Schwing, A.G., Urtasun, R.: Learning to segment under various forms of weak supervision. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3781–3790 (2015) 27. Dai, J., He, K., Sun, J.: Boxsup: exploiting bounding boxes to supervise convolutional networks for semantic segmentation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1635–1643 (2015) 28. Khoreva, A., Benenson, R., Hosang, J., Hein, M., Schiele, B.: Simple does it: weakly supervised instance and semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 876–885 (2017) 29. Sayed, M., Salem, R.K., Khder, A.E.: A survey of Arabic text classification approaches. Int. J. Comput. Appl. Technol. 59, 236–251 (2019)

Real-Time Human Body Detection Based on YOLOv2 Network Xiaopeng Liu, Yan Liu, Hong Wang and Jiangyun Li

Abstract It is a pivotal problem for accurate and efficient human body detection in the field of computer vision. However, the complex backgrounds, various body postures, occlusions, shadow and so forth that usually have a negative impact on the performance of human body detection. Besides, the real-time ability of the existing detection algorithms are limited in the practical application. In this paper, with the excellent learning ability, a fast and efficient deep convolution neural network based on the YOLOv2 network is presented for real-time human body detection. It is a 22-layer network that is capable to handle the dataflow in 93.5 fps, fully meets the real-time requirements. In the same time, it achieves 80.27% average precision in the complex natural scene. Keywords Human body detection · YOLOv2 · DNN · Fast network · Real-time ability

1 Introduction Human body detection is a promising prospect in the field of security monitoring, automatic drive, traffic pedestrian recognition [1], intelligent robot system, etc., that attracting lots of researchers’ attentions in the world. In solving the practical problem, the algorithms of human body detection need to take both the accuracy and efficiency into consideration. On the one hand, the detection performance is sensitive to various human postures and actions, people dress habits, shooting angles, lighting conditions, local occlusions, multi-scale target, etc. These interferences usually deteriorate the perforX. Liu · Y. Liu · H. Wang · J. Li (B) School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China e-mail: [email protected] Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, Beijing 100083, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_44

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mance of detection. On the other hand, it is in demand for the industrial application to develop a more efficient and faster detection algorithm to meet the real-time running requirement [2]. With remarkable learning capability, deep neural networks are widely popular in the study of human body detection. In this paper, an advancing human body detection model based on the YOLOv2 (the full name is You Only Look Once) network is presented. An 22-layer network (named Network22 in short) is adopted as the baseline architecture, just like the name that it is stacked by 22 convolutional layers as well as 5 pooling layers. The presented Network22 is an one-state detecting architecture in such a fashion that receiving the image as input, learning and extracting the representative high-level feature, then predicting the location of the target directly. It could get rid of the cumbersome steps of boxes proposal like the RCNN, fast RCNN and faster RCNN networks, which allows the Network22 running in high speed while maintaining a decent performance. The employed network has a well generalized performance that is robust to the complex background influences and fully satisfies the real-time requirement, which shows favorable attractions in the practical industrial application. The remainder of this paper is organized as follows. We introduce the related works of detection algorithm in Sect. 2. The detailing presentation of the adopted Network22 is illustrated in Sect. 3. We conduct the experiments to validate the performance of the presented method in Sect. 4. In Sect. 5, a conclusion is provided.

2 Related Work The existing approaches of human body detection include the traditional methods and the deep neural network (DNN) methods. Traditional detection algorithms mainly utilize the hand-crafted features, e.g., Haar-based feature [3], SIFT-based (Scale Invariant Feature Transform) feature [4] or HOG-based (Histograms of Oriented Gradients) feature [5], to approximately describe the characteristics of the human body or contour. The hand-crafted feature is fed into the classifiers for recognition, such as SVM (Support Vector Machine) classifiers [6, 7] and Adaboost classifiers [8]. Typically, the DPM (deformable part model) method uses the optimized HOGbased algorithm, which computes the gradient feature of the image to construct the multi-scale pyramid, then uses the SVM classifier for human body detection, which won the champions of the PASCAL VOC Challenges preeminently 2007–2009 [9]. The development of the deep learning methods is reviewed. It is a milestone that Hinton et al. propose the concept of ’deep learning’ in Science journal and point out that the considerably potential learning capability of deep neural network [10]. In 2012, AlexNet is presented [11], the brilliant convolution neural network (CNN) significantly outperforms the runner-up more than ten percent points in the ILSVRC 2012 challenge. Hence, the detection methods are flourishing and numerous novel DNN methods are proposed. These works include the ZFNet network [12], GoogLeNet network [13], VGGNet network [14], etc. The ResNet proposed by

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Microsoft Research Asia reduces the error off to 4.94% [15], which is regarded as a breakout compared to the human error of 5.1%. As the performance increasingly enhancing, ongoing efforts are dedicated to the faster detection networks that are broadly attentive in the industrial practice. There are various kinds of efficient detection network presented, like the RCNN [16], fast RCNN [17] and faster RCNN [18], the SSD network [19] as well as the YOLOv1 network and YOLOv2 network [20, 21], etc.

3 Method 3.1 Motivation The convolution neural network becomes a mainstream of the detection methods. It is developing so rapid that a great deal of deeper and wider networks with encouraging performance are appeared in recent years. However, the increasing complexity of the DNN model brings heavy computational burden and limits the practical application. We focus on the real-time detection network that could take both high-efficiency and high-accuracy into consideration for human body detecting. Out of this, an advancing Network22 that based on the YOLOv2 network is developed.

3.2 Network Architecture The network architecture, as shown in Fig. 1, is stacked by the convolutional layers and max-pooling layers, where the convolution layers are utilized for feature selection and extraction while the pooling layers for downsampling that could reduce the computing cost and slightly improving the generalization. We adopt the batch nor-

Fig. 1 The architecture of the presented Network22. It consists of 22 convolution layers and 5 pooling layers, where ‘×5’ represents the convolution layer is repeated 5 times here. The BN and LRelu are performed after the convolution operation

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malization (BN) as regularization and the leaky rectified linear unit (LRelu) function as nonlinearity after each convolutional operation. As illustrated in Fig. 1, it receives the image as input (i.e., size of 448 × 448), then the interested features that describing the representative information of the human body are learned and extracted by the hierarchical convolutional layers. To heel, the feature maps are obtained and the network is capable to predict the existence of the target and regress their location. 1 to the original image size after five pooling layers. The output feature maps are 32

3.3 Detecting Process Assuming the target’s position is located using the values of x, y, h, w. Where x, y are the prediction center of the target in the image; w, h are referred to the width and height. As stated earlier that the Network22 outputs the feature maps have a size of m × m (i.e., 13 × 13), each point of the feature maps would predict the coordinate center (x, y) of the target. Around the current center, the width, height and the confidence of the target are estimated on the five predetermined anchors. Therefore, the main procedure of the human body detection is completed, as shown in Fig. 2.

Fig. 2 The schematic diagram of the human body detecting process on the output feature maps

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3.4 Dataset The human body data comes from the ’person’ class of the PASCAL VOC 2007 and 2012 dataset, which contains the well-annotated labels for our study. There are totally 8102 images and the corresponding ground-true labels to be available. These data are divided into three parts, including the training set (5112 images), validation set (983 images) and testing set (2007 images). There are several approaches of data augmentation adopted in the training process that could improve the network performance effectively. Commonly, the employed data augmentation approaches include random rotation, random flipping, random saturation and sensitometry transform, random center cropping the images.

3.5 Network Training We train the Network22 for 60,000 iterations using the Adam optimizer, with a batch size of 32 and a learning rate of 0.0001. The flow diagram of the network training process is illustrated in Fig. 3. We perform the model initialization at the beginning, then the training data (i.e., images and labels) are fed into the Network22 batch by batch in a mini-batch training manner, it takes the forward and backward propagation to update the weight iteratively. The validation set is employed to monitor the learning

Fig. 3 The schematic diagram of the network training

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process that training is stopped if the loss curve is not to decrease anymore. Besides, the weight of the model are saved periodically until the training process is over.

4 Experiments The experiments are conducted to validate the presented network in this section. Formally, the performance of human body detection is evaluated by the average precision (AP) and the running time. The presented Network22 is trained and tested using the Nvidia Geforce 1080Ti GPU. The loss curve of the training process is revealed in Fig. 4 (a). From the figure of loss curve, it is observed that the training process is stable and convergent progressively. The Network22 is early stopped and saved at the about 52,000-th step empirically. The average precision is a common evaluation metric of the detection algorithm that is calculated in terms of the recall and precision. As illustrated in Fig. 4b, the average precision is equal to the area between the curve and the x axis. The experimental results of the Network22 with different sizes of the input image is shown in Table 1. It is observed that the presented method could handle the image in high speed with a high precision and high recall rate. For instance, it achieves an average precision of 80.27% while maintains a computational efficiency in 93.5 fps over the 448-resolution image. As the growing size of the input image, it prolongs the running time and brings the performance improvement. No matter what a small size or a large size image to cope with, it is still fast and efficient that fully meeting the real-time requirement. Furthermore, we take a step to detect the head, hand and foot of the object. A Group of examples of the detection results are shown in Fig. 5. It is shown that the well-trained Network22 could effortlessly recognize the targets and locate them accurately that is robust to the influence of the complex background.

Fig. 4 a The loss curve in the training process. b The recall-precision curve on the testing set

Real-Time Human Body Detection Based on YOLOv2 Network Table 1 Performance of the Network22 with different input image sizes Image size Precision (%) Recall (%) AP (%) 352 384 416 448 480 512 544 576

84.56 83.41 84.26 83.81 82.86 82.02 81.65 80.51

71.95 74.27 75.66 77.52 77.61 78.98 80.28 80.90

75.98 77.47 79.66 80.27 81.21 81.94 82.76 82.67

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Speed (FPS) 99.3 99.1 98.1 93.5 87.6 83.5 58.4 56.4

Fig. 5 Examples of human body detection

5 Conclusion In this work, a fast and high-precision human body detection network named Network22 is constructed and developed based on the YOLOv2 network. With favorable performance, its feasibility and effectiveness are examined by the experiments. In future works, we will make effort to optimize the human body recognition, and dedicate to the research of real-time video tracking [22]. Acknowledgements This work was supported by Natural Science Foundation of Beijing Municipality (No. 4182038) and National Science Foundation of China (No. 61671054).

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References 1. Liu, S., Su, T., Wang, B., Peng, S., Jin, X., Bai, Y., Dou, C.: Pedestrian indoor navigation using foot-mounted imu with multi-sensor data fusion. Int. J. Model. Ident. Control 30(4), 261–272 (2018) 2. Liu,Y., Geng, J., Su, Z., Zhang, W., Li, J.: Real-time classification of steel strip surface defects based on deep CNNs. In: Proceedings of 2018 Chinese Intelligent Systems Conference, pp. 257–266. Springer, Berlin (2019) 3. Lienhart, R., Maydt, J.: An extended set of haar-like features for rapid object detection. In: Proceedings. International Conference on Image Processing, vol. 1, p. I. IEEE, New York (2002) 4. Ke, Y., Sukthankar, Rahul, et al.: PCA-SIFT: a more distinctive representation for local image descriptors. CVPR 2(4), 506–513 (2004) 5. Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: International Conference on Computer Vision & Pattern Recognition (CVPR’05), vol. 1, pp. 886–893. IEEE Computer Society (2005) 6. Joachims, T.: Making large-scale SVM learning practical. Technical report, SFB 475: Komplexitätsreduktion in Multivariaten (1998) 7. Gao, K., Su, S., Li, D.-Y., Zhang, S.S., Wang, J.S.: A sentiment analysis approach based on exploiting Chinese linguistic features and classification. Int. J. Model. Ident. Control, 29(3):226–232 (2018) 8. Viola, P., Jones, Michael, et al.: Rapid object detection using a boosted cascade of simple features. CVPR 1(1), 511–518 (2001) 9. Felzenszwalb, P., McAllester, D., Ramanan, D.: A discriminatively trained, multiscale, deformable part model. In: 2008 IEEE Conference on Computer Vision and Pattern Recognition (2008) 10. Hinton, G.E., Salakhutdinov, R.R.: Reducing the dimensionality of data with neural networks. Science, 313(5786), 504–507 (2006) 11. Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097–1105 (2012) 12. Zeiler, M.D., Fergus, R.: Visualizing and understanding convolutional networks. In: European Conference on Computer Vision, pp. 818–833. Springer, Berlin (2014) 13. Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., Rabinovich, A.: Going deeper with convolutions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–9 (2015) 14. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014) 15. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016) 16. Girshick, R., Donahue, J., Darrell, T., Malik, J.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 580–587 (2014) 17. Girshick, R.: Fast r-cnn. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1440–1448 (2015) 18. Ren, S., He, K., Girshick, R., Sun, J.: Faster r-cnn: towards real-time object detection with region proposal networks. In: Advances in Neural Information Processing Systems, pp. 91–99 (2015) 19. Liu, W., Anguelov, D., Erhan, D., Szegedy, C., Reed, S., Fu, C.-Y., Berg, A.C.: Ssd: Single shot multibox detector. In: European Conference on Computer Vision, pp. 21–37. Springer, Berlin (2016)

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20. Redmon, J., Divvala, S., Girshick, R., Farhadi, A.: You only look once: Unified, real-time object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788 (2016) 21. Redmon, J., Farhadi, A.: Yolo9000: better, faster, stronger. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7263–7271 (2017) 22. Jasim, W., Gu, D.: Robust path tracking control for quadrotors with experimental validation. Int. J. Model. Ident. Control 29(1), 1–13 (2018)

Research on the Temperature Field and Thermal Roll Shape of Cold Rolling Model Zichao Sun, Weicun Zhang and Yan Liu

Abstract In the process of cold rolling production, roll shape is a very important parameter. Both the disturbance variables and control variables are existing in the control system that influencing the quality of the strip shape directly. How to predict the thermal crown of the roll is crucial to the control system of the whole set. According to the real data, we set the boundary conditions and the heat transfer coefficient using ANSYS software for large finite element analysis that considering all the affecting factors. We get the temperature spread field and the thermal expansion results of different states after simulation and calculation: in steady state, the highest temperature of the central zone on the surface is about 65 ◦ C, the biggest expansion is about 174 µm which are close to the actual data. We can carry on the subsection control of the cooling system according to the temperature and expansion based on the model to reduce the influence and improve quality of strip shape. Keywords ANSYS · Cold rolling model · Temperature field · Boundary condition · Subsection control

1 Introduction The roll is always in thermal equilibrium in rolling work due to the heat derives from the deformation of plate and the friction between rollers, working rollers and rolling parts during rolling process. The temperature raises and drops in this thermal balance will cause the thermal expansion of the roll, thus forming the corresponding hot roll shape. The hot roll shape is an important factor to determine the quality of plate, its

Z. Sun · W. Zhang · Y. Liu (B) School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China e-mail: [email protected] Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, Beijing 100083, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_45

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expansion rate would directly affect the flatness of the band steel. Therefore, it is the key of rolling process to effectively control the hot roll shape. The main temperature field methods include the analytical methods and the numerical methods. Chen et al. domestic scholars calculate the two-dimensional and three-dimensional temperature fields and the thermal deformation of the strip mill working roll using the large finite element software MAC/NASTRSN; Li et al. adopt the difference method for analyzing. The analytical methods rely on massive assumptions, however, only the simple heat transfer problems could be solved. With the advantage of large calculation and high precision, the numerical methods are able to establish a reliable simulation model. Considering the complex heat transfer behavior and the large heat capability, the finite element method is used for simulating calculation. This study combines the massive variation laws of the temperature field in production process and takes the influence of various possible factors into consideration under the comprehensive environment. With the use of the ANSYS software for thermal-structural coupling analyzing, a simplified method of partition equivalent heat transfer coefficient is developed, we are able to conduct the hot roll shape simulating calculation of the cold rolling. Further, the significantly theoretical foundations for the actual production process are provided [1, 2].

2 Model Parameters and Simplification On the one hand, the temperature field and the shape of hot roll are distributed in a three-dimensional unsteady model factually, on the other hand, the issue of the temperature conduction in the presence of the axial, radial and circumferential directions, the three-dimensional data would generate a huge amount of computation and take the result analysis into troubles. Out of this, it is necessary to simplify and equalize the parameters on the simulating calculation. (1) The rolling period of the roll is the second-order small compared to the response time of the thermal convexity in the rolling conditions, so the temperature change of the roll in the peripheral direction could be ignored and simplified as a twodimensional unsteady system. (2) Assumed that the temperature interferences are ignored except the heat inflow and outflow in the rolling process; the roll material density is uniform; and the initial temperature field is uniform and symmetric along the center line. (3) Considering the characteristics of the cold rolling mill, the heat radiation between the working roll and air, the friction heat between the working rollers, back-up rollers and bearings could be ignored. Moreover, the effect of heat exchange process is expressed by heat exchange coefficient. Due to there are a large amount of influence coefficients in terms of the heat transfer, so we select the coefficients empirically and ensure its reliability through the experimental verification [3].

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3 Boundary Condition Assuming that the initial uniform temperature field of the roll is 30 ◦ C and comprehensively taking account of the thermal influence factors, so the boundary conditions could be divided into eight intervals according to the characteristics of the working roll, as shown in Fig. 1 [4]. Where zone A is the direct contact zone between the strip steel and the roll, which is the most direct heat source of the working roll, and it is the intense convection zone. Zone B and H are radiation heat transfer zones, which are mainly radiation heat transfer of the strip steel and the roll. Zone C and G are the water-cooled zones, and the thermal behavior is mainly in the convection heat dissipation of the cooling water and the roll. Zone D and F are the air radiation zones. The heat exchange in the zone E is mainly the contact heat transfer between the working roll and the supporting roll. As shown in Fig. 2, look down on the working roll, the strip steel is from the below and deformed during rolling in the B and C sections, at this time, part of the heat is transferred by the plastic deformation of the workpiece enters into the working roll, which heating up the working roll gradually. During rolling, the friction heat produced between the rolled piece and the working roll, the temperature of the working roll

Fig. 1 The boundary conditions of the roll in radial direction

Fig. 2 Heat transfer behaviors of the horizontal roll

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reaches the highest due to the elastic deformation heat in the rolled piece export A and D, the thermal crown is also the most obvious. It has less heat exchange in the ABHG zone and CDEF zone because they are not contacted with the strip steel.

4 Simulation Calculation of Finite Element Model 4.1 Two-Dimensional Temperature Field Model The length of the roll used in the model is 1400 mm, the width of the strip steel is 1000 mm, the initial temperature of the working roll is 30 ◦ C, the temperature of the coolant and ambient is 25 ◦ C. In the temperature field analysis, PLANE55 element, a two-dimensional thermal entity, is selected. The grid division should be more precise when dividing because the thermal behavior of the radial external circumference is much more complex, and the temperature at the outlet of the horizontal middle strip steel is the highest, as shown in Fig. 3 [5, 6]. The specific model parameters are shown in Table 1.

Fig. 3 Grid partition of the mill roll

Table 1 Configuration of the model parameters Unit Value Working roll radius r (mm) Rotation speed n (m min−1 ) Specific heat C (J kg−1 k −1 ) Heat conductivity coefficient λ (W m−1 k −1 ) Density ρ (kg m−3 ) Elasticity modulus E (GPa) Poisson ratio μ Coefficient of linear expansion α

180 110 460 45 7800 200 0.3 12 × 10−6

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4.2 Simulation Results of Temperature Field Rolling is a long working period, times are needed for the distribution of the temperature field to reach the equilibrium state. The roll rotates periodically, and each cycle corresponds to a thermal load cycle, therefore, the simulation is conducted on the temperature distribution presented in the roll working process in a cyclic loading of thermal loads manner instead of loading the velocity of roll angular directly in this study. In the experiments, the transient thermal analysis is carried out on the PLANE55 unit of the two-dimensional entities, thermal analysis results is saved and produced as the .rth file. The different periods of the working roll temperature distribution are shown in Figs. 4, 5 and 6, respectively. It is observed that the surface temperature of the transverse middle roll is obviously higher than both sides. At the beginning of rolling, the temperature in the middle reaches out 59 ◦ C approximately, with a temperature difference of about 26 ◦ C that higher than its sides. As it comes to a stable rolling state about one hour, the middle temperature is leveled off to 67 ◦ C, and the temperature difference is reduced down to about 20 ◦ C. Figure 7 is the distribution of the radial temperature, the radial temperature distribution is observed to be uniform and to a

Fig. 4 The horizontal temperature distribution of the working roll with a period of 450 s

Fig. 5 The horizontal temperature distribution of the working roll with a period of 1200 s

Fig. 6 The horizontal temperature distribution of the working roll with a period of 3600 s

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Fig. 7 The radial temperature distribution of the working roll

Fig. 8 The distribution curves of the working roll temperature field at different times

small gradient. Then, the change of the temperature field of the working roll over time as shown in Fig. 8.

4.3 Profile Analysis of Hot Roll The working roll profile is formed by the raising surface temperature. From the experimental results of the temperature filed, it is analyzed that the temperature difference between the middle and the two sides of the working roll would result in the thermal deformation because the middle is more convex than the sides. The hot roll profile analysis is a heat-structure coupling field analysis problem. It provides two methods

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for coupling field analyzing on ANSYS, including the direct coupling method and indirect coupling method. The indirect method uses two or more correlation field analyzes in sequence. It realizes the coupling of the two fields by taking the results of the first temperature field analysis as the load of the second structure field analysis; the direct method uses all the coupled element types including temperature and displacement degrees of freedom to obtain the results of coupling field analysis by only one solution. The temperature field and the structure field of the roll affect each other and iterate continuously, hence the heat-structure is selected for directly coupling analysis. This study adopts two-dimensional coupling field of the eight-node PLANE223 platform unit for solution, we carry out the displacement constraint in the Y direction and X direction on the both sides of the model, the y-direction displacement constraint is applied to the lower end of the model, set the axisymmetric loading on the upper end face, then extracts the thermal analysis results, selects the transient solution and settings the large deflection analysis to observe the deformation results. Figures 9, 10 and 11 are the cloud figures of the thermal expansion distribution of the roll in the beginning, mid-term and steady states, respectively. It could be found that the deformation distribution of the roll is consistent to the temperature distribution results that the expansion is very small at the beginning of rolling, then the middle swell capacity reaches 95 µm in about 26 µs. In the stable working condition, the thermal expansion amount is leveled off to about 174 µm, and the expansion difference between the middle and the two sides is reduced. The result file extracted from ANSYS common postprocessor is able to draw the variation rule of roll surface thermal expansion, as illustrated in Fig. 12.

Fig. 9 The thermal profile of the roll in the beginning

Fig. 10 The thermal profile of the roll in the mid-term

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Fig. 11 The thermal profile of the roll in the steady state

Fig. 12 The thermal expansion of the roll at different time

5 Section Cooling Control System 5.1 Section Cooling Control Strategy The section cooling control technology is realized by spraying the coolant nozzle on the surface of the roll, its principle is to change the distribution of coolant flow along the transverse direction of the roll to control the temperature difference field and thermal deformation by rolling, and achieving the purpose of regulating the strip shape finally. The installation position, injection time interval, injection angle and water pressure of the nozzle can improve the strip shape in different degrees [7]. A common control strategy of the section cooling control is based on the least square method, it is capable to build up the control effect evaluation function of the strip shape with the application of the existing least square principle., and figure out the regulating range of the setting value of the control technology with different strip shapes. Assuming measured roll involves n measuring section, serial numbers from left to right, regard the measured rolls as a number line; let the roll center be the origin, yi is the measured deformation difference of the i-th section, the assumed function relation between xi and yi are established as below:

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Fig. 13 Temperature of the roll at different duty ratios

yi = f (xi ) = a0 + a1 xi + a2 xi2 + a3 xi3 + a4 xi4

(1)

According to the data, we could figure out the coefficients a0 , a1 , a2 , a3 and a4 using the least square method. Afterwards, it is able to control the strip shape according to the function relation, where the high-order component would be used as the control signal of section cooling.

5.2 Section Cooling Effect Analysis In this paper, assuming the heat transfer coefficient is unchanged, as well as the model parameters, the different cooling effects can be achieved by changing the time interval of coolant nozzle. Assuming it has three cooling conditions at the duty ratios of 2:10, 5:10 and 8:10 respectively, the obtained temperature distribution of the roll is shown in Fig. 13.

6 Conclusion In this work, according to the characteristics of the working roll at the scene of the cold rolling, we conduct the finite element analysis method to build up the temperature field model and obtain the temperature field distribution of the working roll under different working durations and conditions. Based on the distribution of the temperature field, the thermal roll shape is simulated through the thermal-structural coupling analysis with the help of the ANSYS software, the thermal expansion amounts in the rolling process are obtained. The effect of nozzle duty ratio on roll shape is analyzed. Compared with the actual rolling parameters on the practical field, the obtained ideal simulation results are able to provide reliable evidence for accurate control of the strip shape, and the control stability could be researched [8–10].

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References 1. Zhuo, X.: Research on Temperature Field Simulation of Work Rolls of Cold Rolling Model with Precision Thin Strip. University of Science and Technology Beijing, Beijing (2014) 2. Guo, Z., Li, C., Jian-zhong, X., et al.: Analysis of roll temperature field and thermal crown in TSCR. Iron Steel 41, 476 (2006) 3. Vladimr, B.G.: Application of coolflex model for analysis of work roll thermal condition in hot strip mills. Iron Steel Eng. 11, 38 (1997) 4. Long, J., Hongbo, G., Jie, Z., et al.: Work roll temperature field calculation and analysis based on multi-objective genetic algorithm. Univ. Sci. Technol. Beijing 36(9), 1255 (2014) 5. Zhang, X.: Simulation and Experimental Research for Temperature Field of Work Roll in 300 Cold Rolling Mill. Yanshan University, Qinhuangdao (2010) 6. Wang, H.: The Research of Sub-Cooling System of Aluminum Foil Rolling Mill. University of Science and Technology Beijing, Beijing (2009) 7. Shengjie, X.: Study on the Stepped Cooling Control System of the Rolls Based on Cloud Model. Yanshan University, Qinhuangdao (2014) 8. Li, P., Zhang, W.: Towards a unified stability analysis of continuous-time TS model-based fuzzy control systems. Int. J. Model., Ident. Control 31(2), 113–123 (2019) 9. Sun, X., Xing, H., Han, G., et al.: Bolt quality testing research using weighted fusion algorithm based on correlation function. Int. J. Modelling, Ident. Control 30(1), 19–29 (2018) 10. Yao, L., Wang, H.: Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model. Int. J. Model. Ident. Control 29(1), 22–30 (2018)

Optimized Control System Design for Two-Wheeled Inverted Pendulums Haifei Si, Yizhi Wang, Xingliu Hu and Zhong Yang

Abstract This paper mainly looks into the attitude angle control of two-wheeled inverted pendulum and validates the reliability of proposed control system via practical model. In order to control the extreme sensible attitude angle, this paper firstly designed Kalman filter to filter noise caused by sensors and to obtain optimized measured angle data, secondly designed a cascade hybrid PID controller respectively for angle control and angle speed control. Specially, an integration control is introduced in major loop to stable the attitude angle caused by accumulated little error, and to improve the response speed compared with single P control. After hardware configuration and manufacture work, the reliability of proposed control system design is validated. Keywords Two-wheeled inverted pendulums · Kalman filter · Cascade control · PID control

1 Introduction 1.1 Two Wheeled Inverted Pendulums Two-wheeled inverted pendulums, also known as two-wheeled self-balanced robots, firstly designed by U.S. Company DEKA and was named as Segway [1]. Initially, this product, Segway, was designed in the purpose to help leg-disabled people. However, H. Si (B) · Y. Wang (B) · X. Hu · Z. Yang College of Intelligent Science and Control Engineering, Jinling Institute of Technology, 99. Hongjing Avenue, 211169 Jiangning, Nanjing, Jiangsu, China e-mail: [email protected] Y. Wang e-mail: [email protected] X. Hu e-mail: [email protected] Z. Yang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_46

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Fig. 1 Two-wheeled inverted pendulum structure

soon researchers found its power in area vehicles unable to reach, such as airports, bus, train stations. With its popularity, for instance, transit efficiency can be largely improved, and then researches and studies about two-wheeled inverted pendulums are followed up. Back to two-wheeled inverted pendulums, characters of its mathematic models are normally, but not limited to, high order equations, flawed stability, multi inputs and multi outputs (like multi-angle movements), nonlinear behaviour, and strongly coupled variables, etc. [2, 3]. It is basically a movable single inverted pendulum, with two wheels set in differential mechanism; each wheel is directly driven by a DC motor through a reducer. As shown in Fig. 1, two-wheeled inverted pendulum can move forward and backward through wheel rotated around the motor axis. Therefore, the two-wheeled inverted pendulum is unlikely to stay stable and balanced under a stationary state but to maintain dynamic balance [4]. Here dynamic balance indicates the robots maintain balance through constant slight adjustment around the balance point.

1.2 Research Aims The research aim of this paper is to optimize the algorithm to balance the two-wheeled inverted pendulums by real-time data sending from sensors.

1.3 Research Objectives The research objectives are listed as follows: (1) Design a Kalman filter to establish an optimized predictive state space model; (2) Design a cascade PID control system to control two-wheeled inverted pendulum’s attitude angle and keep it balanced with required performance; (3) Give type and model selection for parts and components; (4) Validate feasibility and stability of designed system through manufactured twowheeled inverted pendulum with given configuration.

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1.4 Paper Structure This paper will begin with a literature review about wheeled inverted pendulum and some control methods related to this area, and then will mainly focus on algorithm design of the two-wheeled inverted pendulum, including Kalman fusion filter design for attitude angle control and Cascade PID control design, followed by result analysis. Finally a conclusion and future work will close this paper.

2 Research Background 2.1 Wheeled Inverted Pendulum As stated earlier, one of typical features of two-wheeled inverted pendulum is flawed stability. Addition to its complex working space, difficulties in establishing mathematical models and designing control methods leave the performance of two-wheeled pendulum to be improved. In industrial development, Famous JOE model was developed by researchers working in Swiss Federal Institute of Technology. Data from embedded gyroscope and optical-electricity encoder were used to establish a linear state feedback controller for pendulum’s balance. Besides, Xiaomi Corp released Ninebot self-balanced inverted pendulum on 19.10.2015. Sine wave vector control and speed closed loop control were adopted. In research area, a lot of control methods have been developed for wheeled inverted Pendulum, such as neural network control [5], composite control for nonlinear model [6], sliding mode control [7, 8], PID control [9], etc.

2.2 Kalman Filter One of Kalman filter’s applications is to give optimized prediction regard to system’s state based on input/output data of the system via its linear state-space equations [10, 11]. As observed data contains state and noise of system, it can be also considered as a fusion filter algorithm. Via Kalman filter, the states of dynamic systems can be predicted, based on data with measuring noise, if the measurement variance is already known. This advantage makes computer programming and real-time data processing feasible. Kalman filter is the most popular filter method so far, and has been widely used in areas of communication, navigation, guide and control, etc.

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2.3 Cascade Control Method According to its name, in a cascade control system, there are more than one controller connected in series, and the output of one controller is the set value of another controller [12]. In most situations single controller system is applicable, while there are some systems with large lag, long characteristic time, frequent inference or required high performance [13]. Single controller system may apply to these systems no longer, but cascade control system with more than one controller is needed.

3 Control System Design The main design process is shown in Fig. 2. Control system mainly works as follow steps: (1) Accelerated speed and angle speed along axis will be sampled by attitude angle sensor MPU6050; (2) After received the data, micro-controller will calculate an inclined angle around axle through fusion filter; (3) This calculated angle will be further sent to software embedded in microcontroller as the input of control system; (4) Control system will deliver an output data through output pin of micro-controller to drive the motor, and finally keep the pendulum balanced. In remained part, each step combined with control algorithm will be detailed.

3.1 Kalman Filter Design A vital parameter is the attitude angle of its body and the algorithm of attitude angle control plays a decisive role in overall control methods [3]. In practical use, there are two issues in calculating the attitude angle. Firstly, normally, attitude angle data is sampled by gyroscope and accelerometer. As the presence of gravity, it can be inferred that, when placed horizontally, the

Fig. 2 System schematic diagram

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Fig. 3 Acceleration analysis

pendulum will have one G force along Z axis, while inclined in any angle, two force components will be separated from one G force respectively along X and Y axis. Therefore, as shown in Fig. 3, using an arctan function, the attitude angle can be calculated as Eq. 1: angleX = a tan 2(accx, accz) ∗ 180/3,1415926

(1)

Secondly, the mentioned method can only be applied to quiescent state, let’s say, the pendulum stays still. When in moving state, the motor will give the pendulum an added accelerated speed. In this situation, calculation through said arc tan function Eq. (1) will derive a large error far away from the real data. In this case, another way to calculate the attitude angle in moving state is to integrate the angle speed sampled by gyroscope. This is because angle measured by gyroscope is independent from the overall accelerated speed, which will not introduce added error into angle calculation. Consequently, considering measuring error brought by gyroscope and sampling intervals, integration of angle speed will also introduce a noise in attitude angle calculation. Therefore Kalman Filter method here is introduced for fusion filtering data from sensors to obtain the more precise attitude angle result. Considering angle data is sampled by sensors with intervals, the consecutive equation is required discretized, the state equation with random error is established as Eq. 2.

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X (k) = AX (k − 1) + BU (k) + W (k)

(2)

After that, the output equation of the system with measured data is established as Eq. 3. Z (k) = H X (k) + V (k)

(3)

Here: A—State matrix; B—Input matrix; X (k)—State of system at time k; U (k)—Input value of system (also known as control value) at time k; H (k)—Observer matrix; Z (k)—System output (measured data) at time k; W (k)—Random Interference at time k; V (k)—Noise of measurement. For a multi-input-multi-output (MIMO) system, X (k) and U (k) are normally matrix as well. Refer to W (k) and V (k), Gussian white noise is adopted to represent them, hence we use Q and R to denote their covariance respectively. If there exists a Kalman filter that meets these requirements, a Kalman filter is known as optimized predictive filter. Suppose current time is (k); according to Kalman filter model, the following state equation can be predicted from (k−1) state as Eq. (4): X (k|k − 1) = AX (k − 1|k − 1) + BU (k)

(4)

Here, X (k|k − 1) is the predicted current state from last state; X (k − 1|k − 1) is the last state after optimization; U (k) is input of the system, also known as output of control system. If the control system is not active, U (k) defaults as 0. Consequently, we use P to denote covariance of state X (k|k − 1); then the equation for updating P based on last state is as Eq. (5): P(k|k − 1) = A P(k − 1|k − 1)A + Q

(5)

Here P(k|k − 1) denotes the covariance of X (k|k − 1); Accordingly, P(k − 1|k − 1) is the covariance of X (k − 1|k − 1). Combined Eqs. (4) and (5), the predicted state equation is obtained. Consequently, after retrieved measured value of current state, the predicted state of X (k|k) can be calculated through measured and predicted state, as Eq. (6): X (k|k) = X (k|k − 1) + K g(k)(Z (k) − H X (k|k − 1))

(6)

Here Kalman gain is denoted by K g. K g(k) = P(k|k − 1)H  /(H P(k|k − 1)H  + R)

(7)

The last step is to update covariance of X (k|k), as Eq. (8). P(k|k) = (I − K g(k)H )P(k|k − 1)

(8)

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Here I is a unit matrix with all of its elements value equal to 1. For SISO (single input single output) system, I = 1. When system moves into next time sequence, k + 1, current P(k|k) will become P(k − 1|k − 1) of Eq. (5). Follow the algorithm, calculation is manifested convergent.

3.2 PID Control Method Proportional control, derivative control and integration control constitute PID controller in Classic Control Theory. For a continuous system, the attitude angle output is controlled by a group of PID controllers as shown in Fig. 4, and is basically calculated by Eq. (9) as follows: ⎡ 1 u(t) = K p ⎣e(t) + T1

t

⎤ de(t) ⎦ e(t)dt + TD + u0 dt

(9)

0

As micro-controller will be used in this research, data will be obtained through sampling sensors, which is discrete data. Therefore, the said equation should be discretized as follows: u k = K p ek + ki

k  j=0

Fig. 4 PID system block diagram

e j + kd (ek − ek−1 ) + u 0

(10)

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Fig. 5 Cascade control block diagram

3.3 Upright-Balance Control Method As discussed earlier, cascade hybrid PID control method is adopted as the core control method in this research. The minor control loop is angle speed control using PD control method, while the major loop is angle control using PI method as shown in Fig. 5. Therefore, the angle error measured from major loop will become the reference point (set point) of minor loop. According to mathematical model analysis of twowheeled inverted pendulum, the sensitive angle speed plays a very significant role in balancing the pendulum. Hence, the minor loop is also called stability optimized part in this cascade PID control system design. Relatively, the major loop (angle control) performs fine tuning regarding to attitude angle. Lots of researches have been done to prove the feasibility of linear systems control. Refer to inverted pendulum control, as a nonlinear object, the minor loop actually optimizes it to a linear system; Thereupon, only proportional control will be acceptable to stable the pendulum. However, as higher performance is required, integration control is also introduced into major loop. In this case, faster response can be obtained. Additionally, such design will remain some tolerance range, as the mathematical model may also bring error into calculation.

4 Result Analysis The two-wheeled inverted pendulum finished product is shown in Fig. 6.

4.1 Attitude Angle Control Compared with accepted design with P control, integrated control brought into major loop can effectively compensate the deadlock caused by single P control, namely P

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Fig. 6 Finished two-wheeled inverted pendulum

control fails to respond to little error. Therefore, PI controller in major loop will have better control performance refer to frequently changed set-point.

4.2 Cascade Control When moving horizontally, output of speed PI controller will give the pendulum a force along current direction. Due to inertia, the upper half of the pendulum will incline against current moving direction. Under this situation, cascade PID controller will supress the incline of pendulum body and drive the body to move along the inclined direction. The overall control result will reduce the horizontal displacement, until it reaches the dynamic balance state.

4.3 Dynamic Balance Validation The validation process is: As shown in Fig. 7a, firstly the pendulum is forced to stay at the largest angle of inclination, about −30◦ . Then suddenly release the force, the pendulum was moving backward while the body was inclining forward. Overall moving length is about 11.6 cm, which also can be observed from the figure. The inclined angle became 30◦ , as shown in Fig. 7b. After 4 s the pendulum stayed still, with a slight length about 3 cm from original position as shown in Fig. 7c.

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Fig. 7 Reliability validation

5 Conclusions and Future Work 5.1 Conclusions This paper firstly shaped the background and literature of this research, pointed out research aim and objectives, and then briefly introduced the methodology of attitude angle control; after that, a Kalman filter has been designed to filter the measurement noise and to predict optimized system state, which in this case here is the angle and angle speed for attitude angle. Then a cascade PID control system has been designed, taking angle PI control as major loop and angle speed PD control as minor loop. Along with the hardware configuration, the practical model has been manufactured to validate the reliability of control system. Finally the control system’s performance reached expected results.

5.2 Future Work Based on the work in this paper, the future work could be the following: (1) As shown in Fig. 7c, there is about 3 cm horizontal displacement after the pendulum is stable while the expected displacement should be 0. This means the control system brings some residual error. In future study, residual error could be reduced. (2) In validation part, the pendulum is placed at −30◦ but still stays in stable state. Considering unstable situation like excessive inclined angle that would lead the pendulum to overturning. In future study, fuzzy PID could be introduced to reduce response time of PID controller, for instance.

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References 1. Guo, L., Wu, H., Song, Y.: Dynamic modelling of a variable structure two-wheeled robot during the mode switching process between segway mode and bicycle mode. In: Jia, Y., Du, J., Zhang W. (eds.) Proceedings of 2018 Chinese Intelligent Systems Conference. Lecture Notes in Electrical Engineering, vol. 529. Springer, Singapore (2019) 2. Tao, Y., Wang, T., et al.: A dual-redundancy thermal backup control method for the twowheeled self-balancing robot. In: Huang, B., Yao, Y. (eds.) Proceedings of the 5th International Conference on Electrical Engineering and Automatic Control. Lecture Notes in Electrical Engineering, vol. 367. Springer, Berlin, Heidelberg (2016) 3. Mandava, R.K., Vundavilli, P.R: Whole body motion generation of 18-DOF biped robot on flat surface during SSP & DSP. Int. J. Model. Ident. Control 29(3), 266–277 (2018) 4. Liu, Y.J., Gong, M.Z., Tong, S.C., et al.: Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints. Fuzzy Syst. IEEE Trans. 26(5), 2607–2617 (2018) 5. Tsai, C.C., Huang, H.C., et al.: Adaptive neural network control of a self-balancing two-wheeled scooter. IEEE Trans. Industr. Electron. 57(4), 1420–1428 (2010) 6. Liu, X., Liu, D.D.: Composite control of nonlinear robotic system with exogenous disturbance. Access IEEE 7, 19564–19571 (2019) 7. Xiu, C.B., Wang, R.S.: Sliding mode control based on dynamic model for transport vehicle. Access IEEE 6, 33819–33825 (2018) 8. Charles, F., Maarouf, S.: Model-based sliding functions design for sliding mode robot control. Int. J. Model. Ident. Control 30(1), 48–60 (2018) 9. Wu, Y.L., Li, S.Y., Li, K.: Enhanced receding horizon optimal performance for online tuning of PID controller parameters. Int. J. Model. Ident. Control 29(3), 209–217 (2018) 10. Sun, S.L., Peng, F.F., et al.: Distributed asynchronous fusion estimator for stochastic uncertain systems with multiple sensors of different fading measurement rates. Sig. Process. IEEE Trans. 66(3), 641–653 (2018) 11. Chen, Q., Yin, C., et al.: Hybrid consensus-based cubature kalman filtering for distributed state estimation in sensor networks. Sens. J. IEEE 18(11), 4561–4569 (2018) 12. Yang, C.Y., Cheng, J.H., et al.: Design of two-wheel upright self-balance vehicle. J. Zhejiang Shuren Univ. (Nat. Sci.) 13(04), 1–8 (2013) 13. Lin, J.Y., Dai, T.F., Xiong, H.: Design of cascade PID control of current ring of self-balance vehicle. Microcontroller Embed. Syst. 17(05), 63–67 (2017)

A Retinal Vessel Segmentation Algorithm with Convolutional Neural Network Leiming Liu, Jiahao Li, Weicun Zhang and Dongmei Fu

Abstract Accurate retinal vessel segmentation technology plays a critical role due to the changes in retinal blood vessels can be used to diagnose certain diseases. In this paper, we propose an application based on a new convolutional neural network for extracting retinal vessel particularly capillaries, which preserves image details as much as possible with different feature information. We evaluated this model on the DRIVE databases. Our results indicate that the network outperforms most competing approaches in term of accuracy, sensitivity, specificity, F1-score, the area under the ROC curve (AUC). Keywords Retinal vessel · Fully convolution network · Deep learning

1 Introduction In recent years, Deep Learning (DL) has shown great advantages in object recognition, semantic segmentation, image classification, etc. As an important part of deep learning, convolutional neural networks (CNNs) has been employed to deal with medical images including the retinal vessel segmentation, since non-invasive fundus images is helpful to deal with a variety of ophthalmologic diseases such as diabetic retinopathy. Liskowski [1] adopted a deep convolutional neural network to classify retinal vessels and background, considering vessel segmentation as a two-class task. Li [2] implemented auto-encoder to train the network based on patches to segment vessels. Kassim et al. [3] also demonstrated superior performance in the CHASE database. However, the CNN fully connected layer is equivalent to a classifier and it classifies all pixels into several categories, which can not learn well the detailed features. To solve to this problem, Jonathan et al. [4] built a fully convolutional network (FCN), which avoided the problem of overlap between adjacent image blocks and L. Liu · J. Li · W. Zhang · D. Fu (B) School of Automation and Electrical Engineering, University of Science and Technology Beijing, No. 30 Xueyuan Road, Haidian District, Beijing, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_47

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repeated calculation. However, the FCN does not make full use of low-level vessel features and loses shallow semantic information. Therefore, U-Net was proposed [5] to utilize multi-scale information, which is an encoder-decoder structure with skip-connections. Despite vessel segmentation based on fully convolutional network has achieved good performance, there still have difficulties in accurately segmenting vessels. Therefore, we design a new convolutional nerual network for retinal vessel segmentation. We use the residual module [6] to construct the overall architecture, which make the network easier to optimize. Then our model includes a substructure: Atrous Spatial Pyramid Pooling (ASPP), proposed by [7, 8]. We introduce this module on the top of encoder and adjust the expansion rates according to the resolution of minimum feature maps. Based on this network, our method shows superior performance in the improvement of vessel segmentation accuracy and identification of tiny vessel.

2 Method Model Framework. Our network is depicted in Fig. 1. Residual learning avoids the occurrence of gradient disappearance existing in deep network and can enhance the ability of feature propagation. In this paper we use the full pre-activation Residual Unit [6] as the Basic-Residual. In addition, a substructure is involved in the network that we have introduced. Atrous Convolution. Atrous convolution is proposed by Yu and Koltun [9] without increasing the parameters and it can expand the reception fields and retain multiscale features. It adds the “holes” in general convolutional kernel, the size of output feature maps can be controlled by a dilation factor, r. The atrous convolution operation is as follows: y[i] =



x[i + r · k]W [k]

(1)

k

where x and y are the feature maps, i represents the location in y, W is convolution kernel. In this paper, Atrous Spatial Pyramid Pooling (ASPP) is involved the atrous convolutional operation through setting different expansion rates. It consists of five channels in parallel. Since the resolution of the feature map is small at the top of encoder, we set the r is 1, 2, 3 in the 3 × 3 convolution respectively. In addition, we combine a 1 × 1 convolution and image pooling with the module. The ASPP module can be seen in Fig. 1.

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Fig. 1 The framework of our model

3 Experiments Dataset. We evaluated our network on the public database: DRIVE database [10]. It was obtained from a diabetic retinopathy screening program, which consisted of 40 RGB color fundus images with a resolution of 584 × 565. There have been divided into 20 training images and 20 test images. In addition, all the images are equipped with corresponding binary masks. For each test image, the ground truth is annotated by two experts. Image Preprocessing. Each retinal sample is converted into the LAB colorspace and the contrast limited adaptive histogram equalization (CLAHE) algorithm [11] is utilized for L space to improve contrast. Then we extracted image patches with a resolution of 64 × 64 by sliding window on the training images. To prevent overfitting, we further adopt image augmentation methods to increase the number of image patches. Each patch is composed of actions as follows: (a) Rotation by an angel of 90 and 270; (b) Flipping horizontally and vertically; (c) Random brightness transformation by a factor between 0.5 and 1.5. Training Parameters. Stochastic gradient descent (SGD) with a batch size of 128 is employed to optimize our model. Similar to [7–12], we adopt “ploy” policy to index  iter with index adaptively adjust learning rate, which is multiplied by 1 − max_iter = 0.9. The initial learning rate is 0.01 and the momentum parameter is set to 0.9. The weight decay is set to 0.001. Maximum iteration number of training is 100. The experiments are implemented on MXNet framework and conducted on the hardware configurations: Intel E5-2620 CPU with two NVIDIA GTX 1080Ti GPU.

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4 Result We employ five evaluation criteria, including sensitivity (Se), specificity (Sp), accuracy(Acc), F1-score and AUC to evaluate the performance of our methods. Figure 2 shows two test images from DRIVE together with the segmentation results and the ground truth. It can be seen from the figure that there have a good effect on the segmentation of small blood vessels. Then Table 1 gives above evaluation criteria obtained by applying several existing methods and the proposed method to the DRIVE dataset. It shows that the quantitative indicators of our method are completely better than the second expert. From table we can see our method achieved four best values except specificity value, which reveals the overall performance of our network is superior to these existing approaches.

5 Conclusion To accurately segment blood vessels and better detect tiny vessel, we design a new convolutional nerual network and evaluate it on the DRIVE dataset. we introduce the Atrous Spatial Pyramid Pooling (ASPP) to fully utilize and analyze the features of

Fig. 2 a DRIVE images; bSegmentation results; c Ground truth

A Retinal Vessel Segmentation Algorithm with Convolutional Neural Network Table 1 Performance analysis on DRIVE database Methods Year Se Sp 2nd Human Observer Marin [13] Fraz [14] Roychowdhury [15] Li [2] Liskowski [1] Dasgupta [16] Hu [17] Ours

N.A 2011 2012 2015 2016 2016 2017 2018 2019

0.7760 0.7067 0.7406 0.7250 0.7569 0.7811 0.7691 0.7772 0.7900

0.9725 0.9801 0.9807 0.9830 0.9816 0.9807 0.9801 0.9793 0.9809

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Acc

AUC

F1-score

0.9473 0.9452 0.9480 0.9520 0.9527 0.9535 0.9533 0.9533 0.9563

N.A 0.9588 0.9747 0.9620 0.9738 0.9790 0.9744 0.9759 0.9803

0.7881 N.A N.A N.A N.A N.A N.A N.A 0.8205

vessels. The experiments demonstrate the good segmentation results and the superior performance of the network we designed.

References 1. Liskowski, P., Krawiec, K.: Segmenting retinal blood vessels with deep neural networks. IEEE Trans. Med. Imaging 35(11), 2369–2380 (2016) 2. Li, Q., Feng, B., Xie, L.P., et al.: A cross-modality learning approach for vessel segmentation in retinal images. IEEE Trans. Med. Imaging 35(1), 109–118 (2016) 3. Kassim, Y.M., Palaniappan, K.: Extracting retinal vascular networks using deep learning architecture. In: 2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), pp. 1170–1174, IEEE (2017) 4. Long J, Shelhamer, E, Darrell, T.: Fully convolutional networks for semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3431–3440 (2015) 5. Ronneberger, O., Fischer, P., Brox, T.: U-net: convolutional networks for biomedical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 234–241. Springer, Cham (2015) 6. He, K., Zhang, X., Ren, S., et al.: Identity mappings in deep residual networks. In: European Conference on Computer Vision, pp. 630–645. Springer, Cham (2016) 7. Chen, L.C., Papandreou, G., Schroff, F., et al.: Rethinking atrous convolution for semantic image segmentation. arXiv preprint arXiv:1706.05587 (2017) 8. Chen, L.C., Zhu, Y., Papandreou, G., et al.: Encoder-decoder with atrous separable convolution for semantic image segmentation. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 801–818 (2018) 9. Yu, F., Koltun, V.: Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122 (2015) 10. Staal, J., Abrmoff, M.D., Niemeijer, M., et al.: Ridge-based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 23(4), 501–509 (2004) 11. Reza, A.M.: Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement. J. VLSI Signal Process. Syst. Signal Image Video Technol. 38(1), 35–44 (2004)

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12. Chen, L.C., Papandreou, G., Kokkinos, I., et al.: Deeplab: semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018) 13. Marn, D., Aquino, A., Gegndez-Arias, M.E., et al.: A new supervised method for blood vessel segmentation in retinal images by using gray-level and moment invariants-based features. IEEE Trans. Med. Imaging 30(1), 146–158 (2011) 14. Fraz, M.M., Remagnino, P., Hoppe, A., et al.: An ensemble classification-based approach applied to retinal blood vessel segmentation. IEEE Trans. Biomed. Eng. 59(9), 2538–2548 (2012) 15. Roychowdhury, S., Koozekanani, D.D., Parhi, K.K.: Blood vessel segmentation of fundus images by major vessel extraction and subimage classification. IEEE J. Biomed. Health Inform. 19(3), 1118–1128 (2015) 16. Dasgupta, A., Singh, S.: A fully convolutional neural network based structured prediction approach towards the retinal vessel segmentation. In: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017), pp. 248–251, IEEE (2017) 17. Hu, K., Zhang, Z., Niu, X., et al.: Retinal vessel segmentation of color fundus images using multiscale convolutional neural network with an improved cross-entropy loss function. Neurocomputing 309, 179–191 (2018)

A Detection and Isolation of Faults Technique in Automotive Engines Using a Data-Driven and Model-Based Approach Yingmin Wang, Dong Cui and Feng Guo

Abstract Modern Diesel engines with exhaust gas recirculation have achieved a significant progress in intake system, fuel consumption and emissions. So the process became more complex. Therefore, fault detection and diagnosis is difficult to be done and need to be improved. This contribution shows a system of fault detection and diagnosis methods for diesel engines based on physical model and data-driven model. By applying physical dynamic process models, identification with local linear model tree (LOLIMOT), data-driven models and residuals are generated by parity equations. Measured data in fault-free operation is used to build data-driven models. Detectable deflections of these residuals lead to symptoms which are the basis for the detection of faults. In final applications look-up tables can be generated using data-driven models. Experiments with a diesel engine intake system on MATLAB have demonstrated the detection and diagnosis of faults is suitability for application with reasonable calculation effort. Keywords Fault detection · Fault isolation · Fault diagnosis · Data-driven · Diesel engine · Local linear model tree

1 Introduction For modern automotive engines, it is important to find and detect any fault which disrupts its operation. Any fault can lead to the degradation of engine efficiency. Besides, Emission related legislations [1, 2] require on-board diagnosis (OBD) of all faults in automotive engines that may lead to increased exhaust emissions. And, OBD system is necessary for all diesel-driven cars in Europe and will soon be required Y. Wang (B) China Datang Corporation Science and Technology Research Institute, DaTangThermal Power Technology Research Institute, Lugu Village Road West Two Jade Spring District 18 Building Shijingshan District, Beijing, China e-mail: [email protected] D. Cui · F. Guo Inner Mongolia Datang International Tuoketuo Power Generation Co. Ltd., Hohhot 010206, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_48

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also for heavy vehicles in USA and EU [3]. In China, According to a set of relatively complete vehicle emission standards named GB18352.3-2005, not only fault associated with emissions but also fault of sensors, actuators and circuit should be diagnosed in OBD system [4]. All vehicles on sale in Beijing must be equipped with OBD system from 2006 and began to implement in the whole china from 2008 [5]. Therefore, fault detection and isolation (FDI) is necessary for both diagnosis and fault accommodation. In a modern car, about 50% of the on-board software of the engine management system can be applied to fault diagnosis [6]. Early diagnostic programs were based on simple sensor level checks. Nowadays, modern on-board diagnosis systems are employed mostly based on simple threshold monitoring or plausibility checks of measured signals as well as on signal based methods like the frequency analysis of the engine speed signal. In future these methods will no longer be sufficient to meet the growing requirements [7]. There are several challenges and difficulties facing to automotive engines when it comes to design the FDI systems. Typically, engines are optimized for low-cost and high functionality, and not for FDI, which means that there is no hardware redundancy in the form of multiple sensors. Therefore, as long as the embedded control system has sufficient processing capacity, it is necessary to use analytical redundancy and model-based FDI to detect and isolate faults well. To keep up with this, model based fault detection methods developed and tested in recent years can to be used. The fault diagnosis method based on analytical model is firstly applied in fault diagnosis on the intake system. Rizzoni and Min [8], proposed detection filters to diagnose sensor fault in automotive engine control system. A model-based fault diagnosis method of diesel engine intake system is presented by SUN et al. [9], and the fault diagnosis strategy of “detection observer” is formulated. Above model-based methods adopted physics-based models such as mean value engine models (MVEMs). For fault diagnosis, models based on physics have a special appeal for fault isolation since residuals are easily related to physical signals and parameters which are affected by faults. And, in these models, all faults are modeled by signals, or all faults are modeled as parameter changes. However, the faults are considered which appear during steady state operation in these works. This simplification will be used while seeking a unifying approach to sensor and hardware faults that occur in engines during steady state operation [10]. When conditions change or fault location changes, it is hard to get a good diagnostic accuracy, and the portability of the fault system is not high. So, Fault diagnosis method based on analytical model still needs to be further refined and improved. In fault diagnosis techniques, besides the analytical model [11, 12], the datadriven methods may be an alternative solution for the modelling of systems. A comprehensive study of the basic data-driven techniques for modelling and monitoring of complex industrial processes is given [12–15]. They are also applied in a wide range of industrial applications, for example, modelling and monitoring of system processes [16] and health monitoring of systems [16]. However, the classical multivariate statistical methods are used based on the assumption, which think that the measurements are following a Gaussian distribution. This restricts their applications

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because of non-linearity and dynamic behaviors of modern complex systems [17]. For modelling and estimation in combustion engines, neural networks are already integrated with the physically-based approaches for estimation of intermediate variables and as a substitute of look-up tables [18, 19]. The details about data-driven fault diagnosis for Manifold Absolute Pressure Sensor (MAP) of diesel engine can be obtained [20]. The air mass in combustion engine is estimated by using datadriven approaches, considering the non-linear behavior of the system and different settings of actuators and sensors in current engine concepts [21]. A model based on a LOLIMOT model of fault detection system for the injection, combustion and engine-transmission for diesel engines was presented [22]. Wang et al. [23] built intake system model based on LOLIMOT to diagnose faults for diesel engines. In this research, a FDI system for an automotive diesel engine can be designed based on analytical model and data-driven model. The paper is structured as follows. In Sect. 2, presents the design of the FDI system for automotive diesel engine system. Then in Sect. 3, we describe the methods in FDI system. It introduced model–based and data-driven fault diagnosis and residual generation methods. Consequently, the intake system as an example is shown. EGR system model was built by analytical model. LOLIMOT was used to establish the reference model of amplitude and phase of intake pressure fluctuation signal and volumetric efficiency. The models was regarded as a function of engine speed and intake density. Residuals are calculated in the module of Residual Generation using parity equations. Four residual signals were generated. And the mapping relationship between the residual signal and the fault type was achieved. Experiment results analysis is presented in Sect. 5, followed by discussions and conclusions.

2 Overview of Design FDI System In this study, a FDI system for automotive diesel engine was constructed based model and data. Figure 1 displays the overview of the proposed FDI system, in which two dotted boxes represent the on-line module and off-line module, respectively. In offline module, experiment data is preprocessed to build a system analytical model and signal model based on data-driven. And Residual generation, fault signature structure and fault diagnosis strategy were developed for automotive diesel engine for on-line apply. In on-line module, the actual data collected need to be preprocessed by denoising method and feature extraction, residuals are calculated by comparing the measured values of engine with the output values of the model. Then fault can be diagnosed, and if there are faults it turned to decision making module. In on-line module, when no fault, the error need to be calculate to judge whether to modify the model. In this paper, off-line learning and on-line fault diagnosis are combined, parameter adjustment of system diagnosis model by on-line, it is a closed-loop system. The system presented in this paper is shown in Fig. 1. The features generated

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Fig. 1 Fault detection and isolation scheme based on analytical model and data-driven model

from the residual generation are transformed to symptoms through low-pass filtering and thresholds. Then, the features are transformed to symptoms. All symptoms should be zero in fault-free case. The symptoms are transformed to faults using symptom-fault tables.

3 Design of the Model-Based and Data-Driven System 3.1 Model-Based Diagnosis Figure 2 introduces the fault diagnosis scheme based on model, which included: residua generation and decision making. There are a lot of methods to build residual generation, for example: parameter estimation, Sequential [24], state observers or output observers [25], parity equations [26]. Decision making process may be a simple threshold test for residual transient or smoothed values [27], and it can also be based on statistical decision theory, such as the generalized likelihood ratio (GLR) [28] or sequential probability ratio test [29], and hypothesis tests [30], etc. In this paper, parity equations and threshold test were adopted.

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Fault Output

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y (k)

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• ParameterEstimation • Sequential • State observers • Output observers • Parity equations

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Logic detection Residual Decision making

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Fig. 2 Fault diagnosis scheme based on model

In this paper, residuals are generated by parity equations. Partity equations were introduced in the aerospace field in the 1970s [31]. Parity equations are suitably arranged forms of the plant’s input-output model.

3.2 Data-Driven Methods In this paper, model-based and data-driven diagnosis methods are adopted. In Fig. 3, Fig. 3 Fault diagnosis based on data-driven model

Fault Engine U

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Data-driven signal model Fault diagnosis Normal mode Data-driven signal model • • • • •

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signal model was built based on data from ECU (Electronic Control Unit). So, process outputs or special characteristics of process outputs are used for the residual generation. There are a lot of methods to build data-driven signal model, for example: correlation function, Fourier analysis, Vibration analysis, Neural network, etc. Features may be Exceeded threshold, Amplitudes, Frequencies, etc.

4 Fault Diagnosis System on the Air Path of Diesel Engine 4.1 System Description and Considered Faults In Fig. 4, the air path of the considered turbocharged diesel engine is shown. The air path consists of air filter, compressor, intercooler, turbocharger, intake throttle, cylinders, EGR valve and cooler. In this paper, Pin,c and Tin.c represent separately pressure and temperature before compressor, Mair,MAF represents Mass of intake air, Ntc represents speed of compressor, Tout,c and Pout,c represent separately temperature and pressure after compressor, Pexhaust , Texhaust represent separately pressure and temperature of exhaust, Pim and Tim represent separately pressure and temperature of intake manifold, Pem and Tem represent separately pressure and temperature of exhaust manifold. The model-based and data-driven fault detection presented in this contribution is verified on faults of intake system. In following the implemented faults are shortly introduced. Leakage in the intake manifold is implemented by 5 mm orifice. Fault of the EGR actuator is implemented by blocking the EGR valve in bypass-mode. Restriction in the intake manifold is simulated by closing the intake throttle by 70%. The investigated faults in the intake system are summarized in the Table 1. Compressor Air filter

Turbocharger

MAF sensor Pexhaust Texhaust

Pin.c Tin.c m air,MAF

Ntc Tout,c Pout,c F2

intercooler

Fig. 4 Intake system of diesel engine

F1 Intake throttle

F3 EGR valve

Pim Tim

EGR cooler

Cylinders

Tem

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Fault type

Fault description

F1

Leakage in the intake manifold

F2

Restriction in the manifold

F3

EGR actuator blocked

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4.2 Model of Volumetric Efficiency The cylinders of the engine can be modeled as positive displacement pump. The real air mass flow into the engine m˙ r eal,im , this then defined by Eq. (1) with engine speed n, intake pressure pim , intake temperature Tim , universal gas constant R. theoretical. m˙ r eal,im =

Vd · ηv· pim · n 120 · R · Tim

(1)

The volumetric efficiency ηv is defined in Eq. (2) ηV =

m˙ r eal,im m˙ ideal,im

(2)

The theoretical air mass flow into the engine is defined as m˙ ideal,im , Hence, the real air efficiency can be calculated from sensor data, Eq. (3). ηV,measur ed =

m˙ r eal,im m˙ air,M AF = Pim m˙ ideal,im 0.5 · n · Vd RT im

(3)

For the fault detection, a model of the nominal volumetric efficiency in fault-free case is defined as ηv , nominal by Eq. (4). The data-driven model is achieved by a local linear model tree (LOLIMOT) neuronal network [32]. The volumetric efficiency of an engine depends on engine speed, intake density. ηV ≈ f ηV (n, ρim )

(4)

Based on this model, the real engine air mass flow can be calculated according to Eq. (5). m˙ r eal,im ≈ f ηV (n, ρim )

Vd · pim · n 120 · R · Tim

(5)

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4.3 Model of Mass of EGR Value In this section, models of the air mass flows through the EGR paths are built. Hence, EGR valve is modeled as adiabatic throttle. As shown in Eqs. (6)–(8). pem f (π E G R ) m˙ E G R = Cd A E G R √ RTim pim πE G R = pem ⎧ 2 κ+1 κ+1 ⎨ 2κ (π κ − π κ ) , π 2 2(κ−1) E G R > ( κ+1 ) EG R κ−1 E G R f (π E G R ) = κ+1 κ+1 ⎩ κ( 2 ) κ−1 , π ≤ ( 2 ) 2(κ−1) κ+1

EG R

(6) (7)

(8)

κ+1

where Cd is the discharge coefficient through EGR value, AEGR is effective area of EGR value. For the identification of the models, the actual mass flow of EGR has been calculated using the volumetric efficiency and the MAF measurement, Eq. (9). m˙ E G R,measur e = m˙ r eal,im − m˙ air,M AF

(9)

4.4 Amplitude and Phase Models of the Intake Pressure Oscillation Because of the periodic action of the intake valves, the intake air pressure is subject to oscillations, which are mechanically bound to the crank-angle α CA, Eq. (16). The oscillation period is 120° crank-angle for a 6 cylinder 4-stroke engine and φp, meaured,im is the phase delays of the oscillation. pmesur ement,im ≈ pmesur ement,im + A pmesur ement,im × cos(2π

α − φ pmesur ement,im ) (10) 120◦

For the fault detection, models of amplitude and phase of the intake pressure oscillation are defined by Eqs. (11), (12) by a local linear model tree (LOLIMOT) neuronal network. A pmesur ement,im ≈ f A p (n, ρim )

(11)

φ pmesur ement,im ≈ f φ p (n, ρim )

(12)

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4.5 Residuals Generation of the Fault Diagnosis System Residuals set is generated based on model and data-driven. Residual generations are built on parity equations. The four identified reference models are used to set up four independent parity equations yielding to the residuals: rηV = f ηV (n, ρim ) − ηV,measur ed

(13)

r E G R = m˙ E G R − m˙ measur ed

(14)

r A pim = A pmeasur emet,im − f A p (n, ρim )

(15)

r Aϕim = Aϕmeasur emet,im − f ϕ p (n, ρim )

(16)

5 Results of Experiments and Fault Diagnosis 5.1 Selection of Data Experimental research was conducted on DEUTZ-BF6M1015C engine, as shown in Fig. 10. Using 440 kW electric eddy current dynamometer and DEWE–3010 combustion analyser, the cylinder pressure, intake pressure, exhaust pressure and instantaneous speed can be collected based on angle or time. The parameters obtained from ECU include environmental pressure, ambient temperature and intake pressure, intake temperature, intake flow, etc. Due to the limitation of the bench test conditions, the data extraction process needed by the LOLIMOT model was disturbed. In this paper, the diesel engine was modelled by GT-Power, and the simulation test is carried out on the model. In this paper, the data was selected to build the reference model above. When the engine was in different operations. As shown in Fig. 11, the learning test data can represent the main working conditions of the engine, and the validation data represent the typical working conditions. The circle “◯”stands for learning data, to establish the LOLIMOT reference model; The triangle“” stands for validation data which was used to verify the established reference model; Solid square “” stands for the external characteristic engine of the maximum torque point.

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5.2 Data-Driven Models by LOLI MOT The local linear model tree (LOLIMOT) are identified with an orthogonal divided input space and define the placement of radial basis function (RBF). The RBF function is normalized to define the validity of each model. The validity of a local model is almost 100% in its canter, and decreases to its adjacent model, so the local model validity of each point is superimposed to 100%. With the method of local linear model, the parameters of the local model are obtained by one-step least square method, so it has the characteristics of fast neural network training. The input space of the worst performing local models is divided into two local models, resulting in more and more local models. The algorithm stops when a given number of local model or training errors are reached below a given global error limit. In this paper, the given global error limit is 5%.

5.2.1

Reference Model of the Intake Pressure Fluctuation Amplitude

The model of intake pressure fluctuation amplitude is based on LOLIMOT. Engine speed and intake density are as input vectors. Learning data and testing data are as shown in Fig. 5. Figure 6 shows that the global error is up to the experimental requirement when number of iteration is 11 and the segmentation is stopped. Figure 7 shows that it is divided into twelve hyper planes. Figure 8 shows the results of testing data in Fig. 5. In order to evaluate the accuracy of the intake pressure fluctuation model and the simulation results, we used linear regression analysis, the correlation coefficient R2 is as shown in [23]. When the correlation coefficient of R2 is close to 1, the model value y is closed to the simulation value the correlation coefficient R2 of this fit is 0.987. Intake pressure amplitude model value is closed to intake pressure amplitude simulation value. Fig. 5 Experiment data and test data

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Fig. 6 Global training error of intake pressure fluctuation amplitude

Fig. 7 Eleven iterations of the LOLIMOT algorithm

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Fig. 8 Linear regression analysis of intake pressure amplitude

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Reference Model of Volumetric Efficiency

The modelling of volumetric coefficient is based on LOLIMOT. Engine speed and intake density are as input vectors. Learning data and testing data are as shown in Fig. 5. The global error is up to the experimental requirement when number of iteration is 9 and the segmentation is stopped. Figure 9 shows that it is divided into ten hyper planes. Figure 10 shows the identified reference model for volumetric efficiency. The volumetric efficiency increases with the increase of the rotating speed. At low speed, it is affected by the inlet density, while in the middle and high engine speed it is less affected by the intake air density. Fig. 9 Nine iterations of the LOLIMOT algorithm

Fig. 10 Reference model for volumetric efficiency

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Fig. 11 Fourteen iterations of the LOLIMOT algorithm

Phase of the intake pressure CA

Fig. 12 Reference model for phase of the intake pressure oscillation

Intake density Kg .m-3

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Reference Model of the Intake Pressure Fluctuation Phase

The model of intake pressure fluctuation phase is based on LOLIMOT. Engine speed and intake density are as input vectors. The global error is up to the experimental requirement when number of iteration is 14 and the segmentation is stopped. Figure 11 shows that it is divided into fifteen hyper planes. Figure 12 shows the corresponding phase of the intake pressure oscillation. The phased is mainly a linear function of the engine speed. Due to the engine air intake fluctuations in accordance with the local factors in the air intake pipe, due to the smaller density changes, fluctuations in the rate of change is not large, so the density of the phase angle of the smaller. Therefore, the intake pressure oscillation phase is nearly linear with the engine speed.

5.3 Fault Diagnosis Results In the fault free case the residuals are almost zero. But, in fact, the reference models for phase of intake pressure and the reference models for amplitude of intake pressure

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have wider stochastic deviations. Residuals of phase of intake pressure in the fault free case are approximately 6° CA. Residuals of phase of amplitude of intake pressure in the fault free case are approximately 0.2 kPa. The residual of volumetric efficiency has wider stochastic deviations in the fault free case of approximately 0.06. The residual of EGR mass and has wider stochastic deviations in the fault free case of approximately 0.2 kg h−1 . In Fig. 13, the first fault example in 20s is intake leakage. The residuals of volumetric efficiency and EGR mass clearly exceed the thresholds. The second fault example is 30% restriction in 30s, the residuals amplitude and phase intake pressure oscillation show a strong deflection, and with the corresponding symptoms this fault is clearly detected

Fig. 13 Fault diagnosis fault of intake leakage and restriction

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The second fault example is an undesired EGR valve fault in Fig. 14. The residual volumetric efficiency responses intensively and the residuals amplitude and phase intake pressure oscillation and residual of EGR mass show a strong deflection in 20s, too. With the symptom this fault is clearly detected as well. Table 2 summarizes the fault–symptom relation of intake system. It is divided into intense positive, positive, negative and no response. Basing on the features of

Fig. 14 Fault diagnosis fault of EGR valve fault

Table 2 Fault-symptom of intake system Fault

D(rηv )

D(r E G R )

D(r A pim )

D(rϕ pim )

F1

−

+

*

*

F2

*

*

−

+

F3

+

+

+

−

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the deviations different symptom pattern result for each fault, so all faults can be diagnosed. Where di+ is upper threshold, di- is lower threshold. “+” represents that symptom responds positive, “−” represents that symptom responds negative, “*” represents that symptom does not respond. D(ri ) is defined as Eq. (17). ⎧ ⎨ + ri > di+ D(ri ) = 0 di− ≤ ri ≤ di+ ⎩ − ri < di−

(17)

6 Conclusions In this paper, a fault detection (FD) and fault isolation (FI) system of automotive engine MAP were constructed, based on physical model and data-driven model. Residual generations were obtained on parity equations. The fault methods were introduced in details. As an example, the structure of fault diagnosis of intake system with EGR was established by simulation. Four residuals were constructed based on physical model data-driven. The intake pressure fluctuation phase and amplitude and volumetric efficiency and EGR mass were extracted as the characteristic parameters in diagnose. LOLIMOT was used to establish the reference model of three parameters. The models were regarded as a function of engine speed and intake density. Amplitude and phase of intake pressure fluctuation signal and volumetric efficiency reference model were constructed by LOLIMOT. EGR mass model was constructed by physical model. The mapping relationship between the residual signal and the fault type was achieved. Experiments show that the models give good predictions of high linear correlation. Faults can be diagnosed when leakage in the intake manifold, EGR valve blocked and restriction in the intake manifold occurs. (1) According to characteristics of diesel engine, a novel fault detection and isolation (FDI) strategy was proposed based on data-driven and model-based. Experiments demonstrate that the proposed fault diagnosis method is suitable to fault diagnosis for diesel engine system of automotive car, combine mathematical model of engine system and working data. (2) By analysing the characteristics of air path of diesel engine, amplitude, phase of intake pressure fluctuation signal, volumetric efficiency and EGR mass were extracted as the characteristic parameters in diagnose. The residual generations were constructed based on physical models and data-driven models. Local linear model tree (LOLIMOT) was used to establish data–driven model. (3) The data-driven models were regarded as a function of engine speed and in-take density. Through eleven iterations, nine iterations and fourteen iterations, the reference models of intake pressure fluctuation amplitude, volumetric efficiency

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and intake pressure fluctuation phase were built. Experimental results demonstrate data-driven models could give good predictions of high linear correlation, and EGR mass model was consist with the measurement. (4) Finally, the mapping relationship between the residual signal and the fault type was achieved. Leakage in the intake manifold, EGR valve blocked and restriction in the intake manifold were considered in this paper. Experiments on the intake system of engine have demonstrated the detection and diagnosis could diagnose different faults.

References 1. California Environmental Protection Agency: Air Resources Board, Section 1971.1, 1971.5 of title13, California code of regulations: HD OBD and OBDII regulations. California EPA, California(1971) 2. United States Environmental Protection Agency. 40 CFR Part 86,89, et al: control of air pollution from new motor vehicles and new motor vehicle engines; final rule. United States EPA (2009) 3. Nyberg, M.: Model-based diagnosis of an automotive engine using several types of fault models. IEEE Trans. Control Syst. Technol. 10(5), 679–689 (2002) 4. Huang, G.L., Qin, S.R., Wang, J.: Vehicle virtual instrument based on OBD-II system. China Meas. Test (2009) 5. Wu, F., Wang, H., Chen, G. Study on misfire calibration technology for gasoline engine OBD(China III and IV Phase). Automobile Technol. (2008) 6. Nyberg, M.: Model based diagnosis of both sensor faults and leakage in the air-intake system of an SI-engine. SAE Int., Warrendale, PA, USA, SAE Tech. Paper 1999-01-0860, Mar (1999) 7. Vasu, J.Z., Deb, A.K., Mukhopadhyay, S.: MVEM-based fault diagnosis of automotive engines using dempster-shafer theory and multiple hypotheses testing. IEEE Trans. Syst. Man and Cybern. Syst. 45(7), 1 (2015) 8. Rizzoni, G., Min, P.: Detection of sensor failures in automotive engines. Veh. Technol. IEEE Trans. 40(2), 487–500 (1991) 9. SUN, Y., LIU, B., CUI, T., Zhang, F.: Model-based fault diagnosis method of diesel engine intake system. Veh. Eng. (3), 84–87 (2013) 10. Nakai, A., Ohashi, T., Hashimoto, H.: 7 DOF arm type haptic interface for teleoperation and virtual reality system. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Victoria, Canada, Oct 1998: 1 266–1 231 (1998) 11. Yan, Hao, Yao, Lei, Qiu, Li-bo, Chen, Bo, Dong, Lijing: Modelling and fault tolerance analysis of triplex redundancy servo valve. Int. J. Model. Ident. Control 31(1), 27–38 (2019) 12. Wang, M., Sun, X., Xing, H., Zheng, H.: Online fault detection for networked control system with unknown network-induced delays. Int. J. Model. Ident. Control 30(4), 293–302 (2018) 13. Shen, Y., Ding, S.X., Haghani, A., et al.: A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process. J. Process. Control 22(9), 1567–1581 (2012) 14. Liu, B., Huang, S., Fan, W., et al.: Data driven uncertainty evaluation for complex engineered system design. Chin. J. Mech. Eng. 5, 1–12 (2015) 15. Ghodous, P., Martinez, M.T.: Collaborative and standard design and manufacturing model. Int. J. Comput. Appl. Technol. 2017(18), 133–145 (2017) 16. Yin, S., Ding, S.X., Xie, X., et al.: A review on basic data-driven approaches for industrial process monitoring. IEEE Trans. Industr. Electron. 61(11), 6418–6428 (2014)

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17. Yin, S., Luo, H., Ding, S.X.: Real-time implementation of fault-tolerant control systems with performance optimization. Ind. Electronics IEEE Trans. 61(5), 2402–2411 (2014) 18. Nentwig, M., Mercorelli, P.: Throttle valve control using an inverse ocal linear model tree based on a fuzzy neural network. In: IEEE International Conference on Cybernetic Intelligent Systems. pp. 1–6 (2008) 19. Colin, G., Chamaillard, Y., Bloch, G., et al.: Neural control of fast nonlinear systems–application to a turbocharged SI engine with VCT. IEEE Trans. Neural Networks 18(4), 1101– 1114(2007) 20. Wang, Y., Zhang, et al.: Fault diagnosis for manifold absolute pressure sensor (MAP) of diesel engine based on Elman neural network observer. Chin. J. Mech. Eng. 29(2), 386–395 (2016) 21. Kolewe, B., Haghani, A., Beckmann, R., et al.: Gaussian mixture regression and local linear network model for data-driven estimation of air mass. IET Control Theory Appl. 9(7), 1083– 1092 (2015) 22. Kimmich, F., Isermann, R.: Model based fault detection for the injection, combustion and engine-transmission. IFAC Proc. Volumes 35(1), 203–208 (2002) 23. Wang, Y., Cui, T., Zhang, F., Tianpu, D.: Fault diagnosis of intake system of diesel engine based on LOLIMOT. ACTA ARMAMENTARII 38(8), 1457–1468 (2017) 24. Nyberg, M.: Model-based diagnosis of an automotive engine using several types of fault models. IEEE Trans. Control Syst. Technol. 10(5) (2002) 25. Wang, D., Lum, K.Y.: Adaptive unknown input observer approach for aircraft actuator fault detection and isolation. Int. J. Adapt. Control Signal Process. 21(1), 31–48(2010) 26. Isermann, Rolf: Model-based fault-detection and diagnosis—status and applications. Annu. Rev. Control 29(1), 71–85 (2005) 27. Zhou, M., Wang, Z., Shen, Y.: Fault detection and isolation method based on H −/H∞ unknown input observer design in finite frequency domain. Asian J. Control 19(5), 1777–1790 (2017) 28. Svärd, C., Nyberg, M., Frisk, E., et al.: Automotive engine FDI by application of an automated model-based and data-driven design methodology. Control Eng. Pract. 21(4), 455–472 (2012) 29. Nyberg, M., Perkovic, A.: Model based diagnosis of leaks in the air intake system of an SIEngine SAE, 980514 30. Nyberg, M., Stutte, T.: Model based diagnosis of the air path of an automotive diesel engine. Control Eng. Pract. 12(5), 513–525 (2001) 31. Xu, W.L., Wu, R.H.: Lyapunov’s indirect method for stability analysis of fuzzy control system. J. Hunan Univ. (Nat. Sci.) 31(3), 86–89 (1998) 32. Nelles, O.: Nonlinear system identification: from classical approaches to neuralnetworks and fuzzy models. Appl. Ther. 6(7), 717–721 (2001)

Decomposition-Based Gradient Iterative Estimation for Input Nonlinear Model by Using the Kalman Filter Qiuling Fei, Junxia Ma, Weili Xiong and Jing Chen

Abstract This paper considers the joint iterative estimation of the parameters and states for Hammerstein nonlinear state space systems. By applying the model decomposition technique, the unknown parameters to be estimated are distributed into two regression identification models. Furthermore, under the framework of the gradient iterative algorithm and the hierarchical identification theory, a decompositionbased gradient iterative algorithm is proposed to estimate the unknown parameters of nonlinear system. Finally, a numerical simulation example is given to validate the effectiveness of the algorithm. Keywords Input nonlinear model · Kalman filter · Model decomposition · Gradient iterative

1 Introduction Nonlinearities are widespread in actual processes [1, 2]. The problem of parameter identification for nonlinear systems earliest appeared in some specific types of nonlinear models, such as the Wiener model, the bilinear system model, the Hammerstein model and so on [3, 4]. The Hammerstein model is a kind of typical nonlinear model with a specific structure, which concludes a static nonlinear module and a dynamic linear module [5, 6]. The series connection of the two modules can describe a wide variety of nonlinear problems and reflect the process characteristics well. In the Q. Fei · J. Ma (B) · W. Xiong · J. Chen Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China e-mail: [email protected] Q. Fei e-mail: [email protected] W. Xiong e-mail: [email protected] J. Chen e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_49

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literature, Mehmood and Chaudhary proposed a novel evolutionary computational heuristics based on global optimization search methods to estimate the parameters of Hammerstein systems [7]. For the input nonlinear Hammerstein system with exception values and random time delay, Ma et al. deduced a robust EM method to estimate system parameters by representing the noise with t-distribution rather than a Gaussian distribution and treating the unknown delays as latent variables [8]. The Hammerstein model often uses the state space model as its linear subsystem to describe the dynamic situation of practical system [9–11]. However, the state space model contains both unknown system parameters and unmeasurable intermediate states, which brings a difficulty to obtain the estimation of the parameters. Some well-known filtering techniques are often used to compute the unavailable system states, such as Kalman filter (KF), particle filter, and their extended filter methods [12, 13]. Kalman filter is the powerful tool for analyzing and solving a class of estimation problems, which can update the mean and covariance of the state with new measurement in real time. Recently, Dong used the extended KF algorithm and SVM to obtain the parameters of the unmanned marine vehicle’s maneuvering model, which helps to predict the maneuverability of the unmanned ship and provides a great reference for the design of its control algorithm [14]. The computational burden will be heavier when the dimensions of the system become larger and the unknown parameters increase [15]. The model decomposition technique can improve the computational efficiency by dividing a large-scale system into serval subsystems with smaller dimensions [16]. Therefore, this paper considers the iterative estimation algorithm based on model decomposition for the input nonlinear Hammerstein model and uses the Kalman filter to calculate the optimal states. The two objectives of the article are as bellow: first, by applying model decomposition, the input nonlinear Hammerstein model is divided into two sub models to reduce computational load; then, by combining the filter technique and the hierarchical identification method, a gradient iterative identification algorithm is developed to estimate unknown parameters and states. The identification model of the nonlinear system is introduced in the section of System Description. The following section develops the decomposition-based gradient iterative estimation algorithm by means of the Kalman filter. The section named Simulation provides a numerical simulation example to verify the D-KF-GI algorithm. The final section gives some conclusions.

2 System Description Here, we focus on a Hammerstein system as shown in Fig. 1, which can be described as a nonlinear input block followed by a linear state space subsystem. The mathematical expression of the system in Fig. 1 can be described as x(k + 1) = Ax(k) + β u(k) ¯ + ω(k),

(1)

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Fig. 1 The Hammerstein state space system

y(k) = cx(k) + υ(k),

(2)

where (1) and (2) are the process and measurement functions of the system. {ω j (k)} ∼ N(0, Q) and υ(k) ∼ N(0, R) are independent Gaussian noises. u(k) ¯ is the output of nonlinear module with input u(k), x(k)∈Rn is the state, y(k) is measurement output corrupted by the noise. A∈Rn×n is the state transition matrix, β∈Rn and c∈R1×n are the input and output vector: ⎡

−α1 −α2 .. .

⎢ ⎢ ⎢ A: = ⎢ ⎢ ⎣ −αn−1 −αn

1 0 ··· 0 1 .. .. . . 0 ··· 0 0 ··· 0

⎤ ⎡ ⎤T ⎡ ⎤T 0 β1 1 0⎥ ⎢ β2 ⎥ ⎢0⎥ ⎥ .. ⎥∈Rn×n , β: = ⎢ ⎥ ∈Rn , c: = ⎢ ⎥ ∈R1×n . ⎢ . ⎥ ⎢.⎥ .⎥ ⎥ ⎣ .. ⎦ ⎣ .. ⎦ ⎦ 1 0 βn 0

Here, we consider the nonlinear block with the following form: u(k) ¯ = λ2 h 1 (u(k)) + λ2 h 2 (u(k)) + · · · + λq h q (u(k)) = λT h(u(k)), where λ: = [λ1, λ2 , · · · , λq ]T ∈Rq are the unknown coefficients to be estimated, and h(u(k)): = [h 1 (u(k)), h 2 (u(k)), · · · , h q (u(k))]∈R1×q are the known base functions. The model (1) can be transformed into the following form: x1 (k + 1) = −α1 x1 (k) − α2 x1 (k − 1) − · · · − αn xn (k − n + 1) + β1 u¯ k + β2 u(k ¯ − 1) + · · · + βn u(k ¯ − n + 1) + ω1 (k) + ω2 (k − 1) + · · · + ωn (k − n + 1) =

n  j=1

−α j x1 (k − j + 1) +

n  j=1

β j u(k ¯ − j + 1) +

n 

ω j (k − j + 1)

j=1

(3) Define the following information matrix and parameter vectors

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⎡

⎡ ⎤ ⎤ α1 −x1 (k − 1) ⎢α ⎥ ⎢ −x (k − 2) ⎥ ⎢ 2⎥ n ⎢ 1 ⎥ n ⎥∈R , ⎥∈R , ϕ α (k): = ⎢ α: = ⎢ .. . ⎢ . ⎥ ⎢ ⎥ ⎣ . ⎦ ⎣ ⎦ . −x1 (k − n) αn

⎡

⎤ h(u(k − 1)) ⎢ h(u(k − 2)) ⎥ ⎢ ⎥ n×q ⎥∈R H(k): = ⎢ . .. ⎢ ⎥ ⎣ ⎦ . h(u(k − n))

Substituting (3) to model (2) gives the following bilinear-parameter model y(k) = x1 (k) + υ(k) = ϕ Ta (k)α + β T H(k)λ +

n 

ωi (k − j) + υ(k).

(4)

j=1

3 The Decomposition-Based Gradient Iterative Algorithm The model (4) contains a product of parameters β and coefficients λ. It is unpractical to acquire the only parameter estimate, because none identification technique can distinguish λ and β from λ/d, dβ for nonzero constant d. Although we can use the key term separation method to simplified the bilinear-parameter identification model into a pseudo linear regressive identification model. However, the dimension of the identified parameters will increase, and so does the amount of calculation. For this reason, we adopt another method called model decomposition to solve bilinearparameter identification problem. Assuming ||λ|| = 1 and λ1 >0, we redefine a fictitious subsystem as y2 (k): = y(k) − ϕ Tα (k)α = β T H(k)λ +

n 

ω j (k − j) + υ(k)

j=1

= ϕ T2 (k)θ 2 +

n 

ω j (k − j) + υ(k),

(5)

j=1

where θ 2 = [β], ϕ 2 (k) = [H(k)λ]∈Rn . Rewrite (4) in the following new form y1 (k) := y(k) = ϕ Tα (k)α + β T H(k)λ +

n 

ω j (k − j) + υ(k)

j=1

=

ϕ T1 (k)θ 1

+

n  j=1

ω j (k − j) + υ(k)

(6)

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α ϕ α (k) ∈Rn+q . where θ 1 = , ϕ 1 (k) = H T (k)β λ  Let ek := nj=1 ω j (k−n)+υ(k), and we can obtain two identification sub-models y1 (k) = ϕ T1 (k)θ 1 + ek ,

(7)

y2 (k) = ϕ T2 (k)θ 2 + ek .

(8)

Let N be the data length. Define the stacked information matrixes Φ 1,N (k) Φ N (k) and stacked output vectors Y 1,N (k), Y 2,N (k) as Φ 1,N (k) := [ϕ 1 (k), ϕ 1 (k − 1), · · · , ϕ 1 (k − N + 1)]T ∈R N ×(n+q) , Y 1,N (k) := [y1 (k), y1 (k − 1), · · · , y1 (k − N + 1)]T ∈R N , Φ 2,N (k) := [ϕ T2 (k), ϕ T2 (k − 1), · · · , ϕ T2 (k − N + 1)]T ∈R N ×n , Y 2,N (k) := [y2 (k), y2 (k − 1), · · · , y2 (k − N + 1)]T ∈R N Refers to two quadratic criterion functions: J1 (θ 1 ) = ||Y 1,N − Φ 1,N (k)θ 1 ||,

(9)

J2 (θ 2 ) = ||Y 2,N − Φ 2,N (k)θ 2 ||.

(10)

s

s

Define s as the iterative variable. Let θˆ 1 (k) and θˆ 2 (k) be the estimate of θ 1 and θ 2 at iteration s, γ max [Z] be the maximal eigenvalue of Z, μs (k) be the convergence factors, satisfying 0 Tz , it has |x1 − yd | ≤ z .

5 Numerical Results To demonstrate the effectiveness of the proposed control scheme, numerical simulations are conducted for the MDF continuous hot pressing EHSS with the physical parameters listed in Table 1. Next, the assumptions in the numerical simulation are given. The initial states are x1 (0) = x2 (0) = x3 (0) = 0; The MDF slab thickness error is −0.1 mm; The external disturbance is d(t) = 54, 780 + 4000 × sin (4π t). Here we compare the proposed controller with the conventional sliding mode controller (SMC) and the back-stepping controller (BSC) to evaluate the superiority of the designed controller. Since e(0) = x1 (0) − yd = −0.1 mm < 0, the parameters for the performance function are set as ρ0 = 0.2 mm, ρ∞ = 1 × 10−5 mm, κ = 50 As mentioned above, to ensure that the overshooting phenomenon does not emerge in the hot pressing process, we set δ = 0.

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Table 1 The nominal value of system parameters System parameter

Nominal value

System parameter

Nominal value

K sv (m A−1 )

0.01

Bc (106 N s m−1 )

2.25

ω (M)

0.025

Vt

(10−3 m3 )

2.356

ps (MPa)

25

K a (A V−1 )

0.0125

ρ (kg m−3 )

850

cd

0.61

βe (MPa)

685

ps (MPa)

16.67

m (kg)

1000

A (m2 )

0.1256

K (GN m−1 )

2.4

F (N)

54,780

Ct (10−16 m5 N−1 s−1 )

5

Time constant of the first-order filter in the second subsystem is chosen as τ = 0.001. According to the calculation of its initial value in (10), we give x3d (0) = x¯3 (0) = 0.59. The parameters of the ROO are k2 = 600 and k3 = 50. The proposed controller parameters are chosen as c1 = 80, c2 = 120, and c3 = 200. The SMC parameters: a1 = 100, a2 = 2100 and α = 100. The BSC parameters: c1 = 50, c2 = 80, c3 = 100. The simulation results are shown in Figs. 2, 3, 4 and 5. The overall control performance of the proposed control scheme is intuitively reflected in Figs. 2 and 3. In Fig. 2, it is shown that the convergence rate of the proposed controller is obviously faster than the other two controllers. The comparison results of the control inputs are plotted in Fig. 3. Although the peak of the proposed controller is much higher than the BSC and SMC, it exhibits a faster falling trend among these three controllers. In practice, such a phenomenon is accepted since high convergence rate needs high control effort. Fig. 2 Time response of position tracking

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Fig. 3 Time response of control input

Fig. 4 Time response of the performance function and the output tracking error

The capability of the proposed controller in terms of prescribed performance guarantees is explicitly shown in Fig. 4. From Fig. 4, it can be seen that the tracking error of the system output is always confined within the performance envelop specified a priori by the designer. As such, the proposed controller plays a significant role in the closed-loop transient performance, especially overshoot. The estimations of x2 and x3 is shown in Fig. 5, from which one can find that the performance of the ROO is satisfactory with appropriate parameters. It is a significant factor that results in the fact that the proposed control scheme achieves expected control performance.

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Fig. 5 The estimations of x 2 and x 3 . (x 2b : the estimation of x 2 ; x 3b : the estimation of x3 )

6 Conclusions In this paper, an observer-based MDF slab thick-ness tracking output feedback control has been presented for a continuous hot pressing EHSS, while unmeasured states, uncertain dynamics, and unknown disturbances were addressed simultaneously. A reduced-order state observer was presented to estimate the unmeasured system states. It was proved that the estimation error can be governed to zero in a short time interval. Exploiting the estimated information, a novel adaptive output feedback controller was then synthesized and the effect of uncertain dynamics. Moreover, the developed control scheme is able to achieve high precision position tracking control with specific convergence rate, while exhibiting no overshoot, thereby ensuring the production of high-quality MDF. Finally, the effectiveness of the proposed control scheme in terms of transient and steady-state tracking performance and robustness against system uncertainties and disturbance was testified via simulation results. Acknowledgements The authors are grateful for the support of the Fundamental Research Funds of Central Universities (2572018BF02), the Project (2014-4-46) and the Postdoctoral Research Fund of Heilongjiang Province (LBH-Q13007).

References 1. Guo, Q., Zhang, Y., Celler, B.G., Su, S.W.: Backstepping control of electro-hydraulic system based on extended-state-observer with plant dynamics largely unknown. IEEE Trans. Industr. Electron. 63, 6909–6920 (2016) 2. Xie, W.-F.: Sliding-mode-observer-based adaptive control for servo actuator with friction. IEEE Trans. Industr. Electron. 54, 1517–1527 (2007)

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3. Sanfelice, R.G., Praly, L.: On the performance of high-gain observers with gain adaptation under measurement noise. Automatica 47, 2165–2176 (2011) 4. Liu, Y.-J., Tong, S.-C., Wang, D., Li, T.-S., Chen, C.P.: Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems. IEEE Trans. Neural Netw. 22, 1328–1334 (2011) 5. Darouach, M., Zasadzinski, M., Hayar, M.: Reduced-order observer design for descriptor systems with unknown inputs. IEEE Trans. Autom. Control 41, 1068–1072 (1996) 6. Krishnamurthy, P., Khorrami, F., Jiang, Z.-P.: Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form. IEEE Trans. Autom. Control 47, 814–819 (2002) 7. Ding, Z.: Global output feedback stabilization of nonlinear systems with nonlinearity of unmeasured states. IEEE Trans. Autom. Control 54, 1117–1122 (2009) 8. Krishnamurthy, P., Khorrami, F., Chandra, R.S.: Global high-gain-based observer and backstepping controller for generalized output-feedback canonical form. IEEE Trans. Autom. Control 48, 2277–2283 (2003) 9. Bechlioulis, C.P., Rovithakis, G.A.: Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances. In: 2008 16th Mediterranean Conference on Control and Automation, pp. 1035–1040. IEEE (2008) 10. Bechlioulis, C.P., Rovithakis, G.A.: Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. Automatica 45, 532–538 (2009) 11. Liu, Y.-H.: Adaptive control for a class of uncertain nonlinear systems with prescribed performance. Control Theory Appl. 31, 1123–1127 (2014) 12. Zhu, L.K., Wang, Z.B., Liu, Y.Q.: Compound control strategy for MDF continuous hot pressing electro-hydraulic servo system with uncertainties and input saturation. Math. Probl. Eng. 2016(2016-12-8), 1–12 (2016)

Optimization Approaches for Parameters of SVM Jinxiang Chen, Yilan Yin, Lu Han and Feng Zhao

Abstract The method of SVM parameter optimization is discussed. The difference of parameter selection has an important influence on the classification accuracy of the sample. In practical systems it is difficult to obtain thousands of samples. In most cases, it can only rely on hundreds of samples to analysis and forecast. And studies have confirmed that because of the unique kernel function and classification of SVM, SVM has a greater advantage in solving small sample, nonlinear and highdimensional pattern. So, this paper uses SVM to solve small sample classification problem. Moreover, when the parameters of SVM are optimized, higher classification accuracy can be obtained. The grid search and GA are applied to two data sets with different feature numbers, and the prediction effect is analyzed. The results show that the fewer the number of features, the better the effect of the grid search method, the more the number of features, the more obvious the advantage of GA. So GA optimizes SVM is better when higher accuracy and shorter time is required. Keywords SVM · Grid search · Genetic algorithm

1 Introduction With the increasing attention of artificial intelligence and machine learning, the research and application in various fields are becoming more and more intelligent. In the face of classification problems, they also begin to solve with machine learning methods. The relatively accurate classification effect allows researchers to analyze and judge problems more intuitively, and obtain effective and accurate conclusions, which have a positive impact on all walks of life. There are many classification methJinxiang Chen and Yilan Yin are equally contributed to this work. J. Chen (B) · Y. Yin · L. Han · F. Zhao State Key Laboratory of Hybrid Process Industry Automation Systems and Equipment Technology, Automation Research and Design Institute of Metallurgical Industry, China Iron & Steel Research Institute Group, Beijing 100081, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_54

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ods in machine learning, which mainly include supervised learning and unsupervised learning. Support vector machine is a supervised learning method based on statistical learning theory in machine learning. It can realize classification and regression, and in solving small samples, nonlinear, high-dimensional pattern recognition has its own unique advantages, but the simple SVM classification accuracy is not high, the convergence effect is not good. Therefore, it is necessary to combine the optimization algorithms such as cross-validation, grid search, genetic algorithm, particle swarm optimization and other optimization algorithms to optimize the parameters of SVM. The cross-validation method is more suitable for the case of only one parameter. The genetic algorithm is more focused on individual optimization. Therefore, to compare and to analyze the effects of optimizing SVM parameters by the grid search and genetic algorithm used into the data sets with different feature numbers. The results show that the fewer the number of features, the better the effect of the grid search method, and the more the number of features, the more obviously the advantages of the genetic algorithm. Literature [1] introduced several algorithms for optimizing SVM parameters, and using grid search algorithm to train 750 data, which shows the advantage of SVM in small sample classification. Literature [2, 3] introduced the influence of parameters on the accuracy of SVM and its application. Literature [4–6] mainly used genetic algorithm to optimize parameters in the application process, and achieved good results.

2 SVM and Optimization Algorithm Theory 2.1 SVM Principle and Parameters SVM is a nonlinear classifier. The basic idea of SVM is to minimize the risk of structure and sum of square of approximation error. The so called support vector is the last result of structure optimization. That is, to classify samples by hyperplane, but there are many superflats can be classified, and which hyperplane is the best classification effect becomes the core starting point of the problem, so we can turn the problem into how to find the maximum value of the minimum distance from the sample to the hyperplane, and convert this process to the minimum value of the objective function, by traversing all the hyperplanes. The process is transformed into a quadratic optimization problem, which overcomes the defect of local minimum. The obtained extreme solution is the global optimal solution [7]. The biggest feature of SVM is the introduction of a kernel function, which is to convert linear indivisible into linear separable. The main idea is to map lowdimensional linear indivisible samples into high-dimensional space, while in highdimensional space, samples are separable. Mapping samples from low-dimensional to high-dimensional is mainly mapped by inner product operations, but as the number of dimensions increases, the amount of operations increases, and the running speed becomes slower and slower. The kernel function solves this problem. The kernel

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function simplifies the operation of the inner product and speeds up the running of the program. There are usually four kinds of kernel functions, namely linear kernel function, polynomial kernel function, Gaussian radial basis kernel function and S-type kernel function. At present, there is no guiding principle for the choice of kernel function. Therefore, according to many experiences and the generality of the problem that needs to be solved now, the Gaussian radial basis kernel function will gave less deviation and smoother classification effect. Therefore, this paper extends the Gaussian radial basis kernel function in the choice of kernel function [2]. The Gaussian radial basis kernel function formula is: K (xi , x j ) = e(−γ xi −x j ) , γ > 0 2

γ in the Gaussian radial basis function is one of the parameters that need to be adjusted. There may be noise in the data, but the fault tolerance of noise is brought by people’s thinking. People can ignore the sample points of noise subjectively, but the machine does not, so in order to meet the requirements of the distance from some sample points to the classification plane, at the mean time, the classification is also well, the slack and penalty factors play a key role [8]. Existing sample Ω = {(xi , yi )|i = 1, 2, 3 . . . N , x ∈ R d , y ∈ {−1, 1}}. y is the category label, y = 1 is a positive sample, and y = −1 is a negative sample. Then,the hyperplane is: w T x + b = 0, x ∈ R d where w is the hyperplane normal vector and b is the hyperplane offset. Two types of data points close to the critical classification surface satisfy: yi (w T xi + b) ≥ 1, i = 1, 2, 3 . . . N That is to say, the nearest sample point function interval of the distance classification surface is also greater than 1, and when the slack variable is added, fault tolerance is introduced: yi (w T xi + b) ≥ 1 − ξi , i = 1, 2, 3 . . . N , ξ ≥ 0 Introducing a slack variable means giving up the exact classification of the sample, although it is a loss to the classifier, a larger classification interval is obtained while giving up these points [7]. Since SVM is actually a quadratic optimization problem, it can be expressed as: min 21  w 2  s.t.yi (w T xi + b) − 1 ≥ 0, i = 1, 2, 3 . . . N

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What we ask is the minimum value of the objective function  w 2 . And the size of the loss requires a penalty factor C to control it. It can be expressed as: N ξi min 21  w 2  +C i=1 T s.t.yi (w xi + b) ≥ 1 − ξi , i = 1, 2, 3 . . . N , ξi ≥ 0 The outlier point has a corresponding slack variable. The slack variable of unoutlier point can be regarded as 0. The larger the slack variable is, the farther the corresponding outlier point is. The larger the penalty factor C is, the more the loss of the objective function is. Large, means less willing to give up these outliers, that is, the larger C is, the easier it is to fit, and the smaller C is, the easier it is to fit.

2.2 Cross-Validation and Grid Search The core idea of cross-validation is to divide the data into three parts: the training set used to train the model, the verification set used for model selection, and the test set for final evaluation of the learning method, and the K-fold cross-validation as the extension of cross-validation, the principle is also to divide the data, divide the data into several parts, take one of them as the test set, and the other parts as the data set for training. One accuracy will be obtained when an operation is performed each time. And the average accuracy obtained is the final accuracy of the verification set. When the number of hyperparameters is greater than 1, it is necessary to use the grid search to make adjustments. The principle of the grid search algorithm is based on the cross-validation method. Since the grid search algorithm is used, the number of hyper-parameters is already greater than 1, and each parameter has many candidate values, each parameter combination is traversed for cross-validation. A grid search is formed.

2.3 Genetic Algorithm Genetic algorithm is a search algorithm based on Darwin’s biological evolution theory and population genetic mechanism in genetics to search for optimal solutions. It is a global optimization algorithm, which overcomes the problem that general iterative algorithms are easy to fall into local minimum. Disadvantages. When a genetic algorithm is used to solve a problem, each possible solution of the problem is encoded into a chromosome, and several chromosomes constitute a group, that is, the group is a collection of all possible solutions [5]. The core idea of genetic algorithm is based on the principle of “survival of the fittest”. At the beginning, some individuals are randomly generated, and each individual is evaluated according to a

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predetermined objective function, and a fitness value is given, based on this fitness value, individuals are selected to cross and mutate to form a new generation, while eliminating bad individuals. A new generation of individuals inherits the superior traits of the previous generation, and its performance is better than that of the previous generation, that is, it is gradually approaching the optimal solution [9]. Genetic coding: When using genetic algorithm to solve, firstly, the objective function and variables should be clarified, and the variables should be binary coded to form the coding space. The coding is the mapping from phenotype to genotype, that is, mapping the original space. To the coding space required by the genetic algorithm, and decoding is the mapping from genotype to phenotype, that is, the coding space is mapped into the original space. There are three basic operators in genetic operation, namely selection, crossover and mutation. The choice is based on the fitness of the fittest, the evaluation and selection of random individuals according to fitness values, and the elimination of unselected individuals. Crossing refers to replacing and reorganizing part of the structure of two parents to generate new individuals. After crossing, new individuals can be generated in the next generation. Crossover is an important means for genetic algorithms to obtain good individuals [6]. Mutation refers to the random change of an individual’s genetic value with a small probability of mutation. When encoded in binary, the gene changes from 0 to 1 or from 1 to 0. The essence of the mutation operation is actually a local random search. Combined with the selection and crossover operators, it can avoid the permanent loss of some information caused by the selection and crossover operators, which ensures the validity of the genetic algorithm. The genetic algorithm has the ability of local random search, and at the same time enables the genetic algorithm to maintain the diversity of the population, in order to prevent immature convergence. Algorithm specific flow chart (Fig. 1): The advantage of genetic algorithm is that it is based on biological evolution. It has good convergence, global optimization, and it is not easy to fall into local optimum. When calculating accuracy, due to its inherent parallelism, distributed computing can be performed to reduce computation time. The robust is high, the search is dependent by the evaluation function, and the process is simple. However, the local search ability of genetic algorithm is poor, and it is easy to produce the problem of premature convergence. How to maintain good individuals and maintain the diversity of the group is not well solved.

3 Comparison and Analysis of Grid Search and Genetic Algorithm The SVM is trained, optimized, and classified through open source code in the Python language. The grid search and genetic algorithm are applied to two small

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Fig. 1 Genetic algorithm flow chart Table 1 Some parameters in genetic algorithm Name of parameters Ranges population_size chromosome_num chromosome_length max_value iter_num pc pm

– – – – – 0.4–0.99 0.0001–0.1

Defaults 200 2 20 10 50 0.6 0.01

samples with different feature numbers, and the optimization time and optimization accuracy are compared and analyzed. But in addition to the parameters that need to be optimized in the program, there are some things to understand (Table 1). The results obtained by the genetic algorithm after adjusting the SVM are shown in Fig. 2.

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Fig. 2 GA optimization SVM Table 2 Comparison of time and accuracy under four characteristic samples System parameters Grid optimization Genetic algorithm C γ Accuracy Time

0.5 5 0.9333 0.0178

0.5 0.5 0.98 0.1893

3.275 0.077 0.9714 1.0312

In the figure, the abscissa is the number of iterations, and the ordinate is the accuracy. It shows that the accuracy is the highest when the number of iterations is 25, the corresponding parameters C = 9.275 and γ = 0.011. The smooth part of the graph indicates that the genetic algorithm has reached the local optimization during the iterative process. When jumping out of local optimum, a higher accuracy is obtained. In order to compare and analyze the differences of the effects of SVM optimized with no parameter optimization, SVM with grid search optimization and SVM optimized by genetic algorithm in small samples with different feature numbers more intuitively, we use graphs to display (Tables 2 and 3). The tabular data shows that when the number of features is small, the accuracy of SVM, grid search optimization SVM, and genetic algorithm optimized SVM are not much different, and the grid search behave better than the genetic algorithm in time and accuracy. However, when the number of features becomes larger, the accuracy of the SVM without optimization is reduced significantly. Due to the global search ability of the genetic algorithm, the accuracy of the genetic algorithm is better than the grid search optimization significantly, and its time consumption is more significantly.

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Table 3 Comparison of time and accuracy under six characteristic samples. System parameters Grid optimization Genetic algorithm C γ Accuracy Time

0.5 5 0.5797 0.0186

1 0.0313 0.6492 0.2572

9.275 0.011 0.8521 1.2424

It can be seen that advantages of genetic algorithm can not be reflected in the small sample data with a small number of features, while the grid search can obtain higher accuracy in a shorter time. However, genetic algorithm behaves better when high accuracy is desired and timeliness is not critical.

4 Conclusion The core idea of SVM is to find the maximum value of the minimum distance from the sample point to the hyperplane, which has its unique advantages in small sample classification. At the same time, the kernel function is introduced to solve the nonlinear classification problem, which makes the application level of SVM more abundant. In the SVM optimization algorithm selection, it can be seen that the factors affecting the accuracy of the optimized SVM are not only the penalty factor and the parameters in the kernel function, the number of features of the sample is also important. In this paper, the grid search and genetic algorithm are applied to two data sets with different feature numbers, and their prediction effects are analyzed. The results show that the fewer the number of features, the better the effect of the grid search method, the more the number of features, the more obvious the advantage of the genetic algorithm, and because of the global search ability of genetic algorithms, its timeliness is poor and it takes long time. Therefore, genetic algorithm optimization SVM is a better choice without requiring timeliness and for hoping a higher accuracy. Acknowledgements The authors wish to thank the anonymous reviewers and the area editor for their constructive comments and helpful suggestions. This research was sponsored by National Key Research and Development Plan (Grant Nos. 2017YFB0304102).

References 1. Zhang, Shuya: Research on the Old People’s Fall Detection System Based on SVM-KNN Optimized by Grid Search Method. Hubei, China (2017) 2. Wang, L., Xu, G., Wang, J., Yang, S., Guo, L., Ya, W.: GA-SVM based feature selection and parameters optimization for BCI research. In: 7th International Conference on Natural Computation, pp. 580–583. Shanghai, China (2007)

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3. Liu, S., Jiang, N.: SVM parameters optimization algorithm and its application. In: IEEE International Conference on Mechatronics and Automation, pp. 509–513 (2008) 4. Chunni, D.: SVM visual classification based on weighted feature of genetic algorithm. In: 6th International Conference on Intelligent Systems Design and Engineering Applications, pp. 786–789. Marrakesh, Morocco (2015) 5. Sachdeva, J., Kumar, V., Gupta, I., Khandelwal, N., Ahuja, C.K.: Multiclass brain tumor classification using GA-SVM. In: Developments in E-systems Engineering, pp. 182–187. Dubai, United Arab Emirates (2011) 6. Wang, L., Xu, G., Wang, J., Yang, S., Guo, L., Yan, W.: GA-SVM based feature selection and parameters optimization for BCI research. In: 7th International Conference on Natural Computation, pp. 580–584. Shanghai, China (2011) 7. Chen, Z., Liu, C., YangYang, He, X. and Dong, C.: A speedy model parameter optimization algorithm of support vector machines. In: 7th World Congress on Intelligent Control and Automation, pp. 7362–7367. Chongqing, China (2008) 8. Jin, Z., Chaorong, W., Chengguang Huang, Feng, W.: Parameter optimization algorithm of SVM for fault classification in traction converter. In: 10th IEEE International Symposium on High Performance Distributed Computing, pp. 181–184 (2001) 9. Sherin, B.M., Supriya M.H.: GA based selection and parameter optimization for an SVM based underwater target classifier. In: 10th IEEE International Symposium on High Performance Distributed Computing, pp. 181–184 (2001)

The Staffing Optimization Problem for the M-Design Multi-Skill Call Center Based on Queuing Model Chunyan Li, Chunxiao Sun and Jianhua Zhang

Abstract This paper studied the staffing problem of the M-design multi-skill call center with impatient customers. It is very necessary to consider the customer’s impatience characteristics in the model. The queuing model method is used to obtain the system performance index and service level calculation formula. We establish the staffing calculation model for optimal number of the agents in each group, and the model is extended to the general situation of multiple phone types and multiple agent groups. A heuristic algorithm is adopted, which is the ant colony algorithm to solve the model, and the algorithm process is given. The numerical examples are used to further analyze the influence of impatience factors on the whole system, and an example analysis is carried out. Keywords Multi-skill call center · Queuing model · Impatient customers · Service level · Optimization

1 Introduction As an important way for communication between enterprises and customers, call centers are widely used in many industries. A call center is defined as a service system in which agents or servers serve callers or customers over the telephone, fax, email, etc. However, the operation cost of the call center system is very high, and the labor cost is the main part. The greater the number of call center agents, the stronger their service capabilities, but their labor costs also increase. Therefore, the main operational goal of many call centers is to minimize the operating cost under the premise of satisfying certain service quality, that is, to satisfy the required service level with the minimum number of seats. The telephone connection probability and C. Li (B) · C. Sun Zhijiang College of Zhejiang University of Technology, Hangzhou 310024, China e-mail: [email protected] J. Zhang Hebei University of Science and Technology, Shijiazhuang 050018, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_55

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the average wait time of the customer are two important indicators for evaluating the quality of the call center. If the customer fails to get the service directly or the waiting time is too long, the customer may leave because of impatience. This causes the telephone connection probability to decrease. Long wait times or low connection rates will reduce customer satisfaction and cause certain impacts on the company, such as reduced business benefits. In the queuing model, customers who have abandonment behavior, that is, customers who have a waiting time limit, are also called impatient customers. Obviously, after considering the customer’s impatience, the model will be closer to reality. So, this paper studied a queuing model of the M-design multi-skill call center with the impatient customers. In the early research on the call center manpower demand calculation, it was generally considered that all the calls were the same, the agents were the same, and each agent could handle all the calls, called the single-skill call center. In recent years, the size of call centers and the variety of contact methods have made the work of agents more and more complicated, and they need to master more and more skills. However, in fact, it is impossible that every agent has all the skills. These changes have transformed many call centers from single to multiple. In a multi-skilled call center, incoming calls can be divided into different types, and the agents are distinguished by the set of call types they can handle. A typical example is Gan et al. [1], That is an international call center with calls in different languages. An introduction about staffing problems can be found in Aksin et al. [2]. Örmeci [3] studied the dynamic admission control problem about a M-design multi-skill call center where there are two classes of calls and three stations. The rest of this article is organized as follows. In Sect. 2, we describe the Mdesign model for a multi-skill call center with impatient customers. In Sect. 3, by using results of an M/M/c + M queuing system, we obtain the state-transition rates. In Sect. 4, we obtain the staffing calculation model for optimal number of the agents in each group, and the numerical examples are given. Section 5 concludes the paper.

2 System Model In this paper, we study an M-design multi-skill call center model with impatient customers, where there are two types of calls and three groups of servers. A diagram of the model is shown in Fig. 1. Arrival process: There are two types of calls (or customers). which are independent of each other and subject to the Poisson process of arrival rate λ1 and λ2 . The arriving calls are arranged in two queues. Calls of type 1 consist of Queue 1 and calls of type 2 consist of Queue 2. During the queuing process, the customer may leave the queue because of impatience. For the sake of calculation, it is assumed that the impatient time of both types of customers is a negative exponential distribution obeying the parameter θ. Service process: There are three types of agents, each with different skills. Among them, seat group 1 is single-skilled with skill 1, they can only serve call 1, service

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Fig. 1 The queuing model of the M-design multi-skill call center with impatient customers

time is subject to exponential distribution service rate μ1 , and there are N 1 servers. Agent group 2 is also a single-skilled possession skill 2, they can only serve the call 2, the service time is subject to the exponential distribution, the service rate is μ2 , and there are N 2 servers. The agent group 3 has skill 1 and skill 2, and can provide services for the call 1 and the call 2, and the service time is also subject to the exponential distribution, the service rate is μ3 , and the number of servers is N 3 . Routing policy: The routing policy for this model is skill-based routing. When the call arrives, the Type 1 is undoubtedly first assigned to the agent group 1 service, and when the agent group 1 is busy, the agent group 3 service is selected. If the agent group 3 is also busy, the Type 1 is queued for service. The Type 2 is first assigned to the agent group 2 service, and when the agent group 2 is busy, the agent group 3 service is selected. If the agent group 3 is also busy, the queue 2 is queued for waiting. Queuing discipline: The queues for the two types of calls are independent of each other. Assume that the queuing space is infinite, that is, the call will not be abandoned by the system because there is not enough queue space. The agent group 1 and the agent group 2 are first-come-first service for the telephone Type 1 and Type 2, respectively. When the agent ends the service, the agent group 1 selects the Type 1 for service, and the agent group 2 selects the Type 2 for service. For the agent group 3, it can serve both the Type 1 and Type 2. When the agent group 1 and the agent group 2 are all busy, and both Type 1 and Type 2 are queued, the Type 1 and Type 2 are randomly selected (with the same probability).

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3 The Steady-State Probability 3.1 The State Space The queuing model of the M-design multi-skill call center with impatient customers is similar to the model of M-design multi-skill call center, which is studied in paper Yue et al. [4]. The M-design model has three skill groups. Each group has three states: an idle state (denoted by 1), a busy state (denoted by 2), and an overload state (denoted by 3). Similar to the solution method in that paper, the state transition diagram is shown in Fig. 2.

3.2 The State-Transition Rates By analyzing the state transition diagram, it can be seen that the transition between state sets only occurs on the boundary state of the state set. The agent groups in the state set are independent of each other, and the transition between state sets is actually only the state of a certain seat group. Change. For the call center queuing model of this paper, there are only two situations that cause state changes: the phone arrives and the agent group completes the service. The call arrival process is the same as paper [4], but the customer’s departure causes the agent to change not only the agent group to complete the service, but also the customer leaving because of impatience during the queuing process. This situation only occurs when there is a queue in the system. Therefore, the transfer rate caused by the arrival of the phone can be obtained as follows: q1−2 = q3−5 = q6−8 = q9−11 = λ2 P(n 2 = N2 − 1), q1−3 = q2−5 = q4−8 = q7−10 = λ1 P(n 1 = N1 − 1), q2−4 = λ2 P 1 (n 3 = N3 − 1), q3−6 = λ1 P 2 (n 3 = N3 − 1), q5−8 = (λ1 + λ2 )P 3 (n 3 = N3 − 1), q4−7 = q8−10 = q11−12 = λ2 , q6−9 = q8−11 = q10−12 = λ1 , The transfer rate caused by the agent completing the service is as follows: q2−1 = q5−3 = q8−6 = q11−9 = N2 μ2 , q3−1 = q5−2 = q8−4 = q10−7 = N1 μ1 q4−2 = q6−3 = q8−5 = N3 μ3

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Fig. 2 Diagram of the state-transition

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where 

P(n 1 = N1 − 1) =

λ1 1 (N1 − 1)! μ1 

P(n 2 = N2 − 1) =

λ2 1 (N2 − 1)! μ2 

P 1 (n 3 = N3 − 1) =

λ2 1 (N3 − 1)! μ3

 N1 −1   N1





λ2 μ2



λ2 μ3

j (2)

j

j!

j=0

  N3 −1   N3 λ1 1 2 P (n 3 = N3 − 1) = (N3 − 1)! μ3 j=0

(1)

j!

j=0

 N3 −1   N3

j

j!

j=0

 N2 −1   N2

λ1 μ1



 N   3  λ1 + λ2 N3 −1 1 3 P (n 3 = N3 − 1) = μ3 (N3 − 1)! j=0

λ1 μ3

(3)

.

(4)

j

j! 

.

λ1 +λ2 μ3

j!

j .

(5)

The difference is that there is also a state in which the agent completes the service and the state change is from the overload state to the busy state. For example, the agent group 2 in the state set S7 , as the agent group 2 completes the service or the customer leaves because of impatience, the transition from the state set S7 to the state set S4 may occur. The transfer rate can be obtained: q7−4 = q10−8 = (N2 μ2 + N3 μ3 + θ )P(n 2 = N2 + 1), q9−6 = q11−8 = (N1 μ1 + N3 μ3 + θ )P(n 1 = N1 + 1), q12−11 = (N2 μ2 + 1/2N3 μ3 + θ )P(n 2 = N2 + 1), q12−10 = (N1 μ1 + 1/2N3 μ3 + θ )P(n 1 = N1 + 1). where the probabilities of P(n 1 = N1 + 1) and P(n 2 = N2 + 1) can be obtained by using the results of the M/M/c + M queuing system which are given as follows:   N2 λ2 λ P(n 2 = N2 + 1) = P0 (N2 μ2 + θ )N2 ! μ2 ⎡  j   N ⎤−1 λ2   λ2 2 N2 ∞ k    μ2 μ2 λ2 ⎥ ⎢ + P0 = ⎣ ⎦ j! N μ + j − N N ! ( )θ 2 2 2 2 j=0 k=N +1 j=N +1 2

2

(6)

(7)

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Then, we can obtain the equations for the steady-state probabilities of the system like in paper [4]. All of the steady-state probabilities can be calculated numerically by using Matlab software.

4 The Optimization Problem 4.1 The Calculation of the State-Transition Rates The service level of a general call center is defined as: the percentage of calls that are serviced within a certain waiting time, recorded as P/T, generally 80/20 principle, that is, within 20 s of waiting time, 80% of the calls are served. We can derive the service level using the steady-state probabilities. Let Psl1 and Psl2 be the probabilities that the call 1 and call 2 is serviced in a fixed time T 1 and T 2 , respectively. Consider a call 1. Calls 1 form a queue when the process is in states S 9 , S 11 , S 12 . It can be seen that the service rate for call 1 in each state of S 9 and S 11 is N1 μ1 + N3 μ3 , and the service rate in state S 12 is N1 μ1 + N3 μ3 /2, Thus, we get the probability Psl1 that a call 1 can be serviced in time T 1 , as follows:   ∞ ∞ ∞    1 P(n 1 = i) + P11 P(n 1 = i) + P12 P(n 1 = i) (8) Psl = 1 − P9 i=k1

i=k1

i=k2

where k1 = N1 + N3 + [T1 (N1 μ1 + N3 μ3 )]    1 1 k2 = N1 + N3 + T1 N1 μ1 + N3 μ3 2 2   N1 +1 i  1 λ1 P(n 1 = i) = P0 N μ + j − N ( )θ μ1N1 N1 ! 1 1 1 j=N +1

(9) (10)

(11)

1

⎤−1 ⎡  j   N1 λ1 λ1 N1 ∞ k λ    1 μ μ 1 1 ⎥ ⎢ + P0 = ⎣ ⎦ j! μ + j − N ! ( (N )θ)N 1 1 1 1 j=0 k=N +1 j=N +1 1

(12)

1

Similarly, we get the probability Psl2 that a call 2 can be served in time T 2 as follows:

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 Psl2

= 1 − P7

∞ 

P(n 2 = i) + P10

i=k3

∞ 

P(n 2 = i) + P12

i=k3

∞ 

 P(n 2 = i)

(13)

i=k4

where k3 = N2 + N3 + [T2 (N2 μ2 + N3 μ3 )] k4 = N2 +

(14)

   1 1 N3 + T2 N2 μ2 + N3 μ3 2 2

(15)

In actual call centers, they are generally classified according to the number of agents, and different countries have different standards. In China, the size of the call center can be divided into small (50 or less agents), medium (51–200 agents), and large (more than 201 agents). Our service level calculation formula is applicable to call centers of all sizes. Since the state set method is used in this paper, there are 12 state sets and 12 steady state probabilities. The solution of the steady state probability is independent of the agent number N, so in theory, we can solve the call center of any size. Table 1 shows some numerical results for the service levels Psl1 and Psl2 of call Since the model is a multi-skilled call center, the size of the call center is the sum of the total number of three agent groups. Let N be the total number of agents. As can be seen from the table, the service level calculation formula can calculate the call center of any size. At the same time, for the multi-skill call center, the total number of seats is the same, but when the number of seats is different, the service level of the call center is also greatly impact. Therefore, it is necessary to find the optimal number of individual groups so that the service level can be achieved and the total cost of the system can be minimized. Table 1 The numerical results of the service levels Psl1 and Psl2 N

N1

N2

N3

Psl1

Psl2

45

15

18

12

0.8373

0.8607

45

15

15

15

0.9503

0.9457

45

13

17

15

0.9221

0.9627

170

60

60

50

0.9961

1.0000

170

60

50

60

0.8050

0.8163

170

50

50

70

0.8853

0.8611

260

90

90

80

0.9607

0.9765

260

90

100

70

0.9217

0.9380

260

100

100

60

0.8504

0.8835

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4.2 Optimization of a Staffing Problem In this section, the staffing model is promoted. It is assumed that in the system the agent group number is n. The labor cost per person in each agent group is C i , the number of agent in each group is N i , and it is assumed that the system has k types of incoming call. The optimization of a staffing problem can be expressed as follows: min Z =

n 

C i Ni

i=1 j

s.t. Psl ≥ α j , j = 1, 2, . . . , k. ai ≤ Ni ≤ bi , ai , bi , Ni ∈ Z + , i = 1, 2, . . . , n.

(15)

The purpose of this paper is to find the optimal number of agents to minimize labor costs, where the constraints indicate that the service level of each type of telephone j Psl is greater than or equal to α j . The number of people in each group can be selected from the range of (ai , bi ), N i is the unknown positive integers for the solution, finding the optimal N i minimizes labor costs. This is a nonlinear integer programming problem. The objective function in this model is a linear function. There are n variables N i that needs to be determined. The constraint is that the incoming call must meet a certain service level, and the constraint is highly nonlinear. Since there are n variables in this model, traditional methods such as search algorithms are time consuming, which are not applicable here. Since there are many combinations of feasible solutions, searching is very time consuming and it is difficult to get an optimal solution. In recent years, with the development of intelligent evolutionary algorithms, many scholars use heuristic algorithms such as genetic algorithm, particle swarm optimization algorithm, ant colony algorithm and other methods to solve integer programming problems, and the effect is better. Because the ant colony algorithm is mature, programming is easy to implement, and the results are good, here we propose a new improved ant colony algorithm to further solve the staffing calculation model. The ant colony algorithm for solving the staffing problem is as follows: (1) Initializing parameters, initializing the set of the groups to be determined and the pheromone corresponding to each seat group node, the initial pheromone takes the reciprocal of the node value, and sets each parameter at the same time. (2) Initialize the ant colony, place m ants on the nodes of the first agent group, and initialize the node set. (3) Calculate the ant transfer probability, select the node of the next agent group, and each ant travels through n groups. (4) After determining that the ant colony traverses all the nodes, it is judged whether the selected path satisfies the service level, and the pheromone is updated according to different situations.

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Table 2 The numerical results of the optimal N 1 , N 2 and N 3 C1

C2

C3

N1

N2

N3

Cost

2

3

4

20

20

1

104

4

3

2

20

19

2

141

6

3

2

12

21

14

163

8

3

2

1

20

31

130

3

6

2

12

21

14

190

3

8

2

12

21

14

232

2

2

2

20

19

2

82

3

2

4

20

20

1

104

(5) If the maximum number of searches is reached, the current optimal solution is output, otherwise step (2) is turned. In order to verify the effectiveness of the above algorithm to solve the staff problem, there are some numerical results in Table 2. The following table shows the optimal number of agents in different cases. The parameter settings are as follows: λ1 = 80, μ1 = 1.2, λ2 = 60, μ2 = 1, μ3 = 0.8, θ = 2, T 1 = 20, T 2 = 30, α1 = α2 = 0.8. We can see from the Table 2, the number of each group required to reach the required service level of the system is different for the cost of the agent group. When the cost of the three agent groups is similar, the system is more inclined to equip the group 1 and the group 2 with more agents, and the cost of the first group is significantly higher than the cost of the second and third groups. In the high time, more personnel are deployed for the third agent group to achieve the service level. However, if the cost of the third agent group is higher than the cost of the other two agent groups, the system hardly needs to set a third agent group, and the third agent group has few agents. The change in the cost of the second agent group has the least impact on the number of agents, but it also decreases as the cost increases.

5 Conclusions This paper studies the M-design multi-skill call center system with impatient customers, obtains the calculation formula of service level, and gives numerical examples. Established a human demand calculation model with impatient customers. The ant colony algorithm is used to solve the model, and the ant colony algorithm process is given and numerical analysis is carried out. In this work, we studied the exponential model of a multi-skill call center. A further extension of future research will be to study non-index models.

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Acknowledgements This study was financially supported by National Social Science Fund Project(Evolution Mechanism and Symbiotic Performance of Entrepreneurial Ecosystem from the Perspective of Regional Characteristic Towns, Project No.17YBJ036).

References 1. Gans, N., Koole, G., Mandelbaum, A.: Telephone call centers: tutorial, review, and research prospects. Manuf. Serv. Oper. Manage. 5(2), 79–141 (2003) 2. Aksin, Z., Armony, M., Mehrotra, V.: The modern call-center: a multi-disciplinary perspective on operations management research. Prod. Oper. Manage. 16, 655–688 (2007) 3. Örmeci, L.E.: Dynamic admission control in a call center with one shared and two dedicated service facilities. IEEE Trans. Autom. Control 49(7), 1157–1161 (2004) 4. Yue, D., Li, C., Yue, W.: Chapter 14 Performance analysis and optimization of a queueing model for a multi-skill call center in m-design, Springer Nature (2016)

Adaptive Sliding Mode Trajectory Tracking Control of Quadrotor UAV with Unknown Control Direction Lijun Wang, Wencong Deng, Jinkun Liu and Rong Mei

Abstract For quadrotor unmanned aerial vehicle(UAV) with unknown control direction, the Nussbaum gain method is introduced into adaptive sliding mode method to control the position and attitude of the quadrotor UAV. By decomposing the quadrotor UAV system into position subsystem and attitude subsystem, the intermediate control input is introduced to track the 3-DOF position information. The Nussbaum gain function is used to solve the problem of unknown control direction, and an adaptive law is designed to ensure the boundedness of all signals. Based on the Lyapunov theory, the stability of the closed-loop system is guaranteed. Finally the effectiveness of the proposed control method is verified by the simulation results. Keywords Quadrotor UAV · Unknown control direction · Trajectory tracking control · Adaptive sliding mode control · Nussbaum gain function

1 Introduction In recent years, due to the advantages of simple structure, low price, flexible control and easy maintenance, the quadrotor UAV has been widely used in aviation detection, fire monitoring, reconnaissance and patrol, cargo transportation and other aspects [1]. At the same time, because the quadrotor UAV is a nonlinear, multivariable, strongly coupled and under-actuated system, it is challenging to achieve the accurate trajectory tracking control of the quadrotor UAV. Moreover, the four motors of the L. Wang (B) · W. Deng · R. Mei School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China e-mail: [email protected] Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China J. Liu School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_56

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quadrotor UAV cannot be completely symmetrical when they are installed. In the process of flight, due to the uncertainty of the working environment, it is difficult to accurately establish the model, which further increases the design difficulty of the controller [2]. Nowadays, many researches have been done on the trajectory tracking problem of quadrotor UAVs, and many effective control methods have been put forward. The existing control methods for trajectory tracking of quadrotor UAVs include PID control [3, 4], backstepping and dynamic surface control [5–7], sliding mode control [8–10], adaptive control [11, 12] and H∞ control [13]. However, the above studies are all conducted on the assumption that the control direction is known. In some cases, the control direction is difficult to detect, which makes the controller design more difficult [14]. The control direction, the control gain symbol in front of the control variable, determines the motion direction of the system and plays an important role in the design of the controller. If the control direction is different, even the same control input will bring about a huge difference in the control results. In the literature [15], the author first proposed Nussbaum gain method to solve the problem of unknown control direction in a kind of simple first-order system, and named the function Nussbaum gain function. Subsequently, the method was developed and became a common method to solve the problem of control direction. In [16], the authors proposed a sliding mode tracking controller for single-input-single-output uncertain plants with unknown control direction based on output-feedback. In [17], a dynamic surface control method based on adaptive neural network is proposed for a class of nonlinear strict-feedback systems with unknown direction control gains and input saturation. In [18], aiming to a class of single-input and single-output strictfeedback nonlinear systems with unknown control direction and disturbances, the author proposed an adaptive tracking control method. In this paper, Nussbaum gain method is introduced into adaptive sliding mode control for the unknown control direction of quadrotor UAV. First, by decomposing the model of quadrotor UAV with unknown control direction into position subsystem and attitude subsystem, and introducing virtual control input in the middle, the influence caused by under-actuation of the position subsystem is solved. Then, by incorporate the Nussbaum function method into the sliding mode control to realize the trajectory tracking of the quadrotor UAV. Finally, the simulation results show the effectiveness of the proposed control scheme.

2 System Model The following assumptions need to be considered before modeling a quadrotor UAV. Assumption 1 The quadrotor UAV is regarded as a rigid body with uniform mass distribution and structural symmetry. Regardless of the deformation in the process of motion, the geometric center and the center of mass are regarded as coincident.

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Assumption 2 The effects of the gyroscopic effect, the ground effect, the air resistance and the revolution of the earth on the quadrotor UAV are ignored. Assumption 3 Ignore the time when the motor reaches the given speed. Based on the above assumptions, the final nonlinear mathematical model of the quadrotor UAV with the unknown control direction is expressed as: ⎧ ⎪ ˙ ⎨x¨ = α1 u 1 (cosφsinθ cosψ + sinφsinψ) − K 1 x/m y¨ = α1 u 1 (sinφsinθ cosψ − cosφsinψ) − K 2 y˙ /m ⎪ ⎩ z¨ = α1 u 1 cosφcosψ − g − K 3 z˙ /m

(1)

⎧ l K4 ⎪ ⎨θ¨ = α2 u 2 − I1 θ˙ ψ¨ = α3 u 3 − l KI25 ψ˙ ⎪ ⎩¨ φ = α4 u 4 − l KI36 φ˙

(2)

Equation (1) is the position subsystem and Eq. (2) is the attitude subsystem. m represents the mass of the quadrotor UAV and g is the gravitational acceleration. [φ, θ, ψ] represent the roll angle, pitch angle and yaw angle respectively. [x, y, z] represent the position coordinates of the center of mass of the quadrotor UAV in the inertial coordinate system. l represents the length of the quadrotor UAV from the end of each rotor to the center of gravity. Ii represent the moment of inertia around each axis. K i represent the drag coefficients. αi are the control gain coefficients, which are unknown but bounded. Definition 1 ([15]): If a function N (χ ) satisfies the following properties: lim sup

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lim in f

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1 k 



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(3)

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(4)

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Then N (χ ) is a Nussbaum function. Then N (χ ) is a Nussbaum function. According to the Nussbaum function definition, define the Nussbaum function as N (s) = k 2 cos(k)

(5)

The k is real number. Lemmas 1 ([19]): Define V (t) and k(·) as smooth functions on [0, t f ). V (t) ≥ 0, ∀t ∈ [0, t f ). N (·) is a smooth Nussbaum function, and θ0 is a non-zero constant. If the following inequality holds:

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˙ ) dτ + const, ∀t ∈ [0, t f ) (θ0 N (k(τ )) + 1)k(τ

(6)

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˙ ) dτ must be bounded on [0, t f ). + 1)k(τ

3 Control Design Process 3.1 The Design of the Position Controller From the Eq. (1), the position subsystem is an under-actuated system. So three virtual control inputs are composited, and they are given by ⎧ ⎪ ⎨u 1x = u 1 (cosφsinθ cosψ + sinφsinψ) u 1y = u 1 (sinφsinθ cosψ − cosφsinψ) ⎪ ⎩ u 1z = u 1 cosφcosψ

(7)

So the model of the position subsystem is ⎧ ⎪ ˙ ⎨x¨ = α1 u 1x − K 1 x/m y¨ = α1 u 1y − K 2 y˙ /m ⎪ ⎩ z¨ = α1 u 1z − g − K 3 z˙ /m

(8)

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(9)

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(10)

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(11)

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(12)

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V˙x = sx s˙x = sx (cx e˙x + α1 u 1x − K 1 x2 /m − x¨d )

(13)

The virtual control input u 1x is designed as u¯ x = ηx sx + cx e˙x − K 1 x2 /m − x¨d , ηx > 0 u 1x = N (k)u¯ x ˙ k x = γx sx u¯ x , γx > 0

(14) (15) (16)

Then the Eq. (13) is modified as k˙x k˙x − V˙x = sx (cx e˙x + α1 N (k)u¯ x − K 1 x2 /m − x¨d ) + γx γx k˙x = sx (cx e˙x − K 1 x2 /m − x¨d ) + sx α1 N (k)u¯ x + − sx u¯ x γx k˙x = sx α1 N (k)u¯ x + − ηx sx 2 γx

(17)

Substituting Eq. (16) into Eq. (17), we have 1 V˙x = (α1 N (k) + 1)k˙x − ηx sx 2 γx

(18)

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(20) (21) (22) (23) (24) (25)

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3.2 The Attitude Subsystem Intermediate Command Solution In order to obtain the ideal attitude θd and ψd , from the Eq. (7) we can obtain

Since

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(30)

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(31)

It should be noted that if the left value of the Eq. (31) exceeds [−1 + 1], it will result in θd cannot be solved, which is the shortcoming of this method. So this solution is proposed. cosφ(cosφ·u 1x +sinφ·u 1y ) Let X = .When X > 1, we let sinθd = 1. When X < −1, u 1z we let sinθd = −1. So we have θd = ar csin(

cosφ(cosφ · u 1x + sinφ · u 1y ) ) u 1z

(32)

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u 1z cosφcosψd

(33)

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3.3 The Design of the Attitude Controller ˙ For the first attitude subsystem, we have Let θ1 = θ , θ2 = θ. 

θ˙1 = θ2 θ˙2 = α2 u 2 − l K 4 θ2 /I1

(34)

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(35)

˙ 1 − θ¨d s˙θ = cθ e˙θ + e¨θ = cθ e˙θ + θ˙2 − θ¨d = cθ e˙θ + α2 u 2 − l K 4 θ/I

(36)

The time derivative of sθ is

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1 2 sθ 2

(37)

The time derivative of Vθ is V˙θ = sθ s˙θ = sθ (cθ e˙θ + α2 u 2 − l K 4 θ2 /I1 − θ¨d )

(38)

The control input u 2 is designed as u¯ 2 = ηθ sθ + cθ e˙θ − l K 4 θ2 /I1 − θ¨d + sign(sθ ), ηθ > 0

(39)

u 2 = N (k)u¯ 2

(40)

k˙θ = γθ sθ u¯ 2 , γθ > 0

(41)

Then the Eq. (38) is modified as k˙θ k˙θ − V˙θ = sθ (cθ e˙θ + α2 N (k)u¯ 2 − l K 4 θ2 /I1 − θ¨d ) + γθ γθ k˙θ = sθ (cθ e˙θ − l K 4 θ2 /I1 − θ¨d ) + sθ α2 N (k)u¯ 2 + − sθ u¯ 2 γθ 1 = (α2 N (k) + 1)k˙θ − ηθ sθ 2 − sθ sign(sθ ) γθ Integrating both sides, we can get

(42)

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 t  t 1 | sθ (τ )| dτ (α2 N (kθ (τ )) + 1)k˙θ (τ )dτ − ηθ sθ 2 (τ )dτ − 0 γθ 0 0 (43) t According to Lemma 1, Vθ (t) − Vθ (0) + 0 ηθ sθ 2 (τ )dτ is bounded, so sθ 2 and t 2 0 sθ dt are bounded. It is lemma by Barbalat, when t → ∞, sθ → 0, thus eθ → 0 and e˙θ → 0. Similarly, for the second and third position subsystem, the virtual control inputs u 3 are designed as Vθ (t)−Vθ (0) =

t

u¯ ψ = ηψ sψ + cψ e˙ψ − l K 5 ψ2 /I2 − ψ¨d + sign(sψ ), ηψ > 0 u 3 = N (k)u¯ 3 ˙ kψ = γψ sψ u¯ 3 , γψ > 0

(44) (45) (46)

For the third attitude subsystem, the control input u 4 is designed as u¯ φ = ηφ sφ + cφ e˙φ − l K 6 φ2 /I3 − φ¨d + sign(sφ ), ηφ > 0 u 4 = N (k)u¯ 4 k˙φ = γφ sφ u¯ 4 , γφ > 0

(47) (48) (49)

4 Simulations By using simulink, the effectiveness of this method is verified when the control direction is unknown. By establishing the dynamics model of the quadrotor UAV, the control directions of the quadrotor UAV are set to any non-zero constant, and the trajectory tracking control simulation is conducted to observe the position informations and attitude informations of the quadrotor UAV.The parameters of simulation are as follows: the mass of the quadrotor UAV m = 2 kg, gravity acceleration g = 9.8 N/kg, and the length of the quadrotor UAV from the end of each rotor to the center of gravity l = 0.2 m. The moment of inertias around each axis I1 = 1.25 kg m2 , I2 = 1.25 kg m2 , I3 = 2.5 kg m2 . The drag co-efficients K 1 = K 2 = K 3 = 0.01, K 4 = K 5 = K 6 = 0.012. The initial state of the system is given as follows: initial positions [x, y, z] = [2, 2, 0] m, initial speeds v = [0, 0, 0] m/s, initial angles [φ, θ, ψ] = [0, 0, 0], initial angular velocities ω = [0, 0, 0] rad/s. Let the target of the quadrotor UAV [xd , yd , z d , φd ] as [xd , yd , z d , φd ] = [0, 0, 10, π/3]. The performance of the method is illustracted by the simulation as shown in Figs. 1 and 2. Figure 3 illustrates the time history of control inputs. As shown in Figs. 1 and 2, although the six degrees of freedom of the quadrotor UAV eventually converge, the inner loop attitude subsystem has tracked the target value at 2s, and the outer loop position subsystem tracks the desired position at approximately 8.5s. Because in the double-loop control, in order to ensure the stability of the closed-loop system, the method that the convergence speed of the inner loop is greater than the convergence speed of the outer loop is adopted.

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5 Conclusions Aiming at the trajectory tracking problem of quadrotor UAV, this paper proposes an adaptive sliding mode control method. By dividing the system into position subsystem and attitude subsystem, the four controller inputs can control the six degrees of freedom of the quadrotor UAV. For the problem of unknown control direction, an adaptive law is designed to guarantee the boundedness of all signals by introducing Nussbaum gain function. Finally, the feasibility of the method is verified by Lyapunov function and simulation. Acknowledgements This work was supported by the National Natural Science Foundation of China [grant number 61873296] and Beijing Key Disciplines to Build Projects [grant number XK100080537].

References 1. Cole, D.T., Sukkarieh, S., Gökto˘gan, A.H.: System development and demonstration of a uav control architecture for information gathering missions. J. Field Robot. 23(6–7), 417–440 (2006) 2. Zuo, Z.: Trajectory tracking control design with command-filtered compensation for a quadrotor. IET Control. Theory Appl. 4(11), 2343–2355 (2010)

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3. Gautam, D., Ha, C.: Control of a quadrotor using a smart self-tuning fuzzy pid controller. Int. J. Adv. Robot. Syst. 10(11), 380 (2013) 4. Erginer, B., Altug, E.: Modeling and pd control of a quadrotor vtol vehicle. In: 2007 IEEE Intelligent Vehicles Symposium. pp. 894–899. IEEE (2007) 5. Huang, M., Xian, B., Diao, C., Yang, K., Feng, Y.: Adaptive tracking control of underactuated quadrotor unmanned aerial vehicles via backstepping. In: Proceedings of the 2010 American Control Conference. pp. 2076–2081. IEEE (2010) 6. Wang, R., Liu, J.: Trajectory tracking control of a 6-dof quadrotor uav with input saturation via backstepping. J. Frankl. Inst. 355(7), 3288–3309 (2018) 7. Johnson, Y., Ahamed, T.I.: Nonlinear modelling of leader-follower uav close formation flight with dynamic inversion-based control. Int. J. Model. Identif. Control. 30(2), 83–92 (2018) 8. Aguiar, A.P., Hespanha, J.P.: Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Trans. Autom. Control. 52(8), 1362–1379 (2007) 9. Abdessameud, A., Tayebi, A.: Global trajectory tracking control of vtol-uavs without linear velocity measurements. Automatica 46(6), 1053–1059 (2010) 10. Wang, X., Liu, J., Cai, K.Y.: Tracking control for a velocity-sensorless vtol aircraft with delayed outputs. Automatica 45(12), 2876–2882 (2009) 11. Wang, R., Liu, J.: Adaptive formation control of quadrotor unmanned aerial vehicles with bounded control thrust. Chin. J. Aeronaut. 30(2), 807–817 (2017) 12. Dinh, T.X., Ahn, K.K.: Int. J. Precis. Eng. Manuf. International Journal of Precision Engineering and Manufacturing 18(2), 163–173 (2017) 13. Jasim, W., Gu, D.: Robust path tracking control for quadrotors with experimental validation. Int. J. Model. Identif. Control. 29(1), 1–13 (2018) 14. Boskovic, J.D., Bergstrom, S., Mehra, R.K.: Robust integrated flight control design under failures, damage, and state-dependent disturbances. J. Guid. Control. Dyn. 28(5), 902–917 (2005) 15. Nussbaum, R.D.: Some remarks on a conjecture in parameter adaptive control. Syst. Control. Lett. 3(5), 243–246 (1983) 16. Oliveira, T.R., Hsu, L., Peixoto, A.J.: Output-feedback global tracking for unknown control direction plants with application to extremum-seeking control. Automatica 47(9), 2029–2038 (2011) 17. Ma, J., Zheng, Z., Li, P.: Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation. IEEE Trans. Cybern. 45(4), 728–741 (2014) 18. Ma, H., Liang, H., Zhou, Q., Ahn, C.K.: Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans. Syst. Man Cybern. Syst. 99, 1–10 (2018) 19. Ge, S.S., Hong, F., Lee, T.H.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 34(1), 499–516 (2004)

An Aeroengine Adaptive Inverse Control Method Based on U-Model Jiajie Chen, Zhongzhi Hu, Jiqiang Wang and Weicun Zhang

Abstract This paper applies the U-model control method, combined with the traditional adaptive inverse control method, to the aeroengine speed control design, directly obtaining the engine fuel flow through the inverse controller. The proposed method does not need the complex engine model, and greatly simplifies the complex conventional controller design process. The simulation results show that the U-model-based adaptive inverse controller has an acceptable engine speed control performance in small and large transient responses. Keywords Aeroengine · U-model · Self-adaption · Inverse control

1 Introduction Aeroengine is a complex time-varying nonlinear thermodynamic system. It is very difficult to develop suitable nonlinear control laws for such nonlinear systems directly. With the increasing requirements of aero-engine performance, coupled with the harsh working environment of aero-engine control systems and limited hardware computing capabilities, this poses a huge challenge to the design of aero-engine control systems. Therefore, it is very necessary to find a control method with good control performance and low computational complexity to apply to the control system of an aeroengine. J. Chen (B) · Z. Hu · J. Wang College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yu Dao Street, Qin Huai District, Nanjing, Jiangsu 210016, China e-mail: [email protected] Z. Hu e-mail: [email protected] J. Wang e-mail: [email protected] W. Zhang School of Automation and Electrical Engineering, University of Science and Technology Beijing, No. 30 Xue Yuan Road, Hai Dian District, Beijing 100083, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_57

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The theory of adaptive inverse control was first developed in 1986 by Widrow [1]. The basic idea of adaptive inverse control is to use the inverse of the controlled object as the serial controller to open-loop control the dynamic characteristics of the system, thus avoiding the possible instability problem due to feedback. Recently, many researches are focused on the inverse control in nonlinear systems [2, 3]. U-model, which is a polynomial structure that comprises of time-varying system parameters, was originally developed by Zhu [4] in 2002. It can be recognized as an extension of NARMAX structure, which is the typical nonlinear structure with many identified methods [5–7]. U-model can represent a wide range of nonlinear systems. After more than ten years of development, the nonlinear control method based on U-model has been applied to predictive control [8], internal model control [9], adaptive control [10, 11] and so on [12]. Traditionally, there are many disadvantages for the adaptive inverse control of unknown nonlinear dynamic systems, the structure of the controlled object model is complex, and thus the adaptive performance is hard to guarantee, consequently, it is difficult to accurately establish the inverse model. In [13], the transverse filter with different weights is used as the structure of the aeroengine model and the inverse model controller, then corresponding research on the adaptive inverse control of the aeroengine is carried out, but the update of the engine inverse model weight vector is offline, so the real-time performance of the entire control system is difficult to guarantee. Combining the advantages of U-model and adaptive inverse control, this paper uses the second-order U-model as the identification structure of nonlinear model to carry out the simulation research of adaptive inverse control. The inverse controller is used to obtain the aeroengine control parameters online, which simplifies the complexity of adaptive inverse control method. Simulation results show that this method ensures an acceptable control performance, which has application potential in the aeroengine control system with poor working environment. The structure of the article is as follows: Sect. 2 introduces the principle of Umodel based adaptive inverse control method; Sect. 3 introduces the aeroengine component-level model used in simulation; Sect. 4 shows the simulation results in small and large transient responses; Sect. 5 summarizes the method and makes the outlook.

2 Nonlinear Adaptive Inverse Control Method Based on U-Model The U-model structure can be seen as an extension of NARMAX model. Consider a SISO nonlinear dynamic system, using a NARMAX model to describe: y(t) = f [y(t − 1), . . . , y(t − n), u(t − 1), . . . , u(t − n), e(t), . . . , e(t − n)]

(1)

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Here, n is the degree of the model, f is the nonlinear equation, u is the input and y is the output, e represents the error which may be caused by measurement noise, model mismatch, uncertain dynamic performance and so on. Expand the above nonlinear Eq. (1) into a polynomial of the model input u(t−1) y(t) =

N 

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(2)

j=0

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ym(t)

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Calculate control signal u(t-1) using updated weights α j ( t ) and command U(t)

Fig. 2 U-model adaptive update algorithm

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α0 u ( t − 1)

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update weight

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Fig. 3 U-model structure



ˆ T (t)(t) + e(t) y(t) =  ˆ T (t)(t) ym (t) = U (t) = 

(3)

Here,   ˆ T (t) = αˆ 0 (t), . . . , αˆ n (t) ∈ R N    T (t) = 1, u(t − 1), . . . , u n (t − 1) ∈ R N , y(t) is the response of the nonlinear plant, ym (t) is the U-model output, e(t) is the error between y(t) and ym (t). In order to be able to identify and adjust the model parameters online, the forgetting factor recursive least squares (FFRLS) method is used. The principle is as follows: ˆ + 1) = (t) ˆ (t + K (t + 1)ε(t + 1) ˆ ε(t + 1) = y(t + 1) − T (t + 1)(t) P(t)(t + 1) K (t + 1) = T λ +  (t + 1)P(t)(t + 1) 1 P(t + 1) = [I − K (t + 1)T (t + 1)]P(t) λ

(4)

ˆ + 1) is the identified vector of (t); ε(t + 1) is the prediction error Here, (t between the measurement output and the previous step prediction model output; K (t + 1) is the weighting factor vector, which combines ε(t + 1) to construct modified values for different parameter vector elements. P(t + 1) is the covariance matrix. The parameter identification convergence condition is: if the N-order input u(t−1) is persistent and the system unknown parameters can be identified, the dynamic nonlinear system is convergent.

An Aeroengine Adaptive Inverse Control Method Based on U-Model

613

In Fig. 1, the control parameter of the inverse model controller can be obtained through the command signal U(t) and the identification parameters α j (t) of the U-model. Taking the second-order U-model structure as an example, the U-model identification structure is ym (t) = α2 (t)u 2 (t − 1) + α1 (t)u(t − 1) + α0 (t)

(5)

The ideal control target of the control system is ym (t) = y(t) = U (t), through the inverse controller we can approximately get the control parameter by solving the root of Eq. (6), that is α2 (t)u 2 (t − 1) + α1 (t)u(t − 1) + α0 (t) − U (t) = 0

(6)

Considering the case where there may be no positive real roots, select the modulus length of the root as the control parameter:     −α (t) + α 2 (t) − 4α (t)[α (t) − U (t)]    1 2 0 1  u(t − 1)=  2α2 (t)  

(7)

In summary, the aeroengine adaptive inverse control method based on U-model has simple principle and low complexity. At the same time, it can identify nonlinear plants and solve the control parameter through the inverse controller online.

3 Introduction to Aeroengine Component-Level Nonlinear Model The model used in this paper is extracted from the commercial large bypass ratio two-shaft turbofan engine JT9D [14]. The structure diagram is shown in Fig. 4. It mainly consists of eight components: inlet, fan, low pressure compressor (LPC), high pressure compressor (HPC), burner, high pressure turbine (HPT), low pressure turbine (LPT) and nozzle. The JT9D engine component-level nonlinear model is based on data from the engine model in NPSS [14], which includes the characteristics of engine components, constant coefficients and steady-state points data. For components such as fan, compressors, and turbines, the characteristic maps directly use the characteristic maps in the NPSS, and then, using the component characteristics, all the performance parameters of the components in steady-state or dynamic processes can be obtained by physical and empirical formula-based solutions. The aeroengine component-level model can be viewed as a nonlinear system with mathematical expressions as follows:

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Inlet

Bypass Stations 17

19

Duct4

Bypass Nozzle

Duct4

Core Nozzle

Fuel Flow

Flow Splitter Input Air Flow

15

Burner

Fan

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1

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4

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9

Fig. 4 JT9D structure diagram

Table 1 Values at idle and maximum steady-state points on the ground state

Fuel flow (lbf)

Low pressure shaft rotational speed (rpm)

Idle state

0.62

1440

Maximum state

5

3766

y = g(u)

(8)

Considering that this paper only studies the SISO nonlinear system, the input u is the fuel flow, and the output y represents low pressure shaft rotational speed. On the ground state, the steady-state input and output values at both idle and maximum states are shown in Table 1.

4 Simulation Results and Discussion Taking the JT9D aero-engine component-level nonlinear model as the nonlinear controlled plant, which is regarded as a “black box”. Besides, the second-order Umodel is used as the identification structure. The simulation block diagram of the entire adaptive inverse control structure is shown in Fig. 5. Considering the control requirements of the fuel flow in the actual aero-engine system, the control logic for designing the inverse controller is shown in Fig. 6. The filter uses a first-order filter to reduce the changing rate of the fuel flow transient response at the beginning. The specific logic is shown in the following Eq. (9). The corresponding parameters of the filter are set by experience.  W f (t)=

0.035W f (t) + 0.965W f (t − 1), |y(t) − U (t)| > 50 W f (t), other s

(9)

An Aeroengine Adaptive Inverse Control Method Based on U-Model Command Signal U(t)

Inverse controller

Identified parameters

u(t-1)

615 y(t)

JT9D

αi (t )

e(t)

-

Second-order U-model

ym ( t ) = α 2 ( t ) u 2 ( t − 1) + α1 ( t ) u ( t − 1) + α 0 ( t )

ym(t)

Fig. 5 The structure diagram of JT9D adaptive inverse control system U(t)

αi (t )

Root Solver

Filter

Overshoot limiter

u(t-1)

Fig. 6 The structure diagram of inverse controller

A fuel flow overshoot limiter is used to avoid the large amount of overshoot caused by the root solver getting an oversized root due to the U-model identification error. The lower limit is the corresponding fuel flow in the idle state, and the upper limit is set according to the desired command value U(t) and the maximum overshoot in the design requirements. Finally, this adaptive inverse control structure based on the second-order U-model is used to simulate the dynamic process of the JT9D engine from the idle state to the maximum state on the ground. The simulation step is taken as 0.02 s, results of engine’s continuous small transient response are shown in Fig. 7. In Fig. 7a, the dynamic performance of the engine is acceptable in continuous small transients with the overshoot less than 2%. Figure 7b shows the identification error between the U-model and nonlinear JT9D engine, steady-state tracking error is almost zero, and the dynamic tracking error is controlled within 6%. Figure 7c shows that with the restrictions set in the controller, parameters of the second-order U-model are normally identified online. Figure 7d shows that the fuel flow value is calculated based on U-model and the rate of change has little fluctuation. Results of engine’s large transient response are shown in Fig. 8. It can be seen from the simulation results that the U-model tracking engine’s steady-state error is almost zero, and the dynamic error from the idle state to the maximum state large transient response is within 5%, but the dynamic error from the maximum state to the idle state is quite large. The reason may be that it is difficult to track the dynamic process, which may be strongly affected by the nonlinearity in the aeroengine, and the mapping relationship of the second-order U-model is difficult to reflect the nonlinear characteristics of this positive and negative dynamic process response (from idle state to maximum state and from maximum state to idle state).

J. Chen et al. JT9D U-model Command

4000

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0.06 0.04

3500

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0.00 -0.02

2000 -0.04

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(c) Identified parameters of U-model

120

0

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(d) Fuel flow changing curve

Fig. 7 Small transient response simulation results of aeroengine adaptive inverse control method based on U-model

In general, from the actual small and large transient response results of the JT9D, the control performances are acceptable, and the method of adaptive inverse control in the unknown aeroengine based on the U-model is feasible.

5 Conclusions It is the first time that the U-model is used to identify the aeroengine model. With the identified U-model, the inverse controller is obtained, which avoids complex inverse modeling. The simulation results show that the proposed aeroengine adaptive inverse control method based on U-model provides good engine speed control performance, and has potential in the aeroengine control with no need to develop an aeroengine model, which is usually time consuming, costly and not accurate. Future research work will be focused on how to improve the accuracy of the U-model dynamic identification, develop the U-model-based multi-variable adaptive inverse control

JT9D U-model Command

4000

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0.05

3500

0.00

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error

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Fig. 8 Large transient response simulation results of aeroengine adaptive inverse control method based on U-model

system, consider the influence of external disturbance uncertainties, verify the realtime performance of this method and design the implementation in the hardware-inthe-loop platform to improve the technology readiness for the practical applications.

References 1. Widrow, B.: Adaptive Inverse Control. J. IFAC Proc. 20(2), 1–5 (1987) 2. Zhan, S., Bai, J., Li, C.C., et al.: Robustness of adaptive inverse control in solving internal and external disturbance uncertainties for a class of non-linear systems. Int. J. Comput. Appl. Technol. 59(2), 185–192 (2019) 3. Johnson, Y., Ahamed, T.P.I.: Nonlinear modelling of leader-follower UAV close formation flight with dynamic inversion-based control. Int. J. Model. Ident. Control 30(2), 83–92 (2018) 4. Zhu, Q.M., Guo, L.Z.: A pole placement controller for non-linear dynamic plants. J. Proc. Ins. Mech. Eng. Part I: J. Syst. Control Eng. 216(6), 467–476 (2002) 5. Pedro, F., Luis, A.: NARMAX model identification using a randomised approach. Int. J. Model. Ident. Control 31(3), 205–216 (2019) 6. Chiras, N., Evans, C., Rees, D.: Nonlinear gas turbine modeling using NARMAX structures. J. IEEE Trans. Instrum. Meas. 50(4), 893–898 (2001)

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7. Supeni, E., Yassin, I.M., Ahmad, A., et al.: NARMAX identification of DC motor model using repulsive particle swarm optimization. In: 5th International Colloquium on Signal Processing and Its Applications, IEEE press, Malaysia (2009) 8. Du, W., Zhu, Q.M., Wu, X.: Support vector machine based U-model generalized predictive controller for nonlinear dynamic plants. In: 33th Chinese Control Conference, IEEE press, Nanjing (2014) 9. Shafiq, M., Haseebuddin, M.: U-model-based internal model control for Non-linear dynamic plants. J. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 219(6), 449–458 (2005) 10. Wu, X., Liu, L., Zhu, Q.M., et al.: U-model-based adaptive control for a class of stochastic nonlinear dynamic plants with unknown parameters. Int. J. Model. Ident. Control 13(3), 135–143 (2011) 11. Hasan, E., Ibrahim, R.B., Ali, S.S.A., et al.: U-model based adaptive control of gas process plant. J. Procedia Comput. Sci. 105, 119–124 (2017) 12. Xu, F.X., Zhu, Q.M., Zhao, D.Y., et al.: U-model based design methods for nonlinear control systems a survey of the development in the 1st decade. J. Control Decis. 7, 961–971 (2013) 13. Hu, W.F., Huang, J.Q.: Study of aeroengine adaptive inverse control. J. Aerosp. Power 20(2), 293–297 (2005) 14. Chapman, J.W., May, R.D., Lavelle, T.M., et al.: Toolbox for the modeling and analysis of thermodynamic systems (T-MATS) User’s Guide. Technical report (2014)

The Active Fault-Tolerant Control of Reconfigurable Manipulator Based on Iterative Fault Observer Wenfeng Ren and Yanli Du

Abstract In this paper, an active malfunction tolerant control method based on iterative fault tracking observer is proposed for actuator faults of restructurable mechanical arm. Firstly, the interconnection term of subsystems is approximated by fuzzy systems, and the argument self-adaptation laws of fuzzy systems are derived. Secondly, this paper designs an iterative fault tracking observer to discover and predict the malfunctions in the joint subsystems of the reconfigurable manipulator at the same time, and on this basis, this paper designs an active fault tolerant controller for the actuator fault, which can not only estimate the fault in real time when the fault occurs, but also ensure the joint track the preset locus. Finally, the validity of the proposed method is verified by the simulation of the different structures of the 3-DOF (degree of freedom) restructurable mechanical arm. Keywords Reconfigurable manipulator · Active fault-tolerant control · Iterative fault observer · Actuator falu · Fuzzy system

1 Introduction When reconfigurable manipulator performs remote operation and dangerous work such as space mission, and military reconnaissance, once the sensor, actuator and other parts fail, the manipulator will not be able to complete the task, even leading to unpredictable serious consequences. In order to improve the reliability of reconfigurable manipulator, malfunction discernment and malfunction tolerant control technology have become an urgent research topic. Based on iterative technology, Ref. [1] puts forward an observer based method for spacecraft fault detection and reconstruction, which has certain robustness. In Ref. [2], an adaptive terminal sliding mode control method is proposed. This method can realize the limited time control of attitude tracking, and the input saturation problem of the actuator can be W. Ren · Y. Du (B) School of Electrical and Information Engineering, Beihua University, Jilin City, Jilin Province 132021, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_58

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solved explicitly. In Ref. [3], a self-adaption malfunction tolerant control algorithm is designed for nonlinear system with multiple actuators. By observing control performance indexes, the unknown fault actuator is automatically positioned and closed to ensure the gradual stability of the system output. In Ref. [4], a robust control allocation algorithm based on pseudo inverse is proposed for a class of overdriven uncertain systems. This method combines the configuration of the poles of the region with the adjustment of adaptive law to compensate for failure fault and stuck fault, and effectively suppress the adverse impact caused by the fault. In Ref. [5], the adaptive laws are used to estimate the unknown parameters in the controller for the T-S fuzzy system with unknown disturbances and actuator malfunctions, and a fuzzy adaptive fault-tolerant control algorithm is proposed to make the system have good fault-tolerant performance. The research of the above control methods has laid a foundation for solving the fault tolerance of system actuator faults. This article raised a kind of active malfunction tolerant control method on the basis of iterative fault tracking observer in order to actuator faults of restructurable mechanical arm. Based on the advantages of iterative learning, a fault tracking observer is used for supervise the fault, and on this basis, an active malfunction tolerant controller for the actuator fault is designed.

2 Dynamic Model of Reconfigurable Manipulator The dynamic model of n-DOF reconfigurable manipulator is: M(q)q¨ + C(q, q) ˙ q˙ + G(q) = τ

(1)

among them, q ∈ R n is the joint position vector, M(q) ∈ R n×n is the inertia matrix, C(q, q) ˙ q˙ ∈ R n is centrifugal and Coriolis torque, G(q) ∈ R n is a vector of gravitational torque, τ ∈ R n is the joint torque vector. The dynamic model of each joint subsystem of the restructurable mechanical arm [6] is: ˙ q) ¨ = τi Mi (qi )q¨i + Ci (qi , q˙i )q˙i + G i (qi ) + Z i (q, q,

(2)

˙ q) ¨ is an interconnection term between the subsystems, qi , q˙i , q¨i and where Z i (q, q, ˙ q¨ and τ。 τi are respectively the i-th components of vector q, q, Suppose xi = [xi1 , xi2 ] = [qi , q˙i ]T (i = 1, 2, · · · n), then the Eq. (2) can be represented as a state space model in the following form: ⎧ ⎨ x˙i1 = xi2 x˙ = f i (qi , q˙i ) + h i (q, q, ˙ q) ¨ + gi (qi )τi ⎩ i2 yi = xi1

(3)

The Active Fault-Tolerant Control of Reconfigurable Manipulator …

where f i (qi , q˙i ) = Mi−1 (qi )[−Ci (qi , q˙i )q˙i − G i (qi )], h i (q, q, ˙ q) ¨ −1 ˙ q), ¨ gi (qi ) = Mi−1 (qi ). −Mi (qi )Z i (q, q,

621

=

3 Active Malfunction Tolerant Control of Restructurable Mechanical Arm Actuator Malfunction on Basis of Iterative Fault Observer 3.1 Design of Iterative Fault Observer and Its Convergence Analysis The block diagram of active malfunction tolerant control for restructurable mechanical arm actuator malfunctions. See Fig. 1. Considering the state equation of each subsystem and the same proof process, the subscript i of the subsystem of the following equation is omitted, so that the equation and the proof process are more intuitionistic and concise. The dynamic equations of each subsystem shown in Eq. (3) are used, and the model of the subsystem when the actuator failure occurs is shown in the Eq. (4): ⎧ ⎨ x˙1 = x2 x˙ = f (q, q) ˙ + h(q, q, ˙ q) ¨ + g(q)τ + g(q) f a ⎩ 2 y = x1

(4)

For (4), the designed iterative fault tracking observer is as follows:

Fig. 1 The block diagram of fault-tolerant control for restructurable mechanical arm actuator malfunctions

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⎧˙ ⎨ xˆ1k = xˆ2k + L 1 (yk − yˆk ) ˆ θˆh ) + g( ˆ xˆ1k , θˆg )τk + g( ˆ xˆ1k , θˆg ) fˆak + L 2 (yk − yˆk ) x˙ˆ = fˆ(xˆ1k , xˆ2k , θˆ f ) + h(|s|, ⎩ 2k yˆk = xˆ1k (5) γk = y − yˆk = x1 − xˆ1k

(6)

fˆa(k+1) = fˆak + k p γk + kd γ˙k

(7)

   yk (t) − yˆk (t)

∞

≤ε

(8)

where t ∈ [t1 , t2 ] is an optimal time domain, the subscript k represents the k-th iteration in an optimization time domain(No sampling time), xk = [x1k , x2k ] = [qi , q˙i ] is the state of the subsystem, fˆak is the estimated value of the actuator fault, ˆ θˆh ), and g( ˆ xˆ1k , θˆg ) are respectively the fuzzy approximation fˆ(xˆ1k , xˆ2k , θˆ f ), h(|s|, value of f (q, q), ˙ h(q, q, ˙ q) ¨ and g(q), and L 1 , L 2 are the known observer gains of the subsystem. The Eq. (7) is the PD type iterative algorithm for actuator fault, and the iterative update algorithm can also be determined according to specific needs. The basis for judging the fault tracking observer to stop iteration in an optimal time domain is shown in Eq. (8). According to Eq. (5), it can be obtained: 

 where A =

ˆ k + Bˆ f fˆak + L(yk − yˆk ) + Hˆ x˙ˆk = A xˆk + Bτ yˆk = C xˆk

(9)

        

0 01 ˆ 0 0 ˆ L1 , C = 1 0 , Hˆ = ˆ ˆ . ,B = ,L = , Bf = L2 00 gˆ gˆ f +h

Assumption 1 The initial value of the subsystem (4) is known, that is xi (0) = [xi1 (0), xi2 (0)] and yi (0) is known. Assumption 2 The actuator fault and control torque of each subsystem are bounded, that is | f ai | < δi , |τi | < ηi , where ηi and δi are positive constants.     Assumption 3 The coefficient estimation errors in Eq. (9) are bounded, that is  B˜  ≤         α1 xk − xˆk  and  H˜  ≤ α2 xk − xˆk , where α1 and α2 are positive constants. Definition 1 The λ norm of the function f  sup  f (t)e−λt .

: [0, T ] → R n is:  f λ =

0≤t≤T

Theorem 1 For subsystem (4), the iterative fault tracking observer, such as Eqs. (5)–(8), is designed. In the finite optimization time, if the iteration initial condition satisfies xˆk (0) = x(0), then when k → ∞, the iterative learning actuator fault fˆak can infinitely approximate the actual fault f a of the system in the λ

The Active Fault-Tolerant Control of Reconfigurable Manipulator …

623

norm, and the output yˆk of the fault tracking observer can  be guaranteedto converge   to the actual output y of the system, that are limk→∞  f a (t) − fˆak (t) = 0 and λ   limk→∞  y(t) − yˆk (t) = 0. λ

Proof In an optimal time domain [0, tn ], xˆk (0) = x(0), yˆk (0) = y(0), k represents the number of iterations in an optimal time domain.  

t    xk − xˆk  = xk (0) − xˆk (0) + [Axk (s) + Bτ (s) + B f ak (s) + H (s)]d   0  

t  ˆ (s) + Bˆ fˆak (s) + Hˆ (s) + L(yk − yˆk )]ds  − [A xˆk (s) + Bτ   0

t

   A − LCxk (s) − xˆk (s)ds +

≤ 0

t     ˆ    B  f ak (s) − fˆak (s)ds 0

t 

t      ˜  ˜ +  Bτ (s) + B f ak (s)ds +  H (s) − Hˆ (s)ds 0

0

      t  ∧      x x Let h 1 = A − LC, h 2 =  Bˆ , then  −  k k  ≤ 0 h 3 xk (s) − xˆk (s) ds +   t   ˆ 0 h 2  f ak (s) − f ak (s)ds where h 3 = h 1 + α1 (η + δ) + α2 . According to the Gronwall-Bellman [7] integral inequality, it can be obtained:   xk − xˆk  ≤ h 2

t

    exp[h 3 (t − s)] f ak (s) − fˆak (s)ds

0

Let (t) = h 2

t 0

    exp[h 3 (t − s)] f ak (s) − fˆak (s)ds, the above equation is:   xk − xˆk  ≤ (t)

(10)

According to the Eq. (7), it can be obtained that: f ak + fˆa(k+1) − f a(k+1) − fˆak = k p γk + kd γ˙k Because of f˜a = f a − fˆa , so f˜a(k+1) − f˜ak = −(k p γk + kd γ˙k )

(11)

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According to Eqs. (4) and (5), we can get that: 

e˙1k = e2k − L 1 (yk − yˆk ) e˙2k = f˜ + h˜ + gτ ˜ k + g f a − gˆ fˆak − L 2 (yk − yˆk )

(12)

Because of g f a − gˆ fˆak = gˆ f a + g˜ f a − gˆ fˆak = gˆ f˜ak + g˜ f a , so the Eq. (12) is written in the form of a state equation: 

e˙ e˙k = 1k e˙2k



˜ k + B f f˜ak + H˜ = (A − LC)ek + Bτ

(13)

    0 0 . where B˜ = , H˜ = ˜ ˜ g˜ f + h + g˜ f a The Eq. (13) is put into Eq. (11), then we can get: f˜a(k+1) = (I − kd C B f ) f˜ak − [k p C + kd C(A − LC)]

t ˜ k + B f f˜ak + H˜ )dτ − kd C( Bτ ˜ k + H˜ ) + (t, τ )( Bτ 0

Take the norm on both sides of the above equation,        ˜  f a(k+1)  ≤ h 3  f˜ak 

t  

t     ˜  ˜ ˜   ˜ ˜ Bτ + h + h 4 h 5  f ak dτ + h 4 h 6  Bτ + H + H  dτ  k 7 k 0

(14)

0

    where h 3 = (I − kd C B f ), h 4 = k p C + kd C(A − LC), h 5 sup (t, τ )B f , h 6 = sup (t, τ ), h 7 = kd C.

t∈[0,tn ]

=

t∈[0,tn ]

That is:

t       ˜  ˜     f a(k+1)  ≤ h 3  f ak  + h 4 h 5  f˜ak dτ 0

t + h4h6h8

    xk (τ ) − xˆk (τ )dτ + h 7 h 8 xk (τ ) − xˆk (τ )

0

where h 8 = α1 η + α2 . The Eq. (10) is put into the Eq. (15), we can get that:

(15)

The Active Fault-Tolerant Control of Reconfigurable Manipulator …

625

t     ˜    ˜ f a (k + 1) ≤ h 3  f ak  + h 4 h 5  f˜ak dτ + (h 4 h 6 h 8 tn 0

t + h7h8)

    exp[h 3 (t − s)] f ak (s) − fˆak (s)ds

(16)

0

Take h 9 = max{h 4 h 6 h 8 tn + h 7 h 8 , h 3 }, and take the λ norm on both sides of the above Eq. (16), it can be obtained that:    1 − exp(−λtn ) 1 − exp(h 9 − λ)tn     ˜ ] f˜ak  + h9  f a(k+1)  ≤ [h 3 + h 4 h 5 λ λ λ λ − h9 n) 9 −λ)tn By selecting a large enough value λ, we let h 3 +h 4 h 5 1−exp(−λt +h 9 1−exp(h < λ λ−h 9     1, then we can get lim  f a (t) − fˆak (t) = 0. According to the Eq. (10), we can k→∞ λ    get lim x(t) − xˆk (t)λ = 0, that is lim  y(t) − yˆk (t)λ = 0.

k→∞

k→∞

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The parameter self-adaption laws of the fuzzy system are taken as: θ˙ˆi f = ηi1 si ξi f (qˆi , q˙ˆi )

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where ηi1 , ηi2 , ηi3 , ri1 and ri2 are positive constants. Theorem 2 Considering the subsystem dynamics model (4) of restructurable mechanical arm with actuator fault, under the premise of Theorem 1, using the disperse control law such as Eqs. (18a, b) and the parameter adaptive law Eqs. (19)–(23) can guarantee that the locus tracking error of the restructurable mechanical arm with actuator fault will still be asymptotically converging to zero. Proof Define the Lyapunov function as: V =

n 

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(25)

The Eqs. (22)–(23) are put into the Eq. (25), and then it can be obtained that: V˙i ≤ −ki si2 + si u ic + |si |ρˆi + |si |λˆ i

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The Eq. (18b) is put into the above in equation, and according to Babalat lemma, lim we can get that si (t) = 0, that is, the trajectory tracking error ei = xˆi1 − yid t →∞ will be also asymptotically converging to zero.

3.3 Simulation As shown in Fig. 2, the controller is applied to the 2-dof constrained restructurable mechanical arm with different structures. The scheduled locus of the structure a is: y1r = 0.2 sin(t) − 0.5 cos(t) y2r = 0.6 cos(3t) − 0.2t y3r = 0.5 sin(3t) + t Assuming that joints 1 and 3 have random actuator fault and constant deviation actuator fault in 2s and 4s, the designed iterative learning fault tracking observer can be used to reconstruct the joint faults of configuration a, as shown in Fig. 3. Adopting the control law shown in Eqs. (18a, b) and adaptive laws Eqs. (19)–(23), the fault-tolerant locus tracking curves of configuration a are shown in Fig. 4. The desired trajectory of the configuration b is: y1r = 0.5 cos(t) − 0.2 cos(3t) y2r = 0.4 sin(3t) + 0.5 sin(4t) y3r = 0.3 cos(2t) − 0.2t It is also assumed that joints 1 and 3 have random actuator fault and constant deviation actuator fault in 2 s and 4 s respectively, and the joint faults of structure b see Fig. 5.

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The fault-tolerant locus tracking curves of structure b, See Fig. 6. Through the simulation results of Figs. 3, 4, 5 and 6, it can be seen that the designed iterative learning fault tracking observer can well approximate the actuator faults. On this basis, the designed decentralized controller can realize the fault-tolerant control of restructurable mechanical arm with different configurations.

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4 Conclusion (1) The idea of modularization of the reconfigurable manipulator is used to design the decentralized controller, and each joint of the manipulator is considered as a subsystem. (2) A fault tracking observer based on iterative learning is designed to observe faults in real time. This method can not only detect the fault of the system effectively, but also realize the accurate estimation of the fault signal, and it also has good adaptability for different faults. (3) On the basis of the fault tracking observer, an active fault-tolerant controller for actuator fault is designed. Reconfigurable manipulator can still track the desired trajectory when different types of actuator faults occur. Acknowledgements This work is supported by the scientific research project of Jilin Province of China Education Department (JJKH20180340KJ) and Jilin science and technology development plan project (20160101276JC). The corresponding author is Yanli Du.

References 1. Xiao, B., Hu, Q., Ma, G.: Observer based fault reconstruction for spaczcraft under loss of actuator effectiveness. J. Astronaut. 32(2), 323–328 (2011) 2. Hu, Q., Huo, X., Xiao, B., et al.: Robust finite-time control for spacecraft attitude stabilization under actuator fault. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 226(3), 416–428 (2012) 3. Yang, Q., Ge, S.S., Sun, Y.: Adaptive actuator fault tolerant control for uncertain nonlinear systems with multiple actuators. Automatica 60, 92–99 (2015) 4. Zhang, X.Y., Jiang, B., Zhang, K.: Direct adaptive reliable control of overactuated system with actuator failures and external disturbances. Int. J. Adv. Robot Syst. 4961–4966 (2013) 5. Zhang, Wei, Ling, Shaocheng: Adaptive fault-tolerant control with actuator failures and bounded disturbances based on the T-S fuzzy model. Fuzzy Syst. Math. 02, 157–164 (2015) 6. Zhu, M.: Research on Kinematics, Dynamics and Control Methods of Reconfigurable Modular Robots, College of Communications Engineering, pp. 68–69. Jilin University, Changchun (2006) 7. Li, W., Ren, B., Mao, H.: Class method of fault accommodation based on inverse system iterative learning observer. Appl. Res. Comput. 29(5), 1698–1701 (2012)

Prediction for Time Series with CNN and LSTM Xuebo Jin, Xinghong Yu, Xiaoyi Wang, Yuting Bai, Tingli Su and Jianlei Kong

Abstract Time series data exist in various systems and affect the following management and control, in which real time series data sets are often composed of multiple variables. For predicting the future of data, not only the historical value of the variable but also other implicit influence factors should be considered. Therefore, we propose a prediction method based on the convolutional neural network (CNN) and Bi-directional long short term memory (Bi-LSTM) networks with the multidimensional variable. CNN is used to learn the horizontal relationship between variables of multivariate raw data, and Bi-LSTM is used to extract temporal relationships. Experiments are carried out with Beijing meteorological data, and the results show the high prediction accuracy of wind speed and temperature data. It is indicated that the proposed model can explore effectively the features of multivariable non-stationary time series data. Keywords CNN · Bi-LSTM · Time series · Prediction · Multiple variables

1 Introduction Predicting trends in time series plays an important role, such as monitoring data in meteorological management systems [1], trading data in stock markets [2], etc. The time series data in these systems is usually data related to multiple dimensions, that is, there is a relationship between different time series variables. For example, temperature changes are affected by factors such as wind, rainfall, and humidity. The results show that multidimensional correlation variables can improve the accuracy X. Jin · X. Yu · X. Wang (B) · T. Su · J. Kong School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China e-mail: [email protected] Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing Technology and Business University, Beijing 100048, China Y. Bai School of Automation, Beijing Institute of Technology, Beijing 100081, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_59

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of predictive target variables if the intrinsic correlation and historical features are properly mined [3]. Researchers have come up with some ways to solve prediction problems. For example, the traditional method Autoregressive Integrated Moving Average (ARIMA) [4] is good at predicting stationary time series data. However for nonstationary time series data, ARIMA faces the problem of increasing smooth step size and difficulty. In addition, shallow machine learning methods such as artificial neural networks (ANN) and support vector machines (SVM) are applied to the modeling and prediction of time series data because they can process nonlinear data and suppress noise in real systems. However, ANN [5] is not as good as ARIMA in the low frequency range and over-fitting in the excessive frequency phase [6]. SVM is suitable for non-aperture defined non-linear and non-static systems [7], but it is often difficult to determine the parameters in an optimal way. For massive data and high computational performance, deep learning models have recently shown great advantages in automatically extracting and learning multivariate data features. In particular, the Recurrent Neural Network (RNN) and its various improved models [8–10] have been applied to feature extraction of time series data. For example, [11] proposed an RNN for nonlinear data modeling, [8] proposed a method called GRU to improve LSTM by reducing the gating unit. Experiments have shown that GRU has better performance than LSTM on data with missing values [9]. In [10], a bidirectional LSTM (Bi-LSTM) is proposed which increases the input of the LSTM by inputting one step of the time series data into the network in both the forward and reverse directions. Compared to LSTM, Bi-LSTM is more complex in structure than LSTM, introducing more parameters, resulting in increased training time. However, actual data changes usually depend not only on the previous sequence but also on subsequent sequences. Bi-LSTM can remember previous and subsequent information in order to obtain more complete information for higher prediction accuracy. We found that the performance of RNNs declined in the long-term prediction of complex multivariate data. In particular, when the input is multidimensional, the relationship between the variables is also important for prediction. Taking into account the above discussion, we propose a general framework for multivariate prediction problems, including CNN and Bi-LSTM. CNN is used to extract the horizontal relationship of multidimensional variables before the Bi-LSTM network layer, while Bi-LSTM is used to learn the timing relationships of features obtained by CNN and predict based on this. The remainder of this paper is organized as follows: Sect. 2 introduces the proposed method, including convolution of multidimensional time series and Bi-LSTM model. Section 3 describes the experiments and results. We draw conclusions and outlook in Sect. 4.

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2 Model For the prediction problem of multivariable nonlinear time series, this paper proposes a prediction model combining CNN and Bi-LSTM. In this section, we first establish a model framework to explain the prediction process. Then we describe the details of convolutional layer and Bi-LSTM cell structure.

2.1 Model Framework Our model consists of two main parts. CNN is used to extract the lateral features of multidimensional data, and Bi-LSTM is used to extract the temporal features of the data which is shown in Fig. 1. The Bi-LSTM performs exceptionally well in long-term modeling of nonlinear data. One-dimensional convolution allows feature extraction in two dimensions of multidimensional time series data [12]. Theoretically, it is possible to model nonlinear any multidimensional data by Bi-LSTM. Unfortunately, actual data is often multivariate, and these variables have complex relationships themselves. In the prediction, the Bi-LSTM does not learn this complicated relationship on the one hand, and on the other hand, it has a large computational burden because of the excessive number of input features. Therefore, we introduce convolutional layers before Bi-LSTM, and extract the horizontal relationship of multivariate data through convolution operations. The features extracted by these CNN are time-series, which is convenient for LSTM learning.

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Fig. 1 Model framework

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2.2 Convolutional Neural Networks Convolutional neural networks (CNNs) have matured in recent years. Convolution operation refers to the operation of inner product (multiplication by element and then summation) for different window data and filter matrix (a fixed set of weights). The maxpooling layer is used to reduce the eigenvectors of the convolutional layer output to simplify the computational complexity of the network, at the same time, it performs the feature compression and extracts the main features. The one-dimensional CNN model is shown in Fig. 2.

2.3 Bi-LSTM Recurrent neural networks (RNNs) maintain a memory based on history contextual information, which makes them a natural choice for processing sequential data. Long Short-Term Memory network adds cells as the information storage module, which realizes long-term memory of the sequence data, and solves the problem of gradient disappearance and gradient explosion of RNN network. Updating the state of the cell through three gating units is the key to LSTM, as shown in Fig. 3. The three gating units have different calculation methods and function. (1) Forget gate: The forget gate is used to control the memory and forgetting of information, specifically through a Sigmod function. Its input is the state of the current state X (t) and the output H (t − 1) of the previous moment. Then, for each information in the cell state C(t), a value of 0–1 is output, 1 means completely remembered, 0 means completely abandon. (2) Input gate: The input gate mainly controls the update of the cell by the following two pieces of information. One is that the tanh function’s output, and the other is the output of the forget gate.

Prediction for Time Series with CNN and LSTM

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Fig. 3 Structure of LSTM cells

(3) Output gate: The output gate uses different activation functions to filter the current state as well as the previous state and the state in the cell, and multiplies the results to get the final output. The gate units of the bidirectional LSTM are identical to the LSTM. Bi-LSTM is a combination of a forward LSTM and a backward LSTM, that means, one time step of data is input simultaneously in both forward and reverse directions. Although Bi-LSTM needs to train more generations to converge to stability, it also has higher precision because it gets more input information. So we chose the Bi-LSTM as the prediction model.

3 Experiments In this section, we will validate and evaluate the proposed model using a realistic meteorological data set. The prediction performance of the proposed model is verified by comparing LSTM.

3.1 Experimental Setup The data in experiments come from the meteorological dataset of Global AI Challenge. The data are selected from the observation set measured in a meteorological station in Beijing, including the physical quantities in the meteorological factors,

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such as the ground pressure, temperature, relative humidity, and the wind speed. The relative humidity and temperature will be predicted with the proposed model. These meteorological data are measured every hour, and the data set contains 200 time steps for a total of 4800 data and a time step contains data for 24 moments. We select the first 95% of data for training, and the remaining 5% as the test set. The trend of the time series data is shown in Fig. 4, in which the true relative humidity and temperature time series data are dynamic, highly nonlinear, and contain high noise. We use 24 moments’ data to predict the data for 24 moments forward. Therefore, the length of the input data and output data of the network are 24. When we usually use neural networks to build models, the size of the network layer and the number of neurons are not strictly defined. We determined the parameters of each layer of the model through multiple experimental adjustments. Specifically, we set up two layers of convolution layers, the filters size of each convolution layer was set to 3, and the Relu function was used. Two layers of Bi-LSTM, the previous layer of neurons was set to 30, and the latter layer was set to 24 which is determined by the output dimension of the model. In addition, all models are supervised trained using Adam algorithm that optimizes a predetermined objective function, to obtain model

Fig. 4 Relative humidity and temperature trends

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Table 1 Hyper parameters for all experiments Model

Network

Design details

Experiment setup

LSTM

LSTM

Number of layers: 2

Batch size: 20

Size: 37

Epochs: 1500

Conv-BiLSTM

CNN

Number of layers: 2 Number of filters: 5, 5 Filters size: 3

Bi-LSTM

Number of layers: 2

Dence

Size: 33, 33 Number of neurons: 24

Batch size: 20 Epochs: 1500

parameters. The hyper parameters about the models, such as number of layers, batch size, etc. were all empirical figures obtained from experiments and Table 1 shows the details of the model parameters. When we use the data pair to train the network, the data pair is the real current time step data and the next time step data. Each time step contains 24 moments, so the input shape of the network is (24, 1) and the output of the network is also (24, 1). When the network training is completed, we use the test data for evaluation. At this point, we only need to provide the data of the current step size of the network. The output of the network are the predicted values of the next time step. We expect the root mean square error between the predicted values and the observation of the next time step as small as possible. Root Mean Square Error (RMSE) was used to estimate the performance of models, which was frequently used to measure the difference between values predicted by a model and the values actually observed from the environment, RMSE value of 0 indicates that the observed value exactly fit the predicted value and its calculation formula is as follows.   n   (yi − yˆi )2 (1) R M S E =  n1 i=1

where, yˆi represents the predicted value and yi represents the truth value, n represents the number of test data.

3.2 Prediction Results The relative humidity and temperature prediction results are shown in Fig. 5a, b. The green line presents the ground truth of relative humidity (RH) and temperature (T), while the red and blue lines are the predictive results with Conv-BiLSTM and LSTM models respectively. Figure 5 shows the comparison of the ground truth (expected) and the 24-steps forward predictive results of two non-stationary time series data with two models.

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(a) Relative Humidity Predictions

(b) Temperature Predictions Fig. 5 Comparison of ground truth and prediction of RH and T data with models

It can be seen from is the preparation state of a ure that it is not feasible to use the single LSTM model to predict the non-stationary multivariate time series data. This is because the LSTM can extract the time feature of the input variables, but cannot explain the relationship between the input variables. As can be seen from Fig. 4, the LSTM model failed to effectively predict the outlier values such as the wave valley and the wave peak data. We introduce a convolutional layer to achieve feature extraction of the original data in both spatial and temporal dimensions, and closer to the expected value at the peak.

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Figure 6 shows the absolute error of the predictive results and ground truth of non-stationary time series. (a) shows the absolute error of the predicted result of RH, and (b) shows the absolute error of the T. The red, blue and green lines are the difference between the predicted of the Conv-BiLSTM, LSTM models and ground truth, respectively. The closer the difference is to the value of 0, the more accurate the predictions are. Figure 6 is another representation of the predictive performance of all

(a) RH Predictions Absolute Error

(b) T Predictions Absolute Error Fig. 6 The absolute error between the predictive results with models and ground truth of RH and T data

640 Table 2 Comparison of RMSE between our proposed model and the other three models

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models, the general situation is similar to Fig. 5, which also illustrates the advantages of proposed model Conv-BiLSTM in terms of the predictive performance. The quantitative results are shown in Table 2, which gives RMSE comparative analysis of Conv-BiLSTM and LSTM. As indicated in Table 2, our model is superior to other methods in terms of two time series with the smallest RMSE for multi-step forward prediction. The RMSE of the results obtained by the Conv-BiLSTM model is 7.8% lower than the LSTM when predicting relative humidity in 24 steps. The RMSE is reduced by 23% when predicting temperature which proves that the ConvBiLSTM has a significant performance improvement over LSTM in multivariate prediction.

4 Conclusion In this paper, we focus on multivariate noise time series data modeling and prediction univariate, and compare the performance of two deep learning models in multi-step prediction. The performance of the Conv-BiLSTM was verified on the real weather dataset in Beijing. Experimental results show that introducing a convolutional layer is very effective for local spatial feature extraction of multivariate data, and its performance is much better than a single LSTM. In the future, We will consider other methods of analyzing multivariate raw data relationships to train LSTM with more efficient features to improve prediction performance. Acknowledgements This work was supported in part by the National Key Research and Development Program of China no. 2017YFC1600605, National Natural Science Foundation of China No. 61673002, and Beijing Municipal Education Commission No. KM201910011010.

References 1. Soares, E., Costa, P., Costa, B., et al.: Ensemble of evolving data clouds and fuzzy models for weather time series prediction. Appl. Soft Comput. (2017). S1568494617307573 2. Yang, Y., Guizhong, L.: Multivariate time series prediction based on neural networks applied to stock market. In: 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat. No. 01CH37236), vol. 4, IEEE (2001) 3. Du, S., et al.: Deep Air Quality Forecasting Using Hybrid Deep Learning Framework. arXiv preprint arXiv:1812.04783 (2018)

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4. Zhang, G.P.: Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50, 159–175 (2003) 5. Popescu, I., Nikitopoulos, D., Constantinou, P., Nafornita, I.: ANN prediction models for outdoor environment. In: 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications, pp. 1–5. IEEE (2006) 6. Sapankevych, N.I., Sankar, R.: Time series prediction using support vector machines: a survey. IEEE Comput. Intell. Mag. 4(2), 24–38 (2009) 7. Thissen, U., Brakel, R.V., Weijer, A.P.D., et al.: Using support vector machines for time series prediction. Chemometr. Intell. Lab. Syst. 69(1–2), 35–49 (2003) 8. Tang, Y., Huang, Y., Wu, Z., Meng, H., Xu, M., Cai, L.:. Question detection from acoustic features using recurrent neural network with gated recurrent unit. In: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 6125–6129. IEEE (2016) 9. Che, Z., Purushotham, S., Cho, K., et al.: Recurrent neural networks for multivariate time series with missing values. Sci. Rep. 8(1), 6085 (2018) 10. Elsheikh, Ahmed, Yacout, Soumaya, et al.: Bidirectional handshaking LSTM for remaining useful life prediction. Neurocomputing 323, 148–156 (2019) 11. Chalup, S.K., Blair, A.D.: Incremental training of first order recurrent neural networks to predict a context-sensitive language. Neural Netw. 16(7), 955–972 (2003) 12. Suzuki, J., Isozaki, H., Maeda, E.: Convolution kernels with feature selection for natural language processing tasks. In: Meeting of the Association for Computational Linguistics (2004)

CO2 Pipeline Transportation System Optimization Design Based on Multiple Population Genetic Algorithm Qunhong Tian, Aiqin Sun, Kan Shi and Fengde Wang

Abstract Carbon capture, transport, utilization and storage (CCUS) technology is an effective way to reduce the carbon emissions. CO2 transportation system is an important link between the capture source and storage sites, whose cost cannot be neglected. In order to realize the optimization design problem of CO2 pipeline transportation, levelized cost is given as the optimization objective, this paper establishes an optimization model of CO2 pipeline transportation, which is solved by using multiple population genetic algorithm (MPGA). Simulation results indicate the effectiveness of the proposed optimization method for CO2 pipeline transportation. Keywords CO2 pipeline transportation · Levelized cost · Pipeline optimization · Multiple population genetic algorithm

1 Introduction With the continuous increase of greenhouse gas emissions, extreme events have appeared continuously in public observation [1–4]. Carbon capture, utilization, storage (CCUS) technology is a way to decrease the CO2 emissions. CCUS is to separate CO2 from industrial or other emission sources, to transport the captured CO2 to specific sites, and to utilize or store, thus to achieve a long term isolation of CO2 from atmosphere [5]. Compared with the ways to transport CO2 including water carriers, motor carriers and railway, existing studies have shown that pipeline is the most economic and effective way to transport large-scale, long-distance CO2 , pipeline transportation is an important connection for the capture source and storage location, as a vital part of CCUS investment, CO2 pipeline transportation cost should not be neglected. The existing research have been indicated that the optimized design of pipeline transportation system can not only guarantee the safety of pipeline transportation, but also effectively reduce the system cost. A calculation equation of the maximum Q. Tian (B) · A. Sun · K. Shi · F. Wang College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, China e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_60

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distance is proposed for pipeline transportation without intermediate pump station, however, the detailed design scheme is not given [6]. An optimization design scheme is developed in the premise of the fixed distance between pump stations [7, 8]. Based on the established hydrodinamical model, it optimizes the internal diameter of the pipeline and number of pump stations, however, the nominal pipe diameter is not considered in the research, it’s difficult to be used in the actual engineering directly [9]. Based on the nominal pipe diameter sizes, the pipeline transportation is optimized with the optimal configuration of basic parameters [10], however, the optimization results are got by using the enumeration method, the biggest disadvantage of using enumeration method is the large amount of calculation, the more accurate optimization results, the more computational time. Form above analysis, if the number of pump stations is not considered or the distance is fixed between the nearest pump stations, it’s difficult to get the optimization results. Based on considering the number of pump stations, a new optimization method should be proposed, which is important to reduce the cost of pipeline transportation, it should be pointed out that the MPGA method is proposed to realize the goal in this paper. The rest of the structure of this paper is as follows. Section 2 formulates the optimization problem of CO2 pipeline transportation. Section 3 gives the optimization design based on MPGA. Section 4 presents the results. Finally, Sect. 5 gives the conclusions.

2 Optimization Problem of CO2 Pipeline Transportation 2.1 Problem Description of CO2 Pipeline Transportation CCUS technology incudes three sub-systems: carbon capture sub-system, pipeline transportation sub-system, utilization and storage sub-system. Figure 1 shows the process of CO2 transportation, it can be seen that pipeline transportation is the intermediate node to link the capture sub-system and the enhanced oil recovery (EOR) and storage sub-system. To design the CO2 pipeline transportation system simply and effectively in this paper, we assume the major design conditions as follows: (1) The pipeline laid is on the same horizontal plane; (2) Carbon dioxide is transported in a dense phase

CO2 Capture

Pcap PMOP

PMOP

Pinject

Pinlet

Pinlet

Pinject

Pipeline Compressor

Cooler

Compression system Capture

Inter-stage booster pump

Booster pump

Transport

Fig. 1 The process of CO2 pipeline transportation [11]

EOR and storage

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; (3) The type of each booster pump is uniform. (4) Pipeline links one capture source to one oil field. (5) The numerical value of injection pressure is the standard value for the outlet pressure of each pipeline segment.

2.2 Optimization Model of CO2 Pipeline Transportation In order to optimal design for the CO2 pipeline transportation, the optimization model is important, which can be given as follows [10]: min LC s.t. Poutlet < Pinlet < Pmax Vmin < V < Vmax

 Pout = Pinlet − Pact L (N pump + 1)

C R F1 × C P_cap + C R F2 × CC_cap + C R F3 × C B_cap + C T _O M + C T _energy LC = Q m × 10−3 × Hope × 3600

C R Fx =

r 1 − (1 + r )−z x

(1) (2) (3)

 where Q m denotes the CO2 mass flow rate (kg s); Pmax is the maximum pressure of transportation (MPa); LC denotes the levelized cost of CO2 transportation (e/t CO2 ); Poutlet is the outlet pressure for each pipe segment (MPa); Pinlet is the inlet pressure for each pipe segment (MPa); V is the actual velocity (m/s); Vmin is the minimum velocity (m/s); L is the length of the pipeline (m); C B_cap is the capital costs of booster pumps (e); Vmax is the maximum velocity (m/s); N pump is the number of boosting pump stations; C R F1is the capital recovery factors of pipelines; Pact is the actual pressure drop (M Pa m); C R F2 is the capital recovery factors of compressors; C R F3 is the capital recovery factors of booster pumps; C P_cap is the capital costs of pipelines (e); C T _energy are the annual energy costs of compressors and booster pumps (e); z 1 is the lifetime of pipelines (years); CC_cap is the capital costs of compressors (e); C T _O M denotes the annual operation and maintenance of (O&M) costs of pipelines, compressors and booster pumps (e); z 2 is the lifetime  compressors (years); Hope denotes the operation time of the transportation (h year); r is the discount rate (%); z 3 is the lifetime of booster pumps (years).

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3 Optimization Design of CO2 Pipeline Transportation Based on MPGA 3.1 The Theory of MPGA In order to apply the optimization results in engineering practice directly, the nominal pipe size should be considered, however, there exist the mismatch between the calculated and nominal pipe diameter. Genetic algorithm has good global search ability and can search all solutions in solution space quickly. Genetic algorithm can be used to facilitate distributed computing to speed up the solution because of it’s intrinsic parallel characteristic. However, the standard genetic algorithm (SGA) cannot to solve the mismatch problem of CO2 pipeline transportation, which may take longer time on searching or easily running into the local optimization solution. Therefore, a new method should be developed for CO2 pipeline transportation design. Multiple population genetic algorithms (MPGA) develops based on SGA, it can overcome the premature convergence, which is an important factor affecting optimization results in genetic algorithms. MPGA breaks through the framework of genetic evolution closely related to a single population, multiple populations are introduced to search for optimization simultaneously. Different population is assigned with different control parameters, in order to realize different search objective. Each population is connected by migration operator, which can realize the cooperative coevolution of multiple populations. The optimal solution is obtained from the comprehensive result by the cooperative coevolution of multiple populations. The best individual of each population is saved by artificial operator, which is selected as the criterion of algorithm convergence. Therefore, the optimization problem of CO2 pipeline transportation system can be solved with the above advantages of MPGA. Figure 2 shows the structure of MPGA [12–14].

Migration

Migration

Migration

SGA

SGA

SGA

Artificial section

Artificial section

Artificial section

Population 1

Population 2

Population N

Selectness population Fig. 2 The structure of MPGA algorithm

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3.2 The Optimization of CO2 Pipeline Transportation Algorithm 1 gives the steps of the optimization design of CO2 pipeline transportation based on MPGA, Fig. 3 gives the corresponding flowchart. Algorithm 1 Pipeline optimization Step 1: Substitute the established models into (1) in order to construct the pipeline transportation system optimization model. Step 2: Randomly initialize the populations, use the selection, crossover and mutation operation for each population. Step 3: Calculate the value of the objective function of each population, obtain the selectness population after artificial selection. Step 4: Calculate the value of fitness function of the pipeline transportation, use the selection, crossover and mutation operation for each population. Step 5: Calculate the objective function value of each population, use the migration, artificial selection operation, obtain the selectness population. Step 6: Obtain the optimal individual of the selectness population. Step 7: If the current number of iteration (M B P ) is smaller than the maximum number of iteration (M B ), then go to Step 3; otherwise, go to the next step. Step 8: Combined with the nominal pipe size, obtain the optimal pipeline diameter (O D N P S ) and wall thickness (t N P S ), substitute O D N P S and t N P S into (1). Step 9: Calculate the value of fitness function of the pipeline transportation, use the selection, crossover and mutation operation for each population. Step 10: Calculate the objective function value of each population, use the migration, artificial selection operation, obtain the selectness population. Step 11: Obtain the optimal individual of the selectness population. Step 12: If the current number of iteration (M B P ) is smaller than the maximum number of iteration (M B ), then go to Step 9; otherwise, go to the next step. Step 13: Obtain the optimal pipeline inlet pressure (Pinop ) and number of pump stations (N pop ). End the algorithm.

4 Optimization Results and Analysis In order to validate the proposed optimization method, optimization results and analysis are given in this part. Tables 1, 2 and 3 give the parameters of CO2 pipeline transportation systems. It gives the comparison of the MPGA and the SGA methods in Table 4, we can see that the proposed MPGA method saves the pipeline transportation cost.  For example, the soil temperature is assumed to be Tsoil = 9 ◦ C, if Q m is 97 kg s, by using the

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The optimization model of CO2 pipeline transportation

Initialization

Selection, crossover, variation

Objective function value of each population Selectness popultation

Fitness function value

Selection, crossover and mutation Fitness function value

Selection, crossover and mutation Objective function value of progeny population

Migration

Artificial selection

Selectness popultation

Optimal individual Of the selectness popultation

Objective function value of progeny population

Migration

Artificial selection

Selectness popultation

Optimal individual Of the selectness popultation Yes

M BP

MP? No

Yes M BP < M P ?

Pinop

,

No ODNPS , t NPS

Fig. 3 Flowchart of pipeline design

End

N pop

CO2 Pipeline Transportation System Optimization Design Based … Table 1 Basic parameters of CO2 pipeline transportation system [6, 15]

Table 2 Detailed parameter values of pipeline [16, 17]

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Parameter

Symbol

Pipeline length (km)

L

Operation time (h)

Hope

Injection pressure (MPa)

Pin ject

Parameter

Value 325 8760 10

Symbol

Value

Design factor

F

0.72

Longitudinal joint factor

E

1.0

Specified minimum yield stress (MPa)

S

483

Table 3 Parameters of compressor and boosting pump [10, 18, 19] Parameter

Symbol

Value

Universal gas constant (J/mol K)  Molar mass (g mol)

R

8.3145

M

44.01

Isentropic efficiency

ηiso

80%

γ

1.294

Total number of compression stages

N

4

Suction temperature (K)

T1

313.15

Base costs for compressor cost (Me )

I0

21.9

Discharge pressure (MPa)

PM O P

8.6

Suction pressure (MPa)

Pcap

0.101

Mechanical efficiency

ηmech

99%

Scaling factor

y

0.67

Operation time of compressor (h)

TC

8760

Multiplication exponent

n

0.9

Operation time of booster pump (h)

TB

8760

Percentage of the capital cost of booster pumps

f B O&M

0.04

Booster pump efficiency

ηbooster

0.5

Actual velocity (m/ s)

V

0.5 < V < 6

 Specific heat ratio (cp cv )

MPGA method, we can get the optimization results as follows: Dout =3.24 × 10−1 m , t = 6.35 × 10−3 m , Pinlet =12.32 MPa, N pump = 4, LC= 19.85 e/t. By using the SGA method, we can get the optimization results: Dout =3.24 × 10−1 m, t = 6.35 × 10−3 m, Pinlet =12.52 MPa, N pump = 4, LC=20.18 e/t. Although the levelized cost can be saved 0.33 e/t, the total cost saves 25.24 Me in the design lifetime of 25 years, it can be seen that the proposed MPGA method saves LC effectively.

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Table 4 Comparison of the MPGA and the SGA methods  Method Parameter Q m (kg s) MPGA

SGA

97

135

195

290

Dout (m)

3.24 × 10−1

3.24 × 10−1

4.06 × 10−1

4.57 × 10−1

t (m)

6.35 × 10−3

6.35 × 10−3

7.14 × 10−3

7.92 × 10−3

Pinlet (MPa)

12.32

13.02

11.86

11.33

N pump

4

5

6

7

LC (e/t)

19.85

13.06

12.85

11.94

Dout (m)

3.24 × 10−1

3.24 × 10−1

4.06 × 10−1

4.57 × 10−1

t (m)

6.35 × 10−3

6.35 × 10−3

7.14 × 10−3

7.92 × 10−3

Pinlet (MPa)

12.52

13.48

12.26

11.73

N pump

4

5

6

7

LC (e/t)

20.18

13.38

13.21

12.31

5 Conclusion CO2 pipeline transportation optimization design is important for the application of CCUS technology, in order to optimize the CO2 pipeline transportation with the minimum levelized cost, a CO2 pipeline transportation optimization model is proposed in this paper, the nominal wall thickness and pipe diameter are considered in the pipeline design, the MPGA optimization method is developed to optimize the CO2 pipeline transportation. The optimization results and analysis validate the effectiveness of the proposed method, by comparing with the other optimization methods, it can be obtained that the proposed approach saves the costs. Acknowledgements This work was partially supported by the Opening Fund of Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety and the Fundamental Research Funds for the Central Universities (19CX05007A).

References 1. Tian, Q., Zhao, D., Li, Z., et al.: Modelling and evaluating CCUS: a survey. Int. J. Comput. Appl. Technol. 53, 1–12 (2016) 2. Tian, Q., Zhao, D., Li, Z., et al.: A two-step co-evolutionary particle swarm optimization approach for CO2 pipeline design with multiple uncertainties. Carbon Manag. (2018). https:// doi.org/10.1080/17583004.2018.1463782 3. Tian, Q., Zhao, D., Li, Z., et al.: Simulation-based optimisation and analysis for CO2 pipeline transportation system with uncertainties. Int. J. Simul. Process Model. 13, 179–187 (2018) 4. Tian, Q., Zhao, D., Li, Z., et al.: Robust and stepwise optimization design for CO2 pipeline transportation. Int. J. Greenh. Gas Control. 58, 10–18 (2017)

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5. Department of S&T for Social Development, Ministry of Science and Technology of the People’s Republic of China. The Administrative Center for China’s Agenda 21. Technology Roadmap Study on Carbon Capture, Utilization and Strorage in China. (2011) 6. Gao, L., et al.: Cost analysis of CO2 transportation: case study in China. Energ. Procedia 4, 5974–5981 (2011) 7. Wildenborg, T., Holloway, S., Hendriks, C., et al.: Cost Curves for CO2 Storage. Part 2: European sector Utrecht Nederland: IEA Greenhouse Gas R&D. Programme, (2004) 8. Van den Broek, M., Brederode, E., Ramírez, A., et al.: Designing a cost-effective CO2 storage infrastructure using a GIS based linear optimization energy model. Environ. Model. Softw. 25, 1754–1768 (2010) 9. Zhang, D., Wang, Z., Sun, J., Zhang, L., et al.: Economic evaluation of CO2 pipeline transport in China. Energy Convers. Manag. 55, 127–135 (2012) 10. Knoope, M.M.J., et al.: Improved cost models for optimizing CO2 pipeline configuration for point-to-point pipelines and simple networks. Int. J. Greenh. Gas Control. 22, 25–46 (2014) 11. Zhao, D., Tian, Q., Li, Z., et al.: A new stepwise and piecewise optimization approach for CO2 pipeline. Int. J. Greenh. Gas Control. 49, 192–200 (2016) 12. Potts, J.C., Giddens, T.D., Yadav, S.B.: The development and evaluation of an improved genetic algorithm based on migration and artificial selection. IEEE Trans. Syst. Man Cybern. 24, 73–86 (1994) 13. Yu, J., Wu, H., Yang, W.: An improved poly-population gentic algorithm based power distribution network planning. Power Syst. Technol. 29, 36–40 (2005) 14. Ye, Z., Shan, Y.: A new transmission network expansion planning based on multiple population genetic algorithm. Autom. Electr. Power Syst. 24, 24–27 (2000) 15. Chandel, M.K., Pratson, L.F., Williams, E.: Potential economies of scale in CO2 transport through use of a trunk pipeline. Energy Convers. Manag. 51, 2825–2834 (2010) 16. McCoy, S., Rubin, E.: An engineering-economic model of pipeline transport of CO2 with application to carbon capture and storage. Int. J. Greenh. Gas Control. 2, 219–229 (2008) 17. Vandeginste, V., Piessens, K.: Pipeline design for a least-cost router application for CO2 transport in the CO2 sequestration cycle. Int. J. Greenh. Gas Control. 2, 571–581 (2008) 18. Kuramochi, T., et al.: Comparative assessment of CO2 capture technologies for carbon-intensive industrial processes. Prog. Energy Combust. Sci. 38, 87–112 (2012) 19. Zhang, Z.X., et al.: Optimization of pipeline transport for CO2 sequestration. Energy Convers. Manag. 47, 702–715 (2006)

A Train Integrity Monitoring Method Based on GNSS Moving Baseline Resolution Wei Jiang, Yongqiang Liu, Dan Liu, Baigen Cai and Jian Wang

Abstract The traditional train integrity monitoring (TIM) is realized by the wayside equipment like track circuit. However, its shortcomings in high setup and maintenance costs limit further development. In this paper, a novel TIM method based on Global Navigation Satellite System (GNSS) moving baseline is proposed. In this method, the double-difference (DD) algorithm is applied to mitigate the GNSS propagation errors and clock biases to improve the accuracy. Then the DD carrier phase is input as measurement to Kalman filter, which is used to dynamically estimate the length of moving baseline. In order to evaluate the performance of proposed method, a real experiment was conducted on Beijing-Shenyang high-speed railway. The experimental results show that the length difference between the calculated moving baseline and the reference is less than 1.5 m in both scenarios, which further prove the effectiveness of the proposed TIM method. Keywords TIM · GNSS · DD carrier phase · Moving baseline · Kalman filter

W. Jiang (B) · Y. Liu · D. Liu · B. Cai · J. Wang School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China e-mail: [email protected] Y. Liu e-mail: [email protected] D. Liu e-mail: [email protected] B. Cai e-mail: [email protected] J. Wang e-mail: [email protected] W. Jiang · B. Cai · J. Wang Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transportation, Beijing 100044, People’s Republic of China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_61

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1 Introduction Train integrity monitoring system (TIMS) is an important part of train operation control system. Before a train enters a block section, it must be ensured that the previous train has already cleared without leaving any carriages. Currently, several solutions have been proposed to monitor train integrity for different train control systems. Train integrity function is determined by track circuits for Chinese Train Control System (CTCS) [1]. This approach is safe, but the primary limitation is its high setup and maintenance costs for track circuits. Unlike the CTCS, Incremental Train Control System (ITCS) is based on an independent end of train device, which compares wind pressure of the end of train with standard wind pressure value to determine train integrity. However, the wind pressure is detected at a certain rate, therefore the real-time train integrity monitoring (TIM) cannot be guaranteed [2]. In European Rail Track Management System (ERTMS-ETCS) Level 3 and Next Generation Train Control (NGTC) system, trains are required to monitor train integrity by on-board unit without track circuits [3]. Hence, it is necessary to introduce a TIM method to reduce the reliance on track circuits. In recent years, Global Navigation Satellite System (GNSS) has been applied in railway applications especially in train location. GNSS can provide global, allweather, high-precision and real-time positioning results. Due to its positioning advantages, GNSS is suitable to be applied to monitor train integrity. The common TIM method based on GNSS is achieved by calculating the real-time length of the train using pseudo-range measurement, which is the distance between the two GNSS antennas placed at the head and end of train [4, 5]. The calculated length is compared with the real length of the train. If the length difference is within the margin of error, the train is thought to be integrated and vice versa [6]. This TIM method based on GNSS pseudo-range, not only obtain the in real-time train integrity status, but also is independent of the wayside equipment. The general measurements of GNSS include pseudo-range and carrier phase. Compared with pseudo-range, carrier phase performs higher positioning accuracy. To further obtain accurate length of the train, a novel TIM method based on GNSS carrier phase moving baseline is proposed in this paper. The single-difference (SD) carrier phase between the two GNSS antennas is first calculated to eliminate errors caused by the propagation path including ionospheric and tropospheric errors, as well as satellite clock biases. To further improve the accuracy of the carrier phase measurement, the double-difference (DD) algorithm between the other satellites and the reference satellite is introduced to mitigate the receiver clock biases. Then the DD carrier phase difference is input as measurements to Kalman filter, which is used to estimate relative position, relative velocity and integer ambiguity. Based on the estimated relative position, the final moving baseline length is obtained to further compare with the reference length. In addition, the proposed TIM method is proved to be able to judge the train integrity status according to the real experiment. In this paper, we make a step forward to the on-board TIM solution to focus our contribution on the proposed TIM method. The proposed on-board TIM method

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has the advantages of convenient operation and low maintenance cost compared with traditional TIM mode such as the track circuit. In addition, the accuracy is significantly improved compared to the results of directly satellite positioning.

2 DD Carrier Phase Algorithm GNSS is able to provide position and time information when four or more satellites are tracked. GNSS positioning accuracy is typically affected by propagation errors, like ionospheric and tropospheric errors, as well as clock errors including satellite and receiver. Compared with GNSS pseudo-range processing, GNSS carrier phase measurement is also affected by integer ambiguity. Thus, GNSS carrier phase measurement equation can be written as: φ i = λ−1 (r i − I i + T i ) + f (δt − dt i ) + N i + εi

(1)

where φ i is the carrier phase measurement of the ith satellite; λ is wavelength of carrier signal; r i represents the real distance between satellite and receiver; I i is the ionospheric delay; T i is the tropospheric delay; f is carrier frequency; δt is receiver clock error; dt i is satellite clock error; N i is integer ambiguity, and εi is residual errors ignored in this paper [7]. The satellite clock error, ionospheric and tropospheric errors may be estimated, or eliminated using measurement differencing. The SD carrier phase measurement between the rover and base antennas is adopted to eliminate satellite clock error, ionospheric and tropospheric errors. In the SD processing, the carrier phase difference between rover and base receiver for the same satellite is taken as the measurement. Hence, the SD carrier phase measurement equation can be written as: φri b = λ−1rri b + f δtr b + Nri b

(2)

where subscripts r and b represent rover antenna and base antenna respectively. To further mitigate receiver clock errors, the DD carrier phase is calculated based on the SD carrier phase measurement. In the DD processing, the jth satellite is chosen as reference, and carrier phase differences between other satellites and reference satellite are calculated. Therefore, the DD carrier phase measurement equation can be written as: φr b = λ−1rr b + Nr b ij

ij

ij

ij

where rr b denotes distance difference between satellites and receivers.

(3)

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Comparing Eqs. (1) and (3), it can be seen that the DD carrier phase eliminates the satellite clock error, the receiver error, ionospheric and tropospheric errors. Only integer ambiguity and distance difference need to be considered to achieve accurate relative position solution.

3 Relative Position Solution and TIM System Architecture Since the Kalman filter is recursive, only the measurement information at this moment is used to estimate the state vector. Hence, the Kalman filter is used to estimate the relative position epoch by epoch.

3.1 Kalman Filter Model for Relative Position The system model is written as: Xk = AXk−1 + Qk

(4)

where Xk is system state vector; A is state transition matrix and Qk is the system processing noise. The system state vector Xk consists of 6+(n −1) system states, including relative position and velocity in three directions, as well as the DD integer ambiguity. The system state is:   j ˙ y ˙ z ˙ Nr1bj Nr2bj · · · Nr(n−1) XkT = x y z x b

(5)

where (x, y, z) is the relative position between base and rover antennas ˙ y, ˙ z) ˙ represents the designed as constant velocity model in this paper; (x, relative velocity, which is assumed to be first-order Gauss Markov processes, and 1j 2j (n−1) j ) denotes the DD integer ambiguity. (Nr b , Nr b , · · · , Nr b The state transition matrix A can be written as: ⎤ ⎡ I3×3 T · I3×3 03×(n−1) (6) A = ⎣ 03×3 I3×3 03×(n−1) ⎦ 0(n−1)×3 0(n−1)×3 I(n−1)×(n−1) where time interval is T = 0.1s. The system noise matrix Qk is calculated as [8]:  Qk = diag 01×3

2∗T 2 2∗T 2 2∗T 2 τ τ τ

where τ is the correlation time constant.

01×(n−1)

(7)

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The system observation model is: Zk = Hk Xk + Vk

(8)

where Zk is the system observation vector; Hk is the measurement matrix; Vk is the measurement noise; The measurement noise Vk is assumed to be zero-mean white sequences uncorrelated, and its covariance matrix is recorded as R. The system observation vector Zk can be written as:   (n−1) j 1j 2j ZTk = − φrb φrb . . . φrb

(9)

The measurement matrix Hk is calculated as: Hk = [ l(n−1)×1 m(n−1)×1 q(n−1)×1 0(n−1)×3 − λ · I(n−1)×(n−1) ]

(10)

where (l, m, q) consists of n − 1 differences of cosine; I is an order identity matrix. Noise covariance matrix R can be written as: ⎡

2 ⎢1 ⎢ R = 2σ 2 ⎢ . ⎣ ..

1 2 .. .

··· ··· .. .

⎤ 1 1⎥ ⎥ .. ⎥ .⎦

(11)

1 1 ··· 2 where parameter σ is the carrier phase measurement noise standard deviation of signal L1, and it is 0.0008 m [8]. Kalman filtering includes two different information update processes: time update and measurement update [9]. The time update process can be written as: Pk−

Xk− = AXk−1 = APk−1 AT + Qk

(12)

The measurement update process can be written as: ⎧ − − ⎨ Kk = Pk HT (HPk HT + R)−1 − X = Xk + Kk (Zk − HX− k ) ⎩ k Pk = (I − Kk H)Pk−

(13)

The time update process is a prediction of the state vector and the measurement update process is a correction for the prediction. The state vector Xk of each epoch is estimated by the time update process and the measurement update process. Then the relative position of the state vector is used to calculate the length of moving baseline and perform TIM.

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head antenna

SD

Carrier phase end antenna

SD carrier phase between head and end antenna

Carrier phase Eliminate satellite clock ionospheric and tropospheric delay errors

Satellite position

DD DD carrier phase between reference and remaining satellites

Eliminate receiver clock error

YES

H

Zk

Normal

Head or end antenna position

Kalman Filter

X [relative position, velocity, DD integer ambiguity]

L - reference length ≤ ?

Moving baseline length L

Abnormal and Alert

NO

Xk

1

Pk

1

A Qk R

Fig. 1 Train integrity monitoring system architecture based on moving baseline

3.2 TIMS Architecture Based on GNSS Moving Baseline The architecture of TIMS based on GNSS moving baseline is shown in Fig. 1. As indicated, the TIMS consists of four steps: SD solution, DD solution, moving baseline length calculation and train integrity judgment. Step 1: The SD carrier phase solution between two antennas eliminates carrier phase propagation errors including satellite clock error, ionospheric and tropospheric errors using Eq. (2). Step 2: The DD carrier phase solution between reference satellite and remaining satellites is adopted to further eliminate receiver clock error according to Eq. (3). Step 3: The Kalman filter is applied as system filter to estimate relative position, relative velocity and DD ambiguity using Eqs. (4–13). Then the length of moving baseline is calculated by relative position. Step 4: The calculated baseline length is compared with reference length of dual antennas. If the difference between them exceeds the given threshold η, the train may have a decoupling fault. Otherwise, the train is normal. Based on the proposed TIMS, train integrity can be monitored in real-time only relying on on-board equipment.

4 Experiment In order to verify the performance of the proposed TIM method, a real experiment was carried out on Beijing-Shenyang high-speed railway in June, 2018. The test route is about 78 km from Heishanbei to Shenyangxi Railway Station. The speed of test train is about 300 km/h and test time is about 30 min. Figure 2 shows the test train trajectory. The test train is the China Railway (CR) train including eight carriages as shown in Fig. 3a, and the two GNSS antennas were setup on the top of head and end carriages

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Fig. 2 The test train trajectory

HEAD NovAtel OEM6 GNSS receiver

(a) The test train

(b) NovAtel OEM6 GNSS receiver

END UR380 GNSS receiver

(c) UR380 GNSS receiver

Fig. 3 Test train on-board equipment

repressively. The static distance between the two antennas is 186.9 m, which is used as reference for our experiment. The UR380 GNSS receiver and the NovAtel OEM6 GNSS receiver were set in the corresponding carriages of two antennas as shown in Fig. 3b, c. Both the two GNSS receivers are output at a rate of 10 Hz. The experimental results were analyzed in two scenarios including fixed satellites and changed satellites scenarios. In the fixed satellite scenario, the visible satellite remains completely unchanged. Correspondingly, the pseudo random noise code (PRN) number of visible satellites changes in changed satellites scenario. (1) Performance in fixed satellites scenario Figure 4 shows the comparison results between the calculated moving baseline and reference length in fixed satellites scenario. The green dotted line represents the reference, and the blue line is the absolute length of moving baseline. It can be seen that the calculated length of the moving baseline changes frequently. To make the error clear, the difference between calculated length and reference is calculated and marked in red. The maximum offset is about 0.3 m, which indicates that the proposed method shows a good performance in terms of accuracy in fixed satellite scenario.

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Fig. 4 Comparison between moving baseline length and reference in fixed satellites scenario

(2) Performance in changed satellites scenario Figure 5 shows the comparison results between the calculated moving baseline and reference in changed satellites scenario. It can be seen that the maximum offset is close to 1.5 m and the minimum offset is about 0.2 m. Compared to the fixed satellites scenario, the difference between the calculated moving baseline length and the reference in changed satellites scenario has an obvious increase about 1 m. Due to the frequent change of the visible satellites in changed satellites scenario, the relevant matrix dimension of the Kalman filter also changes. The state vector matrix Xk and the corresponding covariance matrix Pk need to be reinitialized when the visible satellites change. However, the reinitialized matrices are in low accuracy compared with fixed satellites scenario, which results in the increased difference. According to the above analysis, the proposed TIM method is able to provide effective moving baseline length in both fixed and changed satellites scenarios. Compared with the reference, the train integrity status can be obtained in real time. The accuracy of positioning is related to the distribution state of satellites. And the Position Dilution of Precision (PDOP) value can reflect the distribution of the satellites. The better the satellite distribution, the higher the positioning accuracy. In general, the satellites are considered to be in good distribution when the PDOP value is less than 3.

Fig. 5 Comparison between moving baseline length and reference in changed satellites scenario

A Train Integrity Monitoring Method Based on GNSS Moving …

661

Figure 6 shows the PDOP, visible satellites number, and PRN number of the reference satellite in the experimental period. It can be seen that the number of visible satellites changes frequently in the experiment process. In most cases, there are eight satellites and the corresponding PDOP value is less than 3. The PRN change of the reference satellite is marked in green, and the abrupt parts indicate that the reference satellite has changed. To make the moving baseline in three directions clear, the relative position is calculated in Single Point Position (SPP) model and used as a reference. Figure 7 shows the comparison results of relative position between moving baseline and SPP. The blue-green line is relative position in SPP. The magenta line is the results based on moving baseline. As indicated in Fig. 7, relative position changes significantly, especially in Y and Z direction. The change trends of moving baseline and SPP results are almost same to each other. However, it is clear that the results in moving baseline are more stable than SPP when the satellites change frequently.

Fig. 6 PDOP, visible satellites number, and PRN number of the reference satellite on test line

Fig. 7 Comparison of relative position based on moving baseline and based on SPP

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5 Conclusion This paper proposes a feasible approach for TIM based on GNSS moving baseline. In order to eliminate measurement biases, the carrier phase difference method is introduced and used to calculate the accurate length of moving baseline. The SD carrier phase between the two antennas is applied to mitigate the ionospheric, tropospheric delay and satellite clocks biases. And the DD carrier phase between the satellites further eliminates the receiver clock errors. The real-time length of the moving baseline is calculated in Kalman filter and compared with reference length to monitor train integrity. In addition, the experiment was carried out on Beijing-Shenyang highspeed railway to prove the effectiveness of the proposed TIM method. The results show that the error of the moving baseline length is less than 1.5 m, and the proposed TIM method is able to monitor train integrity without reliance on the wayside equipment. Acknowledgements This work was supported in part by the Beijing Natural Science Foundation under Grant 4184096 and the National Natural Science Foundation of China under Grant 61703034.

References 1. Zhang, S.G.: General Technical Scheme of CTCS-3 Train Control System. China Railway Publishing House Press, Beijing (2008) 2. Li, S., Cai, B.G., Shangguan, W., Schnieder, E., Toro, F.G.: Switching LDS detection for GNSSbased train integrity monitoring system. J. IET Intell. Trans. Syst. 11(5), 299–307 (2017) 3. Guo, J., Zhang, Y.D., Wang, C.H.: Outlook and thoughts on next generation train control system in china. J. Railw. Trans. Economy. 38(6), 23–28 (2016) 4. Chen, X.Q., Wang, J., Cai, B.G.: Research of GPS application in train integrity monitoring. J. Beijing Jiaotong Univ. 30(2), 69–71 (2006) 5. Neri, A., Rispoli, F., Salvatori, P., Vegni, A.M.: A train integrity solution based on GNSS doubledifference approach. In: 27th International Technical Meeting of the Satellite Division of the Institute of Navigation, pp. 34–50. ION Press, Tampa (2014) 6. An, Y., Cai, B.G., Ning, B., Wang, J., Shangguan, W.: Research on train integrity monitoring method based on GPS and virtual-satellite. J. China Railw. Soc. 34(9), 40–44 (2012) 7. Zheng, J.S.: A Study and Design of Dual-Antenna GPS/INS Integrated Navigation System. Zhejiang University (2017) 8. Liu, T.: Research on Double Antenna GPS Attitude Measurement Technology. Northwestern Polytechnical University (2012) 9. Dong, X.R., Tao, D.X.: An efficient Kalman filtering algorithm and its application in kinematic GPS data processing. J. Acta Geod. et Cartographica Sinica 26(3), 223–227 (1997)

Generalized Extended Stochastic Gradient Algorithm Implemented Parameter Identification for Complex Multivariable-Systems Wei Wang

Abstract In this paper, a new recognition method is deduced based on the theory of model equivalence in order to modify the parameter estimation for the multi-input nonlinear equation-error autoregressive moving average(Multi-variable) system. Using the theory of model equivalence, using the auxiliary model to handle the colored noise, the proposed algorithm reduces the number of unknown noise items in the recognition model information vector and achieves better recognition accuracy. For comparison, we use the recursive generalized extended least squares (RGELS) algorithm. To confirm the effectiveness of the algorithm, an example is shown. Keywords Multi-variable system · Stochastic gradient algorithm · Model equivalence · Parameter estimation

1 Introduction For many years, more and more recognition methods have been developed for linear and single-variable systems, such as the least squares identification methods [1], the auxiliary model identification methods [2], the iterative estimation methods [3], the stochastic gradient methods [4], the maximum likelihood identification methods [5], the multi-innovation identification methods [6], etc. With the development of system modeling, many new multivariable models have been established. Some algorithms have been discussed on the estimation of new multivariable models. Bao et al. presented a least squares based iterative parameter algorithm for multivariable CARMA system [7]. Ding derived a hierarchical least squares based iterative algorithm to estimate the parameters of the multivariable CARMA-like system [8]. Ding presented a iterative least squares parameter estimation algorithms for multiple-input-outputerror systems with autoregressive noise [9]. In this paper, we will extend the classical W. Wang (B) Economy and Information Technology Department, Zaozhuang Vocational College, Shandong 277000, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_62

663

664

W. Wang

stochastic gradient identification algorithm from linear systems to nonlinear multivariable systems and discuss the identification problem of Multi-variable system. Multi-variable system is a commonly used model for describing the systems in industry, such as molecular distillation system and river flow calculation system [10]. It is always a challenge problem for estimating the parameters of the Multi-variable system, which is nonlinear and disturbed by colored noise. This paper adopts the algorithm of the cocoon layer upon layer peeling with which one complex system can be decomposed step by step into many relatively simple systems for identification, respectively. Thereby, the extended algorithm is used to deal with the moving average system and the autoregressive system can be solved by generalized algorithm. The idea of assistant model recognition is used to deal with the case where the information vector contains unknown intermediate variables, and the iterative identification method make sufficient use of the nonlinear system [11]. So we propose the generalized extended stochastic gradient (GESG) algorithm for Multi-variable system. The rest of this paper is shown below. Section 1 gives the identification model for Multi-variable system. Section 2 gives the GESG algorithm for Multi-variable system. Section 3 to confirm the effectiveness of the algorithm, an example is shown. Final conclusion are given in Sect. 4. Let us define some notations: “S =: X ” or “X := S” stands for “S is defined as X ”. The norm of matrix X is defined as X2 := tr[X X T ]. Consider the following Multi-variable system: A(z)y(t) =

r 

B j (z)u j (t) +

j=1

r 

E j (z)u j (t)u j (t − j) +

j=1

D(z) v(t), C(z)

(1)

where u(t) = [u 1 (t), u 2 (t), u 3 (t), · · · , u r (t)]T ∈ Rr is the system input vector, y(t) is the system output sequence, v(t) is the random white noise sequence with zero mean, z −1 is the unit backward shift operator for [z −1 y(t) = y(t − 1), zy(t) = y(t + 1)], A(z), B j (z), C(z), D(z) and E j (z) are polynomials in z −1 A(z) := 1 + a1 z −1 + a2 z −2 + a3 z −3 + · · · + ana z −na ∈ Rna , B j (z) := b j1 z −1 + b j2 z −2 + · · · + b jn j z −n j ∈ Rr n j , C(z) := 1 + c1 z −1 + c2 z −2 + c3 z −3 + · · · + cn c z −n c ∈ Rn c , D(z) := 1 + d1 z −1 + d2 z −2 + d3 z −3 + · · · + dn d z −n d ∈ Rn d , E j (z) := e j1 z −1 + e j2 z −2 + · · · + e jn j z −n j ∈ Rr n j , j = 1, 2, · · · , r. Assume that the orders n a , n c , n d , n j and r are known, when t  0, y(t) = 0, u(t) = 0, v(t) = 0. Define the intermediate colored noise: D(z) v(t) C(z) = [1 − C(z)]w(t) + [D(z) − 1]v(t) + v(t).

w(t) :=

(2)

Generalized Extended Stochastic Gradient Algorithm Implemented …

665

Define the parameter vectors θ := [θ Ts , θ Tn ]T ∈ Rn , n := n a + n c + n d + 2r n j , θ s := [θ Ty , θ Tu ]T ∈ Rna +2r n j , θ n := [c1 , c2 , c3 , · · · , cn c , d1 , d2 , d3 , · · · , dn d ]T ∈ Rn c +n d , θ y := [a1 , a2 , · · · , ana ]T ∈ Rna , θ u := [θ 1 , θ 2 , · · · , θ i ]T ∈ R2r n j , θ i := [bi1 , bi2 , · · · , bin j , ei1 , ei2 , · · · , ein j ] ∈ R2n j , i = 1, 2, · · · , r, and information vectors ϕ(t) := [ϕ Ts (t), ϕ Tn (t)]T ∈ Rn , ϕ s (t) := [ϕ Ty (t), ϕ Tu (t)]T ∈ Rna +2r n j , ϕ n (t) := [−w(t − 1), −w(t − 2),−w(t − 3), · · · ,−w(t − n c ), v(t − 1), v(t − 2), v(t − 3), · · · , v(t − n d )]T ∈ Rn c +n d , ϕ y (t) := [−y(t − 1), −y(t − 2), · · · , −y(t − n a )]T ∈ Rna , ϕ u (t) := [ϕ T1 (t), ϕ T2 (t), · · · , ϕ iT (t)]T ∈ R2r n j , ϕ i (t) := [u i (t − 1), u i (t − 2), · · · , u i (t − n j), u i (t − 1)u i (t − i − 1), u i (t − 2)u i (t − i − 2), · · · , u i (t − n j )u i (t − i − n j )]T ∈ R2n j . then we have A(z)y(t) =

nj 

[b1i u 1 (t − i) + b2i u 2 (t − i) + · · · + bri u r (t − i)]

i=1 nj

+



[e1i u 1 (t − i)u 1 (t − i − 1) + e2i u 2 (t − i)u 2 (t − i − 2) + · · ·

i=1

+ eri u r (t − i)u r (t − i − r )] + w(t) = ϕ Tu (t)θ u + w(t) = ϕ Tu (t)θ u + [1 − C(z)]w(t) + [D(z) − 1]v(t) + v(t) = ϕ Tu (t)θ u + ϕ Tn (t)θ n + v(t). or y(t) = [1 − A(z)]y(t) + ϕ Tu (t)θ u + ϕ Tn (t)θ n + v(t) = ϕ Ty (t)θ y + ϕ Tu (t)θ u + ϕ Tn (t)θ n + v(t) = ϕ Ts (t)θ s + ϕ Tn (t)θ n + v(t) = ϕ T (t)θ + v(t).

(3)

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W. Wang

Suppose that θˆ (t) is the estimate of θ at time t, 1/r (t) is convergence factor or step size. For the system identification model in (3), we can define gradient criterion function: 1 (4) J (θ ) := [y(t) − ϕ T (t)θ]2 . 2 According to the negative gradient search, minimizing J (θ ), we can get 1 ˆ − 1))] grad[J (θ(t θˆ (t) = θˆ (t − 1) − r (t) ϕ(t) ˆ − 1)], grad[y(t) − ϕ T (t)θ(t = θˆ (t − 1) − r (t) r (t) = r (t − 1) + ϕ(t)2 , r (0) = 1.

(5) (6)

2 The GESG Algorithm for Multi-variable System The information vector contains the unmeasurable noise items w(t − i) and v(t − i), so it is impossible to obtain estimate θ(t). We adopt the auxiliary model idea to solve this problem, replace the unknown variables with their estimates, and list the details as follows. Let w(t) ˆ be the estimate of w(t) and v(t) ˆ be the estimate of v(t), referring to the definition of ϕ(t), using the estimates w(t ˆ − i) and v(t ˆ − i) instead of w(t − i) and v(t − i), constructing the estimates of ϕˆ w (t) and ϕˆ v (t): ˆ ϕ(t) := [ϕ Ts (t), ϕˆ Tn (t)]T ∈ Rn , ϕˆ n (t) := [−w(t ˆ − 1), −w(t ˆ − 2), −w(t ˆ − 3), · · · , −w(t ˆ − n c ), v(t ˆ − 1), T n c +n d v(t ˆ − 2), v(t ˆ − 3), · · · , v(t ˆ − n d )] ∈ R . From (2), we have w(t) = ϕ Tn (t)θ n + v(t) = y(t) − ϕ Ts (t)θ s .

(7)

Replacing the θ s in (7) with its estimate θˆ s (t), the estimate of w(t) can be computed by (8) w(t) ˆ = y(t) − ϕ Ts (t)θˆ s (t). using (3), gives v(t) = y(t) − ϕ T (t)θ.

(9)

ˆ Replacing the unknown ϕ(t) and θ in (9) with their estimates ϕ(t) and θˆ (t), the estimate of v(t) can be calculated by

Generalized Extended Stochastic Gradient Algorithm Implemented …

667

ˆ v(t) ˆ = y(t) − ϕˆ T (t)θ(t) T T = y(t) − [ϕ Ts (t), ϕˆ Tn (t)][θˆ s (t), θˆ n (t)]T = y(t) − ϕ T (t)θˆ s (t) − ϕˆ T (t)θˆ n (t)

= w(t) ˆ −

s ϕˆ Tn (t)θˆ n (t)

n

ˆ Replacing the ϕ(t) in (5) and (6) with its estimate ϕ(t), we can obtain the GESG algorithm for estimating the Multi-variable system parameter vector θ : ˆ 1 ϕ(t) θˆ (t) = θˆ (t − 1) + ε e(t), < ε  1, r (t) 2 ˆ − 1), e(t) = y(t) − ϕˆ T (t)θ(t ˆ r (t) = r (t − 1) + ϕ(t) , ˆ ϕ(t) = [ϕ Ts (t), ϕˆ Tn (t)]T , ϕ s (t) = [ϕ Ty (t), ϕ Tu (t)]T , 2

ϕ y (t) = [−y(t − 1), −y(t − 2), · · · , −y(t − n a )]T , ϕ u (t) =

[ϕ T1 (t), ϕ T2 (t), · · ·

, ϕ iT (t)]T ,

(10) (11) (12) (13) (14) (15) (16)

ϕ i (t) = [u i (t − 1), u i (t − 2), · · · , u i (t − n j), u i (t − 1)u i (t − i − 1), u i (t − 2)u i (t − i − 2), · · · , u i (t − n j )u i (t − i − n j )]T , (17) ϕˆ n (t) = [−w(t ˆ − 1), −w(t ˆ − 2), −w(t ˆ − 3), · · · , −w(t ˆ − n c ), v(t ˆ − 1), v(t ˆ − 2), v(t ˆ − 3), · · · , v(t ˆ − n d )]T , w(t) ˆ = y(t) − ϕ Ts (t)θˆ s (t), ˆ = w(t) v(t) ˆ = y(t) − ϕˆ T (t)θ(t) ˆ − ϕˆ Tn (t)θˆ n (t), θˆ (t) =

T T [θˆ s (t), θˆ n (t)]T .

(18) (19) (20) (21)

The ε in (10) is the convergence index. To calculate the parameter estimation vector θˆ (t), the GESG algorithm is used from (10) to (21): ˆ − i) = 1. Let t = 1, take ε. Set the initial values θˆ (0) = 1n / p0 , r (0) = 1, w(t ˆ − i) = 1/ p0 , i = 1, 2, · · · , max[n c , n d ], p0 = 106 , 1n is an 1/ p0 , v(t n-dimensional column vector representing element 1. 2. Collect input and output data u 1 (t), u 2 (t), · · · , u r (t), y(t) and form ϕˆ n (t), ϕ u (t), ˆ using (13) to (18). ϕ y (t), ϕ s (t), ϕ(t) 3. Compute e(t) using (11), compute r (t) using (12). 4. Using (10) to update the parameter estimate vector θˆ (t). ˆ and w(t) ˆ using (19) to 5. Read θˆ n (t) and θˆ s (t) from θˆ (t) in (21), compute v(t) (20). 6. Increase t by 1, go to step 2.

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W. Wang

3 Example Consider the following Multi-variable system: A(z)y(t) =

r 

B j (z)u j (t) +

j=1

r 

E j (z)u j (t)u j (t − j) +

j=1

D(z) v(t), C(z)

−1

A(z) = 1 − 1.620z + 0.994z −2 , B1 (z) = 0.106z −1 + 0.185z −2 , B2 (z) = 0.079z −1 + 0.057z −2 , C(z) = 1 − 0.276z −1 , D(z) = 1 + 0.270z −1 , E 1 (z) = 0.088z −1 + 0.195z −2 , E 2 (z) = −0.013z −1 − 0.044z −2 . the parameter vector to be estimated is θ = [a1 , a2 , b11 , b12 , e11 , e12 , b21 , b22 , e21 , e22 , c1 , d1 ]T = [−1.620, 0.994, 0.106, 0.185, 0.088, 0.195, 0.079, 0.057, −0.013, −0.044, −0.276, 0.270]T . In the simulation experiment, the input {u 1 (t)} and {u 2 (t)} are independent continuous excitation signal sequences with zero mean and unit variance, and {v(t)} as a white noise sequence with mean zero and variance σ 2 = 0.202 , respectively. Apply the RGELS algorithm and the GESG algorithm to identify this Multivariable system, the parameter estimates and errors are shown in Tables 1 and 2, the parameter estimation error δ versus t is shown in Figs. 1 and 2. The GESG algorithm is applied to estimate the parameters of this Multi-variable system, the parameter estimates aˆ i (t), bˆi (t), cˆi (t), dˆi (t) and eˆi (t) versus t are shown in Fig. 3 . From Tables 1 and 2 and Figs. 1 and 2, we can see the following analysis result. 1. The parameter estimation errors δ become smaller with the increasing of the data t length—see Fig. 2. 2. The GESG algorithm converges very fast. The parameter estimation errors δ can reach thirty percent after 50-step and eleven percent after 500-step—see Table 2. 3. Compared with the RGELS algorithm, the GESG algorithm give the parameter estimates of converge to the true values more accurately—see Tables 1 and 2. 4. The proposed algorithm can deal with the identification case where the information vector contains unknown intermediate variables.

a2

0.79916

0.99708

1.00898

1.01685

1.00628

1.00037

0.99952

0.99789

0.99699

0.99688

0.99624

0.99400

a1

−1.63819

−1.55438

−1.61938

−1.63475

−1.62943

−1.62569

−1.62454

−1.62459

−1.62296

−1.62318

−1.62275

−1.62000

t

10

20

50

100

200

500

1000

2000

3000

4000

5000

True values

0.10600

0.12613

0.12819

0.12499

0.12116

0.13450

0.13875

0.13933

0.14316

0.16325

0.19074

0.51604

b11

0.18500

0.12736

0.12568

0.13279

0.12531

0.12901

0.13522

0.13288

0.16793

0.14863

0.24359

0.41700

b12

0.08800

0.12601

0.12806

0.12487

0.12104

0.13437

0.13861

0.13919

0.14302

0.16309

0.19056

0.51553

e11

0.19500

0.12723

0.12556

0.13266

0.12518

0.12888

0.13509

0.13275

0.16776

0.14848

0.24335

0.41658

e12

Table 1 The RGELS estimates and errors(σ 2 = 0.202 , δns = 67.375%)

0.07900

0.04524

0.05379

0.06584

0.05380

0.02980

−0.00882

0.03842

−0.08434

0.10758

0.60982

−1.05933

b21

0.05700

0.00136

−0.01428

−0.04155

−0.02759

−0.01984

0.00877

0.00429

0.12293

0.10284

−0.20588

−1.53460

b22

−0.01300

−0.00488

−0.00580

−0.00710

−0.00580

−0.00321

0.00095

−0.00415

0.00910

−0.01161

−0.06581

0.11433

e21

−0.04400

−0.00015

0.00154

0.00449

0.00298

0.00214

−0.00095

−0.00046

−0.01327

−0.01110

0.02222

0.16562

e22

−0.27600

−0.27405

−0.26016

−0.25995

−0.21616

−0.18304

−0.22477

−0.14551

−0.23217

−0.23484

−0.10452

−0.70215

c1

0.27000

0.25376

0.26452

0.25999

0.29808

0.31810

0.30944

0.36540

0.39711

0.62783

0.52180

−1.54767

d1

6.48855

6.93392

7.36803

7.91570

9.10374

8.20890

10.55968

12.11508

19.46187

35.19394

142.67964

δ (%)

Generalized Extended Stochastic Gradient Algorithm Implemented … 669

a2

−0.01713

0.33190

0.77201

0.91940

0.98253

0.98326

0.99265

0.98442

0.99420

0.99465

0.99116

0.99400

a1

−0.78768

−0.96843

−1.33353

−1.52049

−1.57635

−1.62214

−1.61552

−1.62101

−1.62198

−1.61644

−1.62035

−1.62000

t

10

20

50

100

200

500

1000

2000

3000

4000

5000

True values

0.10600

0.08057

0.08517

0.09098

0.09906

0.11915

0.13717

0.15054

0.15938

0.19408

0.16894

0.18045

b11

0.18500

0.18315

0.19392

0.21069

0.23144

0.27370

0.31828

0.36170

0.39076

0.42745

0.40761

0.56759

b12

0.08800

0.08359

0.08836

0.09440

0.10278

0.12362

0.14232

0.15619

0.16536

0.20136

0.17527

0.18722

e11

0.19500

0.19002

0.20119

0.21859

0.24013

0.28397

0.33022

0.37527

0.40542

0.44348

0.42290

0.58888

e12

Table 2 The GESG estimates and errors (σ 2 = 0.202 , δns = 67.375%)

0.07900

0.05877

0.06278

0.06901

0.07593

0.09326

0.11812

0.15084

0.16875

0.20635

0.19837

0.36047

b21

0.05700

0.06581

0.06743

0.07042

0.07646

0.08923

0.09744

0.10075

0.10449

0.08993

0.08671

0.04937

b22

−0.01300

−0.04233

−0.04522

−0.04971

−0.05469

−0.06717

−0.08507

−0.10864

−0.12154

−0.14863

−0.14288

−0.25964

e21

−0.04400

−0.04740

−0.04856

−0.05072

−0.05507

−0.06427

−0.07018

−0.07257

−0.07526

−0.06478

−0.06245

−0.03555

e22

−0.27600

−0.27202

−0.27398

−0.27752

−0.28082

−0.28879

−0.29772

−0.31017

−0.31327

−0.29801

−0.13105

0.06865

c1

0.27000

0.26890

0.27104

0.27467

0.27850

0.28657

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4 Conclusions This paper proposes a GESG algorithm for estimating the parameters of Multivariable system by using the auxiliary model identification idea. The simulation datas show that the algorithm is effective. On the basis of the research results in this paper, other identification methods can also be used to estimate the parameters of this system, like the recursive generalized extended least squares algorithm [12], the multi-innovation generalized extended least squares algorithm [13], the decomposition based GESG algorithm, the decomposition based recursive generalized extended least squares algorithm, the filtering based GESG algorithm, the filtering based multi-innovation GESG algorithm [14] and so on. Similar examples of Multi-variable system are existed in the areas of technology of multi-core processors. The multi-core processor technology is increasingly mature, but still have some technical bottlenecks, like parallel processing ability of the program [15]. Perhaps in the future, system identification can solve the technical bottleneck of multi-core processors.

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References 1. Hu, Y.B., Liu, B.L., Zhou, Q., Yang, C.: Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circuits, Syst. Signal Process. 33(2), 655–664 (2014) 2. Ding, F.: System Identification—New Theory and Methods. Science Press, Beijing (2013) 3. Ge, Z.W., Ding, F., Xu, L., Alsaedi, A., Hayat, T.: Gradient-based iterative identification method for multivariate equation-error autoregressive moving average systems using the decomposition technique. Circuits J. Frankl. Inst. 356 (2019). https://doi.org/10.1016/j.jfranklin.2018.12.002 4. Wang, Z.Y., Wang, Y., Ji, Z.C.: Filtering based multi-innovation extended stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 39(18), 5724– 5732 (2015) 5. Wang, W., Li, J.H., Ding, R.F.: Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models. Int. J. Comput. Math. 88(16), 3458–3467 (2011) 6. Ding, F.: System Identification—Multi-Innovation Identification Theory and Methods. Science Press, Beijing (2016) 7. Bao, B., Xu, Y.Q., Sheng, J., Ding, R.F.: Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data. Math. Comput. Model. 53(9), 1664–1669 (2011) 8. Ding, F.: Hierarchical parameter estimation algorithms for multivariable systems using measurement information. Inf. Sci. 277, 396–405 (2014) 9. Ding, J.L.: Recursive and iterative least squares parameter estimation algorithms for multipleinput-output-error systems with autoregressive noise. Circuits, Syst. Signal Process. 37(5), 1884–1906 (2018) 10. Chen, K.: Multiple-input single-output linear function model application in the calculus of river flow. Sichuan Water Power 45(3), 69–73 (1994) 11. Jin, Q.B., Wang, Z., Liu, X.P.: Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements. J. Process. Control. 35(11), 154–168 (2015) 12. Liu, Q.Y., Ding, F.: Auxiliary model-based recursive generalized least squares algorithm for multivariate output-error autoregressive systems using the data filtering. Circuits Syst. Signal Process. 38 (2019). https://doi.org/10.1007/s00034-018-0871-z 13. Ding, F., Liu, X.P., Liu, G.: Multi-innovation least squares identification for linear and pseudolinear regression models. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 40(3), 767–778 (2010) 14. Mao, Y.W., Ding, F.: Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory. Int. J. Comput. Math. 93(11), 1869–1885 (2016) 15. Kim, C.G., Kim, J.G., Lee, D.H.: Optimizing image processing on multi-core CPUs with Intel parallel programming technologies. Multimed. Tools Appl. 68(2), 237–251 (2014)

Reinforcement Learning on Robot with Variational Auto-Encoder Yiwen Chen, Chenguang Yang and Ying Feng

Abstract Reinforcement learning enables robot to learn plentiful skills through training. The control based on end-to-end reinforcement learning output joint angle to the robot with image as input. However, using the deep network for end-to-end reinforcement learning makes it hard to converge and need much training time. And it’s also difficult to expand to other tasks because of custom-designed network. In this paper, we propose a reinforcement learning structure with variational autoencoder that can be applied to different goals and reduce training time. Firstly the auto-encoder is trained with images that capture random robot actions. Then the reinforcement learning network is trained with the latent space vectors from autoencoder instead of raw image. After finish training, the robot can reach a state similar to the state in expected image that we input. Keywords Reinforcement learning · Variational auto-encoder · Goal

1 Introduction In the last few years, deep reinforcement learning(RL) has become popular since DeepMind created AlphaGo to master the game of Go based on reinforcement learning [1]. Reinforcement learning can be used in different fields, including video games [2], system control [3] and optimization [4]. Moreover, the application of RL in robots is increasing. RL enables robot to have the power to learn special skills through training. In one way, it can be used for tracking and navigation of mobile robots [5]. In another way, it can also be used for intelligent gripping and obstacle avoidance planning of robot arms [6]. Y. Chen · Y. Feng Key Laboratory of Autonomous Systems and Networked Control, School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China C. Yang (B) Bristol Robotics Laboratory, University of the West of England, Bristol BS16 1QY, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_63

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Fig. 1 Both the image and desired image are input to encoder to generate state vector and goal vector. Then the reinforcement network ouput an action according to the state and goal. After the robot arm interacts with the environment, a new image is collected and replace the original image

Many researches have combined vision with reinforcement learning, and apply it to the robotic arm to enable it to perform assigned tasks autonomously through training. Higgins et al. demonstrate a multi-stage reinforcement learning agent DARLA [7], whose strong migration ability makes it adaptable even in the field without relevant data. The model-based reinforcement learning proposed by Finn and Levine does not require excessive manual supervision. The model can train the unmarked data collected by the robot autonomously [8], enabling it to provide flexible prediction models for a wide range of tasks and environments. Zeng et al. propose the RL algorithm that combine pushing and grasping making them have the synergies [9]. Nair et al. propose the RIG framework that the agent learns from imagined goals generating from β-VAE [10]. In this paper, we use variational auto-encoder(VAE) to extract the feature from the images of environment. The difference between features can be used to measure the difference between images. When the robot is applied to learn a specific task, we set a desired image of this task and RL network will be updated by the difference between image that reflects its current state and desired image, learning to make the robot reach state similar to the state in desired image. The overview of our architecture is shown in Fig. 1. In the experiment part, we will show the process of robot learning to push a puck to the expected position.

2 Reinforcement Learning Structure In this section, details of the variational auto-encoder, RL network, reward function, and some training protocols will be provided.

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2.1 Variational Auto-Encoder Variational auto-encoder is a kind of unsupervised learning [11], which tries to reconstruct image similar to the input image, hoping to generate new images based on the vectors sampled from latent space. The vector in the latent space is the output of the hidden layer, and its dimension is much smaller than the output image’s. The encoder must selectively discard irrelevant data, and includes as much relevant information as possible in the limited vectors. And the decoder needs to learn how to reconstruct the input image from the vector as much as possible. The VAE architecture is shown in Fig. 2. In VAE, the probability of image x is a Gaussian Mixture Model, which can be expressed as  P (x) =

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z is the latent vector, and p (z) is a normal distribution. P (x|z) means the probability of x generating from latent vector, and x|z ∼ N (μ (z) , σ (z)). The μ (z),σ (z) is going to be estimated by the neural network in the encoder. It’s assumed that q (z|x) can be any distribution. Here is  log P (x) =

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K L (q (z|x) ||P (z|x)) means the KL divergence of q (z|x) and P (z|x). And log P (x) has a lower bound because K L (q (z|x) ||P (z|x)) ≥ 0. The lower bound L b can be expected as

Fig. 2 VAE architecture

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 P (z, x) dz q (z|x)    P (x|z) P (z) dz = q (z|x) log q (z|x)     P (z) dz + q (z|x) log P (x|z) dz = q (z|x) log q (z|x) = −K L (q (z|x) ||P (z)) + E q(z|x) [log P (x|z)] 



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Therefore, L b can be divided into −K L (q (z|x) ||P (z)) and E q(z|x) [log P (x|z)]. And we need to maximize L b to maximize P (x). Before training the RL network, a fixed camera is used to collect lots of pictures of the environment, in which the robot is commanded to take random actions related to task. Then VAE is trained to maximize Eq. 3 on these pictures to be capable of extracting useful feature from image. When training the RL network, the vector obtained from the encoder z = e (x) can be directly used to perform operation. There is no need to have the convolutional layer network trained with the RL network, which is time-consuming and may be difficult to converge. Furthermore, the difference between two images in a way can be judged from the distance between their latent vectors, which gives the convenience of defining reward functions for tasks with different goals.

2.2 RL Network Twin Delayed Deep Deterministic policy gradient algorithm(TD3) [12], which is used in our work, is a variant of Deep Deterministic policy gradient algorithm(DDPG). It has two critic networks Q θ1 , Q θ2 and the policy network πφ . There also exits corresponding target networks Q θ  , Q θ  and πφ  . Considering the RL is 1 2 based on the Markov decision process(MDP), the agent at the state s choose an ac tion according to policy network a = πφ (s), and then reach a new state s with the reward r . In addition,  a means the action chosen by policy target network πφ  at state  s , and Q (s, a) is the Q value output from the critic network. In order to reduce the overestimation in TD3, the critic target network output that has relatively smaller value is chosen to update network, which can be expressed as θi ← arg min N θi

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where N is the batch size, γ is discount factor. TD3 is a kind of off-policy RL, which  means it will sample a batch of (s, a, s , r ) from the replay buffer every time it trains. Different from DDPG, the policy network is updated together with target network to slow down update frequency for the purpose of reducing per-update error. The policy network parameter φ is updated by the deterministic policy gradient:

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(5)

One more special part in TD3 is the target policy smoothing. A Gaussian noise is added to the action output from target policy network, which makes it harder for policy to make use of Q value errors. It can be expressed as     a ← πφ s + ε ε ∼ cli p (N (0,  σ ) , −c, c)

(6)

where c is set to be the bound of the noise. In our method, state of the robot is represented by the code from encoder. To be specific, the fixed camera takes a photo of environment, and then photo is input to the well-trained encoder to get latent space vector as a state of the robot. Every time after the robot takes a step, a new photo is captured to be calculated into short code as a new state. Based on the TD3, a goal is added to the input of critic network and policy network, which can be expressed as Q (s, a, g) and π (s, g). The network architecture is shown in Fig. 3. The goal is manually set based on the desired image we enter, and it is also represented by the latent space vector of the desired image. For example, a robot arm is taught to push a puck to a desired position. In this situation, the desired image is the picture of puck on desired position. To set the goal, the puck is put on the desired position manually and then the fixed camera takes a picture of it. Finally the desired image is converted to goal vector by VAE encoder. The goal is set at the beginning of an episode and the agent will make a decision on actions based on its state and goal. After making such a change, the data stored  in the replay buffer becomes (s, a, s , g). The reward is not saved because it can be calculated by the state vectors and goal vectors(details are in the reward function section). Only when updating networks, the reward will be calculated. The reason of adding goal to input is to make this architecture adapt to multiple goals, and to easily extend to other tasks without changing network architecture. In addition, some tasks that are difficultly described in words can be easily expressed in images, which makes our framework more versatile.

Fig. 3 RL network

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2.3 Reward Function Reward function is the key to reinforcement learning, as a well-designed reward can speed up the convergence of RL network. One of the main reasons for using VAE in our work is to calculate the reward function based on latent space vectors. During the training time, the robot is wished to reach the goal state as desired image shows quickly. In other words, difference between the current image and the desired image needs to be reduced as soon as possible. And the Euclidean distance of latent space vectors is used in our work to measure the difference between two pictures. Therefore, it can be seen from the change of the Euclidean distance whether the current state of robot is closer to the completion of the task. The agent will receive a positive reward if the distance is closer after robot performs an action. Otherwise, it will receive a negative reward. The reward function is shown as follows. dist1 = s − g  dist2 = s − g

(7)

r = (dist1 − dist2 ) ∗ α − β 

where s, s , g are latent space vectors. β is a punishment for every step, which pushes the agent to move closer to goal. α is a proportional coefficient coordinated with β. dist1 means the distance from current state to goal state, and dist2 means the distance  from next state to goal state. When the agent reach a new state s from state s after taking a step, the reward will be large if the distance to goal is quickly reduced. If there is no progress, it will continue to be punished.

2.4 Training Protocols 

During training, reward is calculated when the turple (s, a, s , g) is sampled from replay buffer to update network. Before calculating the reward, we modify original goal to a new sampled goal with a possibility of 0.5. This is a thought from Hindsight Experience Replay(HER) [13]. For reinforcement learning, most of initial attempts are failed. By replacing the original goals with other goals, the network can quickly achieve convergence in the tasks of varying goals. This means that although agent doesn’t succeed this time, but it also learns something different in the process. More over, a turple (s, a, s , g) can be expanded to multiple sets of data by changing the goal, which improves sample efficiency. Therefore, the goal is relabeled with possibility of 0.5 in our work to improve the sample efficiency and accelerate convergence of RL network. The whole process of training is shown in Algorithm 1.

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Algorithm 1 The reinforcement learning on robot with VAE 1: Intialize critic networks Q θ1 , Q θ2 and actor network πφ .    2: Intialize taget networks θ1 ← θ1 , θ2 ← θ2 , φ ← φ 3: Intialize VAE encoder and decoder. 4: Intialize replay buffer τ . 5: Set discount factor γ , noise bound c, update frequency d, update rate λ. 6: Collect images of robot random actions. 7: Train VAE on these images. 8: for n = 0 to N − 1 do 9: Sample latent goal g from VAE encoder. 10: Sample initial state s0 . 11: for t = 1 to T do 12: Take an action with noise a = πφ (s, g) + ε, ε ∼ N (0, σ ) 13: Get the observed image x from fixed camera.  14: Convert x to the next state vector s using VAE encoder.  15: Store (s, a, s , g) into replay buffer τ .  16: Sample mini-batch of N transitions (s, a, s , g) from τ . 17: (Probability 0.5) replace g with a new goal. 18: Computereward  r using (7).   19:  a ← πφ s , g + ε, ε ∼ cli p (N (0,  σ ) , −c, c)    a, g 20: y ← r + γ mini=1,2 Q θ  s , i 2

 y − Q θi (s, a, g) 21: Update critics θi ← arg minθi N −1 22: if t mod d then 23: Update φ by the

policy gradient: φ J (φ) = N −1 a Q θ1 (s,a,g) |a=πφ (s,g) φ πφ (s, g) 24: Update target networks:     θi ← λθi + (1 − λ) θi φ ← λφ + (1 − λ) φ 25: end if 26: end for 27: end for

3 Experiments In order to make a comparision with RIG in [10], we used the mujoco simulation environment, in which there is a 7-dof Sawyer arm. The environment is shown in Fig. 4. The robot needs to learn to push the puck on the desk to another desired position with its end effector. And the arm should stay in specified pose at the end. The end effector was limited in the plane parallel to the desk. In this simulation, there was an imaginary camera above the desk to capture 2D pictures of this environment. The dimension of latent vector of VAE was 8. We collected 20,000 images of robot random actions on the puck. The size of image was 84 * 84 * 3. After training VAE with these images for 300 epochs, the results can be seen in Fig. 5.

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Fig. 4 The mujoco simulation environment,in which there is a Sawyer arm, a desk and a puck

Fig. 5 Pictures are captured by fixed camera above the desk. At the first row are the images input to VAE, at the second row are the reconstructed images

For the RL network, the input size of critic network equaled to state dimension plus action dimension and goal dimension. The state dimension and goal dimension equaled to 8, which was the dimension of latent vector of VAE. The action was the plane coordinate that the end effector heads to, whose dimension was 2. The critic network consisted of 4 linear fully-connected layers, including 2 hidden layers with each size of 320 and 400. The architecture of policy network was almost the same as critic network except that it had one more tanh output activation. The update frequency of policy network and target network was 4. In the reward function, α = 10, β = 0.5. The discount factor γ = 0.99. The update rate λ = 0.005. After training, the robot arm learned to finish the task quickly, making the current state similar to the desired state. See it in Fig. 6. We also evaluated the real distance between the final states and goal states using the true coordinate of puck and hand. The final hand distance means the Euclidean distance between the coordinates of hand in final state and in goal state. The final puck distance is the Euclidean distance between the coordinates of puck in final state and in goal state. We made a comparison with the RIG algorithm on the final distance to goal, which equals to final hand distance plus final puck distance. The

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Fig. 6 Each row of images show an epoch. The image is shown about the environment every N steps, the robot tries to push the puck to the desired position shown in goal image, and the pose of arm is also similar to the pose in goal image. Fig. 7 Our method and RIG in [10]

result is shown in Fig. 7. It can be seen that our distance was reduced more quickly and remained lower level.

4 Conclusion In this paper, we propose a reinforcement learning structure for robot based on TD3 and VAE. The state and goal are both described by vectors in the latent space of VAE, and goal is used as input to network. We use the Euclidean distance between latent vectors to compute reward. The goal is relabeled to improve sample efficiency. The experiments about pushing tasks in mujoco environment also prove the availability of this structure. Acknowledgements This work was partially supported by National Nature Science Foundation (NSFC) under Grants 61861136009 and 61811530281.

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References 1. Silver, D., Huang, A., Maddison, C.J., et al.: Mastering the game of Go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016) 2. Human-level control through deep reinforcement learning. Nature 518(7540), 529–533 (2015) 3. Lin, C.T., Jou, C.P.: GA-based fuzzy reinforcement learning for control of a magnetic bearing system. IEEE Trans. Syst. Man Cybern. Part B 30(2), 276–289 (2002) 4. Bello, I., Pham, H., Le, Q.V., et al.: Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940 (2016) 5. Smart, W.D., Kaelbling, L.P.: Effective reinforcement learning for mobile robots. In: Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), vol. 2, 3404–3410. IEEE (2002) 6. Duguleana, M., Barbuceanu, F.G., Teirelbar, A., et al.: Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning. Robot. Comput.-Integr. Manuf. 28(2), 132–146 (2012) 7. Higgins, I. , Pal, A., Rusu, A.A., et al.: DARLA: improving zero-shot transfer in reinforcement learning (2017) 8. Finn, C., Levine, S.: Deep visual foresight for planning robot motion. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 2786–2793. IEEE (2017) 9. Zeng, A., Song, S., Welker, S., et al.: Learning synergies between pushing and grasping with self-supervised deep reinforcement learning (2018) 10. Nair, A.V., Pong, V., Dalal, M., et al.: Visual reinforcement learning with imagined goals. In: Advances in Neural Information Processing Systems. pp. 9191–9200 (2018) 11. Kingma, D.P., Welling, M.: Auto-encoding variational bayes (2013) 12. Fujimoto, S., van Hoof, H., Meger, D.: Addressing function approximation error in actor-critic methods. arXiv preprint arXiv:1802.09477 (2018) 13. Andrychowicz, M., Wolski, F., Ray, A., et al.: Hindsight experience replay. In: Advances in Neural Information Processing Systems, pp. 5048–5058 (2017)

A Multi-Center PSO Algorithm with Memory Ability and Its Application to the Online Modelling of an Underwater Vehicle Thruster Gaofei Xu, Guanqun Wang, Yiping Li, Xiaohui Wang and Xiangyu Qu

Abstract To improve the performance of Particle swarm optimization (PSO) in online optimization problems, a multi-center PSO algorithm with memory ability was proposed. Main strategies of the proposed algorithm include the initial population optimization based on historical optimal solution and improved chaos mapping and the multi-center collaborative search. To verify online optimization performance, the proposed algorithm is applied to the online modelling process of an underwater vehicle thruster to optimize the modeling parameters. Result proves the superiority of the proposed algorithm in online optimization problem. Keywords Online optimization · PSO · Tent mapping · Multi-center collaborative search · Online modeling · Underwater vehicles

1 Introduction Particle swarm optimization (PSO) is one of the most important swarm intelligence paradigms [1]. Due to its simple structure, strong operability and easy to implement, PSO algorithm has many successful applications seen in solving real-world optimization problems, such as controller parameters tuning [2], rectangular packing problem [3], neural network optimization [4], large-scale social network clustering [5], electrophysiological signals modelling [6] and so on. However, as a population-based and global optimizer, PSO has some weakness. Lots of experiments have shown that PSO cannot guarantee to find the global optimal G. Xu · G. Wang (B) · Y. Li · X. Wang · X. Qu State Key Lab of Robotics, Shenyang Institute of Automation, CAS, Shenyang 110016, China e-mail: [email protected] G. Wang Chengde Petroleum College, Chengde 067000, China G. Xu · Y. Li · X. Wang · X. Qu Institutes for Robotics and Intelligent Manufacturing, CAS, Shenyang 110016, China G. Xu · X. Qu University of Chinese Academy of Sciences, Beijing 100049, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_64

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solution and are easy to get trapped in the local optimum, especially in the largescale complex optimization problem [7]. To improve the performance of PSO, many methods are proposed, such as the adjustment of inertia weight, learning factors or social factors [8], improve the search strategy or add auxiliary operations [9], integrate with other algorithms [10] and so on. In engineering applications, there are many online optimization problems, such as the online optimization of control parameters, the online optimization of modeling parameters in online modeling process and so on. In the above-mentioned online optimization problems, it is always difficult to describe the problem using a global model. In addition, for online optimization problems, it is generally desired that to achieve better optimization results with as few iterations as possible. For such online optimization problems, many existing improvement strategies are ineffective or not applicable because those strategies require the global model of the optimization problem or require more iterations. In order to solve the online optimization problems, a multi-center PSO algorithm with memory ability (abbreviated as MMCPSO) was proposed in this paper. Main strategies of the proposed algorithm include the initial population optimize strategy based on historical optimal solution and improved chaos mapping and the multi-center collaborative search strategy. To verify the performance of the proposed algorithm, the MMCPSO is applied to the online modelling process of an underwater vehicle thruster to optimize the modeling parameters.

2 Initial Population Optimize Based on Historical Optimal Solution and Improved Chaos Mapping 2.1 Initial Population Optimize Based on Historical Optimal Solution For the online optimization problem introduced in this paper, the problem to be solved in each optimization process may have certain similarity and continuity. After each optimization process, an optimal solution is obtained. When starting a new optimization, due to the similarity of the optimization problem, the optimal solution of the current optimization problem may be close to the optimal solutions obtained in the previous optimization processes. If these optimal solutions are stored and serve as part of the initial population for the current optimization process, it will help to optimize the initial population and improve the performance of the PSO algorithm.

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2.2 Improved Tent Mapping In the PSO optimization process, it is desired that the initial position is distributed as evenly as possible in the search space to improve the probability of finding the optimal solution. In traditional PSO, the initial position is generally generated by randomly taking values. It may result in uneven initial position distribution and then affect algorithm performance. To overcome the uniformity, the initial position is often optimized by chaos mapping. Tent mapping is a chaos mapping with good ergodicity [11]. In this paper, a randomly selected historical optimal solution is mapped to the search space by tent mapping. The tent mapping is expressed as  tk+1 =

0 ≤ t ≤ 0.5 2tk 2(1 − tk ) 0 ≤ t ≤ 0.5

(1)

Tent mapping have the problem of easy to fall into a small period or several fixed points [12]. To solve this problem, Nie et al. proposed an improved method of multiplying the mapped value by a random number between [0,1] when the mapped value is stuck in fixed points or small period [12]. When initial population is optimizing through tent mapping, the initial value needs to be mapped from the search space to the [0,1] space. Therefore, the initial value of the mapping in the [0,1] space may approximate the infinite loop fraction. In practical applications, it is found that in such case, although the mapped value does not fall into fixed points or a small period, many mapped value points are distributed near each other, which affects the mapping effect. This paper solves this problem by limiting the minimum distance between adjacent values, if |tk+1 − tk | ≤ ε, then  tk+1 =

tk+1 + 0.4 rand tk+1 ≤ 0.5 tk+1 − 0.4 rand tk+1 > 0.5

(2)

where ε is the threshold to limit the minimum distance between adjacent values.

2.3 Comparison of Initial Population Initialization Results In the initialization process of the MMCPSO algorithm, a small number of initial positions are taken as the historical optimal solutions. Through the improved tent mapping method, the remaining initial population is obtained, and the initial population optimization is realized. Figure 1 shows the distribution of 60 points obtained by the improved tent mapping and the method proposed by Nie et al. [12], respectively. The initial value is (0.833333, 0.666667). Figure 1 indicates that points generated by the improved tent mapping distribute more uniformly, while points obtained by the method proposed by Nie et al. concentrated in a small area.

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3 Multi-Center Collaborative Search In the searching process, all particles learn with larger weights to the particles with the best fitness. If the current optimal fitness particles fall into local optimum, it may cause the whole population to aggregate in the local optimal region. At this time, even if a strategy such as particle mutation or secondary search is applied try to jump out of the local optimal region, many searching times have been wasted. In addition, it is difficult to judge whether the population is in the local optimum or not. To reduce the probability of falling into local optimum, this paper proposes a multi-center collaborative search strategy. The basic idea is that, in the search process, particles that are far away from the current optimal fitness particle and have good fitness are allowed to explore independently, and a small number of particles are employed in collaborative search strategy in the peripheral region of the current optimal particle. There are multiple search centers, among them, there is a main center with the best fitness, which guides most of the particles to search around them. In addition, several sub-centers with suboptimal fitness, which guide a small number of particles to search collaboratively in other areas. The multi-center collaborative search strategy mainly affects the speed update process of the PSO. It mainly includes three processes, include calculating the weighted fitness, selecting learning center and speed update. The specific implementation of the multi-center collaborative search strategy is as follows.

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Step 1 For all particles in the population, sort them in ascending order by individualoptimal fitness. Denote particles ranked in the top half according to the k . individual-optimal fitness as set X top k Step 2 For particles in the set X top , calculate its Euclidean distance between the k k and the global-optimal position pgbest . individual-optimal position pibest k dikpg = d( pibest, j

  D  k k k 2 − pgbest, j )= ( pibest, j − pgbest, j )

(3)

j=1 k , calculate its weighted fitness as Step 3 For particles in the set X top

k = f iw

dikpg k f ibest

(4)

k Step 4 Calculate the weighted fitness of all particles in the set X top , and sort the particles in descending order by weighted fitness. According to the number of auxiliary centers set in advance, the sorted particles are sequentially selected as auxiliary center particles, and the individual-optimal positions of the auxiliary center particles are used as auxiliary centers. In this paper, the number of auxiliary centers is set as 2, assume that the auxiliary center particles are particle m and n respectively, the corresponding auxiliary centers k k and pnbest , respectively. are pmbest Step 5 For the central particle c and the auxiliary center particles m and n, we set their learning centers as their individual-optimal positions. For other particles in the population (e.g. particle i), we calculate the distance between their current position xik and the population center as well as the auxiliary center

dikxg = d(x ik , pkgbest ), dikxm = d(x ik , pkmbest ), dikxn = d(x ik , pknbest )

(5)

If dikxg ≤ min(dikxm , dikxn ), that is, the distance between the particle i and the center of the population is not greater than the distance from the auxiliary k . Othercenter, and the learning center of the particle i is set to L ik = pgbest wise, we determine which auxiliary center the particle i is closest to (here, k ), and determine the learning center of it is assumed to be closest to pmbest particle i according to the following rules fk

k k , then L ik = pmbest . otherwise, L ik = pgbest . If rand ≤ 43 f gbest k mbest Step 6 We select the learning centers for all particles in the population according to the above method, and then update the speed of each particle as follows k k k k k vi,k+1 j = wvi, j + c1 r 1 ( pibeset, j − x i, j ) + c1 r 1 (L i, j − x i, j )

(6)

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Start

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NO

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YES Update historical optimal solutions

Output optimal solution

Fig. 2 The schematic flowchart of the MMCPSO algorithm

After the speed update is completed, the location update and subsequent operations can be performed according to the traditional PSO. The complete flow of the MMCPSO is shown in Fig. 2. Figure 3 shows the position and learning centers distribution of each particle during the mid-stage and later-stage iteration of the optimization process described in Sect. 4. There are 20 particles in the population, with one center and two auxiliary centers. In Fig. 3, the number on left side of the arrow is the index of each particle, and the right side is the learning center of the particle during the current searching process. In the mid-stage iteration shows in Fig. 3a, particle 7 is the center of the population, and particle 13 and 14 are the auxiliary centers. In this iteration, there are 13, 3, and 4 particles learned from particle 7, 13 and 14 respectively. Benefit from the collaborative search strategy, particles are widely searched in potential regions and avoid falling into local optimum too fast. In the later-stage iteration shows in Fig. 3b, particles have roughly converged to the optimal region and search within a small range under the guidance of the global center and the auxiliary centers. Owe to the learning center determination rules of this paper, in the later-stage iteration, it is still possible for particles around the auxiliary center to learn from the global center,

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Fig. 3 The position and learning centers distribution of each particle

search the area between the auxiliary center and the global center. This situation further reduces the probability that the optimal solution falling into local optimum.

4 Application of MMCPSO to the Online Modeling of Underwater Vehicle Thruster 4.1 Data Driven Online Modeling of Underwater Vehicle Underwater vehicles play an important role in marine research. To ensure the safety of underwater vehicles, online fault detection is essential. Existing methods are generally based on fixed models, and it is difficult to adapt to the impact of the operating environment or system changes, which affect fault detection performance. Therefore, to meet the actual needs of fault detection, online modeling of the underwater vehicle is needed. Polynomial fitting is a data driven modeling method with the characteristics of simple operation and convenient online implementation [13]. Therefore, this paper uses polynomial fitting to construct the model between control value and thruster speed of an underwater vehicle. During the online modeling, there are two parameters need to be optimized, the model order and the amount of modeling data.

4.2 Modeling Parameter Optimization Based on MMCPSO For the modeling parameter optimization problem in this paper, there are two dimensions in the position of each particle, represent the model order q and the modeling data amount w, respectively. In the modeling process, control value U and thruster

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speed V obtained during the operation of the underwater vehicle is used as the data set for modeling. For a particle at position (q, w), during the modeling process, data for modeling was select according to w as (Uw , Vw ). Then, a thruster model with order q was established by polynomial fitting. We evaluate the accuracy of the model by the mean absolute percentage error (MAPE) as follows MAPE (Uw , Vw ) f q,w

 Nw   vi − vˆ i  1    = Nw i=1  vi 

(7)

Where vˆ is the estimated speed by the model. The fitness value of the particle at position (q, w) is MAPE MAPE f q,w = max( f q,w (Uw , Vw ), f q,w (Utest , Vtest ))

(8)

where (Utest , Vtest ) is the public test data taken from (U, V ). According to the above-mentioned method, the thruster model is established by polynomial fitting according to the optimal modeling parameter (q ∗ , w ∗ ).

4.3 Online Modeling Results Comparison For comparison, the MMCPSO, PSO and SPSO [13] are applied to solve the online optimization problem in the online modeling of underwater vehicle thruster. During the optimization process, related parameters of the three algorithms and modeling 400 Error1 Error2

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steps are set as the same. The online modeling is carried out using data from a sea trial. During the tests, a thruster model is established at first, and then conduct online monitoring of the thruster using the thruster model. If the model residual exceeds the threshold, the online optimization is started, and a new model is established. After each optimization moment, the residual of the newly established model is named as Error 2, at other moment, the model residual is denoted as Error 1. Figures 4, 5 and 6 shows the model residual during the online modeling processes optimized by MMCPSO, PSO and SPSO, respectively. It can be seen from Figs. 4, 5 and 6 that the online monitoring process based on PSO and SPSO optimization 200 Error1 Error2

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has larger model residual and need more times of online modeling than the online monitoring process based on MMCPSO. This indicates that models established based on MMCPSO have better performance than that of PSO and SPSO.

5 Conclusion In order to solve the online optimization problem, a multi-center PSO algorithm with memory ability was proposed. The main contribution of the MMCPSO algorithm is that two new strategies are proposed to improve online optimization performance, namely, the initial population optimization strategy based on historical optimal solution and improved chaos mapping and the multi-center collaborative search strategy. The practical application results show that the above-mentioned strategy can effectively reduce the risk of falling into local optimum and improve the performance of the PSO algorithm. Acknowledgements This work is supported by the National key research and development program (2017YFC0305901), National Natural Science Foundation of China (91648204).

References 1. Evangelin, L.N., Fred, A.L.: Biometric authentication of physical characteristics recognition using artificial neural network with PSO algorithm. Int. J. Comput. Appl. Technol. 56(3), 219–229 (2017) 2. Taeib, A., Chaari, A.: Tuning optimal PID controller. Int. J. Model. Ident. Control 23(2), 140–147 (2015) 3. Wang, J., Qi, Y., Zhang, J.: Research on PSO algorithms for the rectangular packing problem. Int. J. Comput. Appl. Technol. 51(1), 15–22 (2015) 4. Rawashdeh, A., Alkasassbeh, M., Al-Hawawreh, M.: An anomaly-based approach for DDoS attack detection in cloud environment. Int. J. Comput. Appl. Technol. 57(4), 312–324 (2018) 5. Cai, Q., Gong, M., Ma, L., et al.: Greedy discrete particle swarm optimization for large-scale social network clustering. Inf. Sci. 316, 503–516 (2014) 6. Ouali, M.A., Ghanai, M., Chafaa, K.: A new type-2 fuzzy modelling and identification for electrophysiological signals: a comparison between PSO, BBO, FA and GA approaches. Int. J. Model. Ident. Control 29(2), 163–184 (2018) 7. Wang, F., Zhang, H., Li, K., et al.: A hybrid particle swarm optimization algorithm using adaptive learning strategy. Inf. Sci. 436 (2018) 8. Zhan, Z.H., Zhang, J., Li, Y., et al.: Adaptive particle swarm optimization. IEEE Trans. Syst. Man Cyber. Part B: Cyber. 39(6), 1362–1381 (2009) 9. Li, C., Yang, S., Nguyen, T.T.: A self-learning particle swarm optimizer for global optimization problems. IEEE Trans. Syst. Man Cyber. Part B: Cyber. 42(3), 627–646 (2012) 10. Thangaraj, R., Pant, M., Abraham, A., et al.: Particle swarm optimization: Hybridization perspectives and experimental illustrations. Appl. Math. Comput. 217(12), 5208–5226 (2011) 11. Bae, J., Hwang, C., Jun, D.: The uniform central limit theorem for the tent map. Stat. Probab. Lett. 81(10), 1021–1027 (2012)

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12. Nie, R., Zhang, W.G., Li, G.W., et al.: Adaptive chaos hybrid multi-objective genetic algorithm based on the tent map. J. Beijing Univ. Aeronaut. Astronaut. 38(8), 1010–1016 (2012) 13. Zambrano-Bigiarini, M., Clerc, M., Rojas, R.: Standard particle swarm optimisation 2011 at CEC-2013: a baseline for future PSO improvements. In: 2013 IEEE Congress on Evolutionary Computation, pp. 2337–2344. IEEE Press, New York (2013) 14. Garcia-Tejeda, Y.V., Barrera-Figueroa, V.: Least squares fitting-polynomials for determining inflection points in adsorption isotherms of spray-dried acai juice (Euterpe oleracea Mart.) and soy sauce powders. Powder Technol. 342, 829–839 (2019)

Trajectory Tracking of Mobile Robots Based on Fuzzy Control and Extended State Observer Dan Su, Jian Huang and Daqian Yang

Abstract A new trajectory tracking control scheme is proposed for mobile robots based on the fuzzy control and extended state observer in this paper. The fuzzy logic control adjusts the three parameters of the speed controller online, so as to achieve better control effect. The extended state observer is designed to estimate the unknown disturbance information of the system and compensate it. The trajectory tracking controller can track the reference trajectory expeditiously and accurately. And the position errors of the mobile robot eventually converges to zero. The simulation results show that the control scheme is effective and reliable. Keywords Trajectory tracking · Fuzzy control · Extended state observer (ESO) · Mobile robot

1 Introduction In the last several years, Wheeled Mobile Robots (WMRs) have been widely used in many fields. Accurate motion control of WMRs is the prerequisite for accomplishing various tasks. The study about trajectory tracking control is very meaningful [1]. At present, there are many control strategies for WMR’s trajectory tracking. For example, the sliding mode control (SMC) is used to the motion control to enhance the robustness of the system [2]. Huang et al. [3] proposed a terminal SMC scheme to control the velocity and braking of the vehicle system. Robust control methods designed for the robustness of nonlinear systems appeared in the 1950s [4]. Eunju et al. [5] designed the robust controller by Lyapunov theory and backstepping method to reduce the tracking error. Currently, the most widely used intelligent control D. Su · J. Huang (B) School of China-EU Institute for Clean and Renewable Energy, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] J. Huang · D. Yang The Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_65

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methods in robot trajectory tracking are the fuzzy control and neural network control approaches [6–9]. Since there are many uncertainties in the trajectory tracking control system of WMR. These uncertainties are difficult to measure directly, so it’s necessary to estimate and compensate the uncertainties accurately [10, 11]. The extended state observer (ESO) can estimate the uncertainties of the nonlinear system and compensate them dynamically, so as to eliminate the adverse effects. This technology has been generally used in industrial control, especially in motion control where uncertainties exist in the control object [12, 13]. In this article, we propose a method of trajectory tracking control integrating both the fuzzy control and ESO. There are modeling error and external disturbance in the modeling and application. Thus in this research, not only the kinematic model but also the dynamic model of the robot are considered. The fuzzy control is used to adjust the three parameters of speed controller online. Therefore the controller can output the desired speeds of the robot. The ESO is introduced to estimate the system uncertainties in real time, which makes the system have the characteristics of active disturbance rejection, and improve the control accuracy. The simulation results indicate that the control scheme is valid and feasible.

2 Design of Virtual Velocity Controller Based on Kinematic Model 2.1 Establishing Kinematic Model of Mobile Robot For analyzing the issue of motion control of a mobile robot, we need to build the kinematic model of the WMR. The WMR is a nonholonomic mechanical system, as shown in Fig. 1a. The vector q is the position of the WMR in the global coordinate system O-XY, where q = (x, y, θ )T . P-xy is the local coordinate system. x is the moving direction of the mobile robot. Point P is the center of geometry and point G is the center of mass. dg is the distance from P to G. The length between two wheels of the mobile robot is d, and r denotes the wheel’s radius. θ is the angle between the axis x and the axis X. The linear speed and angular speed of the mobile robot are v and ω. qr = (xr , yr , θr )T is the given reference position vector of the WMR. vr is the reference line velocity, and ωr denotes reference angular velocity. The trajectory tracking control scheme is designed for eliminating these three errors. On account of the property of the WMR, it is a kind of nonholonomic constrained mobile robot. We assume that the conditions of pure rolling and no-slip are met. x˙ sin θ − y˙ cos θ = 0

(1)

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Fig. 1 a Kinematics Analysis of Mobile Robot; b Membership functions of s, a, k1 , k2 , and k3

We can obtain the kinematics Eq. (2) of WMR, where x˙ denotes the linear velocity of X direction, y˙ denotes the linear velocity of Y direction, and θ˙ denotes the angular velocity. ⎧ ⎨ x˙ = v cos θ y˙ = v sin θ ⎩˙ θ =ω

(2)

According to [5], we would get the speed control law of the WMR. Where xe , ye are the distance errors in X direction and Y direction respectively, and θe is the angle error.   vr cos θe + k1 xe (3) Vc = wr + k2 vr ye + k3 sin θe It is known that Vc = [vc , wc ]T . k1 , k2 , and k3 are three adjustable positive numbers. The selection of the three parameters k1 , k2 , and k3 has a great influence on the speed controller, but the setting of these three parameters is very difficult. Therefore, in the next section we will design three fuzzy logic controllers to achieve the purpose of adjusting these three parameters in real time.

2.2 Design of Fuzzy Controller Since we need to set three parameters k1 , k2 , and k3 , three fuzzy  controllers are  designed with distance error s, angle error a as the inputs, where s = xe 2 + ye 2 ,

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a = θe . And k1 , k2 , and k3 as the outputs. The variables are divided into seven fuzzy sets {PB, PM, PS, Z, NS, NM, NB}. And the range of all variables are shown in Table 1. Choosing different membership functions is likely to bring different control effects. In this section, we choose the Gauss function as the membership function, because this membership function has good smoothness and symmetry, and there are no zero points. The membership functions are shown in Fig. 1b. Setting up the fuzzy rules is an essential part of designing fuzzy controller. And the establishment of fuzzy rules is usually based on expert experiences. According to the designed speed controller, Eq. (3), the linear velocity vc is affected by the parameter k1 , and the angular velocity ωc is affected by the parameters k2 and k3 . When the distance error of X direction and Y direction is large, the value of k1 should be reduced. When the angle error is large, the values of k2 and k3 should be reduced. Then all fuzzy controllers employ the Mamdani If-Then rules indicated below, where A˜ n , B˜ n , C˜ n (n = 1, 2, 3) is the fuzzy value of inputs and outputs. k1 Control Rule i: If d is A˜ 1 and a is B˜ 1 , Then k1 is C˜ 1 . k2 Control Rule j: If d is A˜ 2 and a is B˜ 2 , Then k2 is C˜ 2 . k3 Control Rule k: If d is A˜ 3 and a is B˜ 3 , Then k3 is C˜ 3 . Therefore, we establish fuzzy rules according to the magnitude of distance error and angle error. In summary, the established fuzzy rules of the three parameters are illustrated in Tables 2 and 3. The process of defuzzification is to transform the fuzzy value received by the fuzzy inference into an accurate control signal as the input of the system. Here the method of defuzzification we selected is the center of gravity method, as the expression (4) shows:

Table 1 The ranges of inputs and outputs Variable s (m) a (rad) Range

[0, 5]

Table 2 Fuzzy rules of k1 k1 s NB a

NB NM NS Z PS PM PB

PM PM PM PM PB PB PB

[0, 5]

k1

k2

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[1, 8]

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PM PM PM PM PM PB PB

PS PS PS PS PM PM PM

Z PS PS PS PS PM PM

NS Z PS PS PS PS PS

NM NS NS NS NS Z PS

NB NM NS Z Z Z PS

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NB NM NS Z PS PM PB

PM PM Z NS NS NM NB

PB PM PS Z NS NS NM

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PB PM PS Z Z NS NS

PB PM PS Z Z NS NS

PB PM PS Z Z NS Z

PB PB PS Z Z NS PM

PB PB PS Z Z Z PB

i vk μv (vk ) vc = k=1 i k=1 μv (vk )

(4)

3 Design of Extended State Observer 3.1 Extended State Observer In practical application, due to the existence of external disturbances, the WMR cannot achieve the ideal speed, and the control effect is not excellent. To ensure the feasibility, the research based on the non-holonomic wheeled robot dynamics model, and seek a method to improve the stability and robustness. The structural block diagram of trajectory tracking control in this paper demonstrated Fig. 2. The mathematical model of mobile robot can be indicated as [12]: q˙ = S(q)V M(q)V˙ + C(q, q)V ˙ + Fd + τd = τ

Fig. 2 Structural block diagram of tracking control system

(5)

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where q = (x, y, θ ) is position of the WMR, V = (v, ω)T includes the linear and angular velocities. τ = (τ1 , τ2 )T denotes the control torque. M(q) denotes a symmetric and positive-definite inertia matrix. C(q, q) ˙ denotes the centripetal and coriolis matrix, Fd denotes the surface friction, and τd is external disturbance. M(q), S(q), C(q, q) ˙ have the same expression as [7]. As the most important part of active disturbance rejection control (ADRC), the extended state observer expands the uncertainties in the system into a new state to estimate and compensate the state to the system controller. Here we assume x1 = V , and then we get the expression (6) based on the dynamic expression (5) of the WMR. ˙ o + F(q) ˙ + τd ] + M −1 (q)τ x˙1 = −M −1 (q) [C(q, q)x

(6)

˙ o + Fd + τd ], u = M −1 (q)τ , Based on (6), by letting xt =−M −1 (q) [Vm (q, q)x and x˙t = h. We can get the following expression: 

x˙1 = xt + u x˙t = h

(7)

The observed values of the state variables of expression (7) are xˆ1 and xˆt . The observation error can be expressed as e1 = xˆ1 − x1 and et = xˆt − xt , so the nonlinear extended state observer we designed indicated as: 

x˙ˆ1 = xˆt − B1 e1 + u x˙ˆt = −Bt f al (e1 , α, σ )

(8)

Based on e1 = xˆ1 − x1 , and et = xˆt − xt , bring e1 , et into the expression (8), we can get: 

e˙1 = et − B1 e1 e˙t = −Bt f al (e1 , α, σ ) − h

(9)

where B1 , Bt are observer gains, and f al (e1 , α, σ ) is a non-linear function. The value of the function can be adjusted according to the error of the observer. The expression of the non-linear function is as follows: f al (e1 , α, σ ) = |e1 |α sign (e1 )

(10)

According to reference [14], the appropriate parameters B1 and Bt are selected, the state variables of the system can be estimated well, and the observation errors e1 and et can satisfy that xˆi − xi ≤ ai , where ai is a very small positive number. Just as the expression (8) of the ESO, we need to adjust the velue of Bt to make e1  (h/Bt )2 hold, then we can obtain bounded error e1 . If the error e1 is bounded, it can be deduced that et is bounded. Therefore, the designed observer is stable.

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3.2 Design of Torque Controller Because of the external disturbance, there is an error ec between the virtual speed Vc output by the speed controller and the actual speed V . Based on the dynamic expression, we can get ˙ c − τ + xt M(q)e˙c = −C(q, q)e

(11)

˙ c + C(q, q)V ˙ c + Fd + τd = τ , K f = diag{k f ,k f }, so the torque where xt = M(q)V controller we designed is as follows: τ = xˆt + K f ec

(12)

According to the reference [12], based on the mobile robot system (5), the ESO is (8), the error system (9), and the torque controller (12), the inequality ec  ≥ Ket fmax min established by adjusting these parameters. So we reason out the closed-loop system is uniformly ultimately asymptotically stable.

4 Simulation Results We would like to clarify the trajectory tracking control strategy as shown in the Fig. 2. An example is given to prove the validity of the design scheme. The external disturbances are Fd = [sin(t), sin(t)]T and τd = [cos(t), cos(t)]T . The digital simulation sampling time is 0.1 s. Consider three reference trajectories on the plane, including a line, a curve, and a circle. Where K f = diag{k f ,k f }, B1 = diag{b1 ,b1 }, Bt = diag{bt ,bt }. we set the real parameters of the WMR system and the parameters of each controller illustrated in the Table 4. The initial position of the WMR is set as (1,0.5,0.8). Demonstrated in Figs. 3a, 4a and 5a, we can obtain the tracking results of the trajectory tracking controller. As the graph illustrates in Figs. 3b, 4b and 5b, we can get the trajectory tracking errors. As Figs. 3c, 4c and 5c show, we can get the estimation errors of the observer. According to the results of trajectory tracking displayed in simulation, we can deduce that whether the reference track is a line, curve or circle, the controller can track it quickly and accurately, and with non overshoot. The tracking error is small

Table 4 Real parameters of the WMR system and the parameters of each controller Parameter m (Kg)

I (Kg m2 ) dg (m)

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Fig. 5 Trajectory tracking, tracking error and estimate error based on circle

and converges rapidly to zero the estimation errors show the validity of the state observer. Figure 6 shows a trajectory tracking controller without fuzzy control to track a circular reference trajectory. Comparing Figs. 5 and 6, the comparative results when they under the same initial conditions about tracking errors and convergence time are obtained. By analyzing Table 5, we can easily know that the trajectory tracking controller based on fuzzy control is able to track the reference trajectory more quickly and has smaller tracking error, better robustness and stability.

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5 Conclusion In this paper, we design a trajectory tracking controller through fuzzy control and extended state observer. The three fuzzy controllers adjust the three parameters online to achieve better control effect. And the extended state observer estimates the external disturbances and compensate the system unknown nonlinear part. Whether the controller tracks a line, a curve or a circular trajectory, it can track quickly and accurately. According to the simulation results shown, we can deduce that the control system is reliable and effective. In this paper, when studying the trajectory tracking control of WMR system, we assume that the conditions of pure rolling and no-slip are met. But if the assumed conditions are not met, we should consider how to get good control effects in the future.

References 1. Xu, J., Guo, Z., Lee, T.H.: Design and implementation of a Takagi-Sugeno-Type fuzzy logic controller on a two-wheeled mobile robot. IEEE Trans. Ind. Electron. 60, 5717–5728 (2013) 2. Huang, J., Guan, Z.-H., Matsuno, T., Fukuda, T., Sekiyama, K.: Sliding mode velocity control of mobile wheeled inverted pendulum systems. IEEE Trans. Robot. 26, 750–75 (2010) 3. Huang, J., Ding, F., Fukuda, T., Matsuno, T.: Modeling and velocity control for a novel narrow vehicle based on mobile wheeled inverted pendulum. IEEE Trans. Contr. Syst. Technol. 21, 1607–1617 (2013)

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4. Mu, J., Yan, X.G., Spurgeon, S.K.: Nonlinear sliding mode control of a two-wheeled mobile robot system. Int. J. Model. Identif. Control (2017) 5. Hwang, E.J., Kang, H.S., Hyun, C.H.: Robust backstepping control based on a Lyapunov redesign for skid-steered wheeled mobile robots. Int. J. Adv. Robot. Syst. (2013) 6. Li, T., Li, W., Bu, R.: A novel decentralised adaptive NN tracking control for double inverted pendulums. Int. J. Model. Identif. Control (2011) 7. Fierro, R., Lewis, F.L.: Control of a nonholonomic mobile robot using neural networks. IEEE Trans. Neural Netw. 9, 589–600 (1998) 8. Huang, J., Ri, M.H., Wu, D.: Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum. IEEE Trans. Fuzzy Syst. 26, 2030–2038 (2018) 9. Jallouli, M., Rekik, C., Chtourou, M.: Optimised fuzzy logic controller for a mobile robot navigation. Int. J. Model. Identif. Control (2010) 10. Han, J.Q.: A class of extended state observers for uncertain systems. Control. Decis. 10, 85–88 (1995) 11. Huang, J., Ri, S., Liu, L., Wang, Y., Kim, J., Pak, G.: Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum. IEEE Trans. Contr. Syst. Technol. 23, 2400–2407 (2015) 12. Yang, H., Fan, X., Xia, Y.: Robust tracking control for wheeled mobile robot based on extended state observer. Adv. Robot. 30, 1–11 (2015) 13. Li, S., Yang, J., Chen, W.: Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans. Ind. Electron. 59, 4792–4802 (2012) 14. Qiang, C., Yu, N.R., Heng, Z.H.: Full-order sliding mode control of uncertain chaos in a permanent magnet synchronous motor based on a fuzzy extended state observer. Chin. Phys. B 24, 110504 (2015)

Design of Wireless Body Area Network with Motion Sensors Using New Materials Guodong Wang, Yanxiao Zhao, Yichun Ding, Jack Yang and Zhengtao Zhu

Abstract Motion detection plays a critical role in wireless body area networks (WBANs) to facilitate patients for physical rehabilitation after an injury or illness. In this paper, we develop motion sensors with new materials and apply these new sensors to monitor motions of fingers as a demonstration. The new materials are low-cost active materials for motion sensors with high compressibility and sensitivity. We design and implement a flexible two-tier WBAN system to remotely monitor and display the motion information of fingers. The system is composed of wireless sensor nodes, wireless receiver, database, Web server, and HMIs. System integration and performance demonstration are conducted. Results show that the proposed WBAN system is capable of remotely detecting finger motions. Furthermore, the proposed WBAN system can be easily extended in other applications by adopting desired sensors. Keywords Motion sensing · WBAN · XBee

1 Introduction Innovative wireless technologies coupled with other emerging technologies, such as the Internet of Things, wearable technologies, and cyber physical systems, are expected to have broad impact on multiple sectors including health care, agricultural G. Wang (B) Department of Computer Science, Massachusetts College of Liberal Arts, North Adams, MA 01247, USA e-mail: [email protected] Y. Zhao (B) Department of Electrical and Computer Engineering , Virginia Commonwealth University , Richmond, VA 23284, USA e-mail: [email protected] Y. Ding · J. Yang · Z. Zhu Department of Chemistry and Applied Biological Sciences, South Dakota School of Mines and Technology , Rapid City, SD 57701, USA © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_66

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monitoring, public safety, security, and surveillance. Wireless body area network (WBAN) with wearable or implantable sensors is a representative example. In recent years, various WBANs have been widely developed to monitor human health status in real-time fashion [1]. In a typical WBAN, a variety of biomedical and strain sensors are attached to human body to monitor physiological parameters and motions of patients. Nowadays, both aged population and young generations often suffer from different diseases, including diabetes, high blood pressure, asthma, heart-related ones, physical impairment or disabilities. Sensing data from WBANs can be used to constantly monitor health condition of aged population or patients to diagnose new diseases, to design optimal maintenance solutions for chronic diseases, or to facilitate recovery from surgeries. It is expected to see a continuous growth of wide applications of WBAN, which will further improve quality of life. WBANs with motion sensors play a critical role in physical rehabilitation to facilitate restoring function for people with injuries of bones, muscles, or nervous systems [2]. In this paper, we focus on developing motion sensors with new materials as well as a flexible WBAN system that integrates with motion sensors. Motion sensors could be placed on figures, hands, arms, knees or ankles to detect the body movement. Flexible and wearable pressure sensors offer convenient, timely, and portable solutions to motion sensors, yet it is a challenge to develop low-cost active materials for pressure sensor with high compressibility and sensitivity. We propose a cost-efficient and scalable approach to prepare highly flexible and compressible conductive sponge for piezoresistive pressure sensor, which will serve as motion sensors. We then develop and implement a flexible WBAN integrated with these motion sensors. The WBAN system is composed of wireless sensor nodes, a wireless receiver (or gateway), a server that runs database and web services, as well as Human Machine Interface (HMI) to display critical sensing information. To test motion detection performance, we place motion sensors on a volunteer’s gloves to test motions when the glove wearer moves figures. The sensing information is transmitted and displayed on the HMI. The main contributions of this paper are summarized as follows: – We develop an practical and flexible WBAN system for motion sensors. This system can be easily extended to support various sensors and further monitor other physiological parameters as needed. – We propose a cost-efficient and scalable approach to produce motion sensor (i.e., piezoresistive pressure sensor) using new materials which is made of highly flexible and compressible conductive sponge. – We demonstrate a simplified WBAN which integrates new motion sensors and interpret how motion is monitored and displayed remotely by the WBAN system. The rest of the paper is organized as follows. Section 2 introduces the existing work in motion sensor materials and WBANs. Section 3 describes the system design of WBAN for motion sensors, including communication system design, motion sensor with new materials, a wireless sensor node based on XBee, components of the WBAN system and HMI. The system integration and demonstration are proposed in Sect. 4. Conclusion is drawn in Sect. 5.

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2 Related Work Strain sensors with high stretchability and sensitivity play a critical role in human motion monitoring and structural health monitoring [3–5]. Conventional strain sensors, which are made of thin metal foils or semiconductors, typically detect only small strain ( 0, bc (˙z s − z˙ u ), ∀ (˙z s − z˙ u ) ≤ 0,

zr

(2)

Fs = ks (z s − z u ) + ksn (z s − z u )3 ,

(3)

Ft = k f (z u − zr ),

(4)

Fb = b f (˙z u − z˙r ),

(5)

The state variables of suspension system can be defined as x1 = z s , x2 = z˙ s , x3 = z u , x4 = z˙ u .

(6)

Then the state-space equation of suspension system (1) can be given as x˙1 = x2 , 1 x˙2 = (−Fd − Fs + u), ms x˙3 = x4 , 1 x˙4 = (Fd + Fs − Ft − Fb − u). mu

(7)

 Let θ = 1 m s , where θ is an uncertain parameter. (1) Ride comfort: Specifically, a PPF is introduced to adjust the convergence rate of x1 , compared with other tracking control methods, the PPF-based scheme can regulate performance of the vertical motion without any prior knowledge of x1 (0).

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(2) Road holding:   |Ft + Fb | < m s min + m u g.

(8)

(3) Suspension movement limitation: |z s − z u | ≤ z max ,

(9)

u min ≤ u ≤ u max .

(10)

(4) Saturation effect of actuator:

3 Control Law Synthesis In this section, a saturated adaptive backstepping controller based on BLF will be designed to realize the desired requirements.

3.1 Adaptive PPF Control and Stability Analysis Step 1: The saturated control law u(t) is defined by ⎧ ⎨ u max , v ≥ u max , u := v, u min < v < u max , ⎩ u min , v ≤ u min ,

(11)

where v(t) is the desired virtual control law. In the controller design, an auxiliary design system [12] is used to compensate the effect of control saturation, which is given by λ˙ 1 = −c1 λ1 + λ2 , λ1 (0) = 0, λ˙ 2 = −c2 λ2 + θˆ u, λ2 (0) = 0,

(12)

where λ1 and λ2 are the state variables of the auxiliary system, θˆ is the estimation value of θ , and u = u − v. To regulate performance of the vertical motion x1 (t), we define an error variable 1 −λ1 , where as z 1 = xϕ(t) ϕ(t) is a positive decreasing smooth function, which is chosen as the PPF. And it can be defined by

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ϕ(t) = (ϕ0 − ϕ∞ )e−r t + ϕ∞ ,

(13)

where ϕ0  ϕ∞  0, and r  0 is the convergence rate. Then we can choose an appropriate convergence rate such that x1 (t) can be constrained by the following bound |x1 (t)| < δ1 ϕ(t) + λ1 ∞ .

(14)

where δ1 is a design parameter chosen by δ1 > |x1 (0)/ϕ0 |, the only prior knowledge that we need to know is the range of x1 (0). Assumption 1 The initial error variable is assumed to be |z 1 (0)| = x1ϕ(0) < δ1 , 0 where δ1 is a tunable positive constant. Step 2: Consider the following BLF [7] candidate

V1 (t) =

1 δ2 In 2 1 2 . 2 δ1 − z 1

(15)

   And we define an error variable as e2 = x1 ϕ − α, where α is the desired virtual function. Then the derivative of (15) can be given by V˙1 (t) =

    z 1 e2 + α − λ1 ϕ δ12 − z 12

.

(16)

     If we choose the virtual function α as α = −k1 δ12 − z 12 z 1 + λ1 ϕ , where k1 is a positive constant. Then (16) can be rewritten as V˙1 (t) =

z 1 e2 − k1 z 12 . δ12 − z 12

(17)

The equation V˙1 (t) = −k1 z 12 ≤ 0 can be guaranteed as long as the error e2 = 0, which further implies that z 1 (t) will converge to zero asymptotically. Clearly, the V1 (t) is bounded and we have V1 (t) ≤ V1 (0). According to Assumption 1, the inequality |z 1 (t)| ≤ |z 1 (0)| ≺ δ1 can be hold in the whole time-domain, then we can get −δ1 ϕ(t) − λ∞ < x1 (t) < δ1 ϕ(t) + λ∞ .

(18)

From (18), the vertical motion x1 (t) can be stabilized within the prescribed bound. Step 3: In this step, a virtual control law v(t) will be synthesized such that the error variables z 1 , e2 and θ˜ = θ − θˆ converge to zero asymptotically.

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Differentiating the error variable e2 along the time, we can get e˙2 =

x˙2 + ϑ, ϕ

˙

(19)

˙ ¨ ˙ 2 )ϕ 1 )ϕ 1 )ϕ where ϑ = − λϕ2 − 2(x2ϕ−λ − (x1 −λ + 2(x1 −λ + k1 δ12 z˙ 1 − 3k1 z 12 z˙ 1 . 2 ϕ2 ϕ3 Defining φ = −Fs − Fd + u and substituting it into (19), Eq. (19) becomes + ϑ. Let ϕ1 = φϕ , then we further have e˙2 = θφ ϕ 2

e˙2 = θ ϕ1 + ϑ.

(20)

Combining (12) with (20), the e˙2 can be rewritten as

e˙2 = θ ϕ1 + θ ϕ1 + ϑ

=

θ (−Fd − Fs + v) + θ ϕ1 + β, ϕ

˙ ¨ ˙ 2 )ϕ 1 )ϕ 1 )ϕ − (x1 −λ + 2(x1 −λ + k1 δ12 z˙ 1 − 3k1 z 12 z˙ 1 . where β = c2ϕλ2 − 2(x2ϕ−λ 2 ϕ2 ϕ3 If the virtual control law v is chosen as:   z1 ϕ −β − 2 − k e v = Fd + Fs + 2 2 , δ1 − z 12 θ

(21)

2



(22)

where k2 is a positive design parameter. Then the closed-loop system (7) is globally asymptotically stable, and all the error variables will converge to zero asymptotically, θ → 0. Specially, the vertical motion can be that is t → ∞ ⇒ z 1 → 0, e2 → 0, stabilized within the prescribed bound. The stability analysis will be shown in Step 5. Step 4: Different from the traditional gradient-based adaptive law, a novel adaptive law is employed in controller design which can makes the error θ converge to zero. Select the auxiliary filtered variables e2 f , ϕ1 f , ϑ f , p1 , q1 as follows k e˙2 f + e2 f = e2 , e2 f (0) = 0,

(23)

k ϕ˙1 f + ϕ1 f = ϕ1 , ϕ1 f (0) = 0,

(24)

k ϑ˙ f + ϑ f = ϑ, ϑ f (0) = 0,

(25)

p˙ 1 = −lp1 + ϕ12 f ,

p1 (0) = 0,

   q˙1 = −lq1 + ϕ1 f e2 − e2 f /k − ϑ f , q1 (0) = 0

(26) (27)

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where k, l are positive design parameters. Then, the adaptive law can be defined by θ˙ˆ = γ e2 ϕ1 − γ σ h 1 ,

(28)



where γ  0, σ  0, h 1 = p1 θ − q1 , and h 1 can be further reformulated as θ based on p1 , q1 . h 1 = − p1 Remark 2 Since Eq. (24) involve the exponent form of er t , if t → ∞, ϕ1 may be infinite. In order to solve this problem, ϕ∞ must be chosen as a positive constant. In this paper, we set ϕ∞ = 0.1 in the controller design. Then the steady-state performance of |x1 (t)| can be stabilized within the prescribed bound δ1 ϕ∞ . Step 5: The stability of close-loop system is analyzed in this step. Substituting (22) into (21), we can get

e˙2 = −

δ12

z1 − k2 e2 + θ ϕ1 . − z 12

(30)

Select a Lyapunov candidate as 1 1 θ 2, V = V1 + e22 + γ −1 2 2

(31)

Differentiating (31) and using (28), (30), we have θ θ˙ˆ V˙ = V˙1 + e2 e˙2 − γ −1 θ2 = −k2 e22 − k1 z 12 − σ p1 ≤ 0.

(32)

Based on Lyapunov-like lemma, the closed-loop system (7) is globally asymptotically stable, and all the error variables will converge to zero asymptotically, that is θ → 0. From t → ∞ ⇒ z 1 → 0, e2 → 0,  (32), it can be seen that V1 (t) ≤ V (0), which further implies that |z 1 (t)| ≤ δ1 1 − e2V1(0) ≺ δ1 , so the prescribed performance (18) can be guaranteed and the vibration damping time can be adjusted by the PPF in (13).

4 Experiment Investigations In this section, the proposed control is implemented in a practical hardware-in-loop (HIL) experiment. The experimental platform is shown in Fig. 2, and the experimental

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PC with QUARC real-time rapid control prototyping software

Data acquisition

Active suspension setup

Power amplifier

EMS

Fig. 2 Experimental setup

components include the following: a motor-actuated active suspension setup, HIL control board; multi-channel power amplifier, Quarc real-time control software, and an emergency switch (EMS). The proposed controller and observer are compiled in Clanguage, and an inline TLC file is created for the hardware acceleration. According to the experimental configuration, the sampling frequency is 0.001 Hz, the maximum suspension deflection is 0.02 m, and the maximum control force is set as 10 N. For brevity, the proposed control scheme is abbreviated as BLF-ABC. For comparison, the following three classical controllers are implemented in the experiment. PD control: u PD = − b1 (k P x1 + k D x2 ), where K p = 5 and K Q = 6.   LQR control: u 1qr = −K x, where K = 24.66 48.87 −0.47 3.68 .   ESO-FLC [11]: u L FC = b1 −K 1 x1 − K 2 x2 − xˆ3 , where K 1 = 401, K 2 = 40, and xˆ3 is obtained by a LESO. The controllers are tested by a sinusoidal input. The excitation frequency and amplitude are set as 3 Hz and 2 mm, respectively. Note that the excitation frequency is the same as the natural frequency of the sprung mass, so the vibration is more observable. The comparative test results are plotted in Figs. 3 and 4. It is clear from Figs. 3 and 4 that the proposed controller acquires a smaller magnitude of the vertical displacement and acceleration when compared with the other controllers. The vibration reduction of the active suspension system is significantly improved by the proposed controller.

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Sprung mass vertical displacement (m)

Fig. 3 Vertical displacement of the sprung mass on the sine excitation

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5 Conclusions A saturated adaptive backstepping controller based on BLF with prescribed performance has been designed to solve the multi-objective control problem of uncertain nonlinear active suspension systems. In order to stabilize the vertical displacement in a given bound, a PPF with adjustable convergence rate is introduced and this method doesn’t require any prior knowledge of initial state values. In order to estimate the sprung mass more accurately, an adaptive law based on error convergence is adopted. The HIL results confirm that the ride quality can be improved by the proposed control scheme.

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Acknowledgements The work is supported by the Joint Research Fund of Department of Science & Technology of Guizhou Province under Grant LH[2015]7093 and Qian-Ke-He platform talent [2017]5789-11 and High-level talent research funding project XJGC20190925.

References 1. Wang, G., Chadli, M., Chen, H., Zhou, Z.: Event-triggered control for active vehicle suspension systems with network-induced delays. J. Franklin Inst. 356(1), 147–172 (2019) 2. Jing, H., Wang, R., Li, C., Bao, J.: Robust finite-frequency H ∞ control of full-car active suspension. J. Sound Vib. 441, 221–239 (2019) 3. Wang, G., Zhou, Z.: Design and implementation of H ∞ miscellaneous information feedback control for vehicle suspension system. Shock Vib. 2019, Article ID 3736402, 15 pages (2019) 4. Yagiz, N., Hacioglu, Y.: Backstepping control of a vehicle with active suspensions. Control Eng. Pract. 16(12), 1457–1467 (2008) 5. Sun, W., Gao, H., Kaynak, O.: Adaptive backstepping control for active suspension systems with hard constraints. IEEE/ASME Trans. Mechatron. 18(3), 1072–1079 (2013) 6. Sun, W., Zhao, Z., Gao, H.: Saturated adaptive robust control for active suspension systems. IEEE Trans. Ind. Electron. 60(9), 3889–3896 (2013) 7. Tee, K., Ge, S., Tay, E.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009) 8. Niu, B., Zhao, J.: Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Syst. Control Lett. 62(10), 963–971 (2013) 9. Sun, W., Pan, H., Zhang, Y., Gao, H.: Multi-objective control for uncertain nonlinear active suspension systems. Mechatronics 24(4), 318–327 (2014) 10. Huang, Y., Na, J., Wu, X., Liu, X., Guo, Y.: Adaptive control of nonlinear uncertain active suspension systems with prescribed performance. ISA Trans. 54(1), 145–155 (2015) 11. Pan, H., Sun, W., Gao, H., Hayat, T., Alsaadi, F.: Nonlinear tracking control based on extended state observer for vehicle active suspensions with performance constraints. Mechatronics 30, 363–370 (2015) 12. Chen, M., Ge, S., Ren, B.: Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47(3), 452–465 (2011)

High Gain Finite-Time Trajectory Tracking Control of Pneumatic Muscle Actuator Tong Shen and Jian Huang

Abstract In this paper, a high gain trajectory tracking control method is proposed for the pneumatic muscle actuator with the tracking errors converging in a finitetime interval. Firstly, we design the sliding surface that ensure the system tracking error reach it within a finite time. Then, an controller with a disturbance observer is designed, which achieves the convergence of the errors within a finite time. At last, numerical simulations, which compare high-gain finite time control with normal finite time control, demonstrate the validity of the method we proposed. Keywords Pneumatic muscle actuator · Tracking control · Finite-time control

1 Introduction The Pneumatic Muscle Actuator (PMA), which can be described by a three-elements model including the contractile, spring and damping, is a novel actuator with numerous advantages such as safety, low-cost, and low-light. It is widely applied in many fields and applications, especially in medical devices, electronic equipments, and industries [1, 2]. However, the trajectory tracking with fast convergence and high accuracy for this kind of actuator has faced challenges due to time-varying parameters, uncertainties and external disturbances in the complex nonlinear dynamics system. To deal with the control difficulties, researchers have concentrated on various control methods for the PMA, such as the artificial neural network (ANN)-based control [3, 4], fuzzy control [5], PID [6], SMC [7] and so on. The fuzzy control of PMA relies on the experience to obtain the fuzzy rules and membership functions. Although the PID technique has been widely accepted in the industrial control, the parameters of PID controller cannot be acquired from sound theoretical support. On T. Shen · J. Huang (B) The Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_73

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the other hand, the key of the ANN depends on choosing the optimal weight for training the neural network. The sliding mode control (SMC) with high robustness against uncertain and disturbance may be a suitable solution for the PMA, while the chattering problem due to discontinuous control laws is undesirable. Also, linear sliding surfaces are used in SMC cannot guarantee globally finite-time stability. In order to improve the convergence performance and anti-disturbance performance of the closed-loop systems, the finite time stability concept and a terminal sliding mode control have been introduced [8]. It indicates that state of the system should reach the origin in a finite time interval. However, there are singular problems in the design of the controller based on the standard terminal sliding surface, because of the existence of nonlinear terms. Moreover, the chattering problem also exists in the control efforts and the initial conditions play a significant role in the convergence rate [9]. To wipe out the singularity, Feng [10] has proposed the nonsingular terminal sliding mode control (NTSMC), which cannot deal with the remaining chattering problems. The second-order NTSMC eliminates the chattering problems in trajectory tracking within a finite time [11]. On the other hand, observer-based robust control methods can get rid of the system uncertainties. One of them is the disturbance observer for estimating the systems disturbance [12]. Another is the state observer e.g. the velocity observers used in the finite-time trajectory tracking [13]. However, most of the asymptotically stable observers cannot ensure the state variables of the closed-loop system to be convergent within a finite time. Although the finite-time control technique is widely used in the control of various nonlinear systems, there are few results of high-gain finite-time control for PMA. The main contribution of this study is that the proposed tracking control gain can be adjusted to increase the flexibility of the design of tracking controller. Thus, it can speed up the convergence of the errors and reduce the convergent time. In this paper, we propose a second-order NTSMC surface with disturbance observer for finite-time trajectory tracking of PMA. In Sect. 2, the model of PMA with three elements and mathematical symbols are introduced. Consecutively, a finitetime control algorithm is proposed to realize our control goal of PMA. Based on the Lyapunov stability theory, a finite-time observer is also given and the convergence of finite-time trajectory tacking of PMA is proved in the Sect. 3. Section 4 describes the simulation of trajectory tacking that verifies the proposed methods.

2 The Model of PMA During the working process of pneumatic muscles, which is shown in Fig. 1, the fibrous layer plays a crucial role. When the PMA is inflated, the rubber bladder begins to expand. Due to the constraint of the fiber layer on the movement of the rubber bladder, the radial expansion force of the rubber bladder is converted into the axial direction force of PMA. Reynolds [14] has proposed the model of PM with three elements (a contractile element, a spring element, and a damping element), which describes the dynamic

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Fig. 1 The working process of PM Fig. 2 Three elements

behavior of PMA approved by many researchers. The principle of the three-elements model is shown in the Fig. 2 and the dynamic equation are given as follows: m x¨ + B(P)x˙ + K (P)x = F(P) − mg

(1)

where m is the mass, and P means input pressure. x describes the three contractile length of PMA, and x = 0 indicates the initial condition that no air is input. g means acceleration of gravity. Moreover, F(P), K (P) and B(P) denote a contractile element, a spring element, and a damping element respectively. And the linear function between pressure and F is:

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F(P) = F0 + F1 P

(2)

The piecewise linear functions K (P) and B(P) describe the relationship between pressure and the spring coefficient, the damping coefficient:  K (P) = K 0 + K 1 P =  B(P) = B0 + B1 P =

K i0 + K i1 P (P > P0 ) K j0 + K j1 P (P < P0 )

(3)

B0z + B1z P (inflation) B0y + B1y P (deflation)

(4)

Let x1 = x and x2 = x. ˙ Considering the existence of the external disturbances and uncertainties, the dynamic model of PMA (1)–(4) can be rewritten as below: 

x˙1 = x2 x˙2 = W (x1 , x2 ) + D(x1 , x2 , t) + Q(x1 , x2 )P

(5)

where W (x1 , x2 ) = m −1 (F0 − mg − B0 x2 − K 0 x1 ), D(x1 , x2 , t) = m −1 d, and Q(x1 , x2 ) = m −1 (F1 − B1 x2 − K 1 x1 ). d is used to denote the lumped external disturbance, errors, and uncertainties of the PMA. And we assume that d and d˙ satisfy the following conditions: ˙ < md1 |d| < d0 , |d| Obviously, D(x1 , x2 , t) also satisfies that ˙ < d1 |D| < d0 m −1 , | D|

(6)

3 Finite-Time Trajectory Tracking with Disturbance Observer for PMA In this paper, our main aim is the finite-time trajectory tracking with high gain for PMA. Firstly, sliding surfaces are designed to ensure the tracking error system reach the sliding surfaces within a finite-time Tr . Secondly, a controller is designed such that the tracking errors converge to the origin in finite-time Ts interval. Therefore, the total convergence time is less than T = Tr + Ts . Let x j = (x1 j , x2 j ) denote the desired trajectory. By defining the tracking errors as e1 = x1 − x1 j and e2 = x2 − x2 j , the dynamics of the tracking error system are obtained:  e˙1 = e2 (7) e˙2 = W (x1 , x2 ) + D(x1 , x2 , t) + Q(x1 , x2 )P − x˙2 j

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Now, we design the second order terminal sliding surface as ξ

s = ϕ + e˙2 + l 1−ξ sig ξ (e2 ) + lsig 2−ξ (ψ(e1 , e2 ))

(8)

where ϕ is a subsidiary vector, and l > 1 which can speed up the convergence of the system. For α is a real number, we have sig α (x) = |x|α sign(x). sign(x) describes the 1 sig 2−ξ (e2 ) where 0 < ξ < 1. signum of the real number x, and ψ(e1 , e2 ) = e1 + 2−ξ The control law P and subsidiary vector Pr are proposed as bellow ξ

P = Q −1 (x1 , x2 )(x˙2 j + Pr − W (x1 , x2 ) − l 1−ξ sig ξ (e2 ) − lsig 2−ξ (ψ(e1 , e2 ))) (9) P˙r = −λs − Dˆ − lγ sig ε (s) − (d0 m −1 + d1 )sign(s)

(10)

where λ, ε, γ > 0 are three constants. The disturbance observer Dˆ is employed for estimating D which is given by Dˆ = −qϕ − W (x1 , x2 ) − plsig ε (ϕ) −|W (x1 , x2 )|sign(ϕ) − d0 m −1 sign(ϕ) θ˙ = Q(x1 , x2 )P − qϕ − x˙2 − plsig ε (ϕ)

(11)

−|W (x1 , x2 )|sign(ϕ) − d0 m −1 sign(ϕ)

(12)

where ϕ = θ − e2 , and p, q > 0 are two constants. Theorem 1 Consider the control law (9)–(10) and the disturbance observer (11)– (12). For PMA (5), state x(t) converges to the desired trajectory x j in a finite-time interval. Proof Considering the sliding surface (8) and the control law (9)–(10), choose a Lyapunov functional 1 V1 = (s 2 + ϕ 2 ) 2 where s = D + ϕ + Pr . By using (7)–(9), s s˙ is given by ˙ s s˙ = −λs 2 − Ds − lγ |s|1+ε − (d0 m −1 + d2 )|s| + Ds

(13)

According to the conditions (6), we have s s˙ ≤ −λs 2 − γ l|s|1+ε

(14)

From (9) and ϕ = θ − e2 , ϕ ϕ˙ is given by ϕ ϕ˙ = −qϕ 2 − pl|ϕ|1+ε − |ϕ||W | − ϕW − ϕ D − d0 m −1 ϕ

(15)

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Note that −ϕ D < ϕ|D| and −|ϕ||W | − ϕW < 0, then we have ϕ ϕ˙ ≤ −qϕ 2 − pl|ϕ|1+ε

(16)

By defining δ = min(λ, q) and ζ = min(γ , p), the derivative of V1 = 21 (s 2 + ϕ 2 ) is given by 1+ε 1+ε (17) V˙1 ≤ −2δV1 − 2 2 lζ V1 2 Then, s and ϕ converge to zero in a finite time interval [10] and the settling time Tr satisfies that δ 2 (1 − ε) 1−ε V1 2 (18) Tr ≤ l From (18), we have ϕ = 0 and ϕ˙ = 0 when t > Tr . Let D˜ = Dˆ − D, then we have D˜ = −qϕ − W (x1 , x2 ) − psig ε (ϕ) − | f (x1 , x2 )|sign(ϕ) − d0 m −1 − D = Q(x1 , x2 )P − qϕ − x˙2 − psig ε (ϕ) − | f (x1 , x2 )|sign(ϕ) − d0 m −1 = θ˙ − e˙2 = ϕ˙

(19)

which implies that Dˆ converges to D after the finite time Tr . Moreover, the errors tracking system can be written as 

e˙1 = e2 ξ e˙2 = l 1−ξ sig ξ (e2 ) + lsig 2−ξ (ψ(e1 , e2 ))

(20)

Consider the following transformation e1 = et1 , e2 = let2

(21)

Then, the tracking error system can be rewritten as 

e˙t1 = let2 ξ e˙t2 = −lsig ξ (let2 ) − lsig 2−ξ (ψ(et1 , let2 ))

(22)

Choose the positive Lyapunov function V2 with 0 < κ < 1, ρ > 1 V2 =

3−ξ 2−ξ ρ |ψ(et1 , let2 ))| 2−ξ + κe2 ψ(et1 , let2 )) + |let |3−ξ 3−ξ 3−ξ 2

Along the system (20), the derivation of V˙2 defined by (21) can be obtained

(23)

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V˙2 = l(−κet22 − κ|ψ(et1 , let2 )| 2−ξ − |et2 |1−ξ |ψ(et1 , let2 )| 2−ξ 1+ξ

2

ξ

−κψ(et1 , let2 )sig ξ (et2 ) − (κ + ρ)sig 2−ξ (et2 )sig 2−ξ (ψ(et1 , let2 )) < 0 (24) Let Φ = {(et1 , let2 ) : V2 (et1 , let2 ) = 1}. Note that the following equalities V2 (k 2−ξ et1 , klet2 ) = k 3−ξ V2 (et1 , let2 ) 1 ˙ 2−ξ 1 V2 (k et1 , klet2 ) = k 2 V˙2 (et1 , let2 ) l l

(25)

hold for any k > 0. Since V˙2 is continuous on Φ, the maximum of V˙2 can be obtained. Define c = − max(e1 ,e2 )∈Φ V˙2 which is always greater than zero. By setting 1 − 3−ξ

k = V2

, we have − 2−ξ − 1 1˙ 1 − 2 V2 (V2 3−ξ et1 , V2 3−ξ let2 ) = V2 3−ξ V˙2 ≤ −c l l

which implies that 2

V˙2 ≤ −clV23−ξ Therefore, the settling time Ts can be obtained Ts ≤

1−ξ 3−ξ V23−ξ (et1 (Tr ), let2 (Tr )) lc(1 − ξ )

(26)

The tracking error system is finite-time stable and the total convergent time T < 1−ε

1−ξ

3−ξ V1 2 + lc(1−ξ V 3−ξ (et1 (Tr ), let2 (Tr )). It is obvious that increasing Tr + Ts = δ (1−ε) l ) 2 the value of l can speed up the convergence time. 2

4 Numerical Simulations To verify the effectiveness of the method we proposed, numerical simulations are carried out on the model of PMA as mentioned before in Sect. 4. Comparison will be made between the high-gain fast finite time control (FFTC) with l = 1.8 and the normal finite time control (NFTC) with l = 1.0 under the same condition. Based on the practical system platform, the parameters of PMA are given in Table 1. We use Matlab/Simulink to establish the model of PMA and realize the finite-time trajectory tracking. The initial condition of the PMA is set as x1 = 0.01, x2 = 0.05, and the disturbance is given by D = 0.1 sin(t), which can verify the robustness of the method we proposed. And the desired trajectories are set as x1 j = 0.015 sin(0.5π(t)) + 0.015 and x2 j = 0.0075π cos(0.5π(t)). The other parameters are set as follows:

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Table 1 The parameters of PMA Parameter Value −91.293 N 0.0016 N/kPa −3653 N/m 0.0406 N/m kPa 495.30 N/m 1 kg

F0 F1 K i0 K i1 K j0 m

Parameter

Value

K j1 B0z B1z B0y B1y g

−0.2839 N/m kPa 52.08 s/m −0.0001245 s/m kPa −3.19 s/m 0.0009022 s/m kPa 9.8 m/s2

0.035 0.03

Trajectory(m)

0.025 0.02 0.015 0.01 NFTC Reference FFTC

0.005 0

0

1

2

3

4

5

6

7

8

9

10

Time(s)

Fig. 3 The trajectory tracking curves of x1

ξ = 0.8, λ = 50, γ = 30,  = 0.9, q = 100,

p = 10.

Figures 3 and 4 show the position tracking curves and the velocity traking curves obtained by the methods of FFTC and NFTC. The states of PMA almost converge to the desired trajectories within total time T ≈ 2.4 s and the chattering phenomenon does not exist even the disturbance exists. Moreover, it is obvious that the convergent speed of FFTC is faster than that of NFTC. Figure 5 shows the convergence of traking errors by the methods of FFTC and NFTC. The result shows that, compared with NFTC, the methods of FFTC has a better perfomance in depressing the overshoot and improving the response speed. The convergence of velocity errors is shown in Fig. 6, which also illustrates that the method of FFTC achieves better performance than that of NFTC.

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0.05 0.04

NFTC reference FFTC

Velocity(m/s)

0.03 0.02 0.01 0 -0.01 -0.02 -0.03

0

1

2

3

4

5

6

7

8

9

10

Time(s)

Fig. 4 The trajectory tracking curves of x2 Fig. 5 The trajectory errors of e1

-3

10

2 0 -2

FFTC NFTC

Trajectory(m)

-4 -6 -8 -10 -12 -14 -16 -18

0

1

2

3

4

5

Time(s)

6

7

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Fig. 6 The trajectory errors of e2

0.02 FFTC NFTC 0.01

Velocity(m/s)

0

-0.01

-0.02

-0.03

-0.04

-0.05

0

1

2

3

4

5

6

7

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Time(s)

5 Conlusion In this paper, a high-gain finite-time trajectory tracking for PMA was proposed. The two stages in finite-time trajectory tracking were introduced and we designed the terminal sliding surface for the PMA. Moreover, we chose the different Lyapunov function candidate for the stages, and the convergence of Lyapunov function had been proved. Finally, numerical simulations demonstrated the validity of our proposed methods.

References 1. Choi, T.-Y., Choi, B.-S., Seo, K.-H.: Position and compliance control of a pneumatic muscle actuated manipulator for enhanced safety. IEEE Trans. Control Syst. Technol. 19, 832–842 (2011) 2. Huang, J., Tu, X., He, J.: Design and evaluation of the RUPERT wearable upper extremity exoskeleton robot for clinical and in-home therapies. IEEE Trans. Syst. Man Cybern. Syst. 46, 926–935 (2016) 3. Huang, J., Cao, Y., Xiong, C.H., Zhang, H.T.: An echo state gaussian process based nonlinear model predictive control for pneumatic muscle actuators. IEEE Trans. Autom. Sci. Eng. (2018) 4. Huang, J., Qian, J.: Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator. J. Franklin Insti. 353, 2761–2782 (2016) 5. Chen C., Huang J.: T-S fuzzy logic control with genetic algorithm optimization for pneumatic muscle actuator. In: 2018 10th International Conference on Modelling, Identification and Control (ICMIC)

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6. Kawashima, K., Sasaki, T., Ohkubo, A., Miyata, T., Kagawa, T.: Application of robot arm using fiber knitted type pneumatic artificial rubber muscles. In: IEEE Conference on Robotics and Automation, pp. 4937–4942. New Orleans (2004) 7. Xing, K., Huang, J., He, J., Wang, Y., Wu, J., Xu, Q.: Sliding mode tracking for actuators comprising pneumatic muscle and torsion spring. Trans. Inst. Meas. Control 34, 255–277 (2012) 8. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43, 678–682 (1998) 9. Du, H. , Li, S.: Finite-time cooperative attitude control of multiple spacecraft using terminal sliding mode control technique. Int. J. Modell. Ident. Control (2012) 10. Saad, W., Sellami, A., Garcia, G.: Terminal sliding mode control-based MPPT for a photovoltaic system with uncertainties. Int. J. Modell. Ident. Control 29(2), 118–126 (2018) 11. Levant, A., Michael, A.: Adjustment of high-order sliding mode controllers. Int. J. Robust Nonlinear Control 19, 1657–1672 (2009) 12. Chen, W.H.: Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatron. 9, 706–710 (2004) 13. Tan, C.P., Yu, X., Man, Z.: Terminal sliding mode observers for a class of nonlinear systems. Automatica 46, 1401–1404 (2010) 14. Reynolds, D.B., Repperger, D.W., Phillips, C.A., Bandry, G.: Modelling the dynamic characteristics of pneumatic muscle. Ann. Biomed. Eng. 31, 310–317 (2003)

Research on Reversing Radar Based on Linear Structured Light Xinliang Tang, Yang Li and Jianhua Zhang

Abstract Aiming at the problem that the existing reversing radar detection method can not accurately detect obstacles, a detection method based on structured light is proposed. Remove the noise point by median filtering the strip image, and the strip area is obtained by using the characteristics of the line structure light in the RGB space and the gray space. The gray center of gravity method is used to extract the initial center of the light strip. Based on this, the Hessian matrix is used to extract the sub-pixel center of the strip, which reduces the number of calculations of Gaussian convolution and improves the extraction speed of the sub-pixel center of the strip. The distance, width and angle information of the obstacle are determined by calculating the light bar parameters. The experimental results show that the reversing radar based on line structure light can meet the real-time and accuracy of detecting obstacles in reversing. Keywords Line structured light · Reversing radar · Obstacle detection

1 Introduction With the continuous progress and development of Chinese society, the people’s living standards have been greatly improved. By the end of 2017, the number of car ownership in the country had reached 217 million, and the construction of roads and parking lots did not keep up with the demand for car growth and became more and more crowded. Due to the limited field of view, accidents that collide with obstacles during the reversing process often occur, posing a great threat to the safety of drivers and public facilities. Therefore, how to quickly and accurately detect obstacles has become one of the key research contents in the parking sensor technology. The current reversing assisted driving technology mainly uses ultrasonic sensors to emit ultrasonic waves, uses ultrasonic principles to detect obstacles, or uses reversing images to display the situation behind the vehicle on the screen. However, the X. Tang · Y. Li (B) · J. Zhang Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_74

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reversing radar has a blind spot. Generally, an object with a height of less than 20 cm is difficult to be detected by a reversing radar within 2 m, such as a ground lock on a parking space or a protruding iron bar. The reversing image uses a wide-angle lens to cover a wide range of fields of view, and the object will be deformed. The distance displayed on the screen is different from the actual distance, which may cause misjudgment. The line structure optical vision technology has wide application in threedimensional measurement, etc. due to its advantages of simple structure, low cost, good real-time performance and high accuracy. Through the research on the application of structured light in different fields, this paper innovatively applies structured light vision to the field of reverse assisted driving. When the line structure light is emitted to the surface of the object, a laser strip is generated. If an obstacle is encountered, some of the strips are offset. Since the real-time image needs to be processed during the reversing process, this paper adopts a CCD camera with better dynamic image acquisition to obtain the light bar image. The median filtering algorithm is used to filter out image noise, and the region of interest is obtained by utilizing the characteristics of the line structured light in the RGB color space and the gray space. The gray center of gravity is used to extract the initial center of the strip, and on this basis, the Hessian matrix is used to extract the sub-pixel center of the strip. Based on the optical triangulation method and the imaging principle of CCD camera, the mathematical model of the line structure optical vision system is established. The distance, width and angle of the obstacle are calculated according to the information of the sub-pixel center parameters of the light strip, and the obstacle is detected during the reversing process.

2 Principle of Line Structured Light Vision System Optical triangulation is a method of active vision measurement, and its threedimensional parameter information is calculated by the angle of the object to be measured offset relative to the optical reference line. The method has the advantages of simple structure, fast measuring speed, and the like, and has wide applications in distance measurement and three-dimensional measurement [1]. The angle between the incident light and the normal to the side can be divided into two types: direct optical triangulation and oblique optical triangulation. According to the research on the detection environment and the installation position, the direct optical triangulation is more concentrated when the surface of the object is irradiated, and the width of the strip is not enlarged by the unevenness of the side surface. The oblique optical trigonometry can make The imaging surface acquires more light strip information. Compared with the direct optical triangulation method, the noise interference is smaller and the sensitivity to the light strip change is higher. The oblique optical triangulation method is more suitable for the detection of obstacles during the reverse driving process [2].

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Fig. 1 Line structured light vision system

The line structure optical vision system is mainly composed of a line structure light emitter, a CCD camera and a lens, as shown in Fig. 1[3]. The system needs to be calibrated before measurement so that the line structured light vision system can accurately calculate the obstacle information through the light bar image. At the standard time, the checkerboard of the checkerboard is placed two meters behind the car, and it is photographed at different angles to extract 20 images. The focal length information can be obtained by measuring the internal and external parameters of the CCD camera using the camera calibrator in Matlab 2015. The actual position of the line structure light and the positional relationship in the image are as shown. Oc is the optical center, AB is the partial line structured light that is irradiated onto the ground, A B is the line structured light image reflected by the line structure light onto the imaging surface of the CCD camera, and C point is any point on the line structured light, C Point is the corresponding point on point C of the light bar image, and L is the distance from the line structure light to the CCD camera. The line structure photo imaging surface is shown in Fig. 2. The imaging plane coordinate system is Oo-X Y , Y is the distance from C to X axis, X is the distance from C to Y’ axis, D is the length of A B , and the pixel coordinates of C point are (x, y). Let A B have the number of pixels N, the CCD camera has a pixel size of e, and the focal length is f, then Y, X, and D can be obtained. The formula is as follows (1): ⎧ ⎨ Y = e × |y| X = e × |x| ⎩ D =e×N

(1)

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X

B Y

A C B

Oc

X

A

D

L

f

C

Oo

B C A Y

Fig. 2 Imaging schematic. Oc is the optical center, AB is the partial line structured light that is irradiated onto the ground, A B is the line structured light image reflected by the line structure light onto the imaging surface of the CCD camera, and C point is any point on the line structured light, C Point is the corresponding point on point C of the light bar image, and L is the distance from the line structure light to the CCD camera. The imaging plane coordinate system is Oo-X Y , Y is the distance from C to X axis, X is the distance from C to Y axis, D is the length of A B , and the pixel coordinates of C point are (x, y)

3 Obstacle Detection Algorithm 3.1 Image Preprocessing During the image acquisition process of the online structured light strip, due to the sway of the CCD camera and the imaging process, the captured image will be affected by the noise. The salt and pepper noise appears as black and white bright and dark point noise in the image. Edge detection has a large impact. In order to accurately extract the region of interest of the strip image, it is necessary to filter the image acquired by the camera. This paper uses median filtering to effectively filter out salt and pepper noise and preserve edge information. The R, G, and B channels of the color image are extracted, and median filtering is performed on the three channels, and the denoised color image is obtained by recombining the filtered three-channel image.

3.2 Image Region of Interest Extraction After the filtering operation, it is necessary to extract the region of interest of the image, that is, extract the strip region. The line structure light appears red after being projected onto the surface of the object and has a higher brightness than the surrounding environment. In the R channel of the RGB color space, set the appropriate threshold to extract the red area. A region matching the Gaussian distribution is longitudinally searched in the grayscale image and extracted. The area where the red area coincides with the area corresponding to the Gaussian distribution is the area of interest [4].

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3.3 Optical Strip Sub-Pixel Center Extraction Algorithm In the process of camera imaging, the obtained image data is a process of discretizing the image, and each pixel on the imaging surface represents only a nearby color. The two pixels are macroscopically connected, and there are countless tiny things between them on the microscopic [5]. These pixels, which exist between two actual physical pixels, are called “sub-pixels”. Since the light beam will become thicker when the structured light is irradiated onto the surface of the object, the position of the light bar cannot be positioned. In order to accurately measure obstacle parameters, the sub-pixel center of the strip is required [6]. The Hessian matrix method calculates the normal direction of the strip by Hessian matrix, and uses Taylor expansion to obtain the sub-pixel center of the strip in the normal direction. The precision is high, but multiple convolution calculations are needed, and the operation speed is slow [7]. Therefore, this paper first uses the gray center of gravity method to calculate the light bar column by column along the normal direction of the light bar, and finds the gray center of gravity of each column as the initial center of the light bar. The calculation formula is as follows (2): n yi =





j=1 f x i , y j ∗ y j  n  j=1 f x i , y j

(2)

Assume that along direction of the   light bar, the pixel coordinates of  the normal of the i-th column are xi , y j , the gray value is f xi , y j , i is 1 to m for the length   the light bar, and j is 1 to n for the light bar. Width, the center of the strip is xi , y j . The initial center of the strip is calculated as the base point in the Hessian matrix method. This method can reduce the number of Gaussian kernel convolutions in the calculation process of the sub-pixel center of the strip by using the initial center extraction, and effectively improve  the running speed [8]. It is assumed that the normal direction of the strip is n x , n y corresponding to the eigenvector of the maximum absolute eigenvalue of the Hessian matrix. The Taylor sub-pixel center is obtained by using Taylor expansion along the normal direction of the light strip. The second-order Taylor expansion is as follows (3):  g(x, y) = g(xi , yi ) + [(x − xi )(y − yi )]

gx (xi , yi ) g y (xi , yi )



  1 gx x (xi , yi ) gx y (xi , yi ) (x − xi ) + [(x − xi )(y − yi )] gx y (xi , yi ) g yy (xi , yi ) (y − yi ) 2

(3)

The partial derivative of the image and the Gaussian kernel can be obtained gx , g y , gx x , g yy , gx y , For any point on the light bar (x, y). The Hessian matrix can be expressed as (4):

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gx x gx y H(x, y) = gx y g yy

(4)

  In the strip image, the strip center n x , n y The first order of direction is 0, And the second order is negative [9]. Taking the initial center of thestrip (xi , yi ) as the base point, the second-order Taylor expansion along the n x , n y direction is (5):   1 g xi + tn x , yi + tn y = g(xi , yi ) + tn x gx (xi , yi ) + tn y g y (xi , yi ) + t 2 n 2x gx x (xi , yi ) 2 1 2 2 2 (5) + t n y g yy (xi , yi ) + t n x n y gx y (xi , yi ) 2

  The first derivative from the center of the strip n x , n y is 0, as shown in (6):  ∂  g xi + tn x , yi + tn y = 0 ∂t

(6)

In turn, it can be obtained from the above two formulas (7): t=−

n 2x gx x

n x gx + n y g y + 2n x n y gx y + n 2y g yy

(7)

The point where thefirst derivative is 0 is located at the current pixel, and the  second derivative of the n x , n y direction is smaller than the specified threshold [10].  As shown in the following Eq. (8), the extreme point of the pixel xi + tn x , yi + tn y is the light bar. The sub-pixel center.   tn x , tn y ∈ [−0.5, 0.5] × [−0.5, 0.5]

(8)

3.4 Obstacle Parameter Calculation When there is no obstacle in the process of reversing, the line structured light strip is a straight line parallel to the X axis. When the line structure light encounters an obstacle, some of the light strips will be offset [11]. From the length of the strip in which the offset occurs, the width W of the obstacle can be calculated. From the position of the deflected light bar in the horizontal direction of the overall light bar, the angle γ of the obstacle relative to the car can be calculated. Since the position and angle of the line-structured light vision system remain unchanged in the car, the distance L between the light bar projected onto the ground and the car does not change [12]. If the light bar is offset during the reversing process, it is judged that an obstacle is encountered, and the distance between the obstacle and the car can be approximated as L.

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Oc Og E Q F

b

Oc

γ

L γ

f

F

a

Q

obstacle

E

O

L

Fig. 3 Obstacle parameter calculation model. The coordinate system of the CCD camera is Oc − X c Yc Z c , and the coordinate system of the line structure light emitter is Og − X g Yg Z g . The angle between the line structured light surface and the ground is α, and the distance from the ground is a. The angle between the optical axis of the CCD camera and the ground is β, and the distance from the ground is b. The optical axis intersects the ground at point O. The intersection of the light bar and the obstacle is E, F, and the midpoint is Q, which corresponds to E (u1, v1), F (u2, v2), Q (u3, v3) in the imaging plane

Assume that the coordinate system of the CCD camera is Oc − X c Yc Z c , and the coordinate system of the line structure light emitter is Og − X g Yg Z g . The angle between the line structured light surface and the ground is α, and the distance from the ground is a. The angle between the optical axis of the CCD camera and the ground is β, and the distance from the ground is b. The optical axis intersects the ground at point O. The intersection of the light bar and the obstacle is E, F, and the midpoint is Q, which corresponds to E (u1, v1), F (u2, v2), Q (u3, v3) in the imaging plane [13]. As shown in Fig. 3. The distance, width and angle information of the obstacle can be obtained by the optical triangulation principle. The obstacle distance L is calculated as follows (9): L=

a tan α

(9)

The angle γ of the obstacle relative to the car is the angle between Q Oc and the optical axis of the CCD camera. The calculation formula is as follows (10), (11). tan γ =

γ=

e × |u 3 | f

3| −ar c tan e×|u , u3 < 0 f e×|u 3 | ar c tan f , u 3 ≥ 0

(10)

(11)

Obstacle width W, the formula is as follows (12), (13): EF (u 2 − u 3 ) × e = f L

(12)

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W = EF =

(u 2 − u 3 ) × e ×L f

(13)

4 Experimental Verification 4.1 Light Strip Sub-pixel Center Extraction Experiment In order to verify the effectiveness of the strip center extraction method in the subpixel center extraction of the light strip, the raspberry pie was used to perform experiments under opencv3.2, and the results of the region of interest extraction are shown in Fig. 4. For the image of the region of interest, the gray center of gravity method, Hessian matrix method and this method are used to extract the center of the light bar from the region of interest [14]. The extraction results are shown in Fig. 5. Since the light bar image in the experiment is a straight line, the obtained light bar center data points are respectively straight line fitted. By calculating the mean square error of all the strip center data points to the fitted line, the accuracy of the strip center extraction method can be compared. In the same experimental environment, if the mean square error of the distance between the center data points of the light strips and the fitting straight line is large, the extraction accuracy of the strip center of the method is low, if the center data points of the strips are fitted to the straight line

Fig. 4 Area of interest, red area binarization, Grayscale and area of interest

Fig. 5 Gray scale center of gravity method, Hessian matrix method and this article

Research on Reversing Radar Based on Linear Structured Light Table 1 Comparison of light bar center extraction algorithms

797

Method

Mean variance mean

Average time (t/ms)

Gray scale center of gravity method

0.3827

116

Hessian matrix method

0.1962

245

Method of this paper

0.1737

131

distance If the variance is small, the extraction center of the strip of the method is highly accurate [15]. The average of the mean square error and the average value of the extraction time were obtained after repeated calculations, and the data statistics are shown in the following Table 1. The mean square error of the method is 0.209 lower than the gray center of gravity method and 0.0225 lower than the Hessian matrix method. The average time is 15 ms higher than the gray center of gravity method and 114 ms lower than the Hessian matrix method. It shows that the method is more accurate than the gray center of gravity method, and has little difference from the accuracy of the Hessian matrix method. It is shorter than the average time of the Hessian matrix method and has little difference from the average time of the gray center of gravity method. Speed and accuracy requirements.

4.2 Obstacle Detection Experiment In order to verify the effectiveness of the obstacle detection method in this paper, the parameters of this method are used to calculate the parameters of different obstacles, and the distance, width and angle information are obtained. The average value of each obstacle is compared with the actual parameters. As shown in Table 2. The first and fourth groups are compared, the second and fifth groups are compared, and the third and sixth groups are compared. When the actual widths of the obstacles are the same and the average actual distance is different, the closer the average actual distance is, the more accurate the obstacle measurement distance is. The error is small with respect to the average actual distance, and the closer the average actual distance is, the narrower the actual width is, the smaller the measurement angle error is. The first, second, and third groups are compared, and the fourth, fifth, and sixth groups are compared. When the obstacle measurement distance is the same and the actual width is different, the actual width is wider and the measurement width error is smaller. Using the method in the literature and the method of this paper, 30 test experiments were performed on different obstacles under the same environment, and the average value and detection rate of the detection time were obtained, as shown in Table 3.

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Table 2 Obstacle detection experiment Measuring distance (cm)

Average actual distance (cm)

Average measurement width (cm)

Actual width (cm)

Average measurement angle (°)

Actual angle (°)

First group

100

98.6

11.6

10

−46

−45

Second group

100

98.5

21.5

20

1

0

The third group

100

98.7

31.5

30

47

45

Fourth group

200

196.9

11.9

10

−47

−45

Fifth group

200

196.5

21.7

20

2

0

The sixth group

200

196.8

31.6

30

48

45

Table 3 Comparison of detection algorithms Detection rate (%)

Average detection time (ms)

Literature 1 [1]

97.7

953

Literature 2 [2]

96.4

764

Literature 3 [3]

97.3

882

Method of this paper

98.5

526

The detection rate of this method is 0.8% higher than that of literature 1. It is 2.1% higher than that of literature 2 and 1.2% higher than that of literature 3. The average detection time is 427 ms lower than literature 1 and 238 ms lower than literature 2 and 356 ms lower than literature 3. Compared with the three methods in the literature, the method has faster detection speed and higher detection rate, can meet the real-time detection of obstacle parameters in the reverse environment, and complete the purpose of assisting the driver to reverse.

5 Conclusion Due to the importance of reversing assisted driving and the low speed of the prior art detection, this paper proposes a reversing assisted driving technology based on line structure light. By improving the sub-pixel center extraction method of the light strip, the extraction speed and accuracy of the sub-pixel center of the strip are improved. The optical triangulation method and CCD camera imaging principle are studied, and the accurate calculation of obstacle distance, width and angle information in the reversing environment is realized, and the fast and accurate detection of obstacles

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is realized. The parameter information of the obstacle is reminded by the voice to realize the reverse driving assistance. The experimental results show that the proposed method has obvious advantages compared with other methods in detection rate and detection time, which can meet the real-time and accuracy requirements of obstacle detection during reversing.

References 1. Zhou, W., Yang, Y., Wang, Z.: Structural light measurement technology based on binocular stereo vision. Comput. Eng. 44(07), 244–249 + 258 (2018) 2. Lavrinov, D.S., Khorkin,. A.I.: Problems of internal calibration of precision laser triangulation 2D scanners. In: International Conference on Industrial Engineering. IEEE (2017) 3. Rodríguez-Quiñonez, J.C., Sergiyenko, O., Flores-Fuentes, W., Rivas-lopez, M., HernandezBalbuena, D., Rascón, R., Mercorelli, P.: Improve a 3D distance measurement accuracy in stereo vision systems using optimization methods’ approach. Opto-Electron. Rev. 25(1), 24–32 (2017) 4. Bo, L., Xiaogang, L., Mingxing, W.: Research on non-contact optical measurement methods for the dimension of inner diameter. In: Fifth International Conference on Instrumentation & Measurement. IEEE (2016) 5. Toriya, H., Kitahara, I., Ohta, Y.: A mobile camera localization method using aerial-view images. In: Pattern Recognition. IEEE (2014) 6. O’Toole, M., Mather, J., Kutulakos, K.N.: 3D shape and indirect appearance by structured light transport. In: Computer Vision & Pattern Recognition. IEEE (2014) 7. Lilienblum, E., Al-Hamadi, A.: A structured light approach for 3-D surface reconstruction with a stereo line-scan system. IEEE Trans. Instrum. Measur. 64(5), 1258–1266 (2015) 8. Wang, C., Li, Y., Ma, Z., et al.: Distortion rectifying for dynamically measuring rail profile based on self-calibration of multiline structured light. IEEE Trans. Instrum. Measure. PP(99), 1–12 (2018) 9. Wang, Z.Z., Yang, Y.M.: Single-shot three-dimensional reconstruction based on structured light line pattern. Opt. Lasers Eng. 106, 10–16 (2018) 10. Green, O.: Efficient scalable median filtering using histogram-based operations. IEEE Trans. Image Process. Publ. IEEE Sign. Process. Soc. 27(5), 2217 (2018) 11. Esakkirajan, S., Veerakumar, T., Subramanyam, A.N., et al.: Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. IEEE Sign. Process. Lett 18(5), 287–290 (2011) 12. Ivanov, M., Kartashov, V., Sergiyenko, O., Hernandez, W., Tyrsa, V., Sheiko, S., Mercorelli, P., Kolendovska, M.: Individual scans fusion in virtual knowledge base for navigation of mobile robotic group with 3D TVS. In: Proceedings: IECON 2018—44th Annual Conference of the IEEE Industrial Electronics Society, pp. 3187–3192 (2018) 13. Garcia-Cruz, X.M., Sergiyenko, OYu., Tyrsa, V., Rivas-Lopez, M., Hernandez-Balbuena, D., Rodriguez-Quiñonez, J.C., Basaca-Preciado, L.C., Mercorelli, P.: Optimization of 3D laser scanning speed by use of combined variable step. Opt. Lasers Eng. 54, 141–151 (2014) 14. Barner, K.E., Aysal, T.C.: Polynomial weighted median filtering. IEEE Trans. Sign. Process. 54(2), 636–650 (2006) 15. Li, Y., Arce, G.R., Bacca, J.: Weighted median filters for multichannel signals. IEEE Trans. Sign. Process. 54(11), 4271–4281 (2006)

Multi-objective Minimal Time Optimal Control Based Path Planning of Mobile Robots Siqi Tu, Shurong Li, Zhe Liu and Derui Zeng

Abstract This paper proposes a novel approach to solve the minimal time multirobot path planning problem. Firstly, the multi-robot path planning problem is described by a multi-objective minimal time optimal control model. In this process, we mainly study the mathematical description of the trajectory paths without hitting with obstacles and colleagues. Secondly, in order to obtain the numerical solution of the optimal control problem, the model is transformed into multiple single-objective mixed integer programming problems (MSOMIP) by using discretization and lexicographic method. Finally, an improved particle swarm optimization-genetic algorithm (PSO-GA) algorithm is proposed to solve the MSOMIP. The optimal path planning scheme and the corresponding analysis are presented at last. Keywords Multi-objective minimal time optimal control · Mixed-integer multi-objective programming · Lexicographic method · Single-objective mixed-integer programming · Improved PSO-GA

1 Introduction Path planning is one of the most important problems in robotics. It is desired to find a collision-free motion in an obstacle prone environment in order to navigate safely from the start configuration to the goal configuration. In the past decades, different strategies were proposed to solve mobile robots path planning problem. The path planning strategies of mobile robots can be categorized as classical methods and heuristic methods [1]. The classical methods mainly include A* algorithm [2], cell decomposition [3], potential field method [4], Probabilistic Roadmap (PRM). The heuristic methods [5] include neural network (NN) [6], genetic algorithm (GA) [7], differential evolution [8], particle swarm optimization (PSO), ant colony optimization (ACO) and bacterial foraging optimization (BFO). The path planning strategy proposed in this paper belongs to the heuristic methods. S. Tu · S. Li (B) · Z. Liu · D. Zeng Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_75

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In this paper, we propose an improved PSO-GA algorithm to solve the minimal time multi-robot path planning problem. Our research work presents two important contributions. The first one is that we build a multi-objective minimal time optimal control model which precisely describes the minimal time multi-robot path planning problem. In the model, we studied description methods of different shape obstacles, such as ellipse, circle, polygon and so on. How to use the constraint equation to describe the collision between robots and express the robots reach to the destination is discussed as well. The second contribution is that we propose an improved PSO-GA algorithm to solve the model. We transform the optimal control model into multiple single-objective mixed-integer programming problem by using discretization and lexicographic method. To solve the MSOMIP, an improved PSO-GA algorithm is proposed. At last, the numerical result proves the accuracy of the model and the effectiveness of the improved PSO-GA algorithm.

2 Problem Formulation 2.1 Assumptions and Kinematic Equations When we build the optimal control model for the multi-robot path planning, some assumptions are as follows: 1. Suppose there are m round robots in the map. They have the same kinematic model, departure time t0 and radius r. 2. Initial position (I nitxi , I nit yi ) and target position (targetxi , target yi ) of each robot is known in prior coordinate system, where (i = 1, 2, . . . , m). 3. In the map, obstacles are stationary and the envelope of all obstacles can be described accurately or approximately using mathematical equations. 4. Each robot has its own level. The priorities of all the robots have been determined and they are numbered in descending order (robot i is ranked higher than robot j when i < j, i, j = 1, 2, . . . , m). As shown in Fig. 1, a two-wheeled unicycle type robot is considered [9]. The kinematic equations can be expressed as: x(t) ˙ = v(t)cos(θ (t)) =

D (ωl (t) + ωr (t))cos(θ (t)) 2

(1a)

y˙ (t) = v(t)sin(θ (t)) =

D (ωl (t) + ωr (t))sin(θ (t)) 2

(1b)

θ˙ (t)=ω(t)=

D (ωr (t) − ωl (t)), 2r

(1c)

where (x, y) is the coordinates of the robot center in the map, v represents linear velocity, θ is the orientation and ω is the angular velocity for the robot. ωl and ωr

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Fig. 1 Definition of configuration variables

v

θ ω y (x,y)

r

D

x

are the left and right angular velocities of wheels, respectively. r is the radius of the T  robot and D is the wheel radius. u = ωl ωr is considered as the control variable.

2.2 Description of Obstacles The trajectory path for each robot is not allowed to have a collision with obstacles and teammates. In this section, two types of obstacles are presented. The first envelope type is approximated as a conic curve, such as a circle, an ellipse, a parabola and a hyperbola. The second envelope type can be approximated as a polygon. The area where the robot is allowed to travel can be described by the following formulas. Suppose there is an ellipse-shaped obstacle in the map as Fig. 2, we can describe the feasible area as follows: F1 =

(xi (t) − x0 )2 (yi (t) − y0 )2 + − 1 ≥ 0, i= 1, 2, . . . , m, t ∈ [to , ti f ] (2) (a + r + ξ )2 (b + r + ξ )2

Fig. 2 Triangle and elliptical obstacle diagram

y

( x − x0 ) 2 a

y = f1 ( x)

2

+

( y − y0 ) 2 b2

=1

y = f 2 ( x)

y = f3 ( x)

x

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where (x0 , y0 ) is the center of the conic curve. Other conic curves can be expressed in a similar way. The safety distance between the robot and the obstacle is ξ . As shown in Fig. 2, f 1 (x), f 2 (x), f 3 (x) represents the equation for each side of the triangle. For the triangle obstacle, the area where allows the robot pass can be expressed by the following inequalities: [yi (t) − f 1 (xi (t)) − r − ξ ≥ 0]∨ [yi (t) − f 2 (xi (t)) − r − ξ ≥ 0]∨ i= 1, 2, . . . , m, t ∈ [to , ti f ] [ f 3 (xi (t)) − yi (t) − r − ξ ≥ 0].

(3)

Other convex polygons can be expressed in a similar way. It should be noted that the proposition in (3) represents a disjunctive set which includes inequality constrains separated by the operator OR (∨) [10]. There are many ways to transform the disjunctive set into a standard form of constraint equation, such as big-M, convex hull and so on. In this paper, since the scale of the problem is not complicated, we use the form of disjunctive set directly. F2 = 0 if the position (xi (t), yi (t)) satisfies (3). Otherwise, F2 = f (x) where f (x) is a field function to accelerate the solving time in the future. There are many ways to build f (x). We define it as: F2 = f (x) = R 2 − (xi (t) − x0 )2 − (yi (t) − y0 )2 . i= 1, 2, . . . , m, t ∈ [to , ti f ] (4) Equation (4) means the polygon is in a circle field with (x0 , y0 ) as the center and R as the radius. If the non-convex polygon is in the map, we can decompose it into several convex polygons for modeling.

2.3 Objective Function and Other Constraint Equations The velocities of the left and right angular are not infinite during driving, so the speed constraints can be described as follows: 2 − ωir2 (t) ≥ 0, F3 = ωmax i= 1, 2, . . . , m, t ∈ [t0 , ti f ] 2 F3 = ωmax − ωil2 (t) ≥ 0,

(5)

where ωmax represents the maximum speed of the wheel in a unit time. And the speed constraint equality is denoted as F3 . Each robot should be able to reach the destination at ti f . The constraint inequalities are expressed as follows: F4 = r 2 − (targetxi − xi (ti f ))2 − (target yi − yi (ti f ))2 ≥ 0. i= 1, 2, . . . , m (6) When the center of each robot enters a circle with the destination as the center and r as the radius, it is considered to reach the destination.

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The distance between any two robots should satisfy the following inequality at any time: F5 =



(xi (t) − x j (t))2 + (yi (t) − y j (t))2 − 2r − ξ ≥ 0.

i = j, i, j = 1, 2, . . . m t ∈ (t0 , min(ti f , t j f ))

(7)

In this paper, we are interested in the minimal time objective. The objective functions are expressed as: min : F6 = t1 f − t0 min : F6 = t2 f − t0 ....... min : F6 = tm f − t0 ,

(8)

The multi-robot path planning problem has been described by a multiobjective minimal time optimal control problem. The control variables are u i = [ωil (t) ωir (t)]T . The goal is to minimize the control time ti f − t0 (i = 1, 2, . . . , m). The constraint formulations are F1 , F2 , F3 , F4 , F5 . In order to solve the optimal control problem, we use the numerical computation method to obtain the numerical solutions. Discretize the model and the simple length is t. ti f ≈ t0 + Ni ∗ t. i = 1, 2, . . . , m

(9)

t p = t0 + p ∗ t. p = 0, 1, 2, 3, . . . .

(10)

 T And the input u i = ωil (t) ωir (t) is considered as a constant vector during t. Then the model can be transformed into a mixed-integer multi-objective programming problem. The objective functions can be expressed as: min: N1 , min: N2 , . . . , min: Nm

(11)

And the constraint formulations are transformed into algebraic formulations.

3 Mixed-Integer Multi-objective Programming Solving by Using the Improved PSO-GA Algorithm James and Russell proposed particle swarm optimization (PSO) in 1995. The PSO algorithm has an outstanding performance in solving nonlinear optimization problems. In this section, an improved PSO-GA algorithm is presented to solve the multirobot path planning problem. The improved PSO-GA algorithm is introduced:

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The PSO-GA algorithm 1: Set the population size N , cross probability pc , mutation probability pm , cross ratio cr , initialize the velocity and position of each particle randomly. Initial the global best optimal particle pgd and individual best optimal particle pid , and set the generation counter k = 1 . 2: while k < Itermax

3: 4: 5:

for i = 1 to N Update particle speed and position with the following formula: 2 vid = w * vid + c1r1 ( pid − xid ) + c2 r2 ( pgd − xid ) + c3 r3 (ωmax − xid2 ). (12)

6: 7: 8: 9: 10: 11: 12: 13: 14: 15:

(13) xid = xid + vid Generate random numbers r1, r 2 if r1 < pc Select particles based on the value of cr for crossover operation. end if if r 2 < pm Perform a mutation operation on the particle end if Calculate the fitness value. if the updated particle i is better than pid

16: 17: 18:

Update pid end if if the updated particle i is better than pgd

19:

Update pgd

20: end if 21: end for 22: k = k + 1 . 22: end while

The difference with PSO-GA algorithm [11] is velocity update Eq. (12). It is easy to think that if the solution is the shortest time, the speed must be as fast as possible. 2 2 − xid ) represents the tendency for the control variable u The added part c3r3 (ωmax to search for maximum speed. The convergence of improved PSO-GA algorithm is better than the PSO-GA algorithm in our problem. As seen from the model, we cannot find a best solution to let all the objective functions to reach the minimum. So we use the lexicographic method [12] to transform the mixed-integer multi-objective programming model into multiple single-objective mixed-integer programming problems according to the urgency of each robot task. Then, for the robot with the highest priority, only the constraints F1 , F2 , F3 , F4 are considered, and for the robot with the lower priority, constraint equations F5 indicating no collision between robots should be added. For the r oboti (i > 1), Equation F5 are transformed into:

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F5 =

807

 (xi (t p ) − x j (t p ))2 + (yi (t p ) − y j (t p ))2 − 2r − ξ ≥ 0. j = 1, . . . , i − 1 p = 0, 1, . . . , min(Ni , N j )

(14)

By using the penalty function method, we can continue to convert the singleobjective mixed-integer programming into the following problem: T  (1) Finding the smallest N1 and u = ω1l ω1r which satisfy

F = λ1 min(F1 , 0)2 + λ2 F2 + λ3 min(F3 , 0)2 + λ4 min(F4 , 0)2 = 0. λ j > 0 j = 1, 2, 3, 4

(15a)

 T (2) Finding the smallest Ni and u = ωil ωir , i = 2, 3, . . . , m which satisfy

F = λ1 min(F1 , 0)2 + λ2 F2 + λ3 min(F3 , 0)2 + λ4 min(F4 , 0)2 +λ5 min(F5 , 0)2 = 0. λ j > 0 j = 1, 2, 3, 4, 5 (15b) When solving the above problem, the number of input variables u i depend on the times Ni for each robot. Therefore, the time Ni should be initialized firstly. However, Ni is a positive integer variable whose range is (0, +∞). We initialize Ni with Eq. (16). It should be noted that the optimal time must be greater than or equal to the Ni obtained by (16). ⎡ Ni =⎢ ⎢ ⎢

(targetix − I nitxi )2 + (targetiy − I nit yi )2 ωmax ∗ D ∗ t

⎤ ⎥. ⎥ ⎥

(16)

So far, we first discretized the optimal control model, and then transformed the mixed-integer multi-objective programming problem into multiple single-objective mixed-integer programming problems. Finally, using the penalty function method to deal with constraints. Combining the above information with the improved PSO-GA algorithm, we present the main procedure using improved PSO-GA algorithm to solve multi-robot path planning problem.

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Pseudo Code for multi-robot path planning with improved PSO-GA algorithm Input: starting points, end points and maximum velocity Output: the minimal time consumed path with collision free Begin For i = 1: m Step1: initialize Ni according to equation (16). Step2: solve the equation F by calling the improved PSO-GA algorithm for a given Ni . T

Setp3: if the improved PSO-GA algorithm can find a solution ui = [ωil ωir ]

which satisfies all constraints ( F = 0) , save input u and time Ni . Otherwise, Ni = N i + 1 return to step2. End

4 Simulation Results The multi-robot path planning problem is carried out in a simulated environment. The simulation is conducted through programming in Matlab2018a on a Inter i7-4710HQ microprocessor. The basic parameter settings are introduced in this paragraph. Let the size of the map is 10 × 10. The robot with radius r = 0.2,wheel radius D = 0.1, minimal distance between robot and obstacle ξ = 0.1 and ωmax = 10 rad/s. The basic parameters in the PSO-GA algorithm are assigned to N = 100, pc = 0.7, cr = 0.2, pm = 0.1, c1 = c2 = c3 = 1.5. The basic environment information has shown in Table 1 and the path is shown in Fig. 3. As Fig. 3, the left and right picture are performed by the proposed algorithm as t = 1 s and t = 0.5 s, respectively. The optimal solution of three individuals are N1 = 19, N2 = 19 and N3 = 12 while choosing the longer sampling step. Hence, Table 1 Basic information about the environment in a conical and polygon obstacle

Basic information

Starting coordinates

Destination coordinates

Robot1

(0, 5)

(10, 3)

Robot2

(2, 2)

(10, 8)

Robot3

(6, 1)

(4, 9)

Circular and elliptical obstacle equation

(x − 4)2 + (y − 2)2 = 1 (x − 8)2 + (y − 3)2 /3 = 1

The vertices of polygons

(1, 8), (2, 6), (2, 4), (1, 4) (7.5, 9), (7.5, 7.5), (9, 7), (9, 9) (4.5, 6), (5, 7), (6, 7), (6.5, 6), (6, 5), (5, 5)

(x − 5)2 + (y − 4)2 = 0.5

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Fig. 3 These two pictures show a path planning result with different t in a clutter environment

the minimal time are t1 f = 19 s, t2 f = 19 s and t3 f = 12 s. When we select a shorter sampling step t = 0.5 s, the optimal solution of three individuals are N1 = 37, N2 = 38 and N3 = 23, respectively. The corresponding minimal time are calculated as t1 f = 18.5 s, t2 f = 19 s and t3 f = 11.5 s.

5 Conclusions and Future Works A multi-objective minimal time optimal control model for multi-robot minimal time path planning was proposed in this paper. The optimal control model was transformed into multiple single-objective mixed-integer problem by using discretization and lexicographical method. At last, we obtained the optimal path by solving the MSOMIP model using an improved PSO-GA algorithm. By simulating in a clutter environment, the feasibility of the algorithm was verified. In the future, researches with respect to more efficient algorithms in different environments and the modeling problem of dynamic obstacles should be concentrated. Acknowledgements This work is supported by National Natural Science Foundation under Grant No. 61573378, BUPT Excellent Ph.D. Students Foundation under Grant No. CX2019113.

References 1. Zafar, M.N., Mohanta, J.C.: Methodology for path planning and optimization of mobile robots: a review. Procedia Comput. Sci. 133, 144–152 (2018) 2. Tan, Y., Yang, L.I., Zhou, J.: Path replanning approach for UAV based on A* algorithm in complex environment. Syst. Eng. Electron. 39(6), 1268–1273 (2017) 3. So, B.C., Jung, J.W.: mobile robot path planning with opposite angle-based exact cell decomposition. Adv. Sci. Lett. 15(1), 144–148 (2012)

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4. Li, G.S., Chou, W.S.: An improved potential field method for mobile robot navigation. High Technol. Lett. 22, 1–23 (2016) 5. Jiang, Y., Pan, F.: Improved heuristic algorithm for modern industrial production scheduling. Int. J. Model. Ident. Control 30(4), 284–292 (2018) 6. Glasius, R., Komoda, A., Gielen, S.C.A.M.: Neural network dynamics for path planning and obstacle avoidance. Neural Netw. 8(1), 122–133 (1995) 7. Ammouri, A., Salah, T.B.: PCB-planar transformers equivalent circuit model identification using genetic algorithm. Int. J. Model. Ident. Control 29(4), 295–303 (2018) 8. Parida, S.M., Rout, P.K.: Small signal stability analysis and optimised control of a PMSG-based wind turbine using differential evolution. Int. J. Model. Ident. Control 29(1), 66–77 (2018) 9. Kim, B.M., Tsiotras, P.: Controllers for unicycle-type wheeled robots: theoretical results and experimental validation. IEEE Trans. Robot. Autom. 18(3), 294–307 (2002) 10. Noriega, J.R., Vera-Marquina, A.C.: Automation of an I-V characterization system. J. Appl. Res. Technol. 8(2), 200–210 (2010) 11. Garg, H.: A hybrid PSO-GA algorithm for constrained optimization problems. Appl. Math. Comput. 274, 292–305 (2016) 12. Arunkumar, N., Karunamoorthy, L., et al.: Linear approach for solving a piecewise linear vendor selection problem of quantity discounts using lexicographic method. Int. J. Adv. Manuf. Technol. 28(11–12), 1254–1260 (2006)

Modeling and Simulation in Distributed Cooperative Simulation Platform of Aircraft Fuel System Zhiyong Fan, Da Teng and Zhexu Liu

Abstract Based on the comprehensive design and airworthiness verification of civil aircraft fuel system, the simulation modeling of fuel system is completed. The aircraft fuel system model is designed by using AMESim software under the environment of distributed cooperative simulation platform. It can realize the fuel quantity change of aircraft fuel system, and ventilation and pressurization, and inerting. The functions of pressure refueling, engine supply and oil discharge are realized through the heat transfer and pipeline analysis of fuel system. The simulation results show that the fuel system can effectively realize the functional characteristics of the actual fuel system, which is of great significance for the optimization design of the aircraft system and the modification integration test. Keywords Fuel system · Distributed cooperative simulation platform · Integrated test

1 Introduction The distributed cooperative simulation platform of aircraft system connects the hydraulic system, landing gear, engine and other systems with the simulation soft bus to realize the distributed cooperative simulation of various systems [1]. The platform is used to test and verify the retrofit design scheme in the process of aircraft integrated retrofit test. At present, most aircraft system simulation verification is implemented separately. Li et al. [2] proposed a design method of integrated test system. It can complete the function and performance test of aircraft fuel system accessories, and can also carry Z. Fan Engineering Techniques Training Center, Civil Aviation University of China, Tianjin 300300, China D. Teng (B) · Z. Liu College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_76

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out fault detection experiments. But the analytical modeling of fuel pipeline is not considered. Zhou and Zhang [3] put forward a new type of fuel system fault system fault simulation training system. The fuel model system is mainly established from the perspective of fluid pipeline system, but the heat transfer of fuel is not considered. Agrawal et al. [4] indicated a fuel system model. However, the modeling process is very complex and has poor universality. In this paper, by analyzing the fuel heat transfer and pipeline, we established the fuel model. The remaining chapters of this article are as follows: Section 2 introduces the description of aircraft fuel system. Section 3 presents the fuel system modeling in this paper. Section 4 describes simulation and verification. In the end, the conclusion is put forward in Sect. 5.

2 Description of Aircraft Fuel System Aircraft fuel system consists of fuel tank system, fuel distribution system, emergency discharge system, ground pressure refueling system and fuel related indication system [5]. The main functions of the fuel system are as follows. First, storage fuel. The aircraft’s fuel tank stores all the fuel that needs to complete its mission, including emergency return and post-landing spare fuel [6]. Secondly, reliable supply of oil. The aircraft fuel systems ensure a safe and reliable supply of fuel to the engine and APU, under a variety of prescribed flight conditions and operating conditions. Third, adjust the center of gravity. The aircraft horizontal and longitudinal center of gravity can be adjusted through the fuel system. The lateral center of gravity position adjustment can maintain the aircraft balance and reduce the force on the wing mechanism, while the longitudinal center of gravity position adjustment can reduce the plane flat tail leveling angle, the leveling resistance and fuel consumption [7]. Finally, cool the medium. The fuel oil can be used as cooling medium, cooling lubricating oil, hydraulic oil and other accessories [8].

3 Fuel System Modeling In this section, we build a fuel system model by analyzing calculation model of heat transfer and fuel pipeline model. The accuracy of the model is guaranteed in two ways: (1) The accuracy of component level, subsystem level, mission level, system level and mission level are ensured by the detailed data parameters, design parameters and simulation results comparison. (2) The strong coupling and separation of the model ensures that the established model has high precision and accuracy.

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3.1 Fuel Quantity Within the modern airframe, the fuel system is the largest fluid system, and it consists of several fuel tanks. The size, shape and installation position of the tank not only determine the flight distance, but also have a great influence on the stability and safety of the aircraft. The fuel system consists of three fuel tanks: the left main tank, the central fuel tank and the right main tank.

3.2 Calculation Model of Heat Transfer in Fuel System In the working process, the fuel system is responsible for heat dissipation of environmental control system and hydraulic system. According to its physical nature, fuel system can be divided into three different heat transfer modes: conduction, convection and radiation. For fuel systems, the three heat transfer modes exist at the same time, but the influence is different. The main heat transfer modes of fuel system and fuel components are analyzed in this paper. In this paper, it is considered that the basic resistive component does not contain hydraulic cavity, and its space span is very small, so it can be considered as adiabatic component. For the components containing capacitive components, the hydraulic cavity is included, so the heat transfer analysis of capacitive components is carried out. For the lumped parameter model, the volume of the oil in the capacitive component is usually regarded as an oil node, and the shell of the capacitive component is regarded as a mass node, which is called the flow node and the mass node respectively. The flow node can reflect the inflow and outflow of a certain quality of oil, thus reflecting the thermal motion of the oil flow, and the mass node can reflect the thermal motion of the component structure in three heat transfer modes: convection, radiation and conduction. The convective heat transfer refers to the heat transfer between the fluid and the solid surface when the fluid flows through the solid. As shown in Fig. 1. When the fluid flows through the solid surface, the fluid close to the solid surface is stationary due to its viscosity, and the heat transfer can only be carried out in the form of heat conduction. Away from the solid surface, the fluid has a macro-motion, thermal convection will occur. The convective heat transfer can be calculated by Newton’s cooling formula. Fig. 1 Convection heat transfer between fluid and solid

Convecctive heat transfer Fluid Solid

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Q˙ conv = h · A · (T f − Tw )

(1)

In formula (1), h is the average surface heat transfer coefficient of the whole solid surface. Tw is the average temperature of the solid surface. T f is the temperature of the fluid, for external flows (for example, fluid skimming through flat plates, tubes, etc.). T f is the mainstream temperature, that is, the fluid temperature away from the wall. It takes the average temperature of the fluid for internal flow (such as the flow in various shape slots). The convective heat transfer between heat exchanger fluid and wall is usually forced convection heat transfer. The forced convection refers to the flow of fluid flowing through a solid wall under external forces. The calculation formula of forced convection heat transfer is as follows. Q˙ f or ced = h f or ced · A · (T f − Tw )

(2)

In the formula (2), h f or ced is the coefficient of forced convection heat transfer, Tw is the average temperature of the solid surface, and T f is the temperature of the fluid. The coefficient of forced convection heat transfer can be expressed as h f or ced =

λ · Nu l

(3)

The λ is the thermal conductivity of the fluid and l is the characteristic scale. The Nussel number Nu can be expressed as a function of the Prandtl number Pr and the Reynolds number Re . N u = f (Pr , Re )

(4)

The specific expressions vary depending on the component. The expression of the Prandtl number Pr is given by the following formula (5). Pr =

μ · cp λ

(5)

In the formula μ is the dynamic viscosity of the fluid, c p is the specific heat capacity of the fluid, and λ is the thermal conductivity. However, due to the complex geometry of most hydraulic components, the characteristic dimension l can not be given accurately. The total heat transfer coefficient between the fuel and the outer air flow is calculated according to the following equation: Ua = In the formula (6):

1 1 hm

+

x k

+

1 h

(6)

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h m —The intrinsic heat transfer coefficient between fuel and skin in kW/mm2 °C. For the intrinsic heat transfer coefficient h m , the value of h m is 300 kW/mm2 °C. x—The thickness of oil tank wall. It is generally between 0.005 and 0.01 m. k—Thermal conductivity of fuel tank wall material and the unit is kW/mm2 °C, k = 0.28. h—Heat transfer coefficient of outer skin and outer air flow W/mm2 °C.

3.3 Fuel Pipeline Model The pipeline model is a relatively difficult model in fuel components, almost all hydraulic components are connected by pipeline. However, the pipeline models are not included in all fuel system models. When we select and build pipeline models, we need to deal with these two situations: (1) Connection between components through short pipe path. Because the outer wall of the pipeline is thicker, the dynamic characteristics of the pipeline have little effect on the system. (2) Connection between components through long pipe path, and the dynamic characteristics of pipes have an effect on the system. The pipeline model is used to connect the fuel component model, and all the angles from the port data flow are divided into three types. (1) When one of the two component ports to be connected is resistive and the other is capacitive, the line port data and direction are shown in Fig. 2. (2) When both components need to be connected with a capacitive port (the port is a basic capacitive component), the line port data and direction are required as shown in Fig. 3. (3) When both components are resistive (the port is a basic resistive component), the line port data and direction are shown in Fig. 4. The AMESim provides a model in a pipeline model that responds to pipe impact pressure (water hammer). In order to reflect the oil inertia of pipeline, the piecewise lumped parameter model of pipeline can be considered as the discretization of wave equation in one-dimensional space. The wave equation is used to describe the motion of a pipe. Fig. 2 Pipeline port data flow for a resistive and capacitive component

Fig. 3 Pipeline port data flow for two capacitive components

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Fig. 4 Pipeline port data flow for two resistive components

Fig. 5 Calculating node distribution of pressure and flow in pipelines

P0 + + Q0

P1 + + Q1

P2 + Q2

Pn + Qn

Pn+1 + Qn+1

The main idea is to divide the pipeline into multiple segments, the internal pressure of each segment is the same, the pressure is the state quantity, and its derivative is calculated by the continuous equation of flow rate. Between the two adjacent pipe sections, the inner half length of the two pipe sections is taken together to form a pipe section. Inside the segment of the pipe, the flow rate is considered to be the same, and the flow rate is a state quantity. The derivative is calculated by momentum conservation equation, and the distribution of pressure and flow is shown in Fig. 5. Thus, the dynamic model equations for section i of the pipeline are as follows: βT ( pi ) dpi = (qi−1 − qi ) dt Vi

(7)

A( pi−1 − pi ) m˙ i · |m˙ i | d m˙ i = − f dt L 2ρ ADh

(8)

The friction coefficient f is the friction coefficient of the pipeline. The specific value can be calculated by the Moody diagram with the Reynolds number and the roughness of the inner surface of the pipe. Whether the pipe port ends with a flow node or a pressure node needs to be determined according to the connection rules that the port of pipe connection component. As for long lines should be divided into several sections, derived from formula (9). N > 10 ·

L· f c0

(9)

In the formula N is the number of segments in the pipeline, L is the length of the pipe, and f is the highest frequency of interest. c0 is the propagation velocity of sound waves in the oil, and the formula is as follows:  c0 =

βT ρ

(10)

This means that the length of the longest segment of the pipeline is 10 times longer than the wavelength corresponding to the frequency of maximum interest.

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4 Fuel System Modeling and Verification The fuel tank model of the fuel system takes full account of the aircraft attitude effect on the fuel tank. The fuel tank model provided by AMESim is shown in Fig. 6. The fuel system model is built using AMESim, as shown in Fig. 7. The schematic diagram of the refueling principle is shown in Fig. 8. The diagram of the change in fuel volume is shown in Fig. 9. The model diagram of ventilation pressurization and inerting system is shown in Fig. 10. From the simulation results, the pressure at each point of the fuel system and the change of the fuel tank’s center of gravity can be clearly seen as shown in Fig. 11.

Fig. 6 The effects of aircraft attitude angle, acceleration etc. considered in the fuel tank model

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heat transfer

Fig. 7 Fuel system model diagram

Fig. 8 Refueling principle diagram

5 Conclusions In this paper, under the background of aircraft cooperative simulation, AMESim is used to model the basic functions of the fuel system, and the fault simulator is considered in the modeling process. The model of fuel system is managed and displayed by man-machine interface. Finally, a series of simulation analyses are carried out, and the system model can be used to simulate the operating characteristics and working conditions of some key components in the aircraft. Through this modeling and analysis method, the design time and test cost can be greatly reduced in the integrated stage of aircraft modification. Acknowledgments This research was funded by the Joint Funds of the National Natural Science Foundation of China Key Project (grant number U1533201), the Natural Science Foundation of Tianjin (grant number 18JCQNJC05000) and the National Natural Science Foundation of China (grant number 61703406). The authors would also like to express their sincere appreciation to the

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Fig. 9 Chematic diagram of gravity refueling principle

Ventilation pressurization inerting

Fig. 10 Ventilation pressurization model diagram

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Fig. 11 Diagram of variation of fuel system pressure, fuel tank center of gravity

Higher Education Innovative Team Training Program of Tianjin, and comments from the reviewers and the editor are very much appreciated.

References 1. Marino, A.: Distributed adaptive control of networked cooperative mobile manipulators. J. IEEE Trans. Control Syst. Technol. 99, 1–15 (2017) 2. Li, X., Zhou, Z., Hou, Y., Cao, K.: Design and simulation of integrative testing system for accessories of aircraft fuel system. In: 2017 International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), pp. 642–646. Shanghai (2017) 3. Zhou, Y., Zhang, W.: The research of aircraft fuel system fault simulation training system. In: 2012 IEEE International Conference on Automation and Logistics, pp. 484–488. Zhengzhou (2012) 4. Agrawal, A., Djenidi, L., Agrawal, A.: Simulation of gas flow in microchannels with a single bend. J. Comput. Fluids 38, 1629–1637 (2009) 5. Bu, X., Lin, G., Sun, B., et al.: Experimental study of an aircraft fuel tank inerting system. J. Chin. J. Aeronaut. 28(2), 394–402 (2015) 6. Gao, Z., Ma, C., Dong, S., et al.: Deep quantum inspired neural network with application to aircraft fuel system fault diagnosis. J. Neurocomputing 238, 13–23 (2017) 7. Yuan, Z.H., Cao, N.X.: Design of flow simulation subsystem of ground simulation test for aircraft fuel system. J. Adv. Mater. Res. 466, 1172–1175 (2012) 8. Yang, M., Wang, S.: Health management system based on airworthiness of the aircraft fuel system. J. Procedia Eng. 80, 34–43 (2014)

Adaptive Neural Network Dynamic Surface Control Algorithm for Pneumatic Servo System Gang Liu, Guihai Li, Zhengyang Peng and Huihui Pan

Abstract Pneumatic servo system is widely applied in many industries, which has advantages comparing with electromechanical and hydraulic system because of its fast response, high-performance quality and low-cost. However, the servo control methods for pneumatic system still have some inevitable drawbacks and problems remaining to be researched. In this paper, a position feedback dynamic surface control is designed which is based on our pneumatic actuator model. More importantly, in order to overcome model uncertainties, noise interference and external force disturbance, an adaptive neural network dynamic surface controller is proposed to overcome the negative effects. Besides, the stability of the pneumatic system is substantiated by Lyapunov stability theorem. Finally, the results of simulation experiment also prove that the adaptive neural network dynamic surface controller has more advantages than the traditional controllers in pneumatic position servo control. Keywords Pneumatic servo system · RBF neural network · Dynamic surface control · Adaptive control

1 Introduction The pneumatic servo systems have greater advantages comparing with electromechanical systems, such as dynamic performance, safety, and strong environment adaptability. Therefore, they have the great potential to take place of electromechanical systems. For example, according to the experimental system demonstrated in paper [1], a rotary pneumatic simulation model was put forward and then verified. Jonathan I. A damping observer based on sliding mode is presented in [2] to restrain moving large-scale vehicles. Algorithm raised in [3] was analyzed to prove its astringency applying the procedure of a related ordinary differential equation. In comparison to traditional PID controller, the superiority of a dynamic surface G. Liu (B) · G. Li · Z. Peng · H. Pan Research Institute of Intelligent Systems and Control, Harbin Institute of Technology, Harbin 150001, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_77

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controller is exhibited in consequences of several simulations and experiments in pneumatic position servo control [4]. The position control plays a significant role in pneumatic servo systems. However, there are still some technical difficulties to design a high-efficiency position tracking controller. There have been some representative designs proposed to approve the realization of robot compliance control. In order to keep the stability and accuracy, some innovative and high-performance control methods are proposed during the past decades. A controller for supporting forceps has been developed which has 3DOFs actuated by pneumatic cylinders in [5]. An impedance controller based on multiple-surface sliding control is proposed in [6] to manipulate highly nonlinear pressure-sensor pneumatic servo systems with mismatched uncertainties. Besides, a great numbers of control methods has been proposed to optimize the control accuracy of the pneumatic executor, such as adaptive control [7], iterative learning control [8], and sliding mode control [9–11]. The main contribution of this paper is summarized as follows: on the one hand, we establish a more realistic model through local linearization basing on the pneumatic position servo system, On the other hand, in order to eliminating the negative influence of uncertainty part, we attempt to add RBF neural network to appropriate the uncertain properties. This paper is demonstrated as follows: dynamic analysis including force analysis in the pneumatic actuator, gas continuity equation,friction analysis and pressure equation. On the basis of above analysis and equation, we could establish the transfer function. Through the control algorithm of adaptive neural network dynamic surface control, we could track the input signal with relatively small errors.

2 The Mathematical Model of Pneumatic Actuator 2.1 Force Analysis of the Executing Agency in Pneumatic System The simplified structure of the pneumatic executing agency is illustrated on the left side of Fig. 1. Define the transmitting force of the pneumatic executor as F1 , the force on m as F2 , the response force from the left organization as FL and the tilt angle of the executor according to the vertical direction is α. A photo of the pneumatic executor is shown on the right side of Fig. 1. Basing on the Newton’s Second Law, the force equilibrium equation could be established as F1 + F2 − FL + G α − f = m x¨ + K V x˙

(1)

where G α is a constituent part of the gravity in α direction and G α = mg sin α, f is friction, K V is the viscous friction coefficient.

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Fig. 1 Schematic and photo of the pneumatic actuator

2.2 Gas Continuity Equation in the Cylinder Assuming that gas flow in the executor is consecutive, according to law of conservation of mass, it could be deduced that the total mass of gas does not change during transmission between adjacent part of the system. Therefore, the difference of mass between input and output gas can be described as follow: dρ dV + M˙ in − M˙ out = ρ dt dt

(2)

The initial condition is S A p A0 = S B p B0 . The effective area of the two chamber is S A and S B , and their ratio is n = S B /S A . Assuming the initial volume ratio of the two chambers as r = VB0 /V A0 . Then we can obtain the mass gradient gas, M˙ in =

d VA dp A 1 (k S A p A + V A0 ) RT0 k dt dt

(3)

M˙ out =

d VB dp B 1 (k S B p B + r V A0 ) RT0 k dt dt

(4)

2.3 Pressure Equation of Cylinder In the cylinder, define the pressure in chamber A as p A , and the capacity of the chamber is V A . The pressure in chamber B is p B , and the capacity is VB . The length of the cylinder block is D. According to Law of Conversation of Energy, assuming the whole process is adiabatic, the energy differential equation of chamber A and chamber B is respectively established: dp A M˙ A kp A x˙ = RT0 k − dt VA x

(5)

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dp B M˙ B kp B x˙ − = RT0 k dt VB D−x

(6)

2.4 Differential Function of the Pneumatic System The opening area and exit pressure of the valve are the influence factors of the mass flow through the valve. Hence, the mass flow is the function of pressure and the size of the opening area. Above all, we could obtain the function as follows: M˙ i = pu X V ψi ( pu , pd )

(7)

In this formula, b is a constant which represents the critical pressure ratio. ψ˙ A ( pc , p A ) = K p A pc + K c1 p A

(8)

ψ˙ B ( pc , p B ) = K p B pc + K c2 p B

(9)

Then we can linearize the equation with the Tylor formula. Where KcA

    ∂ ψ˙ A  ∂ ψ˙ B  ∂ ψ˙ A  ∂ ψ˙ B  = , K cB = , K pA = , K pB = ∂ p A  p A =0 ∂ p B  p B =0 ∂ pc  pc =0 ∂ pc  pc =0

3 Control Algorithm of the Pneumatic System Differential equation into the state-space form x˙1 = x2 x˙2 = h 2 (x2 ) + a2 x3 + 2 (x, t) x˙3 = h 3 (x1 , x2 , x3 ) + a3 μ + 3 (x, t)x3

(10)

2 (x, t) and 3 (x, t) are indeterminacy parts which meet the conditions i (x, t) ≤ δi , δi is the positive real number. First, design the dynamic surface function Z 1 = x1 − x1d , then it can be written as Z 1 = x2 − x1d , and then define control variable x 2 = −c1 Z 1 + x˙2d . Where c1 is the adjustable parameter for stabilizing the controller. In order to dispel differential explosion produced by the derivation of virtual control variables, let x 2 traverse a first-order filter and a new parameter variable τ2 x˙2d + x2d = x 2 is

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produced, and τ2 is the filter time constant. τ2 x˙2d + x2d = x 2

(11)

Second, similarly, the surface function Z 2 = x2 − x2d could be obtained and the dynamic function is as follows:   h˙ 2 (x2 ) 2 − x2d + Z 2 = a 2 x3 + a2 a2

(12)

Then apply the first RBF neural network to approximate h 2 (x2 ) = β2∗T ξ2 (x2 ) + σ2∗ a2   where σ2∗ is an ideal weight variable, and σ2∗  ≤ σ M . σ2∗ is approximation error, and σ2∗ ≤ σ M .   Define the ideal weight σ2∗ = σ2∗ , a12 , at the time define the approximation error  ϕ2 =

δ22 Z 2 2ε

ξ2 (x2 ) . − x2d +˙c2 Z 2

(13)

δ2 Z

ε is arbitrarily small arithmetic number. Besides, 22ε 2 is nonlinear damping term which is used to overcome uncertainty part. Similarly,  Z 3 = a3

.

1 h 3 (x1 , x2 , x3 ) a3 u + (3 − x˙3d ) + a3

h 3 (x1 , x2 , x3 ) = β3∗T ξ3 (x1 , x2 , x3 ) + σ3∗ a3

(14) (15)

c3 is arithmetic number, and ε is arbitrarily small arithmetic number. In addition, is nonlinear damping term which is used to overcome uncertainty part. Define the control law, δ32 Z 3 2ε

u = −βˆ3T ϕ3

(16)

Above all, the adaptive neural network dynamic surface controller has already been designed.

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4 Lyapunov Stability Verification of the Controller Define the filter error variance variable li = xid − x i , i = 2, 3

(17)

It can be obtained from the two filters above. li x˙id = − , i = 2, 3 τi β i = βˆi − βi , i = 2, 3 From the above formulas, we can know that there are nonnegative continuous functions B2 , B3     l˙2 + l2  ≤ B2 (Z 1 , Z 2 , l2 , x d , x˙ d , x¨ d ) (18) 1 1 1  τ2      l2 + l2  ≤ B2 (Z 1 , Z 2 , Z 3 , l2 , l3 , β˜2 x d , x˙ d , x¨ d ) (19) 1 1 1  τ2  So that li l˙i ≤ −

li2 + Bi |li | τi

(20)

Take Lyapunov function L=

 1

 1 1 2 Z 1 + Z 22 + Z 32 + l22 + l32 + a2 β˜2T 2−1 β˜2 + a3 β˜3T 3−1 β˜3 2 2 2

(21)

Find their derivatives separately  

2 ˙L 1 = Z 1 Z 2 + Z 2 a2 Z3 + l3 − β˜2T ϕ2 + σ ∗ + 2 − δ2 Z 2 − c2 Z 2 2ε  

2 δ Z3 − c3 Z 3 + Z 3 a3 −β˜3T ϕ3 + σ ∗ + 3 − 3 2ε

(22)

l2 l2 L˙ 2 ≤ 2 − B2 |l2 | − 3 − B3 |l3 | τ2 τ3

(23)

L˙ 3 = a2 β˜2T 2−1 Z 2 − a2 β˜2T η2 β˜2 + a3 β˜3T 3−1 Z 3 − a3 β˜3T η3 β˜3

(24)

When V ≤ p is workable, consider the following two compact sets 1 and 2 ,

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If the function attribute to the compact set 1 × 2 , it has the Maximum value δ2 Z 2 Mi . Because of i2ε i + 2ε ≥ i Z i , i = 2, 3. On the basis of the Young inequality and the following formula 2β˜iT β˜i ≥ (||β˜i ||2 − ||βi ||2 ), i = 2, 3

(25)

3  a2 ˙L i ≤ 1 (Z 12 + Z 22 − c1 Z 12 ) + a2 (Z22 + Z 32 ) + a2 (Z22 + l32 ) − ci Z i2 + (Z22 + σ2∗ ) 2 2 2 2 i=2    3    l2 B 2l 2 ε a 2 η2  a2  ˜ 2 2  β β −i + i i + − − + (Z23 + σ3∗ ) +  2 2 2 τi 2ε 2 2 i=2    a 3 η3   ˜ 2 (26) − β3  − β3 2 + ε 2

Therefore     2

˙L ≤ −c1 Z 12 + 3a2 + 1 − c2 Z22 + a2 + a3 − c3 Z23 + B2 − 1 l22 2 2 2 2 2ε τ2   2 B 1 2 a2 a 2 η2 a 3 η3 l3 − + 3 − + β˜2T 2−1 β˜2 − β˜3T 3−1 β˜3 −1 2 2ε τ3 2λmax (2 ) 2λmax (3−1 ) a3 a 2 η2 a2 a 3 η3 β2 2 + β3 2 + 2ε + + + 2 2 2 2 where λmax (i−1 ) is the Maximum eigenvalue of i−1 . Design parameters according to the following conditions: c1 ≥ r, c2 ≥

1 a3 3a2 a2 + + r, c3 ≥ + +r 2 2 2 2

1 1 M2 a2 M 2 ≥ 2 +r, ≥ + 3 +r, η2 ≥ 2r λmax (2−1 ), η3 ≥ 2r λmax (3−1 ) τ2 2ε τ3 2 2ε

(27) (28)

where r is parameters to be designed.  Considering σ2∗ ≤ σ M , βi∗  ≤ β M , i = 2, 3, we can obtain that a

a 2 + a2M η2 + a3M η3 β 2 L˙ ≤ −2r L + 2ε + 2M + 3M σ M M 2 2 2 2   3 2 2 2  M B i i − Mi l 2 + 2ε M 2 2ε i i=2

(29)

i

Therefore, L˙ ≤ 2r L + Q +

3  M2 B2 ( i2 − 1)li2 i 2ε Mi i=2

(30)

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where, Q = 2ε +

a

2M

2

+

a3M 2 a2M η2 a3M η3 2 σM + + θM 2 2 2

Above all, we can know that all error signal of the closed-loop system is semiglobal uniformly ultimately bounded in the following compact set. =





Q ˜ ˜ ˜ Z 1 , Z 2 , Z 3 , l2 , l3 , β1 , β2 , β3 : L ≤ 2r

(31)

It means that the compact set , the tracking error Z 1 and the estimation error β˜1 , β˜2 , β˜3 could be arbitrarily small. This method based on Lyapunov theory and the closed-loop system proves to be stable.

5 Experiment on Pneumatic Servo System The simulation of the RBF neural network dynamic surface controller is designed as Fig. 2. The simulation experiment is designed to verify the RBF-DSC control algorithm shown in Fig. 3. First, input ideal position signal x1 = 8 + 5 sin(t) to this controller, and then observe the position response under step tracking signal. The dynamic surface error is shown in the left figure as follow. The observation value of the statement variable

Fig. 2 Block diagram of the RBF neural network dynamic surface controller

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Fig. 3 Simulation results and comparison between ideal signal and tracking signal

is shown in the right figure as follow. Our simulation confirm that the adaptive neural network dynamic control algorithm is convergent, and the pneumatic system is stable.

References 1. Tillett, N.D., Vaughan, N.D., Bowyer, A.: A non-linear model of a rotary pneumatic servo system. J. Proc. Inst. Mech. Eng. Part I. J. Syst. Control Eng. 211(I2), 123–133 (1997) 2. Miller, J.I., Cebon, D.: A high performance pneumatic braking system for heavy vehicles. J. Veh. Syst. Dyn. 48(sup1), 373–392 (2010) 3. Stojanovic, V., Nedic, N.: Identification of time-varying OE models in presence of nonGaussian noise: application to pneumatic servo drives. J. Int. J. Robust Nonlinear Control 26(18), 3974–3995 (2016) 4. Lin, W., Guan, R., Yuan, L.: Position feedback dynamic surface control for pneumatic actuator position servo system. J. Syst. Sci. Control Eng. 6(1), 388–397 (2018) 5. Tsai, Y.-C.: Robust impedance control of pressure-sensor free pneumatic servo systems. In: 2011 International Conference on Electric Information and Control Engineering, vol. 3, pp. 2549–2553 (2011) 6. Tadano, K., Kawashima, K.: Development of a master slave system with force sensing using pneumatic servo system for laparoscopic surgery. In: IEEE International Conference Robotics and Automation (ICRA), Roma, Italy, pp. 947–952 (2007) 7. Abd. Rahman, R., Sepehri, N.: Design and experimental evaluation of a dynamical adaptive backstepping-sliding mode control scheme for positioning of an antagonistically paired pneumatic artificial muscles driven actuating system. J. Int. J. Control 90(2), 249–274 (2017) 8. Yu, S., Bai, J., Xiong, S.: A new iterative learning controller for electro-pneumatic servo system. In: ISDA, 2008 8th International Conference on Intelligent Systems Design and Applications, Kaohsuing, Taiwan, pp. 101–105 (2008) 9. Li, Y., Xueli, W., Zhu, Q., Zhang, J.: Adaptive terminal sliding mode control for finite-time chaos synchronisation with uncertainties and unknown parameters. J. Int. J. Comput. Appl. Technol. 49(3-4), 340–351 (2014) 10. Wu, J., Hua, Z., Wang, Y., Huang, J., Xing, K.: Sliding mode control with fuzzy compensator of pneumatic muscle actuator. J. Int. J. Comput. Appl. Technol. 44(4), 257–268 (2012) 11. Chiang, C.-J.: Incremental fuzzy sliding mode control of pneumatic muscle actuators. J. Int. J. Innov. Comput. Inf. Control 14(5), 1917–1928 (2018)

Data Aggregation Point Placement in Energy Harvesting Powered Smart Meter Networks Asif Hassan, Lina Pu, Yu Luo, Guodong Wang and Yanxiao Zhao

Abstract Wireless smart meter network is a crucial component in the smart grid that collects customer information (e.g., gas, oil, and water consumptions) and links the customers to the utility company. The data aggregation point (DAP) acts as a data center that gathers metering information from surrounding smart meters and relays the data to the utility server. The positions of DAPs significantly affect network efficiency, which has been extensively studied in the literature. However, the DAP placement in energy harvesting powered smart meter network is still an open issue. In this paper, we investigate the DAP placement considering that smart meters harvest energy from surrounding DAPs. The position of DAP not only affects the network performance in terms of throughput but also alters the energy harvesting efficiencies. We conduct simulation evaluations and provide in-depth analysis aiming to shed light on the optimal DAP deployment for energy harvesting driven smart meter networks (SMNs). Keywords Smart meter network · DAP placement · Energy harvesting

A. Hassan School of CIS, Florida International University, Miami, FL, USA L. Pu (B) School of CSCE, University of Southern Mississippi, Hattiesburg, MS, USA e-mail: [email protected] Y. Luo Department of ECE, Mississippi State University, Starkville, MS, USA G. Wang Department of CS, Massachusetts College of Liberal Arts, North Adams, MA, USA Y. Zhao (B) Department of ECE, Virginia Commonwealth University, Richmond, VA, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_78

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1 Introduction The smart grid technology not only provides utility companies more efficient control over their assets and services but also benefits the customers with reduced cost on energy without degradation in life quality [1]. Wireless smart meter network is a critical component of the smart grid, which consists of a large number of smart meters and multiple data aggregation point (DAPs). A smart meter is an electronic device that is installed at residential or commercial sites to record energy consumption. The DAP acts as a fusion center that gathers metering information from surrounding smart meters and relays data to the utility server. It is well recognized that the positions of DAPs significantly affect the network efficiency of the conventional battery powered wireless smart meter networks (SMNs) [2]. In energy harvesting driven SMNs, the DAP serves as both data fusion center and dedicated energy sources to charge the energy harvesting meters through wireless power transfer. Therefore its placement affects the network performance in two folds. First, the efficiency of data aggregation is affected by DAP positions like in traditional SMNs. Second, when the position of DAP varies, the amount of energy that can be harvested on energy harvesting meters changes accordingly [3]. Following this direction, in this paper, we explore potential solutions to tackle the efficient DAP placement in energy harvesting powered SMNs, where the position of DAP as a data center and an energy source at the same time affect the efficiency of energy charging and data communication. A smart meter can only send a packet when it has sufficient energy. Each smart meter harvests energy and then stores energy in its battery, typically a supercapacitor. The majority literature assumes linear charging function for energy harvesting devices. Under the smart meter context, it implies that smart meter harvests energy depending on the distance between DAP and itself. In this paper, the practical nonlinear charging function is integrated to calculate harvested energy at smart meter which does not solely depend on distance but also depends on the current residual energy of smart meter. In this paper, we fully consider the power transfer in the energy plane and the data aggregation in the data plane of energy harvesting driven smart meter networks. Specifically, we use three different metrics to investigate the optimum DAP placement problem. The first metric merely focuses on the performance of data communication. DAP is placed to minimize the cumulative path distance in the data plane. This metric is called the minimum shortest path. The second metric focuses on the performance of energy plane only. It places the DAP in the position where the smart meters can harvest the maximum amount of energy, which we call the maximum energy harvesting metric. The third one jointly considers the performance of the data plane and energy plane to achieve the optimal throughput performance.

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2 Related Work The DAP placement in conventional SMNs has been extensively studied in the literature. In [4], the authors reduced the DAP placement to a Set Covering Problem and proposed a heuristic solution obtaining near-optimal positions for DAPs. In [5] author proposed a solution of DAP placement problem jointly considering power and communication network. In [6], the topology of the power network, as well as a communication network, are both considered in the DAP placement. The authors formulated a mixed-integer nonlinear optimization problem to obtain the optimal number and locations of DAPs. A similar problem is investigated in [7] to minimize the DAP installation cost under the constraint of necessary QoS requirements. Due to the features of self-sustainability, pollution-free and perpetual operation, the energy harvesting is emerging as a promising technique to power the numerous sensors and smart meters in the future home area networks [8]. With the energy harvesting technique, wireless devices that equipped with energy harvesting module are capable of receiving energy from ambient or dedicated energy sources, such as solar, wind or radio frequency (RF) signals [9]. Along with the remarkable progress on low-power semiconductors, RF-based energy harvesting technique has drawn considerable attention in recent years [10, 11]. Existing research on RF-based energy harvesting communications mainly aims to maximize the utilization of the harvested energy from ambient signal [12] or to schedule the optimal energy transfer strategy at dedicated energy resources to efficiently charge surrounding devices [13]. The authors in [14] proposed a MAC protocol for RF energy harvesting wireless sensor networks that has active/sleeping period adapting to the varying network traffic.

3 DAP Placement in Energy Harvesting SMNs In this section, we investigate the problem of DAP placement following the three metrics to shed light on the optimal DAP placement in energy harvesting driven SMNs. These three metrics are the minimum shortest path, maximum energy harvesting, and optimal network throughput.

3.1 Minimum Shortest Path Metric The shortest path metric is primarily used in the conventional DAP placement to minimize the sum length of the path for data collection in the SMNs. We represent the SMN with a graph, G (V, E), where, V is a set of vertices (i.e., smart meters) and E is the set of edges (i.e., routes). Each edge is associated with a weight that equals the length of the path connecting two communication entities. The shortest

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path metric is to add up the weights of all paths through which the DAP collects data from all smart meters. In this paper, we use the well known FloydWarshall algorithm for computing the shortest path in a weighted directed graph [15]. The shortest path from vertex i to vertex j with all intermediate vertices in the set {1, 2, k} is calculated as k−1 k−1 (1) dikj = min(dik−1 j , dik + dk j ), where di j is the shortest path between vertex i and j.

3.2 Maximum Energy Harvesting Metric In the maximum energy harvesting metric, we place the DAP in the location where the smart meters can harvest the maximum amount of energy. The energy captured from DAP will be stored in batteries (e.g., Li-on, supercapacitor, etc.) on the smart meters. Here we use the supercapacitor as an example in the problem formulation and consider the nonlinear charging feature of the supercapacitor. In terms of the energy harvesting process, we assume that the smart meter harvests energy from DAPs constantly. That means in each time slot it harvests energy from DAPs. To achieve this, each smart meter is equipped with two antennas: one is used for energy harvesting and another is used for data transmission. Both of them operate in two different frequencies. The harvested energy is considered as discrete energy packets of length t. Pt represents the sending power of the DAP and PR is the receiving power on the smart meter. Let d be the distance from a smart meter to the DAP. We assume the resistance of the RC circuit is R = 500 , the impedance of the receiving antenna is Z = 50 , and the capacitor value is C = 50 mF. Vm is the highest voltage the supercapacitor can be charged to, which depends on the power of the energy packet and the charging circuit. Correspondingly, the maximum energy can be charged to the supercapacitor is denoted by em . r = 0, E i=0

Vm =



(PR Z ),

Pt 1 G G ( )t, 2 t r d2 ( 4π ) λ 1 em = C Vm2 , τ = RC 2 PR =

The amount of harvested energy can be formulated as [13] 1

E ih = Ai1 (Ai2 )2 + Ai1 Ai3 (E ir ) 2 + Ai1 Ai4 E ir where Ai1 = 3

Ai3 = (2) 2 Ai2 ,

1 2Tie e τ , 2

Ai4 = 2(1 − e

1

Ai2 = (2em ) 2 (e 2Tie τ

),

2Tie τ

(2)

− 1),

r E i+1 = E ih + E ir .

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Here E h is the harvested energy, Tie is the length of energy packet i, G t the antenna gain of DAP, G r antenna gain of smart meter. The amount of harvested energy on smart meters depends on the transmission power of DAP, the distance from smart meters to DAP, and the residual energy at the time of energy harvesting. In this metric, we search for the position that can maximize the harvested energy on all smart meters.

3.3 Joint Consideration of Energy Harvest and Shortest Path Different from the metrics that merely consider the energy harvest or the shortest path in DAP placement, we jointly consider both metrics and aim to maximize the network throughput performance. The network throughput will be taken into account in the optimal DAP placement. Data transmission can only be executed when a smart meter has sufficient energy and data cumulated. In this metric, we count all the successful transmissions in the hop by hop manner. The maximum transmission range of the smart meter is set as 100 meters. In addition to this, the ultimate goal is to deliver the data from smart meters all the way to the DAP in a multi-hop routing [16]. In terms of network throughput, we calculate the number of data packets successfully received on DAP.

4 Simulation Settings In this section, the settings and procedure of simulation are introduced. To avoid collisions among data transmissions, we assume smart meters access channel in the time division manner. When no transmission occurs, the data that is newly generated or relayed to the smart meter will be stored in the data buffer. Meanwhile, the harvested energy in this time slot will be conserved in the supercapacitor for future usage. Only when data buffer is not empty and the smart meter has sufficient energy for transmission, a data packet will be sent out in the assigned time slot. The amount of energy required for packet sending from a smart meter is calculated as follows [17] E c = (Sw +

P(u, v) packet ∗ 8 ) . k br

(3)

Here E c is the energy consumption for a single data transmission, Sw is the power of smart meter which is set as 90 mW in this work, and P(u, v) is power needed for baseband processing to send the packet from smart meter u to smart meter v. In the test, each smart meter generates data packets following Uniform distribution. When the DAP is out of the direct transmission range of a smart meter, the packet will need to be delivered through a multihop route, which is selected following the shortest

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Fig. 1 Grid deployment of smart meters

path rules. The data packet will be stored on a smart meter for future use if the device has no sufficient energy to transmit or it’s not the node’s turn to access the channel. The location of DAP will significantly affect the performance of a network in terms of length of paths from DAP to smart meters, distance-dependent energy harvesting rate, and finally network throughput. The investigation is divided into two cases, which are grid topology and real deployment of smart meters. Case I: In this case, we deploy 12 smart meters in grids as shown in Fig. 1. The dimension of the network is 4 m by 3 m. Case II: In this case, there are 55 smart meters are deployed in a suburban area as shown in Fig. 2 from Rapid City, South Dakota, USA. The coordinates are latitude and longitude of each houses is obtained from Google map. Each point indicating the position of smart meter. For both cases we deploy one DAP in the target area and investigate the optimal DAP position that follows the minimum shortest path, the maximum energy harvesting, and joint shortest path and energy harvesting metrics.

5 Simulation Analysis 5.1 DAP Placement in Grid Topology We first investigate the optimal DAP placement in Case I with grid deployment of smart meters. In each time slot, we check the available energy and number of stored packets for all smart meters. A smart meter, si , will initiate a transmission if

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Fig. 3 Optimal DAP placement to (1) minimize shortest path (magenta circle), (2) maximize harvested energy (black circle) and maximize network throughput (red circle)

it has sufficient energy as well as data packet available in its buffer. The data will be forwarded to its next hop neighbor, sn , that has the shortest path to the destination, DAP. The packet will be traversed through multi-hop shortest path from source smart meter to DAP. We search the optimal position of DAP to maximize three metrics and demonstrate the optimal positions in Fig. 3.

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In order to learn the capability of energy harvesting in the field, we assume to have 12 dedicated energy sources deployed in the same positions of smart meters and calculate the amount of energy that can be harvested in the network. The yellow color means the sufficient energy can be harvested. If there are smart meters in the yellow circle, it can harvest enough energy for data communications. In other words if we have smart meters at the center of the yellow circle, the smart meter will be able to harvest sufficient energy when a DAP is deployed within the circle, considering the channel symmetry in the wireless power transfer. The darker the color is, the more energy gap between the amount of energy required for data transmission and the amount that it can harvest. This energy distribution will help us understand the optimal positions of DAP in this smart meter network. We can observe that when the energy harvesting is not a concern in the minimum shortest path metric, the optimal DAP position is in the middle of the network (magenta circle in Fig. 3), where the minimum multi-hop shortest distance achieved. The black marker indicate the position of DAP that maximizes the harvested energy on smart meters in the network. We notice that the optimal placement of DAP to maximize network throughput (i.e., red marker) is on the edge of the bright circle, where the DAP as energy source provides sufficient power to the corresponding smart meter and meanwhile, attempts to get closer to other smart meters. We also observe that the result from maximizing throughput is close to the result from maximizing the harvested energy. The reason is that in the energy harvesting SMN, the thin energy is the main restriction to the network communications. In other words, due to scarce energy supply, the data packets cannot be transmitted but buffered in the data storage. The throughput performance improves as the more energy the smart meters can harvest. However, when the harvested energy is sufficient to send out all data packets that travel through a smart meter, the increased energy replenishment on that node will not increase the throughput. Therefore, the position of red circle (to maximize the network throughput) is slightly different from that of the black marker. We also varied the traffic rate of smart meters and the transmission power of DAP to evaluate their impact on the DAP placement. Our results indicate that the range of the yellow regions (i.e., sufficient energy for communication) changes with the variation of both factors. To be specific, we observe that the radius of the bright yellow circles reduces with the growth of traffic generation rate on smart meters. When the data packets are generated more frequently, smart meters will need more energy for the data transmission and the DAP as energy source has to be placed closer to a smart meter to provide to sufficient power. As the yellow circle shrinks, the red marker, which is the optimum position maximizing network throughput, moves accordingly to stay on the edge of the yellow circle. Similarly, increasing the transmission power from 3 w to 9 w will increase the radius of the yellow circles. Meanwhile, the red marker moves and keeps on the edge of bright yellow circle, as the energy harvesting rate remains the bottleneck of the network throughput. However, in practice, providing transmission power higher than 3 w is very unrealistic as it exceeds the FCC restriction on the 900M band RF signal.

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5.2 DAP Placement in Real Suburban Area In this subsection, we investigate the DAP placement in a real suburban area, where there are 55 number of smart meters and one DAP deployed in the area as shown in Fig. 2. Similar to Fig. 3, the yellow circles indicate that when DAP is placed inside the yellow circle, the corresponding smart meter that locates in the center of the circle will harvest sufficient energy for communications. Figure 4 shows the optimal DAP positions using different metrics. We can see that when the energy harvesting is not a concern in the minimum shortest path metric, the optimal DAP position is in the middle of the network (magenta circle). In the center of network, the minimum multi-hop shortest distance achieved. We also observe that the result from maximizing throughput is close to the result from maximizing the harvested energy similar to the result in grid topology. This further verifies that in the energy harvesting based SMN, the thin energy is the main restriction to the network communications. The throughput performance would improve as the more energy the smart meters can harvest. However, when the harvested energy is sufficient to send out all data packets that travel through a smart meter, the increased energy replenishment on that node will not increase the throughput. 10 -3

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6 Conclusion In this paper, we investigated the problem of optimum DAP placement in energy harvesting enabled smart meter networks. We compared the optimal positions of DAP that minimizes the shortest path, maximizes the energy harvesting, and maximizes the network throughput. In the energy harvesting model, we incorporated the nonlinear charging feature of batteries to calculate the amount of energy harvested by each smart meter. To optimize the network throughput, the impact of DAP position on both energy harvesting and data transmission has been considered. From the simulation results, we observed that the optimum position to maximize network throughput is close to the position that maximizes the energy harvest in both grid deployment and real suburban deployment. This is essentially caused by the fact that the limited energy supply is the major restriction on network performance. In this situation, the higher the energy supply, the higher the network throughput would achieve.

References 1. Farhangi, H.: The path of the smart grid. IEEE Power Energy Mag. 8(1), 18–28 (2010) 2. Tavasoli, M., Yaghmaee, M.H., Mohajerzadeh, A.H.: Optimal placement of data aggregators in smart grid on hybrid wireless and wired communication. In: IEEE Smart Energy Grid Engineering, pp. 332–336 (2016) 3. Erol-Kantarci, M., Mouftah, H.T.: DRIFT: differentiated RF power transmission for wireless sensor network deployment in the smart grid. In: IEEE Globecom Workshops, pp. 1491–1495 (2012) 4. Rolim, G., Passos, D., Moraes, I., Célio, A.: Modelling the data aggregator positioning problem in smart grids. In: IEEE International Conference on CIT/IUCC/DASC/PICOM, pp. 632–639 (2015) 5. Mahdy, A., Kong, P.-Y., Zahawi, B., Karagiannidis, G.K.: Data aggregate point placement for smart grid with joint consideration of communication and power networks. In: IEEE International Conference on Modeling, Simulation, and Applied Optimization, pp. 1–5 (2017) 6. Wang, S., Huang, X.: Aggregation points planning for software-defined network based smart grid communications. In: IEEE International Conference on Computer Communications, pp. 1–9 (2016) 7. Kong, P.-Y.: Cost efficient data aggregation point placement with interdependent communication and power networks in smart grid. IEEE Trans. Smart Grid 10(1), 74–83 (2017) 8. Kamalinejad, P., Mahapatra, C., Sheng, Z., Mirabbasi, S., Leung, V.C.M., Guan, Y.L.: Wireless energy harvesting for the internet of things. IEEE Commun. Mag. 53(6), 102–108 (2015) 9. Kazmierski, T.J., Beeby, S.: Energy Harvesting Systems (2014) 10. Ulukus, Sennur, Yener, Aylin, Erkip, Elza, Simeone, Osvaldo, Zorzi, Michele, Grover, Pulkit, Huang, Kaibin: Energy harvesting wireless communications: a review of recent advances. IEEE J. Sel. Areas Commun. 33(3), 360–381 (2015) 11. Noble, F.K., Alam, F., Potgieter, J., Xu, W.L.: Energy harvesting and current state of the technology with application to traffic monitoring. Int. J. Comput. Appl. Technol. 39(1/2/3), 166–175 (2010) 12. Luo, Y., Pu, L., Zhao, Y., Wang, W., Yang, Q.: Revisiting Transmission Scheduling in RF Energy Harvesting Wireless Communications. arXiv preprint arXiv:1802.09328 (2018) 13. Luo, Y., Pu, L., Zhao, Y., Wang, G., Song, M.: Optimal energy requesting strategy for RF-based energy harvesting wireless communications. In: IEEE International Conference on Computer Communications (2017)

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14. Nguyen, T.D., Khan, J.Y., Ngo, D.T: An adaptive MAC protocol for RF energy harvesting wireless sensor networks. In: IEEE Global Communications Conference, pp. 1–6 (2016) 15. Hougardy, Stefan: The Floyd-Warshall algorithm on graphs with negative cycles. Inf. Process. Lett. 110(8–9), 279–281 (2010) 16. Zohdy, M., ElBatt, T., Nafie, M., Ercetin, O.: RF energy harvesting in wireless networks with HARQ. In: IEEE Globecom Workshops, pp. 1–6 (2016) 17. Vazifehdan, J., Prasad, R.V., Jacobsson, M., Niemegeers, I.: An analytical energy consumption model for packet transfer over wireless links. IEEE Commun. Lett. 16(1), 30–33 (2012)

Bipartite Consensus Control for Coupled Harmonic Oscillators Using Sampled Data with Measurement Noise Jun Liu, Hengyu Li and Jun Luo

Abstract This paper investigates the bipartite consensus issue of coupled harmonic oscillators by considering measurement noise under cooperation–competition network topology. By introducing the definition of bipartite consensus in mean square associate with networked harmonic oscillator systems, a bipartite consensus algorithms which only use sampled velocity data of agents in network are given. Finally, we present an example to illustrate the corresponding theoretical results. Keywords Harmonic oscillators · Cooperation–competition network · Measurement noise · Bipartite consensus

1 Introduction The networked harmonic oscillator system has extensively been investigated by many researchers due to that it plays an important role in many modern industrial production systems, such as mobile robots [1] and electrical networks [2]. Specially, many synchronization or consensus control protocols were designed for networked harmonic oscillator systems from different perspectives, including continuous damping [3], event-triggered control algorithm [4], impulsive approach [5] and sampled data technique [6]. On the other hand, noise is common in nature and therefore it is meaningful by considering such problem with measurement noise. Many control strategies involving measurement noise or stochastic jumps. For example, Wang et al. [7] proposed a synchronization control protocol for networked harmonic oscillator systems J. Liu Department of Mathematics, Jining University, Qufu 273155, Shandong Province, People’s Republic of China e-mail: [email protected] J. Liu · H. Li (B) · J. Luo School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_79

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by considering measurement noise, and established the convergence criteria for the giving protocol. Furthermore, such issue was also studied in networked harmonic oscillator systems subject to stochastic jumping driving by Markovian process [8]. For more details on the synchronization or consensus topic of coupled harmonic oscillators, one can refer to Refs. [1–8] and the references therein. As an important cooperative behavior form in networked multi–agent systems, bipartite consensus has been studied extensively in recent years for its intrinsic advantages over the traditional complete consensus or synchronization in describing modern multi-objective production process [9]. Unlike complete consensus or synchronization, bipartite consensus requires all agents to be divided into two subgroups, the agents in the same group reach complete consensus and the final states of the agents in different subgroups have the same modulus, but opposite signs [10]. Since the concept of bipartite consensus was given by Altafini in [10], the bipartite consensus problem of networked system has aroused great interest of many researchers in recent years. Reference [11] discussed the collective behaviors of networked multi– agent systems under cooperation–competition network topology and presented some geometric conditions to guarantee realizing bipartite consensus. Moreover, bipartite consensus issue is also discussed in the context of event–triggered control strategy [12], finite–time control method [13] and so on [14, 15]. All the above–mentioned work concerning with coupled harmonic oscillators focused mainly on complete consensus or bipartite consensus without stochastic noise. Given this situation, this paper investigates the bipartite consensus problem of networked harmonic oscillator systems with measurement noise under cooperation– competition network topology. Compared with synchronization control with stochastic noise theme discussed in Ref. [7], the cooperation–competition network topology studied in this paper can exist negative communication weights, which leads to different structure of the Laplacian matrix. Some notations: 1n = [1, 1, . . . , 1]T ∈ Rn , On ∈ Rn×n and In is the n dimensional identity matrix. For a random variable ς , the expected value of ς is denoted as E(ς ).

2 Preliminaries 2.1 Graph Theory We borrowed the graph G = {V , ξ, A } to display information communication between agents in the networks, where V = {1, 2, . . . , n}, ξ ⊆ V × V and A = [aij ] ∈ Rn×n are, respectively, agent set, edge set and adjacency matrix. A node sequence o = {i1 , i2 , i3 , . . . , is } is called as a directed path if (i1 , i2 ), (i2 , i3 ), . . ., (is−1 , is ) ∈ ξ ; and is called as a directed semipath if either (ik−1 , ik ) ∈ ξ or (ik , ik−1 ) ∈ ξ for k ∈ {2, 3, . . . , s}. A directed path {i1 , i2 , i3 , . . . , is } is said to be a directed semicycle if i1 = is . A semicycle {i1 , i2 , i3 , . . . , is } is positive if the product of

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ai2 i1 , ai3 i2 , . . . , ais is−1 is positive. For arbitrary i, j ∈ V , if there exists at least one directed path from i to j in G , then G is strongly connected. G is said to be structurally balanced if all the semicycle are positive. G has a spanning tree if there exists i ∈ V , such that i has a directed path to every other agent.

2.2 Problem Formulation The dynamics of coupled n harmonic oscillators can be formulated by the following equation as, r˙i (t) = vi (t), v˙ i (t) = −αri (t) + ui (t), i = 1, 2, . . . , n,

(1)

where ri (t), vi (t) and ui (t) are, respectively, the position, velocity and control input of the agent i. α is a positive constant. We need give the definition of bipartite consensus in mean square in this sequel. Definition 1 The systems (1) is said to reach bipartite consensus in mean square under control input uk , k = 1, 2, . . . , n, if for almost all initial conditions, the states ri (t) and vi (t) satisfy limt→∞ E[|ri (t)| − |rj (t)|]2 = 0 and limt→∞ E[|vi (t)| − |vj (t)|]2 = 0 for all i, j ∈ {1, 2, · · · , n}; limt→∞ E[ri (t) + rj (t)]2 = 0 and limt→∞ E[vi (t) + vj (t)]2 = 0 for some i = j.

3 Bipartite Consensus in Coupled Harmonic Oscillators This section will study the bipartite consensus issue in the case of a structurally balanced network topology. The Laplacian matrix L = [lij ] ∈ Rn×n corresponding with the network graph G in this section is defined as lij = −aij , if i = j; and lii =  n j=1,j=i |aij |. Then the bipartite consensus control protocol can be given as ui =

∞  n  

    − μaij sgn(aij )vi (tk ) − vj (tk ) − ωk aij sgn(aij )vi (tk ) − vj (tk ) δt−tk ,

k=1 j=1

(2) 

+∞ 0, t = 0; satisfies −∞ g(t)δ(t)dt = g(0). The sequence {tk }∞ k=0 +∞, t = 0, satisfies 0 = t0 < t1 < · · · < tk < · · · , with limt→∞ tk = +∞ and h = tk+1 − tk , where k = 1, 2, 3, · · · . Here we assume vi (tk+ ) = vi (tk ), i = 1, 2, . . . , n. {ωk }, where δ(t) =

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k = 1, 2, . . . , are independent and identically distributed random variables, whose mean and variance are, respectively, 0 and σ 2 . Then by using (2), system (1) can be formulated as ⎧ ⎪ ⎪ ⎨r˙i (t) = vi (t), v˙ i (t) = −αri (t), t  = tk , Δri (tk ) = 0, t = tk , ⎪      ⎪ ⎩Δvi (tk ) = n j=1 − μaij sgn(aij )vi (tk ) − vj (tk ) − ωk aij sgn(aij )vi (tk ) − vj (tk ) , t = tk ,

(3) where i = 1, 2, . . . , n, Δvi (tk ) = vi (tk+ ) − vi (tk ). By denoting r(t) = [r1 (t), r2 (t), . . . , rn (t)]T and v(t) = [v1 (t), v2 (t), . . . , vn (t)]T , one has ⎧     ⎪ r ˙ (t) O r(t) I ⎪ n n ⎪ , t  = tk , ⎪ ⎨ v˙ (t) = −αI O v(t)    n n   (4) ⎪ r(tk+ ) I r(t) O ⎪ n n ⎪ , t = tk . ⎪ ⎩ v(t + ) = O I − μL − ω L v(t) k

n n

k

With above preparation, we can give our first main result. Theorem 1 If the cooperation–competition network G is strongly connected and structurally balanced, √and the following conditions are satisfied, (1− α1 ) sin( αhk )ξn +1−ξn −1 √ ; (2) α > 1 + 1−ξ +ξξnsin > 0; (3) hk = √jπα , (1) 0 < λn < (α−1) 2 √ sin2 ( αhk )+1−ξn ( αhk ) n n for all k, j ∈ N, where ξn and λn are, respectively, the biggest eigenvalues of (In − Ξ )T (In − Ξ ) and (In − Ξ − μΦL Φ)T (In − Ξ − μΦL Φ) + σ 2 ΦL T L Φ, Ξ = , ξ2 , . . . , ξn )T is a left eigenvector of ΦL Φ satisfying ξi ≥ 0, i = 1n ξ T and ξ = (ξ1 1, 2, . . . , n, and ni=1 ξi = 1, then using control law (2), the networked harmonic oscillators (1) reach bipartite consensus in mean square. Furthermore, the states ri (t) and vi (t) of harmonic oscillators in system (1) converge in mean square to γi (t) and πi (t), respectively, as

and

  √ √ 1 T T γi (t) = φi ξ Φr(0) cos( αt) + √ ξ Φv(0) sin( αt) α

(5)

 √ √ √  πi (t) = φi − αξ T Φr(0) sin( αt) + ξ T Φv(0) cos( αt) .

(6)

Proof Firstly, we will proof the existence of the vector ξ . Obviously, the matrix ΦL Φ is a standard Laplacian matrix with nonnegative weights. Since G is strongly connected, one has that the eigenvalues of ΦL Φ denoted by λi , i = 1, 2, . . . , n, satisfy λ1 = 0 and Re(λi ) > 0, i = 2, 3, . . . , n. Moreover, the left eigenvector of T ΦL Φ associated with n0 can be taken as ξ = (ξ1 , ξ2 , . . . , ξn ) satisfying ξk ≥ 0, k = 1, 2, . . . , n, and k=1 ξk = 1.

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Denote γ (t) = (γ1 (t), γ2 (t), . . . , γn (t))T and π(t) = (π1 (t), π2 (t), . . . , πn (t))T . Define the bipartite consensus error 

         e(t) r(t) γ (t) r(t) χ (t)Φ1n , = − = − σ (t)Φ1n s(t) v(t) π(t) v(t)

(7)

√ √ √ where χ (t) = ξ T Φr(0) cos( αt) + √1α ξ T Φv(0) sin( αt) and σ (t) = − αξ T √ √ Φr(0) sin( αt) + ξ T Φv(0) cos( αt). By computing based on Ref. [16], we have ⎧     ⎪ Φ e ˙ (t) O Φe(t) I ⎪ n n ⎪ , t  = tk , ⎪ ⎨ Φ s˙ (t) = −αI O Φs(t)    n n   ⎪ Φe(tk+ ) I Φe(t) − Ξ O ⎪ n n ⎪ , t = tk , ⎪ ⎩ Φs(t + ) = On In − Ξ − μΦL Φ − ωk ΦL Φ Φs(t) k (8)  T  T with initial condition (Φe(0))T , (Φs(0))T = r T (0)Φ, vT (0)Φ . Note that √ √      √1 sin(s α)In cos(s α)In On In α √ √ √ s = , then in order to show exp −αIn On − α sin(s α)In cos(s α)In the mean convergence ofzero solutionfor Eq. (8), it only needsto evalu square    T   T Φe(tk+ ) Φe(tk+ ) Φe(tk+ ) Φe(tk+ ) ate E such that E → 0 as Φs(tk+ ) Φs(tk+ ) Φs(tk+ ) Φs(tk+ ) k → ∞. By the same computing process in Ref. [7], we have  E

Φe(tk+ ) Φs(tk+ )

T 

Φe(tk+ ) Φs(tk+ )



 T     T + + Φe(tk−1 Φe(tk−1 ) ) ≤ ρ eA hk BkT Bk eAhk E , (9) + + Φs(tk−1 Φs(tk−1 ) )



   On In In − Ξ On where A = . Next, we , Bk = −αIn On O In − Ξ − (μ + ωk )ΦL Φ n  T should need to proof ρ eA hk BkT Bk eAhk < 1. As the same discussion in Theorem 1 in  T  Ref. [7], it is easy to show that ρ eA hk BkT Bk eAhk < 1 if the conditions (1)–(3) hold.     Then we can conclude that E (Φe(t))T (Φe(t)) → 0 and E (Φs(t))T (Φs(t)) → 0, which leads to immediate consequences of Theorem 1.

4 Simulation Study Consider a cooperation–competition network containing ten harmonic oscillators shown in Fig. 1. Here, we take α = 1.2, hk = 1.3, μ = 0.2 and σ 2 = 0.003. Then, the conditions in Theorem 1 are all satisfied. It can be derived from Theorem 1 that by

848 Fig. 1 Topology graph (coexisting of positive and negative weights) of ten coupled harmonic oscillators

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using the control strategy (2), the whole system can asymptotically reach bipartite consensus. Figure 2 shows the evolutionary process of bipartite consensus of this harmonic oscillator networks.

References 1. Ren, W., Cao, Y.: Distributed coordination of multi-agent networks: emergent problems, models, and issues. Springer, London (2011) 2. Tuna, S.E.: Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks. Automatica 75, 236–243 (2017) 3. Ren, W.: Synchronization of coupled harmonic oscillators with local interaction. Automatica 44(2), 3195–3200 (2008) 4. Wei, B., Xiao, F.: Event-triggered control for synchronization of coupled harmonic oscillators. Syst. Control Lett. 97, 163–168 (2016)

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5. Zhou, J., Zhang, H., Xiang, L., Wu, Q.: Synchronization of coupled harmonic oscillators with local instantaneous interaction. Automatica 48(8), 1715–1721 (2012) 6. Zhang, H., Zhou, J.: Synchronization of sampled-data coupled harmonic oscillators with control inputs missing. Syst. Control Lett. 61(12), 1277–1285 (2012) 7. Wang, J., Feng, J., Xu, C., Chen, M.Z., Zhao, Y., Feng, J.: The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise. Automatica 66, 155–162 (2016) 8. Wang, J., Feng, J., Xu, C., Zhao, Y.: Almost sure exponential synchronisation of networked harmonic oscillators via intermittent coupling subject to Markovian jumping. IET Control Theor. Appl. 12(11), 1658–1664 (2018) 9. Liu, J., Ji, J., Zhou, J., Xiang, L., Zhao, L.: Adaptive group consensus in uncertain networked EulerLagrange systems under directed topology. Nonlinear Dyn. 82(3), 1145–1157 (2015) 10. Altafini, C.: Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58(4), 935–946 (2013) 11. Hu, J., Zheng, W.X.: Emergent collective behaviors on coopetition networks. Phys. Lett. A 378(26), 1787–1796 (2014) 12. Hu, J., Geng, J., Zhu, H.: An observer-based consensus tracking control and application to event-triggered tracking. Commun. Nonlinear Sci. Numer. Simul. 20(2), 559–570 (2015) 13. Wang, H., Yu, W., Wen, G., Chen, G.: Finite-time bipartite consensus for multi-agent systems on directed signed networks. IEEE Trans. Circ. Syst. I Reg. Pap. 65(12), 4336–4348 (2018) 14. Xia, W., Cao, M., Johansson, K.H.: Structural balance and opinion separation in trustmistrust social networks. IEEE Trans. Control Netw. Syst. 3(1), 46–56 (2016) 15. Liu, J., Li, H., Luo, J.: Bipartite consensus control for coupled harmonic oscillators under a coopetitive network topology. IEEE Access 6, 3706–3714 (2018) 16. Yang T.: Impulsive control theory, vol. 272. In: Lecture Notes in Control and Information Sciences. Springer (2001)

Adaptive Sliding Model Controller Design of Carlike Robot Speed and Steering Angle Based on Characteristic Model Zhen Xu, Mingchu Xu and Qingwei Chen

Abstract Time-varying dynamical parameters, which exist in carlike robot’s formation control under complex tasks or rugged terrain environment, bring inaccuracies or even instability. This paper presents an adaptive sliding model controller based on characteristic model to realize high precision carlike robot formation control. The main contributions are as follows. First, one can consider the carlike robot dynamical system model as a Multi-Input Multi-Output (MIMO) system, rather than two independent variables. Complementarily, the new controller, considering the dynamical inner loop, has better adaptive ability to the time-varying system, such as sprinkler, mine layer and so on. The improvement of the performance is verified by MATLAB for time-varying kinetic parameters and MRDS4 three-dimensional physics engine for the rugged terrain environment. Keywords Car-like mobile robot · Rough terrain · Formation control · Characteristic model

1 Introduction With the continuous development of servo motors drive, sensors and control theory, the core components performance of robots continues to improve, and the multi-robot formation control and high precision trajectory tracking have gradually become the research hotspots in [1]. But so far, most researches on the field of trajectory tracking and formation control of vehicle-based mobile robots still stay in the design of kinematic controllers [2, 3]. There are two reasons for this. First, most of the carlike robots used to study formation control are finished robots with their own motor drives and control module, and they can automatically complete the command signal for tracking the given speed command. In other words, the controller of the dynamical inner loop is already included. Second, most of the researched carlike robot is small in quality. In addition, their speed is slow in flat task environment and the formation Z. Xu (B) · M. Xu · Q. Chen School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_80

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is simple. Even if only the kinematic control was thought about, fast response speed and high pose accuracy can be obtained. However, as the performance of robots increases, the field of multi-robot formation is also developing in the direction of large-scale, high-speed, environment-poor and task-complexing. Therefore, higher requirements are also placed on the control of multi-robot formation in the fields of transportation, exploration, reconnaissance, rescue, environmental cleaning, etc. The research on dynamical analysis and control methods of vehicle-based mobile robots has become an indispensable part. The characteristic model theory based on adaptive control method is proposed by Academician Wu in [4], which is to identify the system in real time according to the input and output signals. Based on this approach, one can obtain the feature model of the second-order discrete system and design the controller. The main feature of this method is that one does not need accurate mathematical model, and the designed controller has better adaptability to system parameter changes. Therefore, this method has certain advantages in solving the problem that the dynamical inner loop model of the finished vehicle robot is unknown and the dynamical parameters of the vehicle mobile robot in the special task environment are time-varying. The research on the formation control of vehicle-type mobile robots through dynamical controller design has achieved fruitful results. Gonzalez [5] proposes a vision-based dynamical formation controller that there is no information interaction between the robots, and the followers estimate the motion parameters based on the acquired video information to complete the formation control. To solve the time-delay of information transmission between agents, a PD kinematics controller in the [6] is designed to compensate the influence of time-delay. The stability of the system is proved. The kinematic trajectory tracking controller in [7] is designed for the follower by the backstepping method and the formation control of the carlike robots is realized. In addition, there are some studies on the controller design for the dynamical inner loop. Chen and Jia [8] introduces the simplified dynamical model of the vehicle robot and proposes a dynamical sliding mode controller design method. The neural network dynamical controller is further designed for the driver and steering system in [9] by using the carlike robots’ dynamical model. The effectiveness of the controller is verified by simulation. In this paper, ones consider the formation control problem of the carlike robots with the time-varying dynamical parameters in complex terrain environment. The outer loop obtains the error state equation of the robots and design kinematics. The inner loop uses the characteristic model method to design the dynamical inner loop controller or the compensation controller, and realize the high-precision formation control of the carlike mobile robot. The MRDS is used to design 3D physical simulation to verify the effectiveness of the proposed method in rugged terrain. The simulation is carried out in MATLAB to verify the effectiveness of the proposed control method under the time-varying dynamical parameters.

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2 Dynamical Modeling Based on Characteristic Model 2.1 Description of Dynamical System The kinematics model of the carlike robot is as follows: ⎧ ⎨ x˙ = v cos θ y˙ = v sin θ ⎩˙ θ = v tan φ/l

(1)

(x, y)T is the coordinates of the center of rear wheel shaft in the global coordinate system; θ is the angle between body direction and x axle; φ is the deflection angle of front wheel; (v, φ)T are the control inputs of robot; v is the velocity of rear wheels. ⎡ ⎤ cos θ 0 Assume that qc = [x, y, θ ]T , G c (qc ) = ⎣ sin θ 0 ⎦, Vc = [v, φ]T , Considering tan φ/l 0 longitudinal sliding and lateral force, the dynamical model is as follows: ⎧ ⎨ q˙c = G c (qc )Vc v˙ = g F − gu Fu − gs Fs − g p T f (v) ⎩ ¨ p p J θ = Fu l sin(φ) + Fw l cos(φ)

(2)

where F p is traction; Fs is the steering force; T f (v) is the friction between the tire and the road; Fu and Fw are the net force in the x and y axis direction of the robot coordinate system respectively; g p , gu , gs are kinetic coefficients. If the longitudinal sliding and lateral force are not considered, the simplified dynamical model can be expressed as:

v˙ = τ1 /m v˙ = τ1 /m in other words ˙ v˙ tan φ ¨ φ = τ2 l−I θ = τ1 /I I v sec2 φ

(3)

From the formula (3), it can be seen that the dynamical inner loop control input of the mobile robot is [τ1 , τ2 ]T . By designing the dynamical controller, the actual speed of the robot and the steering angle of the front wheel [v, φ]T are achieved by tracking the desired signal [vd , φd ]T .It’s the control target of the dynamical inner loop. With the expansion of the application range of mobile robots, the time-varying dynamical parameters are gradually increasing. Therefore, it’s necessary to design a dynamical internal loop controller with adaptive ability to improve formation accuracy.

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2.2 The Characteristic Model of the System Consider the following multi-input multi-output (MIMO) nonlinear system:  ˙ . . . , u (m) y˙ = F y, y˙ , . . . , y (n) ; u, u,

(4)

T and y = y1 y2 · · · y p are the input and output T  of the system respectively, y (r ) = y1(r ) y2(r ) · · · y (rp ) , r = 0, 1, · · · , n, u (s) =   (s) (s) , s = 0, 1, . . . , m. u (s) 1 u2 · · · uq Assume that the nonlinear system has the following characteristics:

where u =

u1 u2 · · · uq

T

(s) (s) (1) The variable y1(r ) (t), y2(r ) (t), . . . , y (rp ) (t), u (s) 1 (t), u 2 (t), . . . , u q (t), r = 0, 1, . . . , n, s = 0, 1, . . . , m in F(·) are the input and output vectors of the system respectively; (2) All independent variables in F(·) differentiable  and each partial    are  continuously   (r )  (s)  derivative is bounded. That is ∂ Fi ∂ yk  ≤ Mir k , ∂ Fi ∂ y j  ≤ Mis j , i, k =

1, . . . , p, j = 1, . . . , q , Mir k , Mis j ∈ C + .

        (3) The derivative of u, y is bounded. That is  yk(r )  ≤ M yr k , u (s) j  ≤ Mus j , M yr k , Mus j ∈ C + . Lemma 1 ([11] lemma 1) For the non-linear MIMO system represented by the formula (4) which satisfies the above assumptions, the characteristic model can be described by the following second-order difference equations: yi (k + 1) =

p 

f i j (k)y j (k) +

p 

j=1

+

q 

f i, p+ j (k)y j (k − 1)

j=1

gig (k)u g (k) +

g=1

q 

gi,q+g (k)u g (k − 1)

g=1

If for a given ε > 0, sampling time T satisfies T < min {min{1, ε/3Mi }} 1≤i≤ p

Mi =

p n   r =1 k=1

Mir k · M yr k +

q m  

Mis j · Mus j , i = 1, . . . , p.

s=1 j=1

where f i j (k), f i, p+ j (k), gig (k), gi,q+g (k) slow time-varying parameters in characteristic model. According to characteristic model theory, when T → 0, f i j (k) → 2, f i, p+ j (k) → −1, gig (k)  1, gi,q+g (k)  1. The dynamical model of the mobile robot satisfies the assumptions (1)–(3), so one can transfer the tracking error to:

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e1 = y1d − y1 = vd − v e2 = y2d − y2 = φd − φ

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(5)

According to the kinetic Eq. (5), one can know:

v˙ = f (v,τ1 ) φ˙ = f (v,φ, τ1 , τ2 )

Therefore, the error characteristic model, removing the coupling term with zero coefficient, can be expressed as: ⎧ ⎪ ⎨ e1 (k + 1) = f 11 (k)e1 (k) + f 12 (k)e1 (k − 1) + g11 (k)u 1 (k) + g12 (k)u 1 (k − 1) e2 (k + 1) = f 21 (k)e1 (k) + f 22 (k)e2 (k) + f 23 (k)e1 (k − 1) + f 24 (k)e2 (k − 1) ⎪ ⎩ + g21 (k)u 1 (k) + g22 (k)u 2 (k) + g23 (k)u 1 (k − 1) + g24 (k)u 2 (k − 1) (6) 

     f 11 (k) 0 f 12 (k) 0 g11 (k) 0 , F2 = , G0 = , where F1 = f 21 (k) f 22 (k) f (k) f 24 (k) g21 (k) g22 (k)     23   g (k) 0 e (k) v , E(k) = 1 , U (k) = G 1 = 12 . e2 (k) g23 (k) g24 (k) φ

3 Dynamical Controller Design and Stability Analysis The method based on feature model is adopted to identify the dynamical inner loop of the system, and to design the dynamical controller [12]. The system structure diagram is shown in Fig. 1. Where [xd , yd , θd ]T is the expected position and posture of robot; [xe , ye , θe ]T is the error of position and posture; [vd , φd ]T is the output of position controller, which is the input of speed and steering angle controller. [v, φ]T and [x, y, θ ]T are actual robot speed, front wheel steering angle, position, attitude angle respectively.

Fig. 1 System structure diagram of controller design

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For the error system (6), the recursive least square method with forgetting factor is adopted to identify the parameters online. The recurrence formula is as follows: ⎧ P(k−1)ϕ(k−1) ⎪ ⎨ K (k) = λ+ϕ T (k−1)P(k−1)ϕ(k−1) ˆ ˆ − 1) + K (k)[y(k) − ϕ T (k − 1)θˆ (k − 1)] (7) θ(k) = θ(k ⎪ ⎩ P(K ) = 1 I − K (k)ϕ T (k − 1) P(k − 1) λ where the λ is forgetting factor; K (k) is the Kalman  gain vector, P(K ) is the covariance matrix. θ T (k) = F1 F2 G 0 G 1 , ϕ T (k) = e (k) e2 (k) e1 (k − 1) e2 (k − 1) ]. [ 1 u 1 (k) u 2 (k) u 1 (k − 1) u 2 (k − 1) After parameter identification, the error characteristic model is obtained as follows: E(k + 1) = Fˆ1 E(k) + Fˆ2 E(k − 1) + Gˆ 0 U (k) + Gˆ 1 U (k − 1) + (k)

(8)

where Fˆ1 , Fˆ2 , Gˆ 0 , Gˆ 1 is the value of parameter identification; (k) = T

δ1 (k) δ2 (k) represents the sum of identification error, uncertainty and disturbance. For discrete error systems (7), the controller is designed as follows: U (k) = Ueq (k) + Us (k)

(9)

The adaptive control law is:   ˆ ˆ ˆ F U − 1) + F − 1) + G Ueq (k) = −Gˆ −1 (k (k)E(k) (k)e(k 1 2 1 0

(10)

Sliding mode control law is: Us (k) = Gˆ −1 0 {(1 − qT )E(k) − εT sgn[E(k)]} Assuming that

(11)

δ1 (k) < dmax 1 , the range of parameters need to be satisfied is δ2 (k) < dmax 2

as follows:  ⎧ ⎨ T < 2|e0 | (2ε + q|e0 |) d +d ε > max1 T max2 ⎩ q>0

(12)

    where |e0 | = e1min  + e2min  is the sum of the two error bounds; T is sampling time; ε, q ∈ C + ; sgn(·) is sign function; Define

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sgn



f1 f2 · · · fn

T 

857

T  sgn( f 1 ) sgn( f 1 ) · · · sgn( f 1 ) .

Theorem 1 Formula (6) error systems is boundedly stable, if the range of parameters meets the condition (12) in control law (9). Proof Take (9) into (8), and it is known that E(k + 1) = (1 − qT )E(k) − εT sgn[E(k)] + (k)

(13)

So, on one hand:

T [E(k + 1) − E(k)]T sgn[E(k)] = −qT E(k) − εT sgn[E(k)] + (k) sgn[E(k)] < −εT + T (k)sgn[E(k)] = −εT + δ1 (k)sgn[e1 (k)] + δ2 (k)sgn[e2 (k)] (14) Considering the condition ε > [E(k + 1) − E(k)]T sgn[E(k)] < 0. On the other hand:

 (dmax1 + dmax2 ) T in (12), denote

T [E(k + 1) + E(k)]T sgn[E(k)] = (2 − qT )E(k) − εT sgn[E(k)] + (k) sgn[E(k)] > (2 − qT )[|e1 (k)| + |e2 (k)|] − 2εT + dmax1 + dmax2 + (k)sgn[e(k)] > (2 − qT )[|e1 (k)| + |e2 (k)|] − 2εT

(15)

 Considering the condition T < 2|e0 | (2ε + q|e0 |) in (12), one can obtain  2 − qT > 4ε (2ε + q|e0 |) and (2 − qT )|e0 | − 2εT > 0, so [E(k + 1) + E(k)]T sgn[E(k)] satisfies that: [E(k + 1) + E(k)]T sgn[E(k)] > (2 − qT )[|e1 (k)| + |e2 (k)|] − 2εT > (2 − qT )[e0 (k)] − 2εT >0

(16)

In conclusion, the system satisfies [E(k + 1) − E(k)]T sgn[E(k)] < 0 and [E(k + 1) + E(k)]T sgn[E(k)] > 0, which is the bounded stability condition for discrete sliding mode control [13].

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4 Simulation Analysis 4.1 Characteristic Model Theory Verification According to the characteristic model theory in Sect. 3, one can obtain the MIMO characteristic model of carlike robot and the time-varying parameters of the discrete characteristic model are obtained by the least square parameter identification method. The equivalence between characteristic model and factual system model is embodied in that the same input obtains the same output. In other words, the dynamical error of system output is bounded, and the stable error is zero. Next, the equivalence between the discrete characteristic model and the original dynamic model is verified. The system’s characteristic model verification simulation is based on MATLAB2012b. The system parameters of carlike robot are as below [10]: mass m = 2000 kg, rotary inertia I = 2000 kg m2 , wheel base l = 1.9 m, forgetting factor λ = 0.995. The original value of the identification parameters: [ f 11 (0) f 12 (0) g11 (0)g12 (0) ]= [1.6 −0.5 0 0], [ f 21 (0) f 22 (0) f 23 (0) f 24 (0) ]= [1.1 1 1.3 1], [g21 (0) g22 (0) g23 (0) g24 (0)]=[00.0005 0.0004 0.0002], P(0) = 108 × I8×8 T

Input signal u 1 u 2 is sinusoidal signal with the 500 amplitude and 1 Hz frequency. The simulation results are shown as Fig. 2. From the simulation results, one can see that the simulation verifies the equivalency between the characteristic model and factual model.

4.2 The Simulation Under Time-Varying Dynamical Parameters In this section, the simulation aims at verifying the reliability of the proposed control algorithm under time-varying dynamical parameters. The specific content is: the leader R1 does uniform circular motions on smooth ground, and control the follower R2 to complete formation control for specified formation parameters. The parameters of initial formation are ρ=5m, ϕ=0◦ , (xe0 , ye0 , θe0 )T = (5, 5, 0)T , initial mass of R2 m 0 = 2000 kg and m(t+1) = m(t) − 5. At 60 s, ρ=5m, ϕ= −90◦ when changing formation. The contrast test uses the partitioning PID without integral and differential terms, the parameters are shown as below:

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0.1

0.1 e1 e2

0.08

0.08

10 -4

4 3

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model output error e2 (°/s)

model output error e1(m/s)

5

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7

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Fig. 2 Characteristic model output error

⎧ ⎨ 4.8 |ev | ∈ [0, 0.5) kv = 3.2 |ev | ∈ [0.5, 2) ⎩ 2.0 |ev | ∈ [2, +∞)

⎧ ⎨ 3.6 kφ = 1.8 ⎩ 0.8

    eφ  ∈ [0, 2) eφ  ∈ [2, 10)   eφ  ∈ [10, +∞)

The formation pattern and the position error are shown as Fig. 3. From Fig. 3a, b, one can obtain that the two methods can finish the high precision formation with fine convergence speed and stability precision before 60 s. After 60 s, for the ceaseless change of the mass and rotary inertia of the carlike robot, the

R1

R1

R2

R2 position error/m

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8

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(a) the sketch of formation

(b) the change of position error

Fig. 3 Time-varying dynamic parameters of robot formation simulation

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adaptive controller has better adaptive ability and shorter convergence time than the partitioning PID controller.

4.3 The Formation Control Simulation on Rugged Terrain In this section, the adaptive sliding model controller is designed for rugged terrain. The simulation is run in MRDS4 which can provide a physical simulation engine with wind, gravity, inertia and friction [14] (Fig. 4). The system parameters of carlike robot formation are set as below: Wheel base l = 1.9 m, ρ = 7 m, ϕ2 = 30◦ , ϕ3 = −30◦ for triangular formation; ρ2 = 5 m, ρ3 = 10 m, ϕ = 0◦ for vertical formation when passing through the valley; ρ = 7 m, ϕ2 = 90◦ , ϕ3 = −90◦ for horizontal formation. The formation result are shown as below. From the results in Fig. 5, one can see that when adopting the origin dynamical PID controller in switching formation, the position error has low convergence speed. By comparison, the adaptive sliding model controller improves the mobility and

Fig. 4 Simulation environment scene

R3 position error/m

20

Sliding model dynamical compensation Origin dynamical controller

15 10 1 0

5 0

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(a) R2 position error

Fig. 5 Formation switching control on undulating terrain

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(b) R3 position error

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manipulation of carlike robots, and the position error convergence speed are raised obviously.

5 Conclusions and Future Work In this paper, a method on designing dynamical controller or dynamical compensation controller based on characteristic model is proposed for the formation control of carlike robot. The second order time-varying difference equation is obtained according to the identified parameters, and the adaptive sliding mode dynamic controller is designed. The simulations of the unknown and time-varying dynamic parameters verify the effectiveness of the proposed method. Acknowledgements This work was supported by National Natural Science Foundation of China under Grant Nos. 61673217, 61673214, 61673219 and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant No. KYCX19_0299.

References 1. Mehrjerdi, H., Ghommam, J., Saad, M.: Nonlinear coordination control for a group of mobile robots using a virtual structure. Mechatronics 21(7), 1147–1155 (2011) 2. Consolinia, Luca, Morbidib, Fabio, Prattichizzob, Domenico, et al.: Brief paper: leaderfollower formation control of nonholonomic mobile robots with input constraints. Automatica 44(5), 1343–1349 (2008) 3. Shao, J., Xie, G., Yu, J., et al.: Leader-following formation control of multiple mobile robots. In: IEEE International Symposium on Mediterrean Conference on Intelligent Control. IEEE (2005) 4. Wu, H., Hu, J., Xie, Y.: Characteristic model-based intelligent adaptive control. China Science and Technology Press, Beijing (2009) 5. Gonzalez, R., Fiacchini, M., Alamo, T., et al.: Adaptive control for a mobile robot under slip conditions using an LMI-based approach. Eur. J. Control 16(2), 144–155 (2010) 6. Corradini, M.L., Leo, T., Orlo, G.: Experimental testing of a discrete-time sliding mode controller for trajectory tracking of a wheeled mobile robot in the presence of skidding effects. J. Forensic Sci. 24(2), 282–290 (2002) 7. Liu, G., Zhang, Y.: Trajectory tracking of mobile robots based on fuzzy PID-P type iterative learning control. Acta Electronica Sinica 41(8), 1536–1541 (2013) 8. Chen, X., Jia, Y.: Adaptive leader-follower formation control of non-holonomic mobile robots using active vision. Control Theor. Appl. Iet 9(8), 1302–1311 (2015) 9. Xu, Z., Schroter, M., Dan, N., et al.: Formation control of car-like autonomous vehicles under communication delay. In: China Control Conference, pp. 6376–6383 (2012) 10. Zhang, B., et al.: A chattering-free adaptive second-order non-singular fast terminal sliding mode control scheme for a class of nonlinear uncertain systems. Int. J. Model. Ident. Control 29(3), 255–265 (2018) 11. Shi, W., Huo, W., Wu, H.: Direct adaptive fuzzy predictive control of flexible structure based on characteristic model. Control Theor. Appl. 22(5) (2005) 12. Ramaswamy, S.A.P., Balakrishnan, S.N.: Formation control of car-like mobile robots: a Lyapunov function based approach. In: American Control Conference (2008)

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13. Li, P., Zhang, W.: Towards a unified stability analysis of continuous-time T-S model-based fuzzy control systems. Int. J. Model. Ident. Control 31(2), 113–123 (2019) 14. Belkacem, B., et al.: On λ-matrices and their applications in MIMO control systems design. Int. J. Model. Ident. Control 29(4), 281–294 (2018)

Inventory Control Strategy on High-Value Aviation Spares at Line Maintenance Shiwei Zhao, Guihang Liu and Peng Zhang

Abstract Line maintenance is very important guarantee for airlines operation, and maintenance quality is inseparable from the support of aviation spares. High-value aviation spares inventory usually accounts for a large proportion of airline’s fixed assets, whose turnover speed directly affect airlines profit. For the dynamic process of aviation spare inventory in line maintenance scenario, “high-value aviation spare purchasing—line maintenance consuming—high-value aviation spares inventory” is considered as generalized physical system, and engineering control strategy could be used to optimize inventory management. Based on actual aviation spare loss data during route maintenance process, typical statistical characteristics about the aviation spare data is analyzed and researched, and the linear inequality robust variance control theory is applied to design high-value aviation procurement strategy. Simulation of inventory optimization process is performed using MATLAB Simulink toolbox, and whose result shows that variance of inventory of high-value aviation spares are significantly reduced. Keywords Line maintenance · High-value aviation spare · Inventory control · Linear matrix inequality

1 Introduction The civil aviation transportation industry has three characteristics: high technology, high risk, high capital occupation, which lead to the industry with low average profit rate. In recent years, with the rapid development of the civil aviation industry, the maintenance cost in the operating cost of airlines is increasing with the fleet grown [1]. S. Zhao (B) · G. Liu Engineering Techniques Training Center, Civil Aviation University of China, 2898 Jinbei Road, Dongli District, Tianjin 300300, People’s Republic of China e-mail: [email protected] P. Zhang Airworthiness College, Civil Aviation University of China, 2898 Jinbei Road, Dongli District, Tianjin 300300, People’s Republic of China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_81

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As the basic support for line maintenance, it is extremely important that aviation parts timely and accurately meet the comsuming demand. Most of aircrafts operated by Chinese airlines are from Europe and the United States, although the manufacturer provides the Recommanded Spare Parts List (RSPL) during aircraft delivery, which is severe conservative advice [2] based on the operation experience of aircraft in Europe and the United States. Due to various differences in operating environment, culture, maintenance technology level etc. in china, the following problems often occur in the actual aviation spares management [3]: (1) The overall inventory configuration is high, however turnover rate is low, resulting in high cash occupancy rate. At present, the largest proportion of fixed assets in most airlines are aviation spares; (2) The inventory configuration is not balanced, there are some aviation spare too much or others too few, Especially aviation parts are insufficiently guaranteed, which resulted in aircraft on ground(AOG). If that case happen, which usually trigers urgent order, and greatly increase purchasing cost and operating cost of the aviation parts. Due to structure of civil aviation transportation, flights operation is subject to multiple regulations, so the consumption of aviation parts is stable too. Line maintenance is the most important and basic maintenance activity of airlines daily flight operation, which has significant meaning. In order to improve the maintenance efficiency of airlines and decrease the number of flight delay events, The paper supplies a proposal that it is considered that “aircraft spares supplementary-line maintenance consumingaviation spare inventory” as a generalized physical system, applying engineering control theory for purchasing strategy of high-value aircraft spares to improve inventory, The dynamic management flowchart is shown in Fig. 1.

Fig. 1 Airline aviation spares inventory dynamic management flowchart

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2 Modeling of High-Value Spares Loss Process in Line Maintenance 2.1 Aircraft Line Maintenance and Spare Loss Process Description According to the regulations of the Civil Aviation Administration of China, the line maintenance occurs before flight departure, short stop, and after the flight is completed. The main duty of line maintenance is the routine inspection of the aircraft according to the airline’s task card, effective aircraft and engine maintenance manuals etc., for detecting fault, failure, or defect of aircraft that maybe occur during flight, and repair. In most maitenance events, it is usually involved in the disassembly and installation of the aircraft parts. If there are insufficient good spares, the flight delay even cancellation case would arise. So requirement of aviation spares has property of randomness [4, 5]. Aviation parts refers to the smallest physical component of each system installed on the aircraft, such as the engine control computer(EEC) on the aircraft, the transceiver of the radio communication system, and the aircraft wires, bolts and nuts. aviation part has two type: comsumable part and turnover part. The one must be discarded once replacement is comsumable parts, the other could be restored after failure by the shop maintenance is turnover parts. The high-value aviation part means whose price keep high over a long period, whether it is a turnover or a comsumable part. In the paper, we define high-value part whose long-term average price is more than 2k US dollars [6]. In order to facilitate establishing system model, the following assumptions are set based on line maintenance and aviation parts dynamic management: (1) there is only removal and installation events related aviation parts in line maintenance so that there is no difference between consumable parts and the turnover parts. Besides, only the high-value aviation parts are considered in the research. (2) Because there are little difference between turnover parts restoring time and consumable parts purchasing time, both two types parts is asked for exportation and importation, so the delay is almost same. (3) Turnover parts could be restored almost as the new one after maintenance. (4) Improper removal or installation events are regarded as interference events of aviation spares inventory dynamic management system. (5) The aviation spares inventory has unlimited capacity, in other word, the parts could purchase as many as line maintenance need.

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2.2 High-Value Aviation Parts Loss Process Model The high-value parts loss takes place in two process, the storage process and the line maintenance process. The storage process is related to storage technology, storage time, transportation and other factors, resulting in a certain loss rate of high-value parts. Since this part of the loss is a natural loss, it is basically independent of external factors, so the loss ratio coefficient can be determined. The loss model in the storage process is shown in Formula (1). L 1 (k) = αS(k)

(1)

Here L 1 is the amount of loss in the storage process, S(k) is the total amount of spare in inventory, and α is the loss factor. The line maintenance process is closely related to fleet operation, and the aviation parts consumption is a typical stochastic process. Take the aviation part labeled 3885007-1 part number as an example, which is installed in 737NG type fleet, which has 52 aircrafts. We get 200 weeks actual maintenance record. After data cleaning, the Table 1 is shown data distribution. Data fitting analysis is carried out by SPSS, aviation parts consumption obviously follows Possion distribution in a short period, and tends to be normally distributed in the long period. The high-value aviation parts loss model is set as L 2 (k). the parameters of L 2 (k) is obtained from actual disassembly and installation data identification. Take 38850071 as an example, the one order and two orders models are quite different from the actual data, while the calculation results of the three orders and above models are not much different from the actual data. Considering that the simple controller design is more practical and realization, the three orders model applies to high-value parts loss process in line maintenance is shown Formula (2), here N(k) is gaussian white noise. L 2 (k) =

1 N (k) 1 + β1 z −1 + β2 z −2 + β3 z −3

(2)

3 Research on Purchasing Strategy of High Value Aviation Spares Since the loss of the aviation part is random, macroscopically, the inventory quantity is positive correlation with inventory management cost, such as storage, transpotation. If inventory is too more, the management cost will increase, while the insufficient inventory will lead to flight delay event, the airlines maybe suffer from economic and social losses. In order to ensure that the shortage of inventory is a very small

1

1

0

0

0

0

0

1

0

0

…

2

3

4

5

6

7

8

9

10

…

1 week

Duration

1

Week SN

…

1

0

2

3 weeks

…

2

7 weeks

…

3

10 weeks

Table 1 Time distribution of aviation parts removal/installation record

0 1

200

0

0

0

1

0

2

0

0

0

…

1 week

Duration

199

198

197

196

195

194

193

192

191

190

…

Week SN

0

3

0

…

3 weeks 3

…

7 weeks

4

…

10 weeks

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probability event, we take the variance of inventory of aviation parts as the inventory optimization target in a certain period, decreasing inventory variance could cut down the average inventory cost. Considering various uncertain conditions, the paper proposes a controller design with robust variance inventory control strategy.

3.1 Dynamic Model of High-Value Spares Inventory Management It takes a certain period for aircraft spares accomplishment from order to be available, which could be regarded as a delay link from engineering control theory point of view. Generally speaking, the delay period is several times of the calculation cycle. Therefore, the model of the purchasing process of aviation spares is shown in Formula (3). P(k) = u(k − d) = z −d u(k)

(3)

P(k) is the variables to be solved, which stand for quantity of spares in current week, u(k) is the order for spares quantity, and d is the delay periods from place the order to spares in inventory and be available. The complete model of the dynamic process of high-value spares inventory management in line maintenance scenario is shown in Formula (4). S(k + 1) = S(k) + P(k) − L 1 (k) − L 2 (k) = (1−α)S(k) + z −d u(k) +(β1 z −1 +β2 z −2 +β3 z −3 ) L 2 (k) − N (k)

(4)

3.2 Robust Variance Control of High-Value Aircraft Spares Linear matrix inequality (LMI) methods [7–10] are widely used to solve complex control problems. Since the inventory dynamic management system has the properties of a discrete event dynamic system, the model parameters will vary within a certain range. Convert Formula (4) into a state-space description, and rewrite the original model of high-value spares dynamic management system as Formula (5). 

X (k + 1) = AX (k) + Bu(k) + D N (k) y(k) = C X (k)

(5)

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T  Here X[k] is X (k) = x1 (k) x2 (k) x3 (k) x4 (k) x5 (k) , and the variable x2 (k) = u(k − 1) is the control value of the previous period or last order of high-value spares, x3 (k) = L 2 (k − 2) is the consumption of aviation spares before the previous period in line maintenance, x4 (k) = L 2 (k − 1) is the consumption in last period, x5 (k) = L 2 (k) is the consumption of aviation spare in current period. Since all state variables are measurable, the observer does not need to design. Considering that parameters in system matrix are affected by uncertain factors and maybe change within a certain scope, the Formula (5) is rewritten again as Formula (6). 

X (k + 1) = (A + A)X (k) + (B + B)u(k) + D N (k) y(k) = C X (k)

(6)

factors, parameters of system matrix could be expressed as   For uncertain   A B = H F E 1 E 2 . According to actual storage records of 3885007-1 spares, we select α from [0.9 0.99], H and E 1 matrix parameters are selected as follow: ⎤ ⎤ ⎡ ⎡ 3111 10000 ⎢0 0 0 0⎥ ⎢0 1 0 0 0⎥ ⎥ ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎢ E1 = ⎢ 0 0 1 0 0 ⎥ H = ⎢0 1 0 0⎥ ⎥ ⎥ ⎢ ⎢ ⎣0 0 1 0⎦ ⎣0 0 0 1 0⎦ 0001 00001 Due to u(k) is calculated from the above equation, B = 0, and the matrix is E 2 = 05×1 . Because α < 1, we could arrive the result F T F < I5×5 . The aim of closed-loop system design should meet following rules, even above parameters have some change with in desired range: (1) aviation spare inventory dynamic management system is asymptotically stable; (2) closed-loop system shall ensure that closed-loop pole is within the specified range by the state feedback controller; (3) The variance of aviation spares inventory should be significantly reduced compared to the no LMI control. In order to achieve the above requirements, the system design is further transformed into the perturbation range of given system parameters, and is the allowable range disc of the closed-loop system pole D(q, r). Here q is the center of the disk on the complex plane and r is the radius of the disk, given the allowable value σ i for the standard deviation of the system state, find constant ε > 0 and symmetric positive definite matrix P and Y, and make those parameters have the relationship as Formula (7).

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⎡

⎤ −P (A P + BY − q P)T (E 1 P + E 2 Y )T ⎣ A P + BY − q P −r 2 P + D D T + ε H H T ⎦ vmax viq = −vmax , i f viq < vmax

(8)

(9)

In (8) and (9), c1 represents the weight coefficient of the historical optimal value of the particle search, which is self “cognition”. c2 represents the global optimal weight coefficient of the particle, that is a global “cognition”, and the alias is “social knowledge”. rand1 and rand2 are random numbers, both value interval is [0, 1]. vmax represents the maximum speed limit and viq represents the velocity component in an one-dimensional space. The position updating formula of the particle in the q(q = 1, 2, . . . , Q) dimensional space: xiq = xiq + r viq

(10)

In which, r is the elastic coefficient of velocity variable and its initial value is 1. The velocity position of a population particle is the result of a series of factors, including the velocity and position of the particles in the past, as well as the state and position of the population in the past. Each particle and population interact with each other to find the optimum solution.

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3.3 Modeling of PSO-LSSVM In practical application, the kernel parameter of LSSVM is always difficult to attain the optimal value, which affects the prediction accuracy to a certain extent. In this paper, the PSO-LSSVM model is created by using the advantages of PSO algorithm in global search and iterative optimization, so as to predict the related parameters of the motor. The specific process is as follows: (1) Preprocessing: determine samples of the training set, normalize and smooth the data. (2) Select PSO parameters and initialize particle swarm to get initial particles and their population. (3) Evaluate the population contains all particles and determine their fitness. (4) Update particles based on existing data to generate new species. (5) If the recognition meets the training requirements, the parameters will be forwarded to LSSVM. If not satisfied, then step back to step 2. (6) Output prediction results and function adaption values.

4 Tests and Results In order to reveal the accuracy of the new model in prediction aspect, we use two groups of actual data of an air fan to predict the next sampling value by three adjacent groups of data, and compare the accuracy of the results with the standard prediction results. For a period of time after the failure of the fan, the voltage keeps the normal working voltage of about 36 V. The working voltage is slowly rising and fluctuating when test continued going. The following Figs. 1 and 2 respectively reveal the prediction

Fig. 1 The comparison between the PSO-LSSVM, LSSVM, PAO-ACO, and SVM for data one

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Fig. 2 The comparison between the PSO-LSSVM, LSSVM, PAO-ACO, and SVM for data two

Table 1 Comparison of predictive parameters Dataset

Error mean

Error standard deviation

Execution time (s)

1

0.41

3.16

2.41

2

0.35

4.22

2.53

LSSVM

1

3.23

4.25

3.23

2

1.87

5.63

4.87

PAO-ACO

1

2.85

8.66

6.78

2

3.89

9.43

6.91

1

3.56

14.48

8.34

2

4.39

15.52

9.43

PSO-LSSVM

SVM

errors of the four models of PSO-LSSVM, PSO-ACO, LSSVM and SVM. When using two models, the relevant parameters are as follows Table 1. Compared the calculation parameters of the PSO-LSSVM and the standard SVM prediction models, it is found that PSO-LSSVM has a greater advantage over the standard SVM in the mean error and the error standard deviation, and the error mean and error standard difference can be raised about 80%. However, the execution time of the program is more than twice as much as that of the standard SVM. For the reason that the PSO algorithm is added, and the kernel function parameter optimization of the support vector machine consumes a higher time cost. The fitness training curve in the PSO-LSSVM prediction process in Fig. 3 shows that the fitness has reached more than 0.996 after many times optimization, which also proves the effectiveness of the prediction model.

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Fig. 3 Fitness training curve

5 Conclusion As a part of the airborne surveillance system, the airborne weather radar can detect the dangerous weather areas in front of the aircraft. Excellent heat dissipation is an important link to ensure the normal work of the weather radar and is used to ensure the safety of the flight. Considering the characteristics of the particle swarm optimization, we deployed the particle swarm optimization based on least square support vector machine kernel function prediction model in this paper. Through the optimization of the PSO algorithm and the support vector machine algorithm, the kernel function of the least squares support vector machine is optimized. It can optimize the parameters of the kernel function quickly and dynamically, realize the complementary advantage, and make up the defect of the previous support vector machine effectively. The experimental results demonstrate that compared with the standard SVM, the particle swarm optimization least squares support vector machine (PSO) algorithm is more accurate than the standard SVM algorithm, which proves the effectiveness of the scheme. The following research direction will head to how to reduce the computational complexity and improve the prediction efficiency under the premise of guaranteeing the accuracy of prediction.

References 1. Wu, X., Chen, B., Niu, H.: Research on fault diagnosis of fan based on EEMD and SVM. Coal Technol. 36(4), 252–254 (2017) 2. Shuqing, Z., Yongtao, H., Jiang, A.: Bearing fault diagnosis based on particle swarm optimization and support vector machine based on dual tree complex wavelet and adaptive weight and time factor. China Mech. Eng. 28(3), 327–333 (2017) 3. Sain, S.R.: The Nature of Statistical Learning Theory by V. N. Vapnik. The nature of statistical learning theory, pp. 988–999. Springer, Berlin (1995)

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4. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol. 4. pp. 1942–1948. IEEE, 2002 (1995) 5. Li, L., Chang, W., Zhou, S.: An identification and prediction model of wear-out fault based on oil monitoring data using PSO-SVM method. In: Reliability and Maintainability Symposium. IEEE, (2017) 6. Tian, Z.D., Gao, X.W., Shi, T.: A combined kernel function least squares support vector machine for chaotic time series prediction. Acta Phys. Sinica 63(16), 66–76 (2014) 7. Yaoqin, S.U.N.: Application of improved particle swarm optimization and support vector machine in fault diagnosis. Comput. Meas. & Control. 25(3), 48–50 (2017) 8. Zhang, S.: Prediction of coal demand in Shandong Province Based on particle swarm optimization and support vector machine. Inner Mongolia Goal Econ. 7, 57–58 (2017)

Research on Harmonic Current Functional Analysis of AC Arc Furnaces and Evaluation of Harmonic Level Pu Deng, Shi Zeng, Yongzhong Li, Xiaojun Peng, Jing Nong, Zhuo Chen and Aiping Pang

Abstract This paper analyses the synchronous measuring data of harmonic current in AC arc furnaces with method of functional analysis, calculates the interaction angle between serial data of harmonic current in two arc furnaces, gets the conclusion that serial data of harmonic current in two arc furnaces are orthogonal, derives superposition formula for synthesizing harmonic currents of multi-arc furnaces and formula for evaluating harmonic voltage level beforehand in construction of power supply area of AC arc furnaces. Keywords AC arc furnace · Synthesizing harmonic current · Function analysis · Orthogonal · Evaluation of harmonic level introduction

P. Deng (B) · J. Nong Power Grid Planning and Research Center, Guizhou Power Grid Corporation, Guiyang 550002, Guizhou, China e-mail: [email protected] J. Nong e-mail: [email protected] S. Zeng · Z. Chen · A. Pang College of Electrical Engineering, Guizhou University, Guiyang 550025, Guizhou, China e-mail: [email protected] Z. Chen e-mail: [email protected] A. Pang e-mail: [email protected] Y. Li · X. Peng Guizhou Power Test and Research Institute, Guiyang 550025, Guizhou, China e-mail: [email protected] X. Peng e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_85

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1 Introduction AC arc furnace is a load with large harmonic release. Before construction, harmonic level assessment and targeted planning and design cannot be carried out, but only deal with after construction. The harmonic current synthesis released by multiple-AC arc furnaces makes the evaluation technically difficult. The formula for synthesizing harmonic currents is recommended in the annex to Harmonics in Public Supply Network (GB/T 14549-93), and the relationship coefficient kh is defined by homologous table another equation was recommended by Conference International des Grands Reseaux Electriques (CIGRE) 36–05 working team, and the relationship coefficient α is obtained as homologous table. International research on synthetic harmonic current of multiple-AC arc furnaces [1, 2], and some analytical methods are proposed [3–6]. However, there is no effective synthesis formula and algorithm. It is still an unsolved problem to evaluate the harmonics of the arc furnace area composed of multiple AC arc furnaces. This paper analyses the statistical characteristics of harmonic current in AC arc furnace, the synthetic harmonic current is studied.

2 The Orthogonality and Functional Analysis of Synthesis Harmonic Current in AC Arc Furnace 2.1 Synchronous Measurement of Harmonic Current in AC Arc Furnace Four signals were synchronously measured, including the in-phase harmonic current at the high voltage side of A and B two AC arc furnace transformers, the in-phase synthetic harmonic current of a feeder and bus voltage. The measurement process covers the entire smelting cycle of AC arc furnace, and the harmonic data formed in chronological sequence at about 1400 moments are obtained. Each data of measurement at one moment is synchronous, the interval between measurements Δt is 10 s. At each moment, Fourier analysis is performed in a single cycle mode. The data at each moment contains the value of each harmonic amplitude and phase of A, B AC arc furnaces and their synthesis current, therefore, the amount of binary data obtained by A whole-process synchronous measurement is greater than 0.8 Mbyte.

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2.2 Functional Definition of Measured Sequences of Harmonic Currents in an AC Arc Furnace T = 1, 2… The measurement sequence at time n is defined as a functional f h A (t) = i h A (t) cos ϕh A (t) + j · i h A (t) sin ϕ h A (t)

(1)

(t = 1, 2,…, n; h = Harmonic number) f hA (t) is a complex number sequence, arranged in chronological order of measurement. Where ihA (t) is the amplitude of the hth harmonic current of AC arc furnaces at time t. ϕ hA (t) is the lag angle between hth harmonic current and bus hth harmonic current. Similarly, the complex sequence of h harmonic currents measured by furnace B is functional f hB (t). f h B (t) = i h B (t) cos ϕh B (t) + j · i h B(t) sin ϕ h B (t)

(2)

(t = 1, 2,…, n; h = Harmonic number) Functional f hA (t) and f hB (t) are complex Numbers belonging to n-dimensional unitary linear space, as shown below f h A (t) ∈ V n , f h B (t) ∈ V n

(3)

The dot product of functional f hA (t) and f hB (t) is  ( f h A (t) · f h B (t)) =

f h A (t) × f h B (t)dt t

= t ×

n 

( f h A (t) × f h B (t))

(4)

t=1

 where, t f h A (t) × f h B (t)dt is the Lebesgue Integral, f h B (t) is conjugate complex number of f h B (t). Δt is the interval between measurements. Notice that the dot product space to which ( f h A (t) · f h B (t)) belongs is the Hilbert space. In Hilbert space, the norm of functional f hA (t) and f hB (t) is    n      | f h A (t)| =  f h A (t) × f h A (t)dt = t × (i h A (t))2 t=1

t

  n   | f h B (t)| = t × (i h B (t))2 t=1

(5)

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In Hilbert space, the angle Φ between functional f hA (t) and f hB (t) is cos Φ =

  

  n  n sgn r eal f (t) × f (t) × ( f (t) × f (t))   h A h B h A h B t=1 t=1 | f h A (t)| × | f h B (t)|

(6)



  n f (t) × f (t) is the sign function of the real part of where sgn r eal h A h B t=1 n t=1 f h A (t) × f h B (t). If Φ = 90°, f hA (t) and f hB (t) are orthogonal to each other.

2.3 The Orthogonality of Harmonic Current Measurement Sequences in Two AC Arc Furnaces Fourier transform is an orthogonal mapping, so that the different-order harmonic current are orthogonal to each other. The purpose of this step is to analyze whether the same-order harmonic current measurement sequence of two AC arc furnaces is orthogonal. According to formula (8), the angle between the complex numbers sequence of the same-order harmonic current of two AC arc furnaces is calculated with synchronous measurement data, as shown in the follow Table 1. As can be seen from Table 2, the Angle of the complex numbers sequence of the same-order harmonic current of two AC arc furnaces is approximately 90°, which is approximately orthogonal to each other. Table 1 Interaction angle  between measuring serials of same order Harmonic Current in two AC Arc furnaces Harmonic number

Two silicon-manganese furnaces

Two phosphorus furnace

Silicon-manganese furnaces and ferrosilicon furnace

2

99.7°

100.2°

98.1°

3

93.0°

79.7°

82.2°

5

94.3°

82.8°

93.2°

7

93.3°

81.4°

92.0°

9

94.8°

86.6°

94.7°

11

93.7°

87.0°

89.7°

13

92.9°

85.6°

91.0°

15

90.8°

94.9°

88.3°

17

85.5°

85.1°

96.3°

19

88.7 °

84.1°

91.5°

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Table 2 Correlation coefficient between harmonic currents Harmonic number

Two silicon-manganese furnaces

Two phosphorus furnace

Silicon-manganese furnaces and ferrosilicon furnace

Real axis

Virtual axis

Real axis

Virtual axis

Real axis

Virtual axis

2

−0.1

−0.13

−0.24

0.03

−0.15

0.10

3

−0.05

−0.17

0.16

0.11

0.06

0.12

5

−0.07

−0.08

−0.05

−0.06

−0.04

−0.10

7

0.00

0.04

0.14

−0.11

0.03

−0.01

9

0.02

−0.02

0.11

−0.10

0.12

−0.17

11

0.00

−0.01

0.14

0.01

0.07

0.05

13

−0.02

0.00

−0.12

0.10

−0.08

0.17

15

−0.10

0.06

0.18

−0.03

0.12

−0.09

17

−0.01

−0.01

0.14

0.15

0.02

0.05

19

−0.06

0.01

−0.04

0.08

−0.07

0.04

2.4 Synthesis Formula of Harmonic Current Content in AC Arc Furnace If the complex numbers sequence of the each-order harmonic current, statistical superposition formula for synthesizing harmonic currents can be derived. The synthetic harmonic current of two AC arc furnaces is defined as functional f h (t). f h (t) = f h A (t) + f h B (t)

(7)

(t = 1, 2,…, n; h = harmonic number) f hA (t) and f hB (t) are functions that orthogonal to each other, according to the pythagoras theorem, the functions of synthetic harmonic current can be deduced as | f h (t)|2 = | f h A (t)|2 + | f h B (t)|2

(8)

Equation (8) can be simplify as n 

i h2 (t) =

t=1

n 

i h2 A (t) +

t=1

n 

i h2 B (t) (h = 2, 3, . . . , ∞)

(9)

t=1

Equation (9) can be deduced as n  ∞  t=1 h=2

i h2 (t)

=

n  ∞  t=1 h=2

i h2 A (t)

+

n  ∞  t=1 h=2

i h2 B (t)

(10)

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∞ 2 2 i (t) and h=2 h A h=2 i h B (t) are the synthetic harmonic current content at time t, and the harmonic current content of A and B arc furnaces, respectively, write as I H (t), I HA (t) and I HB (t).

∞ 2 h=2 i h (t),

∞

n  t=1

(I H (t))2 =

n 

(I H A (t))2 +

t=1

n 

(I H B (t))2

(11)

t=1

If measurement of harmonic current is strictly orthogonal, the measured data at time n satisfies the following equation (I H (n))2 = (I H A (n))2 + (I H B (n))2

(12)

in a statistical sense, I H = I H2 A + I H2 B . This indicates that if the harmonic currents are strictly orthogonal to each other, the relation coefficient of formula given by Public Supply Network is 0 and that of formula recommended by CIGRE is 2. If the harmonic currents of 1-m AC arc furnaces are strictly orthogonal in pairs, it can be inferred as   m  I H2 i (13) IH =  i

I Hi is the ith harmonic current content of the arc furnace.

2.5 Independence of Harmonic Currents in Two AC Arc Furnaces Because of the orthogonality between the harmonic currents of two arc furnaces, it also shows that the harmonic vectors of two arc furnaces are independent in theory. The measured data are calculated according to the regularized correlation coefficient E[(x − E(x))(y − E(y))] corrcoef(x, y) =   E (x − E(x))2 E (y − E(y))2

(14)

Since harmonics are complex (vector) sequences, it is necessary to project the harmonic vector onto the real and imaginary axes of the complex plane, that is, the real components of parallel and perpendicular to the voltage harmonics for calculation with formula (14).

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The correlation coefficient of current harmonic measurement sequences of two AC arc furnaces are shown in Table 2. Set the correlation coefficient between −1 and 1. If the correlation coefficient is positive and the value is large, it means the probability that the current harmonic of two arc furnaces increases or decreases simultaneously. The correlation coefficient is negative, indicating that the current harmonic of one arc furnace increases, the harmonic of the other arc furnace decreases at the same time. The correlation coefficient is 0, which indicates that harmonics increase and decrease in two arc furnaces are independent of each other. The data in Table 2 show that the values of each-order harmonic content between two arc furnaces are approximately independent (weakly correlated). According to the independent property of each-order harmonic current, the harmonic content of each arc furnace can be measured separately.

3 Definition and Synthesis Formula of Harmonic Current Number Product The harmonic current times product is defined as  ∞  JH =  (Ih · h)2

(15)

h=2

where, h is the number of harmonics, and I h is the magnitude of the hth harmonic current. If the harmonic current sequence of multiple-AC arc furnaces is strictly orthogonal, according to Eq. (10), it can be proved that the times product of harmonic current synthesized by 1 ~ m AC arc furnaces as   m  J H2 i JH = 

(16)

i

where J Hi is The times product of the ith harmonic current of AC arc furnace. It’s important to note that Eq. (16) derived by functional analysis method only has statistical significance, and the harmonic current of AC arc furnace is approximately orthogonal rather than strictly orthogonal. Therefore, the error analysis of formula (16) is necessary. (1) The measured error of the whole production cycle According to the statistics of the measured data of 3 whole production cycles in different sites, when the 95% probability value of the measured value of AC arc furnace J Hi is taken, the error of formula (16) is between −10.01 and 1.03%.

914 Table 3 Measuring data of THDJ in AC arc furnaces

P. Deng et al. 35 kV AC arc furnace

THDJ

Silicon-manganese refining furnaces (3.4 MVA)

0.937

Silicon Manganese crude furnace (3.4 MVA)

1.027

Silicon-manganese refining furnaces (8 MVA)

0.338

Ferrosilicon rough smelting furnace (5 MVA)

0.929

Ferrosilicon refining furnace (9 MVA)

0.286

Phosphorus furnace (6 MVA)

0.119

Phosphorus furnace (6 MVA)

0.0975

(2) The error probability Because of the independence between harmonic current vectors of AC arc furnace, the measurement data can be statistically analyzed by Monte Carlo Method. The error analysis shows that the relative error of formula (16) in the confidence interval of 2.5 to 97.5% is −5.9 to 5.1%, which indicates that formula (16) can be used for evaluation and calculation. The total distortion rate of harmonic current time product is defined as T H DJ =

JH × 100% I1

(17)

where, I 1 is the rated industrial frequency current of electric furnace transformer. The measured values of each harmonic at each moment are obtained by the harmonic meter, and the THDJ is obtained after statistics. The measured value of THDJ AC arc furnace (95% probability value of measured value) is shown in fellow Table 3 models and production processes of Ac arc furnace are different, THDJ vary greatly.

4 Evaluation of the Harmonic Voltage Level in the Power Supply Area of AC Arc Furnace 4.1 Definition of Total Distortion Rate of Harmonic Current Time Product Assuming that the AC arc furnaces is connected to the point of common coupling of the grid, the harmonic impedance of the point is inductive, and the hth harmonic impedance is X h = 2π h L = h X 1

(18)

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where X 1 is short-circuit impedance of industrial frequency for point of common coupling. The total harmonic voltage distortion rate THDu of the common access point can be obtained as ∞ ∞ 2 2 h=2 (X h · Ih ) h=2 Uh T H Du = = U1 U1 ∞ m 2 2 X1 · (h · I ) · X h 1 h=2 i JH i X 1 · JH = = = U1 U1 U1  

2 m J m 2 U1 · I1i · IH1ii i i (Si · T H D J i ) (19) = = U12 S X1

where, U 1 is the rated industrial frequency voltage of point of common coupling, U h is the hth harmonic voltage, I h is hth synthesizing harmonic current, J H is the synthesizing harmonic current time product, S is the short circuit capacity, I 1i , THDJi and S i are the rated industrial frequency current, short circuit capacity and total harmonics distortion of harmonic current time product in the ith AC arc furnace. The formula for evaluating the harmonic voltage level of multiple AC arc furnaces can be obtained as m 2 i (Si · T H D J i ) (20) T H Du = S

4.2 Definition of Total Distortion Rate of Harmonic Current Times Product Take a silicon (silicon iron, silicon manganese) smelter as an example, Powered by 220 kV self-contained substation, short-circuit capacity of 220 kV busbar is 2705 MVA, short-circuit capacity of 35 kV is 1072 MVA, and 34 sets of 6300 kVA AC arc furnace are connected to 35 kV busbar. The total harmonic distortion of the 35 kV bus voltage in the factory is evaluated as  T H DU =

34 × (6.3 × 1.027)2 = 3.67% 1072

(21)

It can be directly connected to the grid without taking control measures. In the actual measurement, 25 AC arc furnaces are running. The test value of 35 kV bus voltage of total harmonic distortion (95% probability) is 3.2%. The formula (10)

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is the rechecking value:  T H DU =

25 × (6.3 × 1.027)2 = 3.15% 1072.7

(22)

5 Conclusion The research on harmonic current functional analysis of AC Arc furnaces and evaluation of harmonic level realizes the harmonic currents in the same phase of multiple ac arc furnaces are orthogonal and independent. The harmonic current of ac arc furnace is synthesized according to the rule of the sum of squares. Ac arc furnace harmonic current is synthesized by the root of the sum of squares. Therefore, the increase in the number of ac arc furnaces does not increase the resultant harmonic current much. It is advisable to gather multiple ac arc furnaces in an independent power supply area and access the point of common coupling of the grid with large short-circuit capacity. The evaluation in the construction planning can make the harmonic power quality in the Ac arc furnace reach the standard without adopting the harmonic control measures, so as to achieve remarkable economic benefits. The classified measurement of total harmonic current time product distortion of Ac arc furnace should be carried out to meet the needs of pre-construction evaluation. This strategy has certain guiding significance for the measurement of total harmonic current. Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Fund of China (51567005) and Guizhou Province Joint Fund Project (LH[2017]7230, [2017]5788). Guizhou Science and Technology Innovation Talents Team Project [2018]5615.

References 1. Fu, Y., Wang, Z., Wang, Z., et al.: Splattering suppression for three-phase AC electric arc furnace in fused magnesia production based on acoustic signal. IEEE Trans. Ind. Electron. 64, 4772–4780 (2017) 2. Lim, C.C., Ramiah, H., Yin, J., et al.: An inverse-class-F CMOS oscillator with intrinsic-high-Q first harmonic and second harmonic resonances. IEEE J. Solid-State Circ. 1–12 (2018) 3. Zhao, H., Wang, S., Moeini, A.: Critical parameter design for a cascaded H-bridge with selective harmonic elimination/compensation based on harmonic envelope analysis for single phase systems. IEEE Trans. Ind. Electron. 66, 2914–2925 (2019) 4. Yuan, R., Qu, T.: Synthesis of the same harmonic in public power grid. China Electric Power 7, 47–49 (1994) 5. Xia, D., et al.: Theory of real variable function and functional analysis. Higher Education Press (1983) 6. Xu, Y.: Evaluation of harmonic limits and nonlinear load access for public power grids. Power Syst. Equip. 2, 66–69 (2004)

Minimax Optimization for Capacitors Composited with Two Kinds of Series Reactance Rates Pu Deng, Tinghao Lei, Fengyuan Wang, Zhuo Chen and Aiping Pang

Abstract For the reasonable series reactance rate in capacitor of substations, the full parametric harmonic circuit and model for 220 and 110 kV substations are established, which consists of transformer, load, short impedance and harmonic source, capacitors that two reactance rates are adopted. Moreover, the resonance objective function is proposed, which reflects the degree of resonance, such as, harmonic voltage amplification factor on load bus, etc. With the method of minimax optimization, the maximum values of objective function in all the power grid parameter space are minimized by changing reactance rate. The optimization results show that resonance is eliminated with the best effect by using a set capacitor with 12% series reactance rate and another groups of capacitors with 4.5%, and the result also reduces the loss and cost. At the same time, this conclusion is suitable for all 220 and 110 kV substation. Keywords Harmonic · Resonance · Harmonic amplification · Reactance ratio · Harmonic impedance

P. Deng (B) · F. Wang Power Grid Planning and Research Center, Guizhou Power Grid Corporation, Guiyang 550002, Guizhou, China e-mail: [email protected] F. Wang e-mail: [email protected] T. Lei (B) · Z. Chen · A. Pang College of Electrical Engineering, Guizhou University, Guiyang 550025, Guizhou, China e-mail: [email protected] Z. Chen e-mail: [email protected] A. Pang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_86

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Fig. 1 The equivalent circuit of resonance caused by capacitor

1 Introduction In areas with large harmonics of the power grid, power shunt capacitors are prone to harmonic resonance, not only damage to the shunt capacitor, but also cause the common connection point (PCC) harmonic voltage amplification and deteriorating the power quality of the grid. The harmonic resonance of the capacitor is caused by the following two factors: First, the capacitor impedance and the grid impedance have parameters, so that the resonant frequency coincides with the integer harmonic frequency. Secondly, the substation injects a larger, resonant harmonic components with the same frequency. The harmonic current source is directly injected into the bus of the access capacitor device [1–3]. A parallel equivalent circuit is formed by the harmonic current source, the impedance of the capacitor device and the short-circuit impedance of the bus [4, 5]. And all of these form the basic model of capacitor resonance as shown in Fig. 1. In order to solve the problem of series reactance selection in the design of new substation capacitors, it is necessary to study the generality of the series reactance rate harmonic elimination ability. In a word, the universality under the conditions of various factors including the power grid.

2 Circuits, Models and Parameters According to the equipment and electrical wiring of a typical 220–110 kV substation, a substation equivalent resonant circuit including capacitor device, transformer, load, and short-circuit impedance of the power grid is established. The harmonic source uses a constant current source model, which can be the background harmonic injected from the main transformer high-voltage side busbar, or the nonlinear load harmonic injected into the load busbar. Therefore, four resonant equivalent circuits are formed,as shown in Fig. 2.

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Fig. 2 Harmonic injection mode and resonance equivalent circuit

The values of the individual harmonic impedance values in the circuit of Fig. 2 are derived as following figures. (1) Harmonic impedance of system short-circuit impedance

(Q/ST ) h (Q/ST ) 0.15 + j√ ZSh = √ 2 2 (S/S ) 0.15 + 1 0.15 + 1 (S/ST ) T 0.15 in the equation is the ratio of resistance to inductance in the short-circuit impedance, which has little effect on the capacitor resonance. h is the harmonic order, and S/ST is the transformer short-circuit ratio. More specifically, S is the high-voltage side short-circuit capacity of the main transformer, and ST is the transformer capacity. (2) Two harmonic reactance capacitor harmonic impedance Set the total capacity of the capacitor put into the substation is Q, the capacitance capacity of the reactance ratio x is ε Q, the capacitance capacity of the reactance rate y is (1 − ε)Q, ε is the proportional coefficient, and 0 ≤ ε ≤ 1. A capacitor harmonic impedance circuit using a mixture of two reactance rates is shown in Figure 3. The reactance of the capacitor with the reactance of x and y is: X Zh =

    1 1 1 1 k L x + j hx − j Y Zh = k L y + j hy − j ε h ε h

The total impedance of the capacitors put into the substation is: Z Ch = X Z h ||Y Z h The symbol “||” indicates the parallel operation of the impedance, at the same time, x and y are between 0 and 0.13.

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Fig. 3 Two kinds of reactance mixed capacitor harmonic impedance circuit

The reactance rate x is the control variable to be solved, and the remaining variables are the parameters of the grid, which can form the vector z˙ . z˙ = (δ, γ , S/ST , Q/ST , cos φ, a2 , a3 , . . . , an ) z˙ ∈ D ⎫ ⎧ ⎨ (δ,  γ, S/ST , Q/ST , cos φ, a2 , a3 , . . . , an ) ⎬  D =  0.7 ≤ δ ≤ 1.3, 0.1 ≤ γ ≤ 1, 3 ≤ S/ST ≤ 100 ⎭ ⎩ 0 ≤ Q/ST ≤ 0.3, 0.7 ≤ cos φ ≤ 1, 0 ≤ a2 , a3 , . . . , an ≤ 1  Each variable, that constitutes the parameter vector z˙ , has a certain range of values. The grid parameter space D where z˙ is determined. The author believes that D contains all the parameters of the grid.

3 Objective Function Reflecting the Resonance Level The degree of deterioration of the harmonic resonance power quality of the capacitor connection to the common connection point (PCC) is measured in (1). λ is the ratio of the total harmonic distortion of the load bus voltage taking into account the resonance of the capacitor and the capacitor not resonating (without the input capacitor), λ(x, y, z˙ ) =

THDL lim (THDL )

(1)

Q/ST →0

THDL is the total harmonic distortion rate of the load bus voltage  THDL =

h

V2Lh

V1

THDL is affected by both the harmonic source and the capacitor resonance factor (the impedance of the impedance). Analytic expression of λ in the circuit is shown in 3(a).

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h

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ah2 |ZLh ||[XT2h +(ZSh + XT1h )||(ZCh + XT3h )]|2  2 2 h ah |ZLh ||(XT2h + ZSh + XT1h )|

It is noted that the load bus fundamental voltage V1 and the nonlinear load fundamental current I1 have been approximately eliminated. It can be found that the multivariate function consists of independent variables (x, y, z˙ ), and the analytical expressions of the remaining circuits are also easily deduced.μ is the ratio of the total harmonic distortion rate of the voltage on the capacitor element when the capacitor device resonates, the effect of the resonance of the capacitor device on the overvoltage of the capacitor component is measured, which reflects the degree of damage of the capacitor device resonance to the device itself. μ(x, y, z˙ ) =

THDC lim (THDC )

(2)

Q/ST →0



h

THDC =

V2ch

Vc1

THDC is the voltage total harmonic distortion rate on the capacitor element. Vc1 is the fundamental voltage on the capacitor element, and Vch is the h-th harmonic voltage on the capacitor element. As shown in Fig. 2.

4 Maximum Optimization of the Objective Function The objective function λ(x, y, z˙ ) is a multivariate function of the control variable x and the parameter vector z˙ , z˙ ∈ D, and D is the grid parameter space. For a value of the control variable x, there is a z˙ in the parameter space D, so that λ(x, y, z˙ ) has the maximum value. The mapping of x and the maximum value constitutes the target maximum function max (x). λmax (x, y) = max[λ(x, y, z˙ )] z˙ ∈D

λmax (x) maximum function is a single-valued function with x as an independent variable. Similarly, a target maximum function max (x) for the reactance rate x can be defined. μmax (x, y) = max[μ(x, y, z˙ )] z˙ ∈D

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The minimax optimization of the objective function λ(x, y, z˙ ) with respect to x is expressed as, min[λmax (x, y)].

x,y  That is, min max λ(x, y, z˙ ) . x,y

z˙ ∈D

Optimization Interpretation: A combination of series reactance rates x, y is obtained to minimize the value of the maximum value of the objective function μ(x, z˙ ) in all grid parameter space D, which is suitable for the grid parameter space D. Similarly, the minimum optimization of the maximum value of x for the objective function μ(x, z˙ ) is expressed as: min[μmax (x, y)].

 x,y That is, min max μ(x, y, z˙ ) . x,y

z˙ ∈D

In Fig. 4, each point on the surface is the target function maximum in all grid parameter spaces D corresponding to the combination of x, y reactance rates. The vertical coordinate value of the surface point is larger, the degree of resonance is greater. On the other side, the vertical coordinate is smaller, so the resonance is smaller. The optimized reactance rate x, y combination value is to find the area

Fig. 4 Binary maximum function graph of two reactance rate combinations

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with small vertical coordinates. That is, the x, y region with the smallest maximum function is called the maximum minimum optimization. And the optimized value is suitable for the entire grid parameter space D, which is called the optimization for the grid parameter space D. The figure shows that the minimum area of the maximum function is: x ∈ (0.039∼0.06) and y ∈ (0.11∼0.13), the 4.5 and 12% reactance rates are optimized for the combination of D.Accurately, the 4.5% capacitor capacity accounts for 75% of the total capacity and 12% of the capacitor capacity accounts for 25% of the total capacity. The effect of suppressing resonance is the best, and it is an optimization result suitable for D. It must be pointed out that this calculation is only for the case where the ratio of the capacitor capacity of the reactance rate x, y is 75 and 25%, respectively, and the other ratios still have no clear conclusion. In order to further clarify the above problems, and also for clarifying the problem of the retreating order in the operation of the capacitor bank, and the mixing problem of 12 and 4.5% reactance rate, in the case of including all the substation operating conditions, the capacitors of the two reactance rates are in various capacities. The number of capacitor banks installed on the low-voltage side of each transformer is mostly designed as 2 or 3 groups, and there are also 4 groups and a maximum of 5 groups. The composition of each group is as shown in Table 1. In the manner of Table 1, the following combinations of different reactance capacitors were investigated. In the process of capacitor switching, the capacity ratio and reactive power compensation rate of the two reactance capacitors are changed. In order to study the resonance under the combined conditions, according to the 7 ratios listed in Table 2, with the reactive power compensation rate the various points the change, the maximum Table 1 Minimax optimization while S/ST ≥ 15 and Q/ST ≤ 0.2

Number of capacitor banks 1 group

Capacitor capacity ratio 4.5%

12%

100%

0%

0%

100%

2 group

50%

50%

3 group

33.3%

66.7%

66.7%

33.3%

25%

75%

50%

50%

75%

25%

20%

80%

40%

60%

60%

40%

80%

20%

4 group

5 group

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Table 2 Capacity ratio of substation capacitor hybrid reactance rate

Capacitance ratio

4.5%

12%

1

100%

0%

2

80%

20%

3

66.7%

33.3%

4

50%

50%

5

33.3%

66.7%

6

20%

80%

7

0%

100%

value of the objective function is calculated. The maximum curve of the objective function is plotted for each combination ratio, as shown in Fig. 5. It can be seen from the figure that the ratio of 12% capacitor capacity is larger, the ratio of 4.5% capacitor capacity is smaller, and the effect of suppressing resonance is better. The harmonic elimination is better than the 12% single reactance rate of each group, and it is the best harmonic elimination performance. Moreover, it has a universal combination, and the way is adapted to 110 and 220 kV substations.

(a) Single λmax reactancecurve

(b)λmax ( 4.5%,12% ) curve of each capacity combination

(c)Single μmax reactancecurve

(d) μmax ( 4.5%,12% ) curve of each capacity combination

Fig. 5 Curves of objective maximum functions while

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In the operation sequence of the capacitor, the 12% capacitor is input firstly, and the 4.5% capacitor is input. When exiting, the 4.5% capacitor is removed firstly, and finally the 12% capacitor is removed. This method can effectively prevent resonance.

5 Conclusion By establishing a voltage total harmonic distortion amplification factor and a capacitor component voltage total harmonic distortion rate amplification factor, the objective function of capacitor resonance is established. And according to the minimax optimization of the way for the combination of two reactance capacitors. The general conclusion is obtained: A set of 12% capacitors is used, and the other groups adopt a combination of 4.5% capacitors, which is not only the optimal combination of harmonic elimination performance, but also an economical and reasonable combination mode. Moreover, this method is suitable for 110 and 220 kV substations. Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Fund of China (51567005) and Guizhou Province Joint Fund Project (LH[2017]7230, [2017]5788).Guizhou Science and Technology Innovation Talents Team Project [2018]5615.

References 1. Lim, C C., Ramiah, H., Yin, J., et al.: An inverse-class-F CMOS oscillator with intrinsic-high-Q first harmonic and second harmonic resonances. IEEE J. Solid-State Circ. 1–12 (2018) 2. Mannen, T., Fukasawa, I., Fujita, H.: New control method of suppressing dc-capacitor voltage ripples caused by third-order harmonic compensation in three-phase active power filters. IEEE Trans. Ind. Appl. 1 (2018) 3. Chakravorty, D., Meyer, J., Schegner, P., et al.: Impact of modern electronic equipment on the assessment of network harmonic impedance. IEEE Trans. Smart Grid 8(1), 382–390 (2016) 4. Andersen, T., Krismer, F., Kolar, J., et al.: Modeling and pareto optimization of on-chip switched capacitor converters. IEEE Trans. Smart Grid. 1 (2016) 5. Shuming, L., Chenying, L., Qionglin, L., et al.: Characteristics analysis of power system series harmonic resonance and sensitivity calculation. Power Syst. Prot. Control. 43(9), 21–27 (2015)

GRU-Based Estimation Method Without the Prior Knowledge of the Noise Xuebo Jin, Aiqiang Yang, Tingli Su and Jianlei Kong

Abstract The state estimation method is one of the important techniques for target tracking and those techniques based on Kalman filtering have attracted the attention of many researchers. Among these existing methods, the very basic and necessary premise is that the model of the target is with high precision and good prior knowledge of process noise as well as measurement noise are also available. However, it is quite difficult to achieve in the practical applications. Therefore, in this paper, the Gated Recurrent Unit (GRU)-based estimation method is proposed to estimate the actual moving trajectory via the simulated GPS data with noise. GRU has a good advantage in the processing of time series data, and it has a memory function for data information. In the experiment part, by comparing with the traditional Kalman method, it is found that the GRU can obtain better estimation results. Keywords Object tracking · State estimation · Kalman filtering · GRU

1 Introduction As an important technique for target tracking, state estimation has a wide range of applications, such as video surveillance [1], region tracking [2] and human-computer interaction [3]. Since there are various uncertain dynamics and different complex X. Jin · A. Yang · T. Su (B) · J. Kong School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China e-mail: [email protected] Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing Technology and Business University, Beijing 100048, China X. Jin e-mail: [email protected] A. Yang e-mail: [email protected] J. Kong e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_87

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backgrounds in the moving target [4], there is a need for a possible method to better capture the features of the moving target and provide a reasonable estimate afterwards. Kalman filtering is one of the most classic target tracking algorithms, which can effectively estimate the target state, so the kalman estimation is also called “optimal estimation”. When accomplishing the whole estimation process, it is necessary to know the measurement noise R and the measurement matrix C of the measurement equation, as well as the parameters of the process matrix A and the process noise Q in the process equation. However, in practical applications, the Kalman method has two difficulties: (i) those parameters and true values may be inaccurate or difficult to obtain, and (ii) if accurate estimates are to be obtained, those parameters must be as accurate as possible. In view of this, there are many improved modes of Kalman filter. For example, in order to obtain more accurate value of parameters, Yi et al. [5] proposed an online noise reduction algorithm, which can realize the optimal noise reduction by adaptively changing the model parameters. Jin et al. [6] developed a model with adaptive parameters, and estimated the system parameter Q online, so that the parameter selection of the system is more consistent with the actual states. Su [7] proposed an initial alignment method based on Sage-Husa adaptive filter, which could realize automatical on-line estimation and correction for the noise parameters, the state of the system and the state estimate covariance by the observed data. The basic idea of these improvements is to use adaptive parameters to adjust the precision of the system model or some noise variance according to the collected data. However, it is so difficult to adjust all of the required parameters simultaneously, therefore certain prior knowledge of the target or the noise is still required. This paper attempts to adopt another solution, using a deep learning network to fit the estimation mechanism, and proposing an estimation model to achieve end-toend estimation. In fact, the deep learning-related method has already been applied to target tracking in recent years. Recurrent neural network (RNN) is a promising choice for target tracking task with time series data. According to “human cognition is based on past experience and memory,” RNN is proposed [8], which means that the current output of the network is related to the previous output. Using the memory function of the previous output information, the cyclic neural network is suitable for the study of problems related to chronological order. For example, Jiang [9] investigated a new variant of RNN Simple Recurrent Unit (SRU) in MEMS IMU based navigation system, which contains fewer parameters that need to be determined and can improve navigation system accuracy. Zhang et al. [10] proposed a tracking framework based on RNN, which could predict the object’s direction in the next frame according to the time relevance and realize target tracking. However, due to the simple structure of RNN, it will be difficult to learn and adjust the parameters of early neurons and learn long-term dependencies. With the time lags increasing, gradients of RNN may vanish or explode because of the back-propagation algorithm, which causes the error of the training process to accumulate over time. To learn long-term dependence information, Long Short Term Memory(LSTM) was proposed and has been promoted nowadays [11]. As a variant that is as popular as LSTM, Gated Recurrent Unit (GRU) has a simpler structure as well as less parameters, which contributes to a learning time

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saving. Therefore, GRU is applied to GPS data estimation in target tracking in this paper. The GRU network structure is simple, with few parameters and can guarantee accuracy. The structure of this paper is organized as follows: The second part will mainly introduce the GRU-based state estimation method, the third part is to verify the effectiveness of the proposed method via simulated GPS data and comparison with the Kalman filter. Conclusion will be presented in the final section.

2 Method The algorithm flow used in the paper, as shown in Fig. 1, consists of four parts: acquisition of data, data preprocessing, GRU estimation, denormalization of results and estimation results. First, some historical data would be necessary to well train a GRU network to achieve the following estimation purpose. The data could either be the simulated data or the actual measurements from various sensors. Second, data preprocessing mainly includes interpolation and normalization. If the available data is too less, the information that can be learned by the network will be less as well, and the cubic spline interpolation method is employed to interpolate the available data to expand the data volume. For the normalization operation, the model convergence speed can be improved, and the state can be well unified when using this model and other types of data for state estimation. Third, the training set is input to the GRU network, and the time series data relationship is learned. The loss curve is used to

Fig. 1 The flow of GRU learning

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determine whether the model learning result is acceptable. When the loss continues to decrease and eventually stabilizes at a small value, the model training is effective. Finally, the results are denormalized to obtain the final results. The algorithm pseudo code is shown in Algorithm 1. The above is the whole process of training. When the model is tested or used, only the noise data is needed, and the actual data can be estimated through the learned relationship. Algorithm 1: The flow of GRU estimate Input: GPS data with noise Output: Estimate data 1. Data interpolation and normalization 2. for i = 1:itrs () 3. GRU training 4. end 5. Estimated results are denormalized 6. Get results

2.1 Gated Recurrent Unit The internal structure of the GRU is shown in Fig. 2. Use the formula to represent the structure of the GRU module is as follows, rt = σr (Wr h h t−1 + Wr x xt )

Fig. 2 The structure of internal GRU

(1)

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z t = σr (Wzh h t−1 + Wzx xt )

(2)

  h˜ t = φh Whh (rt ◦ h t−1 ) + Whx xt

(3)

h t = (1 − z t ) ◦ h˜ t + z t ◦ h t−1

(4)

where h t−1 is the state relative to the current time t, the previous time; xt and h t are the input and output of the GRU module at the current time; rt and z t are the two key structures in the GRU module, i.e. reset gate and update gate, each gate is a simple neural network. In order to make the gate output fixed between 0 and 1, the activation function of the neural network uses the sigmoid function, which are σz and σr . h˜ t is the candidate value of output after the reset gate processing and φh is the hyperbolic tangent function. Symble ◦ denotes element-wise multiplication. The whole workflow of GRU is as follows: At each moment, the GRU unit receives the current state xt and the hidden state h t−1 of the previous moment through the update gate. After receiving the input information, the activation function determines whether the neuron is activated by the matrix operation. Similarly, the reset gate also receives xt and h t−1 , and the result of the operation determines how much past information needs to be forgotten. The current moment input is superimposed by the operation and reset gate output, and the current memory content h˜ t is formed by the activation function. The current memory h˜ t and the previous step input h t−1 determine the output content h t of the final gating unit by dynamically updating the gate, and h t will also be passed to the next GRU unit.

3 Experiments 3.1 Dataset The experimental data of this paper comes from MATLAB simulation, specifically the maneuvering target trajectory simulation of GPS tracking system. The GPS system can measure two-dimensional space, and the measurement is not related to the horizontal and vertical coordinates. In general, both the horizontal and vertical coordinates contain noise, and the variance is known. Therefore, the simulated measurement data needs to contain horizontal and vertical coordinates, which is 2-dimensional data. Upon completion, the real trajectory without the measurement noise passed by the maneuvering target and the sensor measurement output with the measurement noise can be obtained. White noise and colored noise are included in these experiments.

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3.2 Results Since the GPS data is 2D, we interpolate the noise data and real data of the X and Y axes respectively, and use the GRU training for the two sets of data. For the twentyfive trajectories obtained from the simulation, we divided 20 of them into training set, five as test set, and conducted two sets of experiments. The first one is to train the training set, and use the results to test the five trajectories separately, and also use kalman to estimate. In the whole experiment, GRU with one layer is used. The input of the network is set to one data point and the output is the same, i.e. if the first observation point value of X axis is used to be input and the output will be the estimate result of the first point. According to the experience, the firts key parameter of Kalman, Q are set as 1 and the second one, R is set as 10 due to the noise data generation in simulation. After a training of 50 iterations, the network is used to estimate with testing data. The RMSE results are shown in Table 1. As can be seen, GRU usually has a lower RMSE with bose white and colored noise. Figures 3 and 4 are some of the comparisons of real and estimate data for the two trajectories, which comes from the best GRU estimated results with white and colored noise, respectively. And Fig. 5 shows the trajectories composited via two axes data. Although there are a little error in the beginning and end of the trajectory, GRU could still revert the track very well comparing to Kalman. It is indicated that when estimating using the GRU method, even if only real data and noise data are available, an acceptable estimation result also can be obtained. Evenly, the difficulty of selecting the model parameters as described above is avoided. Based on the first set of experiments, we set up a second set of experiments. The benefits of using the GRU method are further illustrated by indicating the effect of the Kalman model parameters on the results. In the second set of experiments, the second group is selected due to the reason that both GRU and Kalman results are acceptable in Table 1, and changed the parameters Table 1 RMSE of testing set via GRU and Kalman Test trajectories

With white noise GRU

Kalman (Q = 1, R = 10)

GRU

Kalman (Q = 1, R = 10)

1

X axis

1.0319

0.9834

0.8060

1.0529

Y axis

0.6562

1.1019

0.9378

0.9301

2

X axis

0.9615

1.0269

0.6941

0.9952

Y axis

0.6557

1.0919

0.8355

0.9992

X axis

1.0577

0.9821

0.6747

0.9430

Y axis

0.7159

1.0074

0.9129

0.9211

4

X axis

0.9903

1.0488

0.7137

1.0625

Y axis

0.6336

0.9974

0.8355

0.8414

5

X axis

1.0298

0.9330

0.8091

0.8125

Y axis

0.8698

1.0433

0.7613

0.9699

3

With colored noise

GRU-Based Estimation Method …

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(a) Comparetion of X axis and its partial enlargement

(b) Comparetion ofY axis and its partial enlargement Fig. 3 Estimation result of trajectory 2 with white noise in lowest RMSE of GRU

of the Kalman model to compare the results, as shown in Table 2. As can be seen, as the parameters are not precise, the results can be various, which means Kalman estimate result will be fluctuate with the uncertain parameter values. However, GRU will not have that kind of problem, once the model is well trained, the result is fixed for the same data.

4 Conclusion Based on the development of target tracking technology, this paper finds that the existing estimate model has complex parameters, so the deep learning method is applied to it. The GRU method is used in this paper because of its ability of memory in time series data learning. The GRU can estimate the GPS trajectory only by knowing the actual data. This method also avoids the disadvantage such as the various

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(a) Comparetion of X axis and its partial enlargement

(b) Comparetion of Y axis and its partial enlargement Fig. 4 Estimation result of trajectory 5 with colored noise in lowest RMSE of GRU

(a) Trajectory 2 Fig. 5 The composition trajectory using GRU estimation results

(b) Trajectory 5

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Table 2 RMSE of testing set via GRU and Kalman Axis

Kalman (Q = 5 R = 10)

Kalman (Q = 10 R = 10)

Kalman (Q = 1 R = 1)

Kalman (Q = 1 R = 20)

Kalman (Q = 5 R = 20)

Kalman (Q = 10 R = 20)

GRU

X

1.5136

1.8590

2.1902

1.0069

1.1681

1.4659

0.9615

Y

1.5706

1.9275

2.2763

1.1141

1.2247

1.5220

0.6557

parameters in Kalman estimation model, which are difficult to obtain the true values. The future work will be on the direction of exploring a better GRU estimation model. Acknowledgements This work was supported by National Natural Science Foundation of China (No. 61673002), and Beijing Municipal Education Commission with project No. KM201810011005 and KM201910011010.

References 1. Chavda, H.K., Dhamecha M.: Moving object tracking using PTZ camera in video surveillance system. In: 2017 International Conference on Energy, Communication, Data Analytics and Soft Computing (ICECDS), pp. 263–266. IEEE (2017) 2. Mukherjee, K., Kar, I.N., Bhatt, R.K.P.: Adaptive gravity compensation and region tracking control of an AUV without velocity measurement. J. Int. J. Model., Identif. Control. 25, 154 (2016) 3. Shajideen, S.M.S., Preetha, V.H.: Human-computer interaction system using 2D and 3D hand gestures. In: 2018 International Conference on Emerging Trends and Innovations in Engineering and Technological Research (ICETIETR), pp. 1–4. IEEE (2018) 4. Zhou, Y., Zhou X.D., Yuan, J.H., et al.: Tracking method of moving target in complex environment. In: 2017 International Conference on Information Networking (ICOIN).pp. 668–673. IEEE (2017) 5. Yi, S.L., Jin, X.B., Su, T.L., et al.: Online denoising based on the second-order adaptive statistics model. J. Sens. 17, 1668 (2017) 6. Jin, X.B., Lian, X.F., Shi, Y., et al.: Data driven modeling under irregular sampling. In: Proceedings of the 32nd Chinese Control Conference, pp. 4731–4734. IEEE (2013) 7. Su, W.X.: Application of Sage-Husa adaptive filtering algorithm for high precision SINS initial alignment. In: 2014 11th International Computer Conference on Wavelet Actiev Media Technology and Information Processing (ICCWAMTIP), pp. 359–364. IEEE (2014) 8. Han, K., Wang, D.L.: Neural network based pitch tracking in very noisy speech. J. IEEE/ACM Trans. Audio, Speech Lang. Process. (TASLP) 22, 2158–2168 (2014) 9. Jiang, C., Chen, S., Chen, Y., et al.: Performance Analysis of a Deep Simple Recurrent Unit Recurrent Neural Network (SRU-RNN) in MEMS Gyroscope De-Noising. J. Sens. 18, 4471 (2018) 10. Zhang, Y.S., Yue, M., Zhang, R.S.: Object detection and tracking based on recurrent neural networks. In: 2018 14th IEEE International Conference on Signal Processing (ICSP), pp. 338– 343. IEEE (2018) 11. Xiao, Y., Du, S., Xie, X., et al.: A Modified Speaking Rate Estimation Based on Frame-Level LSTM. In: 2018 14th IEEE International Conference on Signal Processing (ICSP), pp. 600– 603. IEEE (2018)

Research on Optimization Method of LEACH Routing Protocol Fan Chao, Zhiqin He, Xiumin Hu, Hongbo Zhou and Aiping Pang

Abstract In view of the problem of cluster head selection in traditional LEACH protocol, this paper considers the residual energy of node, distance from base station, density of surrounding node and so on, and puts forward the method of selecting cluster head by secondary competition law. Then, a simple optimization of intracluster communication is made, and the improved I-Leach algorithm is obtained. Through MATLAB simulation it is verified that the improved algorithm can effectively improve the network life cycle. Keywords Secondary competition law · Wireless sensor network · Network life cycle · I-LEACH

1 Introduction LEACH is a low-power adaptive clustering routing algorithm for WSN [1–3]. Its basic idea is to distribute the energy load of the whole network equally to each sensor node by randomly selecting cluster heads in equal probability. Aiming at the problem that the cluster head election, we propose a method to select cluster head based on quadratic competition, and then optimize the intra-cluster communication, and obtain the improved algorithm I-LEACH.

2 Analysis of Typical LEACH Algorithm LEACH protocol is a self-organizing and self-adaptive clustering protocol, the cluster head node selection is based on: T (n) =

p ,n ∈ G 1 − p[r mod(1/ p)]

(1)

F. Chao · Z. He (B) · X. Hu · H. Zhou · A. Pang School of Electrical Engineering, Guizhou University, Guiyang 550025, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_88

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wherein the setting of the threshold value T(n) can fully guarantee the random distribution of the selected cluster head node in the network [4–7].

3 The Improvement of the LEACH Algorithm The energy consumption of sending kbits data by nodes can be represented as: Ps (k) = E elec × k + E amp × d γ × k

(2)

The power consumption for nodes to receive kbits data is: PR (k) = E elec × k

(3)

The energy consumption for node analysis and processing of kbits data is Pcpu (k) = E cpu × k

(4)

where k is the binary length of the packet, the E elec (nJ/bit) is the energy consumption factor of the RF circuit, and the amplifier energy consumption factor of the circuit is the E amp (nJ/bit/m2 ), d is the transmission distance, γ is the signal attenuation index, and the value is 2 or 4. According to the Formulas (2), (3) and (4), the energy consumption is closely related to the communication distance and the amount of data. The increase of communication distance and the amount of data will lead to a sharp increase in energy consumption. As a result, we propose the second competition law to select the cluster head, and when the cluster head is selected, the candidate cluster head is selected for the first time, and the final cluster head node is determined by the second competition.

3.1 Selection of Candidate Cluster Head When the candidate cluster head is selected for the first time, the distance between the node and the base station and the energy of the node itself are taken into account, and the concepts of distance factor and energy factor are proposed. Distance factor There is a great relationship between wireless communication energy consumption and communication distance [8–10]. Based on the relationship between sending data and receiving data power: Pr = (Pt /r) ∗ n

(5)

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where r is the distance between nodes, n is the propagation factor, and is related to the environment, Pr is the receiving power, Pt is the transmission power [11–13]. At the beginning of the cluster head election, the broadcast is first transmitted by the base station, and the node I is transmitted by the distance between itself and the base station according to the Formula (5). At the same time, we return our current energy information to the base station; from this, the distance factor is: Di = (d Bi − dm )/(dm − dn )

(6)

Of which Di is the distance factor of the node, dm is the furthest distance from the node i and the base station, dn is the nearest distance from node i base stations. Energy factor The energy factor is not taken into account in the selection of cluster head in the original LEACH protocol. If the node with lower remaining energy is selected as cluster head, the lifetime of the network will be greatly affected. The energy factor is: E re =

Ec Et

(7)

Of which E re Is the energy factor of the node, E c Is the current energy of the node, E t Is the initial energy of the node. In conclusion, the selection of candidate cluster head is based on A(n) =

p    (λ1 E re + λ2 (1 − Di )), n ∈ G 1 − p rmod 1p

(8)

Of which λ1 , λ2 is constant, and λ1 + λ2 = 1. In the first round of competition, each node selects a random number a (0 < a < 1). If a < A(n) the node becomes a candidate cluster head node, otherwise it goes to sleep until the end of the competition and the formula sub (8) indicates that only those nodes that have not been cluster heads in previous cycles, The node close to the base station can be selected as the candidate cluster head node with less energy consumption.

3.2 Identify Cluster Head Node After the candidate cluster head is selected through the first competition, the neighbor cluster head set of each candidate cluster head is established firstly, and then the competitive weight of cluster head is determined according to the relative residual energy and node density. Then the cluster head node is determined by the second competition.

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We first determine the set of neighbor cluster head nodes for each candidate cluster head node Ich ,   Ich = Ij /Ij is the candidate cluster head, and d(Ii , Ij ) < R

(9)

In the second competition process of candidate cluster head, the residual energy of candidate cluster head I Derived from Formula (7). We can get the density factor from the following formula: ρ=

ich ist

(10)

Of which ρ is the density factor, ich Is the number of neighbor nodes for the candidate cluster header I, ist is the number of neighbor nodes in the fully uniformly dispersed standard cluster. Then the competitive weight of the candidate cluster head is wi = α E re + βρ

(11)

Of which, α, β are weight factor and α + β = 1. Thus the competitive weight value of each candidate cluster head is calculated according to the Formula (11). In the candidate cluster head competition, each candidate cluster head node transmits the broadcast at the power of the communication distance R, and the broadcast content includes the local node id and the node competition weight. Each candidate cluster header node builds a neighbor cluster header set Ich based on a messa. The final cluster head is determined according to Formula (11). If the weight value of the candidate cluster head is the same, the small id cluster head is selected as the cluster head first. In summary, The clustering algorithm process based on quadratic competition is shown in Fig. 1: in the first round of competition, a random number a (0 < a < 1) generated by ordinary nodes is used to select candidate cluster head nodes compared with threshold A(n); In the second round of competition, the candidate cluster head node sets up its own neighbor cluster head node set Through the weights with the remaining candidate cluster headers in the set Finally, the optimal cluster head node can be obtained by competing again.

3.3 Intra-cluster Communication Optimization After the cluster head node is determined, the surrounding common node adds the nearest cluster according to the principle of proximity, and we further optimize the intra-cluster communication, as shown in the Fig. 2, C is the cluster head node, A is the ordinary node, and when D(A, C) < D(A, Sink) then the data collected by A is sent to the cluster head node C, after the data fusion of the cluster head

Research on Optimization Method of LEACH Routing Protocol Fig. 1 Flow chart of selecting cluster head by secondary competition

Fig. 2 Optimization diagram of intra-cluster communication

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node, it is sent to the Sink; when the data of the cluster head node is fused. When D(A, C) > D(A, Sink), the data collected by node A is sent immediately to the base station. Therefore, the load of cluster head nodes can be effectively reduced and the lifetime of cluster head nodes can be improved. According to the research of the above aspects, the improved algorithm establishing process is shown in Fig. 3: at the forming stage of the cluster, according to the threshold A(n), the remaining energy is high, and the node closer to the base station is more likely to be selected as the candidate cluster head node. Then the candidate cluster head node establishes its own set of adjacent cluster head nodes, and then performs secondary competition according to factors such as relative residual energy, density and the like, and finally determines the cluster head node. After the cluster head selection is finished, each common node selects a join cluster according to the proximity principle, and becomes a member node in the cluster, in which some of the member nodes are close to the sink node, let these nodes communicate directly with the sink nod.

Fig. 3 Algorithm flow chart

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4 Algorithm Simulation and Analysis In order to verify that the improved algorithm has better performance, the improved I-LEACH algorithm is simulated by Matlab and compared with the traditional algorithm in several aspects.

4.1 Simulation Environment The simulation tool uses MATLAB2012a, Table 1 to give the main parameters.

4.2 Comparison of Simulation Parameters We analyze the improved algorithm performance by simulation. As shown in Fig. 4, the traditional LEACH algorithm has about 200th cycle when it appears the first dead node, while the improved algorithm I-LEACH only appears the first dead node in the 300th cycle, and the first node’s dead time is delayed by about 100 cycles. The experimental results show that the proposed algorithm can prolong the first node’s dead time. It is clear that the improved algorithm has a larger network life cycle. As shown in Fig. 5, when the program is running, the two algorithm nodes consume almost the same amount of energy. With the running of the program, the total energy consumption of the two algorithms increases, but the speed of the improved algorithm increases slowly. With the increase of the number of wheels, the advantages of low energy consumption of the improved algorithm are more prominent.

Table 1 The main parameters Parameter

Set point

Deployment area

100 m * 100 m

Node number

100

Base station location

(50, 50)

Node original energy

0.5 J

Transceiver circuit energy consumption

50 NJ/bit

Amplifier coefficient 1

10 PJ/bit*m

Amplifier coefficient 2

0.0013 PJ/bit*m

Data fusion energy consumption

50 NJ/bit

Packet size

4000 bit

Cluster head ratio

0.05

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Fig. 4 Comparison of changes in surviving nodes

Fig. 5 Comparison of network energy consumption

As shown in Fig. 6, with the same number of running wheels, the data throughput of the I-LEACH algorithm is much higher than that of the original LEACH algorithm. Therefore, the improved I-LEACH algorithm has been greatly improved in the data transmission capacity.

5 Conclusion Aiming at the problem of limited energy in wireless sensor networks, this paper studies and optimizes the typical LEACH routing algorithms, and proposes a method to select cluster heads based on quadratic competition. Then we optimize the intracluster communication and get the improved algorithm I-Leach which is simulated

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Fig. 6 Comparison of network data transmission

with MATLAB software. We can get the following conclusion: the improved ILEACH algorithm can optimize the overall performance of the system, effectively reduce the energy consumption of the network, and improve the life cycle of the network. Acknowledgements Fund projects: The National Natural Science Fund 61640014; Science and Technology Plan Project of Guizhou province [2016]2302.

References 1. Heinzelman, W., Chandrakasan, A., Balakr Ishnan, H.: Energy efficient communication protocol for wireless microsensor networks. In: Proceedings of the 33rd Hawaii International Conference on System Sciences, pp. 3005–3014 (2000) 2. Karaki, J.N., Kamal, A.E.: Routing techniques in wireless sensor networks: a survey. IEEE Wirel. Commun. 11(6), 6–28 (2004) 3. Anastasi, G., Conti, M., Francesco, M.D., et al.: Energy conservation in wireless sensor networks: a survey. Ad Hoc Netw. 7(3), 537–568 (2009) 4. Hosseinirada, S.M., Ali Mohammadib, M., Basua, S.K., Pouyanb, A.A.: LEACH routing algorithm optimization through imperialist approach. IJE Trans. A: Basics 27(1) (January 2014) 5. Aslam, J., Li, Q., Rus, D.: Three power-aware routing algorithms for sensor networks. Wireless Commun. Mob. Comput. 3(2), 187–208 (2003) 6. Zhao, M., Yang, Y., Wang, C.: Mobile data gathering with load balanced clustering and dual data uploading in wireless sensor networks. IEEE Trans. Mobile Comput. 14(4), 770–785 (2015) 7. Qiao, Y., Li, X.Y., Zhao, T.: Analysis of typical military application of small satellite technology. Foreign Electron. Meas. Technol. 36(3), 47–50 (2017) 8. Zhu, Y.H., Ding, E.N.J., Hu, Y.J.: PSO optimization energy balanced routing algorithm of WSNs. Chin. J. Sci. Instrum. 36(1), 78–86 (2015) 9. Fu, H.-L., Chen, H.-C., Lin, P.: Aps: distributed air pollution sensing system on wireless sensor and robot networks. Comput. Commun. 35(9), 1141–1150 (2012)

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10. Elhoseny, M., Yuan, X., Yu, Z., et al.: Balancing energy consumption in heterogeneous wireless sensor networks using genetic algorithm. IEEE Commun. Lett. 19(12), 2194–2197 (2015) 11. Wu, L., Du, J., Nie, L., et al.: Cluster head selection method using dynamic k value for wireless sensor network. J. Huazhong Univ. Sci. Technol. (Natural Science Edition) 43(10), 37–41 (2015) 12. Huang, T., Yi, K., Gui, G., et al.: Hierarchical routing protocol based on non-uniform clustering for wireless sensor network. J. Comput. Appl. 36(1), 66–71 (2016) 13. Li, A., Chen, G.: An improved clustering routing algorithm for energy heterogeneous wireless sensor networks. Chin. J. Sens. Actuators 30(11), 1712–1718 (2017)

Stochastic Road Condition Identification for Electromagnetic Active Suspension Based on Support Vector Regression Zepeng Gao, Sizhong Chen, Yuzhuang Zhao, Zhicheng Wu, Lin Yang, Jiang Hu, Yong Chen and Baoku Liu

Abstract Accurate road condition identification is conducive to improving the accuracy of vehicle performance. Aiming at electromagnetic active suspension, a novel method is proposed to realize accurate road condition identification using finite unknown samples. Because actual road condition is changeable, it is not exactly consistent with the standard grade road. Therefore, this paper adopts the power spectral density value Gq (n0 ) as the identification object to identify the non-standard road condition. Accordingly, back propagation neural network (BPNN) and support vector regression (SVR) are employed to identify road conditions respectively. The results suggest that these two methods have high accuracy for the identification of standard grade roads. However, the random oscillation of road conditions increases the sample uncertainty, which seriously affects the identification accuracy of BPNN. This also causes that the accuracy of road condition identification obtained by SVR with finite sample data is significantly higher than that obtained by BPNN. Keywords Active suspension · Non-standard road condition · Power spectral density value · Road condition identification · Support vector regression

1 Introduction Difference road excitation, which is regarded as the main disturbance input for suspension system, leads to the different vehicle dynamic responses, thus affecting the vehicle performance. Meanwhile, the constant road conditions used during the simulation process are not consistent with the actual road conditions for the driving vehicle [1]. It is impossible for a vehicle to travel on the standard grade road that completely conforms to the classification criteria of road roughness. Therefore, road identification based on system dynamic responses is conducive to enhance the vehicle comprehensive performance [2]. In order to identify road conditions effectively, it is necessary to select appropriate parameter directly related to road conditions. Z. Gao (B) · S. Chen · Y. Zhao · Z. Wu · L. Yang · J. Hu · Y. Chen · B. Liu School of Mechanical Engineering, Automotive Research Institute, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_89

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Road identification can be divided into two types: direct and indirect measurement. Direct measurement mainly harvests the vertical road elevation data and related statistical parameters of actual road through the experimental measurement. Indirect measurement includes non-contact measurement and system parameter response identification. Direct and non-contact measurements rely on advanced sensors and valid testing technology, which limits its application. Contrarily, system parameter response identification is based on the vibration responses during vehicle driving [3]. It is widely applied because it can reflect the road quality from the passenger perspective and optimize the system parameters by using the identification results. However, traditional parameter response identification focuses on the suspension with fixed parameters, and the identification process is limited to the standard grade road and road has not been investigated too much. Since the power spectral density (PSD) values directly correspond to the road roughness, the identification of PSD value can avoid the conversion of identification of actual road conditions to approximate classification problem. In this paper, SVR is employed to identify PSD value, which overcomes the shortcomings of demand for large amount of data and poor adaptability to non-standard road in previous studies. The characteristic sample set in identification process adopts the responses of electromagnetic active suspension. It includes the signals of sprung and unsprung mass accelerations, suspension deflection and relative velocity, wheel relative dynamic load. Furthermore, the corresponding statistical characteristic values, including the square root of amplitude (SRA), root mean square (RMS), the variance (Var) and maximum value (Max), are also taken into account. Then, BPNN and SVR are employed to identify standard and non-standard grade roads respectively. The structure of this paper is organized as: stochastic road excitation input, linear quadratic regulator (LQR) optimizer, vehicle and linear motor model are established in Sect. 2 respectively; in Sect. 3, the characteristic parameters are selected; then, the road identification methods based on BPNN and SVR are introduced in Sect. 4; finally, the identification results of road conditions and corresponding discussions are summarized in Sect. 5 and the conclusion is listed in Sect. 6.

2 Model Establishment 2.1 Road Excitation Model It is necessary to establish an appropriate road model for road condition identification. In this paper, the road power spectral density (PSD) Gq (n) is constructed as:  G q (n) = G q (n 0 )

n n0

−w

 = G q (n 0 )

f un 0

−w (1)

Stochastic Road Condition Identification …

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where, w is frequency index, n and n0 are spatial frequency and reference spatial frequency respectively, f is time frequency, u is speed. The signal input of road surface in time domain [4] can be expressed as: t



q(t) = 2π n 0 G q (n 0 )u

ω(t)dt

(2)

0

where, q is road excitation.

2.2 Dynamic Model The system dynamic model of electromagnetic active suspension employed in the process of modelling in this paper is exhibited in Fig. 1. The dynamic equation of active suspension is expressed as: m 2 z¨ 2 = K (z 1 − z 2 ) − Fc

(3)

m 1 z¨ 1 = K (z 2 − z 1 ) + K t (q − z 1 ) + Fc

(4)

where, z1 , z2 , z¨ 1 and z¨ 2 are vertical displacements and accelerations of unsprung and sprung mass respectively. The vertical displacements and speeds of vehicle body and tire are selected as the state variables, as shown below: X = [x1 x2 x3 x4 ]T = [˙z 2 z 2 z˙ 1 z 1 ]T

m2

z2

Fc M

K

E

i1 Motor

Rcoil1 i2 Rres

m1

z1 Kt q

(5)

Fkt

Fig. 1 1/4 vehicle model

U0

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Table 1 Vehicle model parameters

Parameter

Symbol

Value

Unsprung mass

m1

30 kg

Sprung mass

m2

300 kg

Spring stiffness

K

11,844 N m−1

Equivalent stiffness of tire

Kt

118440 N m−1

Electromagnetic thrust coefficient

ki

112.4 N A−1

Back EMF coefficient

kv

112.4 Vs m−1

Internal resistance of linear motor

Rcoil

6.8 

Back resistance

Rres

0–30 

Terminal voltage of battery

U0

24 V

where, z˙ 1 and z˙ 2 are vertical unsprung mass velocity and vertical sprung mass velocity respectively. The differential equation of state variable is: 

⎡

0 − mK2 ⎢ ⎢1 0 A=⎢ ⎣ 0 mK1 0 0

0 0 0 1

X˙ = AX + B Fc Y = [¨z 2 z 2 − z 1 z 1 ]T = C X + DFc ⎤ ⎡ 1 ⎤ ⎡ K − m2 0 0 m2 ⎥ ⎢ ⎥ 1 ⎢ 0 −K 1 ⎥ ⎢ 0 ⎥ ⎢ ⎥, B = ⎢ 1 ⎥, C = t ⎣ − mK1+K 0 0 ⎦ ⎣ ⎦ m 2 +m 2 m1 K −1 0 0

(6) ⎤T ⎡ ⎤T 0 − m12 ⎥ 0⎥ ⎢ ⎥ ,D=⎣ 0 ⎦ 1⎦ 0 0 (7)

The system parameters used during the calculation process are shown in following Table 1.

2.3 Linear Motor Model When linear motor works in the electromotor state, it consumes electrical energy to generate force F e which can completely match the required force F c , so there is: Fe = Fc = ki i 1

(8)

It is assumed that the mutual conversion between mechanical energy and electrical energy has no energy loss during the motor working process. Force F c can be obtained by: i1 = i2 =

Fc ki

(9)

Stochastic Road Condition Identification …

Fc = −

951

k i E + U0 k i k v v + U0 =− Rcoil Rcoil

(10)

If the linear motor works in the braking state, it not only does negative work to recovery vibration energy but also consumes battery electric energy so as to ensure the required control force F c . The power supply voltage required in this circuit is:

U0 = Fkic (Rcoil + Rr es ) − kv v, U0 = 0,

Fc ki (Rcoil Fc ki (Rcoil

+ Rr es ) > kv v + Rr es ) ≤ kv v

(11)

The currents in this circuit and electromagnetic force output from linear motor are:

i 1 = i 2 = Fkic , Fe = Fc , U0 > 0 (12) kv v, i = 0, U0 = 0 i 1 = Rcoil E+Rr es , Fe = Rcoilki+R 2 r es

3 Characteristic Parameters Extraction According to [1], four statistical characteristic values, which includes SRA, RMS, Var and Max, are adopted to analyze the characteristic parameters, which is shown as:  n  n √ 2 2 x i i=1 i=1 x i , SRA = , RMS = n N n (xi − M)2 , Max = max|xi | V ar = i=1 (13) n−1 In order to effectively identify the road conditions, it is necessary to select the dynamic response variables of active suspension as the standard feature set. And these variables exist not only in time domain but also in frequency domain. The time domain signals, which include accelerations z¨ 1 and z¨ 2 , dynamic deflection (z2 − z1 ), suspension relative speed v and wheel relative dynamic load σFd are adopted as the identification features. Among them, the stable region of the vehicle state is that the absolute value of σFd should be less than 1. Meanwhile, the acceleration signals under different road grades (A–F grade) in frequency domain are also collected as samples for analysis. As you can know from Fig. 2 that the frequency response ranges of acceleration signals are mainly concentrated in 0–20 Hz, so the low frequency signals are also used as a part of the reference sample during the identification process and the upper-limit frequency is set as 30 Hz. Generally, a total of 20 signals in time domain and 8 signals in frequency domain

700 600 500 400 300 200 100 0 -100

1.4

3

A-grade B-grade C-grade D-grade E-grade F-grade

2

800

PSD of acceleration (m /s )

900

PSD of acceleration (m /s )

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2

952

0

5

10

15

20

25

A-grade B-grade C-grade D-grade E-grade F-grade

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

30

5

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10

15

20

25

30

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Fig. 2 Unsprung mass acceleration and sprung mass acceleration

Table 2 Characteristic sample set Statistical characteristics Time domain

Frequency domain (0–20 Hz)

SRA

RMS

Var

Max

z¨ 1

x1

x2

x3

x4

z¨ 2

x5

x6

x7

x8

z2 − z1

x9

x 10

x 11

x 12

v

x 13

x 14

x 15

x 16

σ Fd

x 17

x 18

x 19

x 20

z¨ 1

x 21

x 22

x 23

x 24

z¨ 2

x 25

x 26

x 27

x 28

are collected as the characteristic sample input set x i , which are shown in Table 2. The PSD Gq (n) corresponding to the sample input is selected as the characteristic sample output set yi . And the above input vector x i and output vector yi constitute the characteristic sample set D = [(x 1 , y1 ), (x 2 , y2 ), …, (x n , yn )].

4 Characteristic Parameters Extraction 4.1 Back Propagation Neural Network BPNN consists of different interaction layers, including input layer, hidden layer and output layer, which is a multi-layer feedforward network structure. Its concrete implementation process and network structure can be seen in [5]. Since the weight can be adjusted to minimize the error, BPNN adjusts system parameters in the target negative gradient direction based on gradient descent strategy. The characteristic sample set D is adopted to fit the PSD values after BPNN has been trained in advance.

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4.2 Support Vector Regression SVR is a predictive learning algorithm for nonlinear regression estimation, which is implemented by introducing the insensitive loss function lε into SVR for pattern identification. For the traditional regression model, the model output f (x) should be as close as possible to the training sample output set yi . However, the loss is calculated in SVR only if the absolute value of the deviation between the output f (x) and sample output set yi is greater than ε. Once it is in [−ε, ε], the predictive result is considered correct. The loss function lε provides a loss-free region for the decision function, and assumes that the main prediction deviation induced from the sample points outside the interval [−ε, ε] [6]. The f (x) and lε can be expressed as: f (x) = wT · ϕ(x) + b  lε = |y − f (x)| =

(14)

|y − f (x)| ≤ ε 0, |y − f (x)| − ε, |y − f (x)| > ε

(15)

In order to obtain the optimal solution under constraint conditions, the relaxation variable ζi and ζˆi is introduced to transform the SVR optimization problem into the convex quadratic programming problem, which can be written as the following form:   1 T min ζi + ζˆi , w w+C 2 ˆ w,b,ζi ,ζi i=1 n

⎧   ⎪ wϕ x − b ≤ ε+ζi ⎨ yi −   i s.t. wϕ xi + b − yi ≤ ε + ζˆi , i = 1, 2, . . . , n ⎪ ⎩ ζi ≥ 0, ζˆi ≥ 0

(16)

In order to guarantee the linear regression of sample points, it is necessary to map the sample points to Hilbert space by the kernel function κ, whose structure as well as weight values is determined by the quadratic optimization algorithm. Furthermore, Lagrange multiplier αi , αˆ i , α j and αˆ j is introduced to solve the optimization problems:           1  αˆ i − αi αˆ j − α j κ x i , x j − ε αˆ i + αi + yi αˆ i − αi 2 i=1 j=1 i=1 i=1 n

max − α,αˆ

s.t.

n

n

n    αi − αˆ i = 0, 0 ≤ αi , αˆ i ≤ C, i = 1, 2, . . . , n i=1

n

(17)

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m2

LQR controller

m1

q

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Control force Fc Active Suspension System

Linear motor

Decision function f(x) ε - insensitive loss function κ(x)

RMS Frequency domain (0~20Hz) signals - 8

Var ¼ vehicle model

Sample set

Max

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x1

Mapping Φ(x) from lowdimension space to highdimension space ζ Convex quadratic programming problem α, α SVR dual problem

xh

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f2

Δ1

fi

zk

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fj

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yl

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Regression estimation function f(x), w*, b SVR

Fig. 3 Structure diagram of road identification

5 Results and Discussion 5.1 System Identification Structure The overall structural design flow chart of road identification process is illustrated in Fig. 3. The extracted sample set of characteristic parameters is used to identify the corresponding road conditions according to dynamic system responses. The actual road conditions are obtained based on the PSD value Gq (n0 ) of road conditions, so the main contents includes are the fitting of PSD value of standard road grades and dynamic non-standard road grades. Therefore, there are the following assumptions: Hypothesis 1. The velocities of sprung and unsprung mass are available, so that (z2 − z1 ) and v can be obtained by integral and differential operation respectively. Hypothesis 2. The speed is set as 80 km/h and grade roads are switched between A and F. Meanwhile, the switching time intervals between different road grades is ignored.

5.2 Road Identification of Standard Grade The variation order of standard grade roads is set to C-E-A-F-D-B, and the identification results and accuracy obtained by regression fitting with RPNN and SVR are exhibited in Fig. 4. It is seen that the identification accuracy of PSD values under good road conditions exceeds 95%, such as standard grades A, B and C, while the identification accuracy of SVR is slightly higher than BPNN. When road condition deteriorates, the identification accuracies of SVR and BPNN corresponding to D

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Road PSD Gq(n0) (10-6m3)

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16000 14000 12000 C

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Fig. 4 Standard road condition identification and its accuracy

and E grade road also decrease, and the identification error of BPNN increases. This indicates that the system responses induced by road excitation has an effect on the road identification accuracy, which also is seen from the identification process of PSD value of F-grade road. It shows that dynamic responses induced by large-scale road excitation leads to the considerable deviation of PSD value fitting produced by BPNN based on the sampling data set D, which directly results in its identification accuracy less than 90%. Contrarily, the identification accuracy of SVR can still be over 90%, which is mainly due to its generalization ability is stronger than that of BPNN. Although the structure of BPNN is simpler than SVR, it is easy to be trapped into the local minimum so that the global optimal value cannot be found during the process of parameter optimization. In addition, the implementation of BPNN depends on the training of a large number of samples, so the scale of sample data will have a significant impact on it. Conversely, SVR is an optimization process based on limited samples. It transforms the regression estimation problem into the convex quadratic programming problem, so that it has the best approximation performance and global optimal characteristics, which leads to its generalization ability is better than BPNN. It also illustrates that the identification results of SVR is more accurate than that of BPNN during the identification process of finite samples.

5.3 Road Identification of Non-standard Grade On the basis of standard road grade, SVR and BPNN are employed to identify the road condition under the non-standard road grades respectively, which means the identification of PSD. The identification results are shown in Fig. 5. With the regard to the road identification of non-standard roads, the identification results of BPNN and SVR has been further compared. It can be intuitively seen from Fig. 5 that there are obvious deviations in road conditions identified by BPNN, which makes its highest identification accuracy within 0–5 s only 86.95% and not more than 90%.

Z. Gao et al. 20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

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Fig. 5 Non-standard road condition identification and its accuracy

The highest identification accuracy of PSD value within 5–30 s obtained by BPNN is less than 80%, which is much lower than that of SVR. It is noteworthy that the sample results identified by BPNN within 5–20 s have greatly deviated from the actual sample range, which also leads to its lowest accuracy reaching only 70.07%, and this is far beyond the tolerance range. Meanwhile, although the identification accuracy of SVR is also reduced, it is still higher than 90%, which is still significantly higher than that of BPNN. The above results further indicate that the generalization ability of BPNN is weaker than that of SVR, especially within 5–10 s and 15–20 s. The road PSD value fluctuates drastically in these two periods, so the sample identification needs to have good adaptability to the system dynamic responses induced by stochastic road excitation so as to ensure the identification accuracy. However, BPNN is less adaptable to finite and unknown samples than SVR, which results in its identification accuracy for stochastic non-standard road surface samples is lower than that of SVR.

6 Conclusions This paper proposes a novel approach to identify actual road conditions in view of system dynamic responses. The results demonstrate that BPNN and SVR have high accuracy for identifying PSD values Gq (n0 ) for standard road, which can reach more than 90%. However, the identification accuracy of BPNN for non-standard road is less than 90%. Conversely, the accuracy of SVR is still higher than 90%. Compared with other identification algorithms, SVR doesn’t need an accurate system model and has better generalization performance for unknown samples. Meanwhile, it has good adaptability to road condition fitting with finite data samples, so it has a wide application prospects. Acknowledgements This project is supported by the National Key R&D Program of China under Grant 2017YFB0102600.

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References 1. Qin, Y.C., Xiang, C.L., Wang, Z.F., Dong, M.M.: Road excitation classification for semi-active suspension system based on system response. J. Vib. Control 24(13), 2732–2748 (2018) 2. Du, M.M., Zhao, D.X., Yang, B., Wang, L.L.: Terminal sliding mode control for full vehicle active suspension systems. J. Mech. Sci. Technol. 32(6), 2851–2866 (2018) 3. Mucka, P.: Current approaches to quantify the longitudinal road roughness. Int. J. Pavement Eng. 17(8), 659–679 (2016) 4. Wang, D.Z., Zhao, D.X., Gong, M.D., Yang, B.Y.: Research on robust model predictive control for electro-hydraulic servo active suspension systems. IEEE Access 6, 3231–3240 (2018) 5. Yan, Y., Xu, J., Lee, P.: Mass flow measurement of fine particles in a pneumatic suspension using electrostatic sensing and neural network techniques. IEEE Instru. Meas. Mag. 55(6), 2330–2334 (2006) 6. Utkin, L.V., Coolen, F.P.A.: A robust weighted SVR-based software reliability growth model. Reliab. Eng. Syst. Safe. 176, 93–101 (2018)

Research on Noise Suppression and Edge Reading Algorithms in X-Ray Image Detection Xiumin Hu, Zhiqin He, Fan Chao and Aiping Pang

Abstract The noise in the Gas Insulation Station (GIS) equipment fault picture obtained for the X-ray imaging system cannot be eliminated due to the use of common filters, and the noise will affect the subsequent edge feature extraction. Therefore, MCPDE (Coupling Partial Differential Equation Model of Nonlinear Diffusion) is selected for noise suppression. This model greatly considers the image fidelity after denoising and has good stability. For the denoised image, taking into account the accuracy of the edge contour, the unsupervised nonlinear algorithm based on the McLaughlin function curve fitting is used for contour extraction. The experimental results show that the method is effective. Keywords GIS equipment · MCPDE denoising model · Maclaurin curve fitting

1 Introduction The GIS equipment is a gas-insulated metal-enclosed switchgear. The key parts include isolation switches, circuit breakers, grounding switches, etc., which are filled with SF6 insulating gas. Its long-term work in high-pressure environment, and GIS equipment structure is closed, the existing methods can not accurately detect whether the internal faults, the introduction of X-ray detection and image processing technology, can accurately determine whether the GIS internal faults, improve detection efficiency, reduce cost. In the X-ray imaging process, the following noises are generated: the fluctuation noise of the photocathode emission electrons; the fluctuation noise of the microchannel plate multiplying electrons; the fluctuation noise and particle noise of the fluorescent screen output photons; and the thermal noise of the CCD image acquisition [1]. Among them, the particle noise can be removed by the Gaussian filter, and other noise cannot be removed directly by the common filter. Based on this, this paper has carried out the following research.

X. Hu · Z. He (B) · F. Chao · A. Pang School of Electrical Engineering, Guizhou University, Guiyang 550025, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_90

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2 PDE Model The PDE model is widely used in noise suppression. Some scholars have applied nonlinear diffusion systems to the noise in the image smooth continuous domain. A nonlinear PDE-based method is proposed, as follows: ⎫ ⎧ ⎨ It = ∇(c|∇ I |)∇ I in  × (0, T ) ⎬ ∂I = 0 in ∂ × (0, T ) ⎭ ⎩ ∂n I (x, y, 0) = I0 (x, y) in 

(1)

where, I an image is represented, T represents time, n represents a picture boundary,  a unit representing an image field, ∇ I a local gradient representing, I an input noise image, and C is a diffusion function indicating a local gradient size and greater than zero. C(s) can be expressed as: c(s) =

1 1 + (s/k)2

(2)

where K is the threshold for controlling the diffusion rate must be greater than zero. The difference from the traditional spatial filtering method is that the conventional method does not preserve the image boundary, and the diffusion method removes the noise while retaining the edge. This method has good performance in the case of only additive noise, but it does not have a good effect on X-ray mixed multi-noise images. Therefore, the CPDE model is used to perform multiplicative noise remove. There are two main types of nonlinear coupled partial differential (CPDE) methods for noise removal. One is a log-CPDE model based directly on logarithmic transformation, and the second is a general model for removing noise. Logarithmic transformation, called the MCPDE model.

2.1 Log-CPDE Model In this method, the initial picture is first transformed in the log field, and then the log-CPDE model of the logarithmic transformation is used for noise cancellation [2]. wt = ∇(g(u)∇w) − 2λv in  × (0, T ) u t = ϕ(||∇wξ ||2 − u +

ψ2 u) in  × (0, T ) 2

vt = ∇(∇v) − (log I0 − w) in  × (0, T )

(3) (4) (5)

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∂u ∂v ∂w = 0, = 0, = 0 in ∂ × (0, T ) ∂n ∂n ∂n

(6)

w(x, y, 0) = log I0 (x, y) v(x, y, 0) = 0 u(x, y, 0) = G ξ ∗ |∇ log I0 |2 in  (7) Among them,  is the Laplacian operator, λ is the weighting parameter, T is the average time delay,  and the deformation and smoothness of the edge information are controlled. In general, the result of the bit constraint smoothing is related to the initial image data. The selected bit is inversely proportional to the variance of the noise in a given image. where k > 0 is the threshold parameter, and the equation ut representing the edge u is a parabolic equation, which represents a diffusion-based criterion for calculating the edge information of an image. Get a smoother image w. Finally, an exponential transformation of the denoised image is obtained to obtain a restored image.

2.2 MCPDE Model The MCPDE model differs from the log-CPDE model in that it does not require logarithmic transformation, is more general, and the model is more stable. It is a method based on temporal airspace regularization. Considering the significant influence of the gray level on the variance of some noise images, in order to ensure more effective picture information, in the diffusion process, based on the gray level and diffusion function of the image, the method introduces an energy minimization method, as follows Shown as follows: ⎧ ⎫

⎬   ⎨ I0 1 log I + min E u (I ) = β(I )g(u)|∇ I |2 d + λ (8) ⎩ 2 I ⎭ 



β(I ) =

α

2|I | M α + |I |α

(9)

where α > 0. The minimization problem can be given by the steady state of the Lagrangian equation: I − I0 1 div(β(I )g(u)∇ I ) = 2λ I2

(10)

This is equivalent to the following equation div(β(I )g(u)∇ I ) − 2λv = 0 v−

I = I0 =0 I2

(11)

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ut = ϕ(||∇ I ξ ||2 − u +

ψ2 u) 2

(12)

where ϕ and ψ are normal numbers, Iξ = Gξ*I; Gξ is a two-dimensional Gaussian function. Finally, we obtain a multiplicative coupled partial differential equation (MCPDE) model in which a set of PDE models interact with initial and insulating boundary conditions, which can be expressed as I t = ∇(β(I )g(u)∇ I ) − 2λv in  × (0, T ) u t = ϕ(||∇ Iξ || − u +

ψ2 u) in  × (0, T ) 2

∂u ∂v ∂I = 0, = 0, = 0, in ∂ × (0, T ) ∂n ∂n ∂n I (x, y, 0) = I0 (x, y) v(x, y, 0) = 0 u(x, y, 0) = ξ ∗ |∇ I0 |2 in 

(13)

Among them, g(u) = 1/(1 + uk2), the model is different from the common noise removal model. In this model, it uses the spatiotemporal regularization feature to handle edge variables and fidelity terms, respectively. The proposed coupled PDE model has similar diffusion characteristics for effectively maintaining the denoising of noisy images. That is, the model is used to control the smoothing speed at the boundary of the region. Through this model we are able to incorporate information obtained along scales into the diffusion process [2–6]. This single equation improves the model’s ability to recover better. The gray level indicator β(I) directs the diffusion process according to the gray level to effectively remove the multiplicative noise and preserve the image detail in the low gray level region. The fidelity term between I and I0 can pass the function v, which includes the multiplicative nature of the noise in the proposed model. In other words, the first two evolution equations are used to calculate the denoising equation [7, 8]. It ultimately helps to obtain a preferred result by finding the appropriate edge map and fidelity between the speckle and noisy images in each iteration.

3 Maclaurin Curve Fitting We often use curve fitting to find the relationship between observations and observations. At present, curve fitting method is not only applied in data processing, but also widely used in image boundary fitting [9, 10]. We think of an image as a matrix of countless pixels, and a boundary is a sequence of groups. Use the mathematical idea to get the edge of the target object in the picture. Classic edge extraction methods include canny algorithm, sobel operator and least squares method [11–13]. In this paper, an improved least squares curve fitting method, namely McLaughlin curve fitting method, is adopted. The purpose of this method is also to find the function specified in advance in the data {(x, Ix)}. Find the minimum residual and find the predetermined function f(x). The minimum residual is as follows

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N 1  [ f (x) − Ix ]2 N i=1

(14)

This paper uses the Maclaurin curve fitting algorithm to read the edges. The Maclaurin series function approximation is defined as follows:  ∧

f (x) = f (x) =

L 

cjx j

(15)

j=1

The approximation should be consistent with f(x), f (i) (1) = fˆ(i) (1), i = 1, 2, . . . , L

(16)

where f(i) is the ith derivative of f. For pixels at (p, q) coordinates, the Maclaurin 

family of functions f ( p, q) approximates the following: ∧

x

( p,q)

N

f

=

L  j=1

cj

x j N

(17)

where x/N represents the normalized number of bands, and the coefficient vector C = [c1, c2,…, cL], T can be determined by minimizing the following mean square error: E=

N  x 2 1  ∧ x f − f N i=1 N N

(18)

It can also be expressed in another way: ⎤2 ⎡ N L x 1  ⎣ x j ⎦ E= cj − f N x=1 j=1 N N

(19)

Then, calculate the derivatives of E relative to the coefficients and set them to equal zero. ∂E = 0, ∂c j

j = 1, 2, . . . , L

⎞ ⎡⎛ ⎤2 N L L

j x  x 2  ⎣⎝ x j ⎠ ⎦ cj − f N x=1 N N N j=1 j=1

(20)

(21)

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A sufficient but not necessary condition for solving a system of nonlinear equations is to find C: L  j=1

cj

x j N

= f

x N

, x = 1, 2, . . . , N

(22)

Or in the form of a matrix: A N ×L C L×1 = B N ×1

(23)

among them,

1 1 2 ⎢ N N ... ⎢

⎢ ⎢ 2 2 2 ⎢ ... A=⎢ ⎢N N ⎢...... ⎢ ⎢ 2 ⎣N N ... N N ⎡



L ⎤

⎡ ⎤ ⎤ 1 C1 ⎥ ⎢f N ⎥ ⎥ ⎢ ⎥ ⎢ C2 ⎥ L ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ 2 ⎥ ⎢ ⎥ ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ f C3 ⎥ ⎥, B = ⎢ N ⎥ N ⎥, C = ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢. ⎢. ⎥ ⎥ ...... ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎦ ⎣

. L ⎥ ⎣ N ⎦ N ⎦ f CL N N 1 N

⎡

(24)

In order to make the extracted feature quantity able to express the effective feature of the image without redundancy of the feature quantity, it is necessary to satisfy L  N . That is to ensure that the norm of AC-B is the smallest, generally use the inverse of A to get C, and then solve the equation to find the coefficient of curve fitting of Maclaurin series function.

4 Experimental Analysis On the MATLAB2016a platform, the fault picture of the GIS equipment containing noise is processed, mainly for noise reduction and edge contour extraction. The noise reduction situation is shown in Fig. 1, and the contour reading situation is shown in Fig. 2. From the comparison of various models in Fig. 1, it can be clearly seen that the MCPDE model has better noise reduction effect and it has better fidelity. The comparison of the iterations of the MCPDE model with other models is shown in Figs. 2. Due to the rigor of GIS equipment, its accuracy requirement is 0.01 mm. As can be seen from Fig. 2, the McLaughlin curve fitting method has better accuracy than the classic edge contour reading algorithm (Fig. 3).

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(3) Picture after noise reduction of log-CPDE model of PDE model

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(4) Picture after noise reduction

Fig. 1 Denoising situation

5 Conclusion The image of noise-containing GIS equipment obtained by X-ray imaging is mainly used to compare the denoising effect of log-CPDE model and MCPDE model. Experiments show that the MCPDE model has better denoising effect and fewer iterations in operation., faster, and this model is more stable. Then, the edge of the GIS device image obtained after noise removal is read, and the classic canny operator, sobel operator and McLaughlin curve fitting method are used. The first two methods cannot accurately obtain the exact edge of the isolation switch in the GIS device. The

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Fig. 2 Comparison of the iterations of the MCPDE model with other models

(1) canny operator

(2) sobel operator

(3) Maclaurin curve fitting method

Fig. 3 Edge extraction

McLaughlin curve fitting method can fit the edge well, and the error is within the acceptable range, which can meet the precision requirements of GIS equipment. Acknowledgements National Natural Science Foundation, 61640014.

References 1. Heinzelman, W., Chandrakasan, A., Balakr Ishnan, H.: Energy efficient communication protocol for wireless microsensor networks. In: Proceedings of the 33rd Hawaii International Conference on System Sciences, pp. 3005–3014 (2000) 2. Jain, S.K., Ray, R.K., Bhavsar, A.: A nonlinear coupled diffusion system for image despeckling and application to ultrasound images. Circuits, Syst. Signal Process. 38, 1654–1683 (2018)

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3. Anastasi, G., Conti, M., Ancesco, F.R., et al.: Energy conservation in wireless sensor networks: a survey. Ad Hoc Networks 7(3), 537–568 (2009) 4. Hosseinirada, S.M., Ali Mohammadib, M., Basua, S.K., Pouyanb, A.A.: LEACH routing algorithm optimization through imperialist approach. IJE Trans. Basics 27(1) (January 2014) 5. Aslam, J., Li, Q., Rus, D.: Three power-aware routing algorithms for sensor networks. Wirel. Commun. Mob. Comput. 3(2), 187–208 (2003) 6. Zhao, M., Yang, Y., Wang, C.: Mobile data gathering with load balanced clustering and dual data uploading in wireless sensor networks. IEEE Trans. Mobile Comput. 14(4), 770–785 (2015) 7. Qiao, Y., Li, X.Y., Zhao, T.: Analysis of typical military application of small satellite technology. Foreign Electron. Meas. Technol. 36(3), 47–50 (2017) 8. Zhu, Y.H., Ding, E.N.J., Hu, Y.J.: PSO optimization energy balanced routing algorithm of WSNs. Chin. J. Sci. Instrum. 36(1), 78–86 (2015) 9. Fu, H.-L., Chen, H.-C., Lin, P.: Aps: distributed air pollution sensing system on wireless sensor and robot networks. Comput. Commun. 35(9), 1141–1150 (2012) 10. Elhoseny, M., Yuan, X., Zhengtao, Y.U., et al.: Balancing energy consumption in heterogeneous wireless sensor networks using genetic algorithm. IEEE Commun. Lett. 19(12), 2194–2197 (2015) 11. Wu, L., Du, J., Nie, L., et al.: Cluster head selection method using dynamic k value for wireless sensor network. J. Huazhong Univ. Sci. Technol. (Natural Science Edition) 43(10), 37–41 (2015) 12. Huang, T., Yi, K., Gui, G., et al.: Hierarchical routing protocol based on non-uniform clustering for wireless sensor network. J. Comput. Appl. 36(1), 66–71 (2016) 13. Li, A., Chen, G.: An improved clustering routing algorithm for energy heterogeneous wireless sensor networks. Chin. J. Sens. Actuat. 30(11), 1712–1718 (2017)

Research on Water Monitoring Information Acquisition System of UAV Based on Wireless Sensor Network Junjie Ge, Fan Chao, Zhiqin He and Wenye Shi

Abstract In view of the difficulty of collecting water quality monitoring data, as well as the high cost and inflexibility of data transmission, etc. Utilizing the high maneuverability of UAV, a new type of system is designed, which uses UAV as mobile sink node in WSN waters monitoring, and can collect monitoring node data efficiently and flexibly through wireless transmission of data. According to the characteristics of the system, the flight path of UAV is further optimized in the traditional path planning algorithm. The experimental results show that the system is stable, low-cost, realtime and flexible, and can accurately and effectively collect data from monitoring nodes. Keywords Water monitoring · Wireless sensor network · UAV · Mobile node · Path optimization · Data collection

1 Introduction The rapid development and application of WSN technology provide a new research direction for water monitoring. It has the characteristics of low cost, flexible networking and little influence on the surrounding environment. WSN technology can be used to achieve high efficiency, rapid, real-time and remote monitoring of water quality. But the collection of water monitoring node data has always been some difficult problems, such as, the efficiency of manual collection is low, the cost of establishing fixed wired monitoring base station is high, at the same time, the wireless communication range of node monitoring node is also high. The adoption of 4G communication will increase the power consumption and cost of the system [1, 2]. Introduction of UAV into the WSN Waters Monitoring system, greatly increasing the system’s Spirit Activity, optimize flight path, and save the cost of the system on the basis of ensuring stable collection of detection data.

J. Ge · F. Chao · Z. He (B) · W. Shi School of Electrical Engineering, Guizhou University, Guiyang 550025, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_91

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Fig. 1 System structure diagram

2 Overall Design Scheme of the System The new water monitoring system mainly consists of water quality monitoring data acquisition module, wireless sensor gateway [3], and UAV carrying wireless communication module to store information. In the water area WSN, the data of each sensor monitoring node is sent to the aggregation node of each region uniformly, and then the data of each aggregation node [4] is uniformly collected by UAV through cc2530, so as to ensure the efficiency of data collection. The collected data is brought back to the working base station for analysis and processing through the storage unit module. Figure 1 shows the overall structure of the system.

3 Hardware Design of New WSN Waters Monitoring System Hardware design of the system, UAV type selection can carry a certain weight of large four-axis rotor [5]. Microprocessor stm32f407 [6] mainly realizes the control of UAV. At the same time, it is necessary to carry barometer ms5611, gyroscope, accelerometer mpu6050, and magnetometer ak8975, to ensure the smooth flight of UAV. The wireless communication module uses cc2530 [7] to send the monitored data to the UAV to save and bring it back. The storage unit selects the USB and type c’s u-disk, which has a large capacity and is convenient to read and write in a wide range of applications. The hardware block diagram is shown in Fig. 2.

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Fig. 2 System block diagram

4 Research on Path Optimization Algorithm The problem of UAV flight path in this system can be summed up as the ergodic optimal path problem in the discrete domain [8]. At the same time, the signal of the water quality monitoring node of Zigbee has the characteristics of spatial coverage [9]. Using this feature, the flight path can be further shortened in theory on the premise of stable transmission of positive preserving signals. Firstly, the traditional ant colony algorithm [10] for solving traveling salesman is used to obtain the optimal path quickly. On the basis of this, a new model is established and further analyzed and processed. As shown in Fig. 3, x0 is the initial position of the mobile convergence node, x1 , x2 , x3 is the wireless monitoring node, A1 , a2 is the midpoint y1 , y2 between the two nodes when the signal coverage of different nodes intersects. Y3 is the optimal feasible point considering the spatial coverage characteristics of wireless signals. As you can see, the path traversed by the ordinary traveling salesman is x0 , x1, x2 , x3, x0 . When the wireless signal range intersects, the default path for selecting the midpoint is x0, a1, a2, x0 . When the wireless signal range intersects, the path of the midpoint is selected as x0, y1, y2, y3, x0 , After considering the spatial characteristics, the optimal path is x0, y1, y2, y3, x0 and it is not difficult to find the shortest path is the path x0, y1, y2, y3, x0 . Wireless signal space coverage node path planning, in the plane area, stable communication signal coverage radius r, define a mobile aggregation node x 0, n wireless monitoring nodes X = (x1 , x2 , x3 , Xn ), needs to determine the satisfactory solution [11]. Y = (y1 , y2 , y2 ) for mobile convergence nodes traversing the coverage of each monitoring node. Yn position and traversal order, in order to enable the drone to complete the data collection route of the shortest distance.

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Fig. 3 Optimization model diagram

In the shortest line planning problem of mobile convergence node, there is a direct link between the initial location point of mobile convergence node and the satisfactory solution point, and between the satisfactory solution point and the satisfactory solution point, without considering the obstacles, so there is a direct link between the initial location point and the satisfactory solution point of the mobile convergence node. The initial position point and satisfactory solution point of moving aggregation joint constitute a directed graph [12], which is expressed as G = (V, E). Where G = (x0 , y1 , y2 , yn ), E is the collection of lines in figure G), the S matrix indicates whether the line segment in E is selected as the optimal line section, where Sij = 1 indicates that the section (yi , yj ) is selected, and Sij = 0 indicates whether the line segment in E is selected or not. The section (yi , yj ) is selected. Therefore, the optimal path problem for wireless signal spatial coverage of mobile aggregation nodes can be expressed as follows: n n       Si j  y˙i − y˙ j  M in  Y˙ , S = i=0 j=0

     y˙i − y˙ j  ≤ r : Node space coverage constraint  y˙i − y˙ j : Linear distance between satisfactory solution points n  i=0 n  j=0

⎫ ⎪ Si j = 1 ⎪ ⎬ ⎪ Si j = 1 ⎪ ⎭

Exuberance and ingress are both 1

(1)

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For ease of expression, the next route for the traditional traveling salesman to start with a mobile convergence node is, in turn, s0 , s1 , s2 , . . . , sn The path of the optimized wireless signal space overlay node is: l0 , l1 , l2 , . . . , ln . In the selection of satisfactory solution points, the angular bisection method is used to approximately obtain the satisfactory solution points in the coverage range of each monitoring node. So, the original path: L = l0 + l1 + l2 + · · · + ln

(2)

S = s0 + s 1 + s 2 + · · · + s n

(3)

Space overlay path:

s0 =

 l02 + r 2 − 2rl0 cos ϕ1

Of which, Angle ϕ is half of the angle formed through the original node path, ϕ2 = θ1 + θ1 s1 =



(y1 x2 )2 + r 2 − 2r (y1 x2 ) cos θ1

(4)

y1 x22 = l12 + r 2 − 2rl1 cos ϕ1 cos θ1 =

l12 + d12 − r 2 l1 − r cos ϕ1 = 2l1 d1 d1

θ1 = ϕ2 − arccos cos θ1

(5)

l1 − r cos ϕ1 d1

l1 − r cos ϕ1 l1 − r cos ϕ1 = cos ϕ2 + sin ϕ2 1 − d1 d1  s1 = d12 + r 2 − 2r d1 cos θ1

(6) (7) 2 (8) (9)

So s2 =

 d22 + r 2 − 2r d2 cos θ2

(10)

d2 =

 l22 + r 2 − 2rl2 cos ϕ2

(11)



− r cos ϕ l l2 − r cos ϕ2 2 2 2  cos θ2 = cos ϕ3 + sin ϕ3 1 − d2 d2

(12)

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finally sn−1 =



dn−1 = cos θn−1 

2 dn−1 + r 2 − 2r dn−1 cos θn−1 

 2 ln−1 + r 2 − 2rln−1 cos ϕn−1

(13) (14)



ln−1 − r cos ϕn−1 ln−1 − r cos ϕn−1 2 = cos ϕn−1 + sin ϕn−1 1 − dn−1 dn−1 (15)

Therefore, for any line available, the angular bisection space coverage optimization line is within the original path region, the number of traversing nodes is the same, so there are: L = l 0 + l 1 + l 2 + · · · + l n < S = s0 + s1 + s2 + · · · + sn

(16)

We can find that this method is better.

5 System Software Processing The software design of information collection system for water monitoring UAV based on WSN consists of two parts: one is the design of UAV flight collection, the other is the design of wireless communication transmission of node data. UAV flight control is mainly to complete the initialization of the flight control and wireless communication module on the UAV, fly to the acquisition node to send a signal to the convergence node, and wake up the node to complete the data transmission. In order to ensure low energy consumption, the monitoring points and convergence nodes use the timing sleep mode, which can be awakened by external excitation. The data sender sends the monitored node data to the aggregation node and sets itself to collect regularly [13].

6 System Operation and Experimental Data Analysis The system is tested on the ground, and the nodes are fixed on the surface of the water using a buoy [14], while the nodes are treated with water repellency, as shown in Fig. 4. Before the formal test, the communication quality of the built UAV system was tested, and the physical diagram is shown in Fig. 5.

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Fig. 4 Node deployment and waterproofing

Fig. 5 Object diagram of UAV test

The whole test process is carried out in the visible environment on the edge of the water, and the test distance is continuously extended during the test process. The test results are shown in Table 1, through the test of receiving 1000 packets [15]. As can be seen from the table, with the increase of the test distance, the packet loss rate and the packet error rate will also increase, and the transmission quality after more than 30 m can not be guaranteed, and the transmission can hardly be transmitted after Table 1 Communication quality test results

Distance (m)

Number of packets sent

Packet loss number

Packet loss rate

10

1000

0

0

15

1000

0

0

20

1000

1

0.001

25

1000

23

0.022

30

1000

101

0.121

35

1000

382

40

1000

1000

0.394 1

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J. Ge et al. Acquisition time

System measurement value (°C)

Measuring temperature (°C/ph)

fractional error (%)

14:00

24.5/8.1

24.7/8.2

0.81/1.22

14:30

24.5/8.1

24.7/8.2

0.81/1.22

15:00

24.5/8.2

24.7/8.2

0.81/1.22

15:30

24.5/8.1

24.6/8.2

0.47/1.22

16:00

24.5/8.1

24.7/8.2

0.81/1.22

16:30

24.1/7.9

24.3/8.0

0.82/1.25

17:00

23.9/7.9

24.2/8.0

1.24/1.25

more than 40 m. Therefore, when deploying nodes, the distance should be controlled within 20 m, which can meet the requirements of data transmission. The system collects data once per 30 min at the time of formal collection. Statistical analysis of the experimental data shows that the experimental values and actual measurements of the system can be obtained as shown in Table 2. Through comparison and analysis of Table 2, it can be concluded that the temperature error is between 0.81 and 1.24%, and the ph error is less than 1.3%, which is a reasonable error range. Therefore, the system can be more accurate collection of water monitoring data.

7 Concluding Remarks In this paper, a new WSN water monitoring data collection system is designed, combining UAV with WSN, the characteristics of water monitoring are analyzed, the flight path of UAV is optimized, and the system is designed reasonably from software and hardware. The experimental results show that the information collection system of water monitoring UAV based on WSN is stable and reliable, and has the advantages of flexibility, real-time performance and low cost. Acknowledgements Fund projects: The National Natural Science Fund 61640014; Science and Technology Plan Project of Guizhou province [2016]2302.

References 1. Xiao, T., Guanghua, C., Qinghua, D., et al.: Design of aquaculture environmental monitoring system based on WSN. Comput. Meas. Control. 26(10), 9–13 (2018) 2. Chang, B.: Design of multi-parameter monitoring system for indoor air quality based on wireless sensor network. In: International Information and Engineering Association. Proceedings of 2018 7th International Conference on Advanced Materials and Computer Science (ICAMCS 2018) (2018)

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3. Kong, Y., Li, P.-Y., Chen, Z., Quantao, Q.: The gateway design of an adaptive wireless sensor network monitoring system. Comput. Meas. Control. 23(09), 3178–3181 (2015) 4. Xingang, C., Tang, Z., Jun, M., et al.: Design of on-line temperature monitoring system for vacuum Circuit breaker based on ZigBee wireless network. Instrum. Technol. Sens. 8, 39–42+72 (2018) 5. Xuezhong, G., Lili, Z., Fan, C., et al.: UAV ground monitoring system based on STM32. Chem. Autom. Instrum. 44(03), 277–278+318 (2017) 6. Song, Y., Shaowei, Z., Peizhuang, S., Jun, G.: Agricultural condition Monitoring system of UAV based on STM32 and OV5640. Internet Things Technol. 8(07), 22–25 (2018) 7. Haizhen, W., Zaozheng, L., Yanping, T.: Cc2530 single-chip microcomputer multi-point temperature acquisition experiment design. Lab. Res. Explor. 37(12), 98–101+106 (2018) 8. Huang, F.S.-Y., Tang, S., Tong, Z., et al.: A review of path planning methods for autonomous mobile robots. Softw. Guid. J. 17(10), 1–5 (2018) 9. Jiqiang, T.: Line planning of mobile convergence nodes in wireless sensor networks. Chongqing University (2016) 10. Zhonghua, L.: New progress in the research and application of ant colony algorithm. Comput. Eng. Sci. 41(01), 173–184 (2019) 11. Shumin, F., Haiyue, W., Tiexin, W.: Research on multi-objective shortest path solving algorithm based on ideal point method. Highw. Traffic Technol. 33(03), 97–101 (2016) 12. Xin, L., Yajuan, W.: Trajectory design of WSN mobile convergence node based on Hilbert space filling curve. Mod. Electron. Technol. 39(23), 17–21 (2016) 13. Xiaoming, L.: The enhancement of directed graph-an example of problem solving oriented teaching. Comput. Educ. 02, 1–4 (2019) 14. Changyan, L., Guangzhong, L.: Node location of 3D underwater acoustic sensor network based on buoy. Microcomput. Appl. 32(22), 48–49+52 (2013) 15. Fan, S., Zhao, H.: Delay-based cross-layer QoS scheme for video streaming in wireless Ad Hoc networks. China Commun. 15(09), 215–234 (2018)

Recursive Estimation Method for Bilinear Systems by Using the Hierarchical Identification Principle Ling Xu, Xiao Zhang and Feng Ding

Abstract This paper considers the parameter identification of bilinear systems with unknown states, which are disturbed by an autoregressive moving average noise. The hierarchial identification principle is employed to derive new algorithms for interactively estimating the states and parameters via a bilinear state observer. However, the general bilinear state-space model involves many parameters, which causes heavy computational burden. Motivated by this fact, we propose a hierarchical generalized extended least squares (HGELS) algorithm by decomposing the original system into a series of subsystems with small dimensions for enhancing computational efficiency. The performance of the proposed algorithms is illustrated through a numerical example. Keywords Parameter estimation · Bilinear system · Recursive algorithm

1 Introduction System identification is the theory and methods of studying and establishing the mathematical models of dynamical systems [1–6]. Nonlinear systems widely exist in industry areas. The mathematical models of systems commonly cover the nonparametric models and the parametric models, including the Volterra and Wiener

L. Xu School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi 214153, People’s Republic of China e-mail: [email protected] L. Xu · X. Zhang · F. Ding (B) School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, People’s Republic of China e-mail: [email protected] X. Zhang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_92

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series, the state-space models, the linear-in-parameter models and the nonlinear-inparameter models [7]. Bilinear models are recognized as a special class of nonlinear models and can be applied to many industrial processes [8, 9]. Thus the studies of bilinear systems become wider in parameter identification [10], state estimation [11–13] and model-based controller design [14]. The parameter estimation of bilinear systems has attracted much attention. In this literature, Li et al. converted a bilinear state-space model into an input-output representation by eliminating the state vector of the system and presented a two-stage least squares based iterative algorithm for a special class of bilinear systems [15]. dos Santos et al. extended the subspace identification algorithm to bilinear systems by approximating a bilinear system as a linear system [16]. The problem occurs because the subspace identification algorithm causes the heavy computational burdens. In order to overcome this problem, Verdult et al. utilized the kernel methods to reduce the dimensions of the data matrices and improved the computational efficiency [17]. In this paper, we introduce the hierarchical identification principle to develop highly efficient estimation methods [18–20]. The bilinear state observer based recursive least squares algorithm is presented to estimate the states and parameters of the bilinear systems [21], but the computational burden is heavy for bilinear system identification. Thus this paper applies the hierarchical identification principle to derive an efficient method for joint state and parameter estimation with high computational efficiency. This rest of this paper is organized in the following. Section 2 describes the identification problem for bilinear state-space systems. Section 3 develops a hierarchical generalized extended least squares algorithm for interactive state and parameter estimation. Section 4 provides an example to illustrate the effectiveness of the proposed algorithms. Finally, Sect. 5 gives some concluding remarks.

2 Problem Description This paper considers a bilinear system disturbed by an autoregressive moving average process: xk+1 = Axk + Bxk u k + f u k , yk = hxk + wk ,

(1) (2)

where u k ∈ R, yk ∈ R and xk := [x1,k , x2,k , . . . , xn,k ]T ∈ Rn are the control variable, the output variable and the state vector, respectively, vk ∈ R is a stochastic white noise D(z) vk ∈ R is the measurement noise, with zero mean and variance σ 2 , and wk := C(z) C(z) and D(z) are the polynomials in the shift operator z −1 : C(z) := 1 + c1 z −1 + c2 z −2 + · · · + cn c −1 z −n c +1 + cn c z −n c , D(z) := 1 + d1 z −1 + d2 z −2 + · · · + dn d −1 z −n d +1 + dn d z −n d ,

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and A ∈ Rn×n , B ∈ Rn×n , f ∈ Rn , h ∈ R1×n , ci ∈ R (i = 1, 2, . . . , n c ) and d j ∈ R ( j = 1, 2, . . . , n d ) are the system parameters to be identified and ⎡

−a1 1 0 ⎢ .. . .. ⎢ . A := ⎢ ⎣ −an−1 0 1 0 ··· 0 −an ⎡ ⎤ b1 ⎢ b2 ⎥ ⎢ ⎥ B := ⎢ . ⎥ , bl ∈ R1×n , ⎣ .. ⎦

⎡

⎤ ⎥ ⎥ ⎥, ⎦

⎢ ⎢ f := ⎢ ⎣

f1 f2 .. .

⎤ ⎥ ⎥ ⎥, ⎦

fn l = 1, 2, . . . , n.

bn Define the parameter vectors ϑ, ϑs , ϑa , ϑb , ϑ f and ϑn as ϑ := [ϑsT , ϑnT ]T ∈ Rn

2

+2n+n c +n d

, ϑs := [ϑaT , ϑbT , ϑ Tf ]T ,

ϑa := [a1 , a2 , . . . , an ] ∈ R , ϑb := [b1 , b2 , . . . , bn ]T , ϑ f := [ f 1 , f 2 , . . . , f n ]T ∈ Rn , T

n

ϑn := [c1 , c2 , . . . , cn c , d1 , d2 , . . . , dn d , ]T ∈ Rn c +n d . Then Eq. (1) can be written as T T T ϑa + Φb,k ϑb + Φ Tf,k ϑ f = Φs,k ϑs , x1,k = Φa,k

(3)

where the information vectors Φk , Φs,k , Φa,k , Φb,k , Φu,k and Φn,k are defined as T T Φk := [Φs,k , Φn,k ]T ∈ Rn

2

+2n+n c +n d

,

n 2 +2n

,

Φs,k := [Φa,k , Φb,k , Φu,k ] ∈ R T

T

T

T

Φa,k := [−x1,k−1 , −x1,k−2 , . . . , −x1,k−n ]T ∈ Rn , 2

T T T u k−1 , xk−2 u k−2 , . . . , xk−n u k−n ]T ∈ Rn , Φb,k := [xk−1

Φu,k := [u k−1 , u k−2 , . . . , u k−n ]T ∈ Rn , Φn,k := [−wk−1 , −wk−2 , . . . , −wk−n c , vk−1 , vk−2 , . . . , vk−n d ]T ∈ Rn c +n d . Substituting (3) into (2) gives the identification model of the system in (1)–(2): T T ϑs + Φn,k ϑn + vk yk = x1,k + wk = Φs,k T T T T = Φa,k ϑa + Φb,k ϑb + Φu,k ϑ f + Φn,k ϑn + vk

= ΦkT ϑ + vk , T ϑn + vk . wk = Φn,k

(4) (5)

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Assume that the degrees n, n c and n d are known; yk = 0, u k = 0, vk = 0, wk = 0 and xk = 0 for k  0. The objective of this paper is to explore an efficient identification method for combined state and parameter estimation of bilinear state-space systems.

3 The Hierarchical Generalized Extended Least Squares Algorithm This section presents a hierarchical generalized extended least squares (HGELS) algorithm for the considered system by decomposing the identification model into several sub-identification models based on the hierarchical identification principle. The identification model in (4)–(5) can be written in the following sub-identification models: T ϑa + vk , ya,k = Φa,k

T yb,k = Φb,k ϑb + vk ,

T T y f,k = Φu,k ϑ f + vk , wk = Φn,k ϑn + vk .

According to the least squares principle, defining and minimizing the cost functions J (ϑa ) :=

k 

[ya, j − Φa, j ϑa ] ,

k  T 2 J (ϑb ) := [yb, j − Φb, j ϑb ] ,

[y f, j − Φ Tf, j ϑ f ]2 ,

k  T 2 J (ϑn ) := [w j − Φn, j ϑn ]

2

T

j=1

J (ϑ f ) :=

k 

j=1

j=1

j=1

give the recursive relations for parameter estimation. However, we find that the algorithm cannot work because the information vectors Φa,k , Φb,k and Φn,k contain the unknown states xk−l (l = 1, 2, . . . , n) and the noise terms wk−i and vk− j . According to the method in [21], by using the parameter estimates ϑˆ a,k := [aˆ 1,k , aˆ 2,k , . . . , aˆ n,k ]T ∈ 2 Rn , ϑˆ b,k := [ bˆ1,k , bˆ2,k , . . . , bˆn,k ]T ∈ Rn , ϑˆ f,k := [ fˆ1,k , fˆ2,k , . . . , fˆn,k ]T ∈ Rn and ϑˆ n,k := [cˆ1,k , cˆ2,k , . . . , cˆn c ,k , dˆ1,k , dˆ2,k , . . . , dˆn d ,k ]T ∈ Rn c +n d to construct the estimates of A, B and f : ⎡

−aˆ 1,k ⎢ .. ⎢ . Aˆ k = ⎢ ⎣ −aˆ n−1,k −aˆ n,k

1 0 0

0

..

.

···

fˆk = [ fˆ1,k , fˆ2,k , . . . , fˆn,k ]T ,

⎤

⎥ ⎥ ⎥, 1 ⎦ 0

⎡ ⎢ ⎢ Bˆ k = ⎢ ⎢ ⎣

bˆ1,k bˆ2,k .. .

bˆn,k

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

(6)

(7)

we can derive the following bilinear state observer to generate the state estimate xˆ k :

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T ϑˆ n,k ], xˆ k+1 = Aˆ k xˆ k + Bˆ k xˆ k u k + fˆk u k + L x,k [yk − h xˆ k − Φˆ n,k

L x,k = [ Aˆ k + Px,k+1 = [ Aˆ k +

Bˆ k u k ] Px,k hT [h Px,k hT + 1]−1 , Bˆ k u k ] Px,k [ Aˆ k + Bˆ k u k ]T − L x,k h Px,k [ Aˆ k + Bˆ k u k ]T .

(8) (9) (10)

Define the estimates of Φk , Φs,k , Φa,k , Φb,k and Φn,k as 2 T T Φˆ k := [Φˆ s,k , Φˆ n,k ]T ∈ Rn +2n+n c +n d ,

Φˆ s,k := [Φˆ a,k , Φˆ b,k , Φu,k ] ∈ R T

T

T

n 2 +2n

T

(11)

,

(12)

(13) Φˆ a,k := [−xˆ1,k−1 , −xˆ1,k−2 , . . . , −xˆ1,k−n ]T ∈ Rn , T T T T n2 ˆ (14) Φb,k := [ xˆ k−1 u k−1 , xˆ k−2 u k−2 , . . . , xˆ k−n u k−n ] ∈ R , T n c +n d ˆ Φn,k := [−wˆ k−1 , −wˆ k−2 , . . . , −wˆ k−n c , vˆ k−1 , vˆ k−2 , . . . , vˆ k−n d ] ∈ R , (15) where the estimates of wk and vk are T ˆ ϑs,k−1 , wˆ k = yk − Φˆ s,k

(16)

vˆ k = yk − Φˆ k ϑˆ k−1 . T

(17)

By replacing Φa,k , Φb,k and Φn,k with their estimates, we can obtain the bilinear state observer based hierarchical generalized extended least squares algorithm for computing the parameter estimates ϑˆ k as follows: T T ϑˆ a,k = ϑˆ a,k−1 + L a,k [y(t) − Φˆ b,k ϑˆ b,k−1 − Φu,k ϑˆ f,k−1 T T ϑˆ n,k−1 − Φˆ a,k ϑˆ a,k−1 ], −Φˆ n,k

(18)

T Pa,k−1 Φˆ a,k ]−1 , L a,k = Pa,k−1 Φˆ a,k [1 + Φˆ a,k

(19)

Pa,k = [I − L a,k Φˆ a,k ] Pa,k−1 ,

(20)

T

ϑˆ b,k = ϑˆ b,k−1 + L b,k [y(t) − Φˆ a,k ϑˆ a,k − Φu,k ϑˆ f,k−1 T

T

T T ϑˆ n,k−1 − Φˆ b,k ϑˆ b,k−1 ], −Φˆ n,k

(21)

L b,k = Pb,k−1 Φˆ b,k [1 + Φˆ b,k Pb,k−1 Φˆ b,k ] ,

(22)

Pb,k = [I − L b,k Φˆ b,k ] Pb,k−1 ,

(23)

T

−1

T

T T ϑˆ a,k − Φˆ b,k ϑˆ b,k ϑˆ f,k = ϑˆ f,k−1 + L f,k [y(t) − Φˆ a,k T T ϑˆ n,k−1 − Φu,k ϑˆ f,k−1 ], −Φˆ n,k

(24) −1

L f,k = P f,k−1 Φu,k [1 + Φu,k P f,k−1 Φu,k ] , T P f,k = [I − L f,k Φu,k ] P f,k−1 , T

(25) (26)

T T ϑˆ a,k − Φˆ b,k ϑˆ b,k ϑˆ n,k = ϑˆ n,k−1 + L n,k [y(t) − Φˆ a,k T T ϑˆ f,k − Φˆ n,k ϑˆ n,k−1 ], −Φu,k

(27)

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Table 1 The computational efficiency of the RGELS and HGELS algorithms Algorithms Number of multiplications Number of additions 2(n 2 + 2n + n c + n d )2 + 4(n 2 + 2n + n c + n d ) 2(n c + n d )2 + 7(n c + n d ) + 2n 4 + 11n 2 + 14n

RGELS HGELS

2(n 2 + 2n + n c + n d )2 + 2(n 2 + 2n + n c + n d ) 2(n c + n d )2 + 5(n c + n d ) + 2n 4 + 9n 2 + 10n

T L n,k = Pn,k−1 Φˆ n,k [1 + Φˆ n,k Pn,k−1 Φˆ n,k ]−1 ,

(28)

T ] Pn,k−1 . Pn,k = [I − L n,k Φˆ n,k

(29)

This section employs the hierarchical identification principle to decompose the identification model into several sub-identification models for the purpose of reducing the computational burden – see the computational analysis in Table 1. The computational cost can be evaluated by floating point operation. Table 1 lists the number of multiplications and additions of the RGELS, HGELS algorithms at each step for computational comparison. It is clear that the HGELS algorithm can greatly improve the computational efficiency, especially for large-scale systems.

4 Example In this section, the simulation example is provided to illustrate the efficiency of the proposed algorithms. Consider the following bilinear state-space model:



−a1 1 b11 b12 f1 xk + xk u k + uk , xk+1 = b21 b22 f2 −a2 0 yk = [1, 0]xk − cwk−1 + dvk−1 + vk .

The parameter vector to be identified is given as ϑ = [a1 , a2 , b11 , b12 , b21 , b22 , f 1 , f 2 , c, d]T = [−0.25, 0.20, 0.08, 0.14, −0.07, −0.20, 0.40, 0.30, −0.10, 0.15]T . In simulation, the input {u k } is taken as an uncorrelated persistent excitation signal sequence, and {vk } as a white noise sequence with zero mean and variances σ 2 = 1.002 . Set the data length L = 3000. Applying the HGELS algorithm in (6)–(29) to estimate the parameters of this example system. The parameter estimates and their estimation errors δ := ϑˆ k − ϑ/ϑ × 100% versus k are shown in Fig. 1. The states xi,k and their estimates xˆi,k versus k are shown in Fig. 2. From Figs. 1 and 2, we can draw the following conclusions.

Recursive Estimation Method for Bilinear Systems …

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2 1.8 1.6 1.4

δ

1.2 1 0.8 0.6 0.4

HGELS 0.2 0

1500

1000

500

0

2000

2500

3000

k

Fig. 1 The HGELS estimation errors versus k State estimate of x1

1.5 1 0.5 0 −0.5 −1 −1.5 0

100

200

0

100

200

k

300

400

500

300

400

500

State estimate of x2

1 0.5 0 −0.5 −1

k

Fig. 2 State xi,k and its estimate xˆi,k versus k

1. Figure 1 shows that the parameter estimation errors of the HGELS algorithms become smaller with k increasing. 2. Figure 2 shows that the estimated states fit with the true states well, which illustrates that the bilinear state observer is effective.

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5 Conclusions This paper presents a hierarchial generalized extended least squares algorithm for bilinear systems. The simulation results indicate that the proposed algorithm can solve the identification problem of bilinear systems and improve the computational efficiency. Combined with the statistical tools, the identification algorithms proposed in this paper can be applied to other fields [22–25]. Acknowledgements This work was supported by the National Natural Science Foundation of China (61873111), the Qing Lan Project, the Postdoctoral Science Foundation of Jiangsu Province (No. 1701020A), the 333 Project of Jiangsu Province (No. BRA2018328).

References 1. Ding, F.: System Identification—New Theory and Methods. Science Press, Beijing (2013) 2. Ding, F.: System Identification—Performances Analysis for Identification Methods. Science Press, Beijing (2014) 3. Ding, F.: System Identification—Auxiliary Model Identification Idea and Methods. Science Press, Beijing (2017) 4. Ding, F.: System Identification—Iterative Search Principle and Identification Methods. Science Press, Beijing (2018) 5. Ding, F.: System Identification—Multi-innovation Identification Theory and Methods. Science Press, Beijing (2016) 6. Ding, F.: Modern Control Theory. Tsinghua University Press, Beijing (2018) 7. Nowak, R.D.: Nonlinear system identification. Circuits Syst. Sig. Process. 21(1), 109–122 (2002) 8. Bruni, C., Dipillo, G., Koch, G.: Bilinear systems: an appealing class of nearly linear systems in theory and applications. IEEE Trans. Autom. Control 19(4), 334–348 (1974) 9. Svoronos, S., Stephanopoulos, G., Rutherford, A.: Bilinear approximation of general non-linear dynamic systems with linear inputs. Int. J. Control 31(1), 109–126 (1980) 10. Baheti, R., Mohler, R., Spang, H.: Second-order correlation method for bilinear system identification. IEEE Trans. Autom. Control 25(6), 1141–1146 (1980) 11. Hara, S., Furuta, K.: Minimal order state observers for bilinear systems. Int. J. Control 24(5), 705–718 (1976) 12. Funahashi, Y.: Stable state estimator for bilinear systems. Int. J. Control 29(2), 181–188 (1979) 13. Phan, M.Q., Vicario, F., Longman, R.W.: Optimal bilinear observers for bilinear state-space models by interaction matrices. Int. J. Control 88(8), 1504–1522 (2015) 14. Cheng, D.: Controllability of switched bilinear systems. IEEE Trans. Autom. Control. 50(4), 511–515 (2005) 15. Li, M.H., Liu, X.M.: The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique. Sig. Process. 147, 23–34 (2018) 16. dos Santos, P.L., Ramos, J.A., de Carvalho, J.L.M.: Identification of bilinear systems with white noise inputs: an iterative deterministic-stochastic subspace approach. IEEE Trans. Control Syst. Technol. 17(5), 1145–1153 (2009) 17. Verdult, V., Verhaegen, M.: Kernel methods for subspace identification of multivariable LPV and bilinear systems. Automatica 41(9), 1557–1565 (2005) 18. Liu, Y.J., Ding, F., Shi, Y.: An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–970 (2014)

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19. Ding, J., Ding, F., Liu, X.P., Liu, G.: Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011) 20. Ding, F., Chen, T.: Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst.-I: Regul. Pap. 52(6), 1179–1187 (2005) 21. Zhang, X., Xu, L., et al.: Combined state and parameter estimation for a bilinear state space system with moving average noise. J. Franklin Inst. 355(6), 3079–3103 (2018) 22. Suresh, A., Jha, M.: Automated essay grading using natural language processing and support vector machine. Int. J. Comput. Technol. 5(2), 18–21 (2018) 23. Murali, V., Chatrapathy, K.: BuyerPlyGround: agriculture trade market using blockchain with machine learning. Int. J. Comput. Technol. 6(5), 31–36 (2019) 24. Sellami, L., Zidi, S., Abderrahim, K.: Self-adaptative multi-kernel algorithm for switched linear systems identification. Int. J. Model. Ident. Control 31(1), 103–111 (2019) 25. Xue, J., Liu, F., Bai, J., Hou, T.: Modelling of gene signal attribute reduction based on neighbourhood granulation and rough approximation. Int. J. Model. Ident. Control 31(2), 161–168 (2019)

PSO Rapid Ascending Trajectory Planning Method Based on Neural Network Trajectory Surrogate Model Yuhang Zeng, Ye Yang, Yongji Wang and Lei Liu

Abstract To reduce the time cost of Runge-Kutta multi-step prediction calculation process of PSO direct shooting method in solving trajectory planning problem, a fast trajectory planning method based on neural network surrogate model converting multi-step prediction process into single-step prediction is proposed. In this method, the solution space samples consisting of feasible trajectories are designed to approximate the real feasible trajectory solution space, and the training set of neural network is constructed by feasible trajectory database. The samples generation time is reduced by trajectory reusing, and the incremental method of distinguishing reference state vectors at different times is used to reduce the complexity of the model so as to facilitate the training of the model of the neural network. The simulation results show that the method is fast, feasible and adaptable. Keywords Surrogate model · Neural network · Particle swarm optimization · Ascending trajectory planning · Shooting method

1 Introduction Ascending trajectory planning and optimization is a fundamental topic for studying the flight plan and performance of high-speed aircraft. It is beneficial to reduce takeoff weight, reduce cost, and optimize the requirements for each subsystem (propulsion system, material, aerodynamic shape, etc.), and provides the necessary data for subsystem design and has important theoretical and engineering significance [1]. Moreover, as countries continue to increase their aviation exploration, the demand for rapid, flexible, and autonomous mission planning has expanded. There are many influencing factors in autonomous mission planning, including trajectory planning, Y. Zeng · Y. Wang · L. Liu (B) National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, HUST, Wuhan 430074, China e-mail: [email protected] Y. Yang Beijing Aerospace Automatic Control Institute, Science and Technology on Aerospace Intelligent Control Laboratory, Beijing 100854, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_94

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fault tolerance, system identification, adaptive control, sensor fusion, etc. Among them, trajectory planning plays a key role in achieving a mission goal [2]. Therefore, trajectory planning becomes more and more important as the basic application of aircraft mission planning. Rapidity, reliability, adaptability and cost of implementation are the main motivations of this paper. The realization of fast trajectory planning is affected by three basic factors: task complexity, environment uncertainty and implementation complexity of onboard algorithm [3]. Due to the complexity of integration of onboard trajectory planning algorithms, adaptability has become a key factor. Algorithms should be scalable and universal, avoiding the use of limited specific methods. The same planning algorithm should be used in most aircraft in a modular way. This will reduce costs in many ways, such as concept and prototype development, testing and validation, manufacturing and replication, maintenance, etc. Intelligent algorithm is a kind of strong expansibility and good portability algorithm, which is suitable for designing well-adapted and low-cost algorithms. Particle Swarm Optimization (PSO) is a general swarm intelligence algorithm. It has been widely used in flight trajectory planning and optimization, and is one of the most effective tools for trajectory planning. There are many advantages of using PSO algorithm for trajectory planning: (1) Particle Swarm Optimization takes up less hardware resources, which is beneficial to the algorithm migration to ordinary onboard computer; (2) PSO algorithm has inherent parallelism and can improve the efficiency of trajectory planning through parallel computing methods; (3) PSO algorithm has strong scalability and can be mixed with other algorithms to improve the efficiency of the algorithm [4]. Considering the point mentioned above, this paper studies the fast PSO trajectory planning in ascending phase. To some extent, the process of trajectory planning is like a black box. Without knowing its internal working principle in advance, the terminal state can be predicted only according to the input of the current state vector, the characteristic of the control function, the evaluated uncertainty parameter vector, the current time and the end time. For complex trajectory model, the calculation time of terminal state prediction based on dynamic equation is related to integration time and integration step. When integration time is long and integration step is small, the prediction calculation time is also long, which is not conducive to short flight mission [5, 6]. In recent years, surrogate model has attracted widespread attention. This method establishes approximate models to improve the computing speed in the case of complex systems with high computational time cost. Constructing surrogate model based on samples in design space can greatly reduce the calculation cost of agent model in solving optimization problems. When constructing design space samples according to trajectory planning problems, the number of samples is infinite for continuous trajectories. Even the proportion of feasible sample space to the whole trajectory sample space is small, the number of feasible samples is still large, and the trade-off between reducing sample size and ensuring the accuracy is needed, and the reasonable sample distribution can be provided by particle swarm optimization, which is the convenience brought by the high coupling of trajectory planning problem itself [7, 8]. The method of this paper is based on the idea of

PSO Rapid Ascending Trajectory Planning …

991

sampling, interpolation and model approximation, using surrogate model to solve the trajectory planning problem [9, 10]. In [11–13], optimal algorithms are used for solving practical problems.

2 Ascending Trajectory Model In this paper, the multi-stage solid rocket ascending trajectory model is taken as the simulation model. For the ascending trajectory planning problem, only the longitudinal plane motion is considered. The trajectory equation is generally solved as dimensionless form during the process of calculating the trajectory. There are several advantages to the dimensionless form equation: (1) avoid large differences in the scale of the state vector, thereby reducing numerical calculation errors and precision losses; (2) facilitating similar simulations, thus making the results more versatile. There are two problems to be noticed in the dimensionless process: one is that the sequence of coordinate transformation and dimensionless should be considered in practical application of trajectory equation. Generally, it is more convenient to first dimensionless and then coordinate transformation. The second is the selection of characteristic scale, which includes height r, velocity v, time t. R=

v t r , V =√ , τ=√ Re g0 Re Re /g0

(1)

Re is earth radius, g0 is gravity acceleration, Da is drag acceleration, L a is lift acceleration, aT is thrust acceleration, and the definition is as follows: Da = D/mg0 , L a = L/mg0 , aT = T /mg0

(2)

Ignoring the effects of the Earth’s rotation, the simplified longitudinal plane of motion is as follows: ⎧ dR ⎪ ⎪ = V sinγ ⎪ ⎪ dτ ⎪ ⎪   ⎪ ⎪ sinγ dV ⎪ ⎪ = a − D − ⎪ T a ⎨ dτ R2  (3) 1 dγ 1 cosγ ⎪ 2 ⎪ ⎪ = L ) + a sinα + (V − a T ⎪ ⎪ dτ V R R ⎪ ⎪ ⎪ ⎪ dm

T ⎪ ⎪ ⎩ =− Re /g0 dτ Isp R is the distance from the centroid of aircraft to the center of the earth, V is the speed of the aircraft relative to the earth, γ is the flight path angle, m is mass, and Isp is specific impulse.

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3 Neural Network Trajectory Surrogate Method Surrogate method is a single-step prediction method showing as Fig. 1. The idea is to predict the terminal state according to the current state, control vector and aerodynamic parameters bias as shown in Fig. 2. Neural Networks is modeling problem in Euclidean Space, the surrogate model is consisted of control vector space R U , initial and terminal state vector R x0 , R x f , and parameter vector space R p , defining surrogate model as F [14, 15]. The different trajectory problem showing as Fig. 2 is mapping as F(R x0 , R U , R p , tstar t , t f ) → R x f , tstar t is different time point (tstar t = t0 , t1 , . . .) and t f is terminal fixed time point. In this way, the dynamic trajectory planning problem is transformed into multiple static trajectory planning problems, and the trajectory planning problem at different time points is unified by an surrogate model like Fig. 3.

3.1 Surrogate Model Design The following problems need to be solved when using neural network as surrogate model: (1) How to determine the input and output vector of neural network; (2) In fact, the real feasible solutions are infinite, the key problem is how to approximate the spatial distribution of real feasible solutions through representative sample distribution for the trajectory planning problem with finite sample size; (3) How to improve the accuracy of surrogate model; (4) In many cases, sample generation takes a lot of

Fig. 1 Surrogate model problem converting

Fig. 2 PSO surrogate model solving trajectory planning algorithm

PSO Rapid Ascending Trajectory Planning …

993

Fig. 3 Surrogate model for time partitioning

t0

t1

t2

t3

......

tf

time and how to shorten the time of sample generation. (5) How to choose learning algorithm to train neural networks? According to the trajectory equation Formula (3), the input and output vector is designed as Fig. 4. Our ascending trajectory model has three stage, and the first stage fly as procedural angle, we design different model for different flight stage, because the flight environment has great difference in stage2 and stage3, so them are designed independently. [h 0 , v0 , γ0 ] is initial [height, speed, flight path angle] vector, [Ecl , Ecd , Er ho , ET ] is [lift coefficient bias, drag coefficient bias, atmospheric density coefficient bias, thrust bias] vector. f (α) is angle of attack function, representing by Chebyshev polynomial. The sample generation procedure is as following. Feasible trajectory database obtained by height stratified sampling, the height is designed as 93, 94, 95, 96 km, and using PSO algorithm searching trajectory satisfied path constraint and height constraint. In this way, approximating the spatial distribution of real feasible solutions. The total number of samples of the feasible trajectory database can be defined by following formula. M = Mh Mbias Mseg

(4)

Mh is terminal height stratified sampling number, Mbias is bias vector number, Mseg is time segment number. Mh = 4, Mbias = 1000, Mseg = 5. The bias vector is obtained by stratified sampling [16, 17]. Table 1 shows the samples generation algorithm procedure. The accuracy of the surrogate model is related to the terminal state quantity scale. Take the terminal height of 95 km as an example. When the accuracy of the surrogate model is desired to be 1 m, the precision of the neural network mean square error (MSE, Mean Squared Error) for the full-scale output is (1 m/95 km)2 . Such x0 = [h0 , v0 , γ 0 ]

x0 = [h0 , v0 , γ 0 ]

f (α ) = [α 0 ,.., α N , t0 , t f ]

f (α )

p = [E cl , E cd , E rho , ET ]

Fig. 4 Multi-stage surrogate model

p = ET

x f = [h f , v f , γ f ]

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Y. Zeng et al.

Table 1 Sample generation procedure Algorithm: Sample Generation Procedure

S1 , bias vector set S 2

1.

terminal state set

2.

for terminal state vector

3.

for bias vector

p1 in S1

p2 in S 2

p1 , p2 ,control vector range U PSO Algorithm Output p1 , p2 , U sample saving p1 , p2 , U ( p1 is PSO searching terminal state vector)

4.

PSO Algorithm Input

5.

direct shooting method getting control vector

6. 7. 8.

end

9. End 10. Above procedure getting initial samples M initial , M initial resampling is needed according to different time 11. for each

[tstart , t f ] , t start = t0 , t1 ,...

[tstart , t f ] resampling trajectory:

12.

after U =chebyshev polynomial(before

13.

U)

14. end

high precision requirements are difficult for training to learn feasible parameters for complex neural networks. Considering the incremental output, with a reference value of 90 km, the output can be written as (95–90 km), and the scale is (1 m/5 km)2 . The reduced scale can be learned through training algorithm.

3.2 Neural Networks Training After getting the train data set, we can train neural networks. The training procedure is as follows: Step 1. data normalized. The reason for using the incremental input and output to reduce the scale is analyzed in above section. Since the initial state and the scale of the control vector are changing at different times, the incremental reference value is also variety. For different flight stages, the reference vector matrices stage2_ref and stage3_ref are respectively defined, and the reference vector matrix is obtained by statistically averaging the training samples, the matrix shows at Table 2. Where t0 is the start time, tf is the end time, href is the height reference value, vref is the speed reference value, gamref is the flight path angle reference value, [hrange, vrange, gmarange] represents the state range. The data normalized formula is as follows: h˜ = (h − h r e f )/ h range , v˜ = (v − vr e f )/vrange , γ˜ = (γ − γr e f )/γrange

(5)

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Table 2 Different time point state reference vector Stage2

Stage3

t0 (s)

tf (s)

href (m)

vref (m/s)

gmaref (°)

hrange

vrange

gmarange

65

123

21,960.5

1440.1

25.7

10

10

10

70

123

25,134.5

1593.1

23.9

68.2

30.6

10.8

75

123

28,371.9

1757

22.2

285.5

51.4

11.6

80

123

31,735.5

1936.3

20.6

609.3

74

11.8

85

123

35,194.8

2130.3

19.2

958.7

98

12.3

123

165

65,675.8

4310.6

12.6

5353.7

334.9

2.5

128

165

70,360.7

4462.7

11.7

6280

368

3.2

133

165

74,686

4614

10.5

7129.4

382.4

3.2

138

165

78,707

4778.3

9.2

7257.9

429

3.8

143

165

82,337.3

4959.3

8

7799.5

457.1

4.3

 t0 = t0 /t f , α˜ i = αi /90, i = 1, 2, . . . , 10

(6)

Step 2. Design neural network as Fig. 4. Stage2 input vector is 19 dimension, [1:3] dimension is [h 0 , v0 , γ0 ], [4:7] dimension is [Ecl , Ecd , Er ho , ET ], [8:9] dimension is [tstar t , t f ], [11:19] dimension is attack of angle vector. Stage3 input vector is 16 dimension, [1:3] dimension is [h 0 , v0 , γ0 ] [4], dimension is [ET ], [5:6] dimension is [tstar t , t f ], [7:16] dimension is attack of angle vector. Stage2 and Stage3 neural network has two hidden layers, each layer has 30 neurons, and the activation function is sigmoid, the output vector is 3 dimension, the activation function is purline. Step 3. Choosing Levenberg-Marquardt Algorithm to train neural network. Step 4. Test and verify trained neural networks.

4 Simulation The accuracy of the neural network surrogate model is shown in Table 3, and the accuracy test is based on the training set statistics. Since the influence of parameter uncertainty needs to be considered during the flight process, surrogate model under the parameter deviation is considered at different time points by simulating the dynamic flight process, and the stage2 parameter deviation is considered. The 65 s moment is the reference trajectory, and 70, 73, 75, and 80 s indicate deviations at different times. When simulation, we use two type bias as before bias and after bias indicating the parameter deviation. The before parameter bias is [Ecl , Ecd , Er ho , ET ] = [0.05, −0.01, −0.02, 0.02], the after bias is [Ecl , Ecd , Er ho , ET ] = [0.01, 0.01, −0.02, 0.02]. The PSO surrogate model plans the Target terminal state, and the result is show as Table 4. We can see the result is acceptable, and the running time costs only 0.2 s, improving a lot comparing Runge-Kutta costs 10.2 s. And some of states show from Figs. 5, 6, 7, 8, 9 and 10.

Stage3

Stage2

t0

165.0

165.0

165.0

165.0

138.0

143.0

123.0

85.0

133.0

123.0

80.0

128.0

123.0

75.0

165.0

123.0

123.0

123.0

70.0

tf

65.0

tf

Table 3 Surrogate model precision

5.9

5.6

9.1

14.2

9.6

6.1

18.9

40.8

86.9

83.0

5.9 3.4 2.4 1.6 1.4 2.0 1.6 1.2 1.0 1.0

−105.8 −30.7 −48.0 −9.0 −6.0 −11.4 −10.0 −6.9 −5.5 −5.8

2.4

1.8

1.8

2.8

3.0

0.5

0.3

0.4

0.5

0.5

max

−2.0

−3.1

−3.0

−2.6

−4.2

−0.4

−0.5

−0.5

−0.6

−0.6

min

v precision (m/s) std

max

min

h precision (m)

0.3

0.3

0.4

0.4

0.5

0.1

0.1

0.1

0.1

0.1

std

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

max

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

min

gma precision (°)

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

std

996 Y. Zeng et al.

PSO Rapid Ascending Trajectory Planning … Table 4 Different time point bias terminal state

Fig. 5 Different time h contrast

Fig. 6 Different time v contrast

997

time (s)

Terminal h (m)

Terminal v (m/s)

Terminal gma (°)

Target

95,500

6010

1

65

95,597.4

6007.5

0.9

70

95,046.7

6014.5

0.7

73

95,864.5

6002.7

0.5

75

95,282.5

6011.2

1.4

80

95,720.1

6009.3

1.1

998 Fig. 7 Different time gma contrast

Fig. 8 Different time Qs contrast

Fig. 9 Different time m contrast

Y. Zeng et al.

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Fig. 10 Different time afa contrast

5 Conclusion In summary, it is feasible to approximate the feasible solution space by surrogate model and searching the control vector by PSO algorithm, and then use Runge-Kutta integral to obtain the trajectory of the selected vector, which is more efficient and accurate than using Runge-Kutta integral directly. Acknowledgements This work was supported in part by the National Nature Science Foundation of China (Grant nos. 61873319, 61803162 and 61573161).

References 1. Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Guid. Control Dyn. 21(2), 193–207 (1998) 2. Changwan, M., Jianping, Y.: Introduction of military aircraft route planning. Flight Dyn. 4 (1998) 3. Yakimenko, O.A.: Direct method for rapid prototyping of near-optimal aircraft trajectories. J. Guid. Control Dyn. 23(5), 865–875 (2000) 4. Huang, G.Q., Lu, Y.P., Nan, Y.: A survey of numerical algorithms for trajectory optimization of flight vehicles. Sci. China Technol. Sci. 55(9), 2538–2560 (2012) 5. Verma, A., et al.: Neural dynamic trajectory design for reentry vehicles. In: AIAA Guidance, Navigation and Control Conference and Exhibition (2007) 6. Julian, K.D., Kochenderfer, M.J.: Neural network guidance for UAVs. In: AIAA Guidance, Navigation, and Control Conference (2017) 7. Zhang, B., Chen, S., Xu, M.: Application of neural network in trajectory planning of the entry vehicle for variable targets. In: International Conference on Artificial Intelligence and Computational Intelligence. Springer, Berlin, Heidelberg (2011) 8. Dileep, M.V., Kamath, S., Nair, V.G.: Ascent phase trajectory optimization of launch vehicle using theta-particle swarm optimization with different thrust scenarios. Int. Rev. Aerospace Eng. 9(6), 200–207 (2016)

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9. Breitner, M.H.: Robust optimal onboard reentry guidance of a space shuttle: dynamic game approach and guidance synthesis via neural networks. J. Optim. Theory Appl. 107(3), 481–503 (2000) 10. Rao, A.V.: A survey of numerical methods for optimal control. Adv. Astronaut. Sci. 135(1), 497–528 (2009) 11. Huang, J., Qian, J., Liu, L., Wang, Y.J., Xiong, C.H., Ri, S.: Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator. J. Franklin Inst. 353, 2761–2782 (2016) 12. Hou, Z.W., Liu, L., Wang, Y.J., Huang, J., Fan, H.J.: Terminal impact angle constraint guidance with dual sliding surfaces and model-free target acceleration estimator. IEEE Trans. Control Syst. Technol. 25(1), 85–100 (2017) 13. Liu, X., Liu, L., Wang, Y.J.: Minimum time state consensus for cooperative attack of multimissile systems. Aerosp. Sci. Technol. 69, 87–96 (2017) 14. Geiger, B., Horn, J.: Neural network based trajectory optimization for unmanned aerial vehicles. In: 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (2009) 15. Xue, M.: UAV trajectory modeling using neural networks. In: 17th AIAA Aviation Technology, Integration, and Operations Conference (2017) 16. Murillo, O., Lu, P.: Fast ascent trajectory optimization for hypersonic air-breathing vehicles. In: AIAA Guidance, Navigation, and Control Conference (2010) 17. Sagliano, M., Mooij, E., Theil, S.: Onboard trajectory generation for entry vehicles via adaptive multivariate pseudospectral interpolation. In: AIAA Guidance, Navigation, and Control Conference (2016)

A Two-Stage Design of Formation Control for Underactuated Surface Vessels Xiaofei Yang, Chunxiao Ge, Hui Ye and Shuyi Shao

Abstract This paper investigates the problem of formation control for underactuated unmanned surface vessels (USVs). The proposed two-stage formation control method makes the USVs asymptotically track the desired trajectory with desired speed. The control strategy includes two phases: the position and the velocity. Firstly, each USV is steered to the desired initial position in finite time through adding a power integrator in the phase of position. Then, USVs are controlled to obtain a desired forward speed along with the direction of the formation in the phase of velocity. Numerical examples are given to illustrate the effectiveness of our scheme. Keywords Formation control · Finite-time convergence · Underactuated surface vessel

1 Introduction The distributed formation control of USVs has attracted great interests over the years due to both practical and theoretical challenging [1]. Compared with single, the formation can deal with more complex problem and collaborate to improve efficiency [2]. Hence, it has been and still remains a hot research [3]. Among the formation control laws, such as the virtual-leader control scheme presented in [4], X. Yang · C. Ge · H. Ye (B) School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China e-mail: [email protected] X. Yang e-mail: [email protected] C. Ge e-mail: [email protected] S. Shao College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_95

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the behavior-based approach in [5], the graph theory-based method in [6], and so on, their research models are usually considered as fully actuated. However, most of the USVs are underactuated, which means the inputs are fewer than the degrees of freedom (DOF). For formation control problem of underactuated USVs, a cross-track scheme based path following control is proposed in [7]. The agents are guided to asymptotically constitute desired formation with desired speed. Given velocity of unicycle-type nonholonomic vehicles constrained, a leaderfollowing formation control problem is studied in [8, 9]. Sliding-mode control laws are proposed to make USVs constitute arbitrary formations in [10]. A finite-time switching control algorithm is proposed in [11]. Our formation control scheme are consisted of two stages in this work. Firstly, single controller is designed to make each USV reach the desired position in finite time. Secondly, cooperation controllers are designed for USVs to achieve formation consensus. The remainder is organized as follows: Sect. 2 states the model of USV and put forward problem formulation. Section 3 develops controllers for single and formation based finite-time control and distribute cooperation control, respectively. Simulation results and concluding remarks are given in Sects. 4 and 5.

2 Preliminaries and Problem Formulation 2.1 Modeling USV has 6 DOF, including sway, yaw, surge, roll, pitch, and heave. When it comes to the horizontal plane, the generic kinematic and dynamic equations without external disturbance can be described as follows [12]: x˙ = u cos ψ − v sin ψ y˙ = u sin ψ + v cos ψ ψ˙ = r

(1)

where u, v denote the speed of surge and sway, ψ, r denote the direction and angular speed of the vehicle, x and y are the cartesian coordinates of the center of the mass. When ignoring the effects of the roll, pitch, and heave, the motion can be simplified with sway, surge and yaw as follows: m u u˙ − m v vr + du u = τu m v v˙ + m u ur + dv v = 0 m r r˙ − m uv uv + dr r = τr

(2)

where m u , m v , m r and m uv = m u − m v , are components of the mass and hydrodynamic added mass. The du , dv and dr denote the capture hydrodynamic damping effects. The extra force in surge and the external warping force of the vehicle can be expressed with τu and τr , respectively.

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2.2 Problem Formulation The USV gain surge force and yaw torque from thrusters and rudder on the quarter. The sway force is zero because of no side thruster, which means that lateral velocity vr cannot be controlled directly. So, we design formation control scheme using two steps: (a) making each converge to desired initial position and (b) tuning surge speed of each USV to make them achieve coordination control goal.

3 Controller Design for USVs 3.1 First Stage Control of Single USV In this section, the controller for single is designed. The dynamic model can be simplified with the following input changes [13], ⎧ ⎪ ⎨ u˙ = τu v˙ = m1v (−m u ur − dv v) ⎪ ⎩ r˙ = τ r

(3)

For convenience, new coordinate transformation with nonholonomic constraints has been proposed. (x0i , y0i ) denotes the desired initial position of the ith USV, then the coordinate transformation can be introduced as follows, x = x − x0 , y = y − y0 ⎧ ˙ x0 ) = u cos ψ − v sin ψ ⎨ (x + ˙ y0 ) = u sin ψ + v cos ψ (y + ⎩ ϕ˙ = r ⎧ ⎨ u˙ = τu v˙ = −αur − βv ⎩ r˙ = τr

(4)

(5)

(6)

where α = m u /m v , β = dv /m v . Remark 1 lim (x, y) = (0, 0) imply that lim (x, y) = (x0 , y0 ). x→∞ x→∞ As the lemma of coordinate transformation in [12, 14], following state and input transformation can be further introduced.

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u 1 = − βα τ u + βα (x1 + x4 ) − x2 x6 + β1 x5 x6 u2 = τ r ⎧ x1 = x cos ψ + y sin ψ ⎪ ⎪ ⎪ ⎪ ⎪ x2 = −x sin ψ + y cos ψ + β1 v ⎪ ⎪ ⎨ x3 = ψ α ⎪ x 4 = − β u − x1 ⎪ ⎪ ⎪ ⎪ ⎪ x5 = v ⎪ ⎩ x6 = r

(7)

(8)

Then two cascade systems can be obtained as follows, 

x˙2 = x4 x6 x˙4 = u 1  x˙3 = x6 x˙6 = u 2

(9) (10)

Therefore, the control target is to make the x2 , x3 , x4 , x6 asymptotically coverage to zero in finite time. Remark 2 x1 , x5 will asymptote to zero when x2 , x3 , x4 , x6 trend to zero in finite time. Hence, the stabilization problem in (7), (8) is equal to that in system (1), (2). As the transformation of [τu , τr ]T and [τ u , τ r ]T is invertible, Eq. (8) is also invertible, so just need to design [u 1 , u 2 ]T . That is to say, when x1 , x2 , x3 , x4 , x5 asymptote to zero, (x, y, ψ, u, v, r ) will asymptote to (x0 , y0 , 0, 0, 0, 0) too. Based on the conditions above, the adding a power integrator technique [15, 16] can be used to design the following input control. 7/5 7/5

u1 =

−(k1 + k2 + 1)(C x6 x4 C x6

+ 27/5 x2 )3/7

, u2 = 0

(11)

Given x6 (0) = 0 and input u 2 = 0, x6 (t) will be a nonzero constant value, t ∈ [0, T0 ], correspondingly, Eq. (12) can be got 

x˙2 = C x6 x4 x˙4 = u 1

(12)

For convenience, variables can be defined as x 4 = C x6 x4 , u 1 = C x6 u 1 , then (12) can be transformed as x˙2 = x 4 x˙ 4 = u 1

(13)

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Consider the following positive definite Lyapunov function V1 =

1 2 x 2 2

(14)

V˙1 = x2 · x˙2 = x2 (x 4 − x ∗4 ) + x2 x ∗4 = x2 (x 4 − x ∗4 ) − 2ε1

12/7

(15)

with x ∗4 = −2x2 = −2ε1 . Construction technique of strict Lyapunov functions in [12] is adopted to determine stability of our system. Consider the function 5/7

5/7

V2 (x2 , x 4 ) = V1 (x2 ) + W2 (x2 , x 4 ) with W2 (x2 , x 4 ) = Satisfies

 x4 x ∗4

(16)

(s 5/7 −(x ∗4 )5/7 )9/7 ds, ε2 = x 4 − (x ∗4 )7/5 , V2 ≤ 2(ε12 + ε22 ). 7/5

∂ W2 ˙ ∂ W2 12/7 x4 + x˙2 V˙2 = −2ε1 + ε1 (x4 − x ∗4 ) + ∂x4 ∂ x2 =

12/7 −2ε1

+ ε1 (x4 −

x ∗4 )

+

9/7 ε2 u 1

9 ∂(x ∗5 4 ) − 7 ∂ x2

x 4

∗7/5 2/7

(s 7/5 − x 4

)

ds

(17)

x ∗4

Reference to the conclusion in [12], following Eq. (18) can be derived. ε1 (x4 − x ∗4 ) ≤

1 12/7 1 12/7 12/7 ∂ W2 12/7 ε1 + k1 ε2 x˙2 ≤ ε1 + k2 ε2 2 ∂ x2 2

(18)

When k 1 = 2.7289; k 2 = 51.5613; then Eq. (18) is substituted into (12), and Eqs. (20) can be derived. 12/7 9/7 12/7 V˙2 ≤ −ε1 + ε2 u 1 + (k1 + k2 )ε2

(19)

6/7 12/7 12/7 V˙2 + 41 V2 = −(ε1 + ε2 ) ≤ 0, 6/7 V˙2 ≤ − 41 V2

(20)

Reference the lemma (21), V˙ (x) ≤ −εV α (x), x = 0, T (x0 ) ≤ V 1−α (x0 )/(ε(1 − α)) 1/7

(21)

t1 can be derived. When t1 = 28V2 (x2 (0), x4 (0)), x2 (t), x4 (t) can asymptote to zero. As x2 , x4 are bounded in finite time, and that x˙3 = x6 and x6 is constant, x3 , x6

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can be deduced to be bounded. When t ≥ t1 , similar control law can be designed as above to make (x3 , x6 ) asymptote to zero. 1/7

t2 = 28V2 (x3 (0), x6 (0))

(22)

So the conclusion can be drawn that the total convergence time consists of two parts. After the time t (t = t1 + t2 ), each USV arrives to the desired initial position, then the cooperation control begins.

3.2 Second Stage for USV Formation When each USV has reached the desired initial position, formation cooperative control law [17, 18] should be devised to make USVs move in formation.

3.2.1

Surge Control

The USV is only equipped with propellers and rudder on the quarter. Hence, it is an underactuated system and only can be actuated in surge and yaw. Considering the model of USV, u˙ i = τ ui

(23)

Therefore, the control input as follows can be designed, τ ui = −



ai j (u i − u j − u)

(24)

j∈Ni

where ai j is scale factor and u is constant. The control scheme is distributed. The proof can be seen in [19].

3.2.2

Yaw Control

A control law is devised for yaw control τ ri , thereby guarantee ψ asymptote ψ0 exponentially. Hence, the direction of the formation can keep consistent with the leader [20, 21]. Considering the model of USV, ψ˙ = r r˙ = τ r

(25)

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The input control law can be devised as Eq. (26). Different from the surge control above, the scheme of the yaw and angular velocity is a double-integrator control law. ai j , bi j are the proportion of the yaw and angular velocity, respectively. The proof can be seen in [19]. τ ri = −



ai j [(ψi − ψ j )] −

j∈Ni



bi j [(ri − r j )] − k(t)

(26)

j∈Ni

4 Simulation Results Simulation has been made to verify the effectiveness of our scheme. All the USVs are supposed to have the same model parameters, which are given as follows. All the USVs’ initial conditions are listed in Table 1. M = diag[25.8, 33.8, 2.76] ⎡

⎤ 0 0 −33.8v C =⎣ 0 0 25.8u ⎦ 33.8v −25.8u 0

Table 1 initial conditions and desired states of the USVs

⎡ D=⎣

⎤

12 + 2.5|u|

Initial states

17 + 4.5|v|

⎦ 0.5 + 0.1|r |

USV = [x, y, ψ, u, v, r ] USV1 = [0, 20, 0.11, 0, 0, 0.17] USV2 = [0, 5, 0.21, 0, 0, 0.27] USV3 = [0, −20, 0.31, 0, 0, 0.37]

Desired states before formation

USV1[10, 10, 0, 1, 0, 0] USV2[20, 0, 0, 1, 0, 0] USV3[10, −10, 0, 1, 0, 0]

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In order to illustrate convergence, some setting parameters are t = 18 s, k 1 = 2.7289, k 2 = 51.5613, ai j = bi j = 1. Simulation results shown as follows: trajectories in axis x and y illustrated in Fig. 1a, b, respectively. Direction and surge velocity illustrated in Fig. 1c, d. Sway velocity and angular velocity illustrated in Fig. 1e, f. Fig. 1g shows the xy-trajectories of each vessel.

(a)

x-trajectories

(b) y-trajectories

(c) direction of the vehicle

(d) surge velocity

(e) sway velocity

(f) angular velocity

(g)

xy-trajectories

Fig. 1 Simulation results of the formation of the USVs

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5 Conclusion This paper proposed a two-stage control scheme to achieve formation control. Distributed control laws for single-integrator, double-integrator, and model of USV have been presented and proved to be globally stable. It should be mentioned that the interference factors such as delay and noise, have been ignored. This can be a subject for further research. Acknowledgements Supported by Natural Science Fund for Colleges and Universities In Jiangsu Province (18KJB520010) and Natural Science Foundation of Jiangsu Province (BK20180988).

References 1. Qin, J.H.: Recent advances in consensus of multi-agent systems: a brief survey. IEEE Trans. Ind. Electron. (2018) 2. Sun, Z.Y.: Distributed stabilization control of rigid formations with prescribed orientation. Automatica 78, 250–257 (2017) 3. Yu, X., Liu, L.: Distributed formation control of nonholonomic vehicles subject to velocity constraints. IEEE Trans. Industr. Electron. 63, 234–242 (2016) 4. Lu, X.Q., Lu, R.Q, Chen, S.H.: Finite-time distributed tracking control for multi-agent systems with a virtual leader. IEEE Trans. Circuits Systems–I: Regul. Pap. 60, 63–71(2013) 5. Arrichiello, F., Chiaverini, S., Fossen, T.I.: Formation control of marine surface vessels using the null-space-based behavior control. Group Coop. Control 336, 1–19 (2006) 6. Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. Automatic 49(9), 1465–1476 (2004) 7. Børhaug, E., Pavlov, A., Pettersen, K.Y.: Cross-track formation control of underactuated autonomous underwater vehicles. Group Coord. Coop. Control. 336, 35–54 (2006) 8. Wang, J., Liu, J.Y.: Formation control of unmanned surface vehicles with vision sensor constraints. In: OCEANS- MTS/IEEE Washington (2015) 9. Sun, Z.J.: Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation. ISA Trans. 72, 15–24 (2018) 10. Peng, Z.H., Wang, D.: Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics. IEEE Trans. Control Syst. Technol. 21, 334–342 (2013) 11. Peng, C.L., Wang, T.: An improved energy-aware and self-adaptive deployment method for autonomous underwater vehicles. Int. J. Model., Identif. Control. 31, 182–192 (2019) 12. Huang, X.Q., Lin, W.: Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41, 881–888 (2005) 13. Mazenc, F., Pettersen, K.: Global uniform asymptotic stabilization of an underactuated surface vessel. IEEE Trans. Autom. Control. 47, 1579–1762 (2002) 14. Do, K.D., Pan, J.: Global tracking control of underactuated ships with nonzero off-diagonal terms in their system matrices. Automatica 41, 87–95 (2005) 15. Ma, B.L.: Global asymptotic trajectory tracking and point stabilization of asymmetric underactuated ships with non-diagonal inertia/damping matrices. Int. J. Adv. Rob. Syst. 10, 1–9 (2013) 16. Jiang, B.Y., Li, C.J.: Finite-time output feedback attitude control for spacecraft using “adding a power integrator” technique. Aerosp. Sci. Technol. 66, 342–354 (2017) 17. Mehrjerdi, H., Ghommam, J., Saad, M.: Nonlinear coordination control for a group of mobile robots using a virtual structure. Mechatronics 21, 1147–1155 (2011)

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18. Lien, C.H., Vaidyanathan, S.: Robust mixed performance for uncertain Takagi-Sugeno fuzzy time-delay systems with linear fractional perturbations. Int. J. Model., Identif. Control. (IJMIC) 31, 193–203 (2019) 19. Ren, W., Beard, R.W.: Distributed Consensus in Multi-vehicle Cooperation Control. Springer, Berlin (2008) 20. Wang, J.H.: Combining recursive projection and dynamic programming technique in multi UAVs formation anomaly detection. Int. J. Model., Identif. Control. (IJMIC) 31, 53–61 (2019) 21. Wang, N.: Yaw-guided trajectory tracking control of an asymmetric underactuated surface vehicle. IEEE Trans. Ind. Inform. (2018)

Research on 3D Space Target Following Method of Mobile Robot Based on Binocular Vision Xitong Zhao, Lei Cheng, Rui Peng, Chan Li, Xiaoqi Nong, Huaiyu Wu, Ling Xiong and Yang Chen

Abstract In order to solve the problem of the target following in 3D (threedimensional) space, the KCF and SGBM fusion algorithm is proposed. In this method, the position information of the target in the camera image is obtained by KCF algorithm, the depth information of the target is calculated by SGBM algorithm, and the three-dimensional coordinate of the target in camera coordinate system is determined. The binocular vision system is set on the mobile robot, and the mobile robot achieves target following through velocity information and angular velocity information. Experiments in different indoor environments show that the algorithm has low hardware requirements, good real-time performance, and high precision. It is suitable for target tracking by a robot in three-dimensional space. Keywords Binocular vision · KCF algorithm · SGBM algorithm · Three-dimensional space · Target follow

1 Introduction Nearly all of the modern intelligent mobile robot systems use visual technology. Wu et al. [1] proposed a computer vision navigation method for mobile robot tracking, which can realize target recognition, distance estimation, and location. Reference [2] explored how the robot adapts itself to an open environment according to the binocular stereo vision system and makes full use of its own intelligent computing method to realize independent and accurate positioning and to master autonomous control without human participation. An independent visual servo control system and tracking navigation function are realized. David et al. [3] proposed a minimum output sum of squared error (MOSSE) filtering algorithm. MOSSE filter is based on an adaptive training method. It only needs one frame of an image to produce a X. Zhao · L. Cheng (B) · R. Peng · C. Li · X. Nong · H. Wu · L. Xiong · Y. Chen Engineering Research Center for Metallurgical Automation and Measurement Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_96

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stable correlation filter because of its robustness and computational efficiency. Target tracking based on correlation filtering has been paid more and more attention in the field of research. Qi et al. [4] proposed a region Markov Random Field (MRF) segmentation and tracking method based on adaptive weights, which uses the spatial correlation of adjacent pixels to adaptively update the parameters in the capability function of the system. Based on the feature of the gray histogram of the target, the feature template of the piecewise integral histogram was established, and the segmentation and tracking of partial occlusion and light change were realized based on Kalman filtering algorithm. In reference [5], a method of detecting depth information based on the binocular salient region is presented. The error map is calculated by using the deviation of the left and right images, and the chroma is used. The color space of saturation and intensity and mean shift algorithm are used to decompose the image. In recent years, because computer hardware technology is getting better and better, many people use the deep learning method to track the target. Deng et al. [6] proposed a real-time identification method for explosives by selecting the target position of explosives from the grey-scale image and using Kernelised Correlation Filters (KCF) tracking algorithm of kernel correlation filter and distance constraint. Faten et al. [7] proposed a new approach for solving the problem of mobile robot navigation in dynamic environment based on tangent circle algorithm. Danelljan et al. [8] proposed the continuous convolution operators for visual tracking (CCOT). The feature images with different resolution can be used as the input of the filter, so that the traditional features and depth features can be deeply combined. Finally, multiple responses are fused to obtain the estimated position of the target. Based on the idea of transfer learning, using the partial structure of VGG-M. Nam et al. [9] proposed a multi-domain convolution neural network (MDNet), which has high accuracy but poor real-time performance. From the above, we can see that there are some problems in the traditional target tracking algorithm: (1) if the background information is not taken into account, the tracking failure is easy to occur under the interference of object occlusion, illumination change and motion blur. (2) the tracking algorithm cannot meet the requirement of real-time because of its slow execution speed. In recent years, the method of target tracking with the aid of deep learning has solved the problem of traditional target tracking algorithm to a certain extent and has achieved great success, but it needs a large amount of work, such as data collection, calibration and so on. The hardware is demanding and the algorithm is complex. Therefore, based on low-cost purposes, this paper proposes a 3D object-following method for the mobile robot based on binocular vision [10], which combines KCF algorithm with SGBM algorithm. This method has high precision and low hardware requirement. Moreover, the computational complexity of the algorithm is low and the execution efficiency is high.

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2 Binocular Vision Principle The binocular vision system comes from the human visual structure. It can be understood that the camera replaces the human eye and the computer replaces the human brain. The binocular vision in this paper consists of two cameras mounted on the same axis with the same performance. Two images of the same scene are collected at the same time from different angles, the parallax between them is calculated, and the 3D geometric information of the object is recovered based on the parallax principle.

2.1 Mathematical Model of Binocular Vision Measurement As shown in Fig. 1, For any point P in the space projected from the angle of the left camera the image point of the image is P1 but the three-dimensional position of P cannot be determined by P1 . In fact, any point on the line after imaging can be regarded as P1 . Therefore, according to the position of P1 , we can only know that the space point P is on the P P1 connection, and cannot get its exact position. If the left and right cameras project point P simultaneously, and the image point P1 on the left camera and the image point P2 on the right camera are the image points of the same point P in space, then the position of the P point is only certain, which is the intersection of the ray P P1 and P P2 . The distance between the projection centers of the two cameras is the baseline distance b, and the camera focal length is f. The corresponding coordinates of a point P in the left camera image and the right camera image in the space are P1 (u 1 , v1 ) and P2 (u 2 , v2 ) respectively. Because the two cameras are on the same plane, Then the point P has the same vertical coordinates in the camera image, which means v1 = v2 , derived from trigonometric relations: Baseline distance b

xc yc

zc

Focal length f

u

O1

Left camera image v

P1 (u1 , v1 )

O2

P2 (u 2 , v2 )

v

P( xc , yc , zc ) Fig. 1 Binocular vision ranging model

u

Right camera image

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u1 = f

xc zc

(1)

(xc − b) zc yc v1 = v2 = f zc

u2 = f

(2) (3)

Parallax d is defined as the difference between the transverse coordinates of the left and right camera images, namely: d = u1 − u2 =

f ·b zc

(4)

As a result, the coordinates of a point P in the left camera coordinate system can be calculated as follows: ⎧ b·u ⎨ xc = d 1 (5) y = b·v1 ⎩ c b·df zc = d Because the two cameras are on the same horizontal plane, zc is the distance between the point P and the camera.

2.2 Mathematical Model of Binocular Vision Measurement The realization of binocular stereo vision technology [11] can be divided into the following steps: (1) image acquisition, (2) image processing, (3) stereo matching, (4) 3D reconstruction. In these steps, matching is a key technology, its advantages and disadvantages are directly related to the quality of subsequent results. The key of the image matching is to find the effective matching method, and the matching speed of the algorithm is fast, the precision is high, the probability is high, and the method has good real-time performance. In this paper, SGBM algorithm is used to realize stereo matching. As a semi-global matching algorithm, the binocular stereo matching algorithm is better than the local matching algorithm. The parallax image is obtained by matching the left and right camera images using SGBM algorithm, then the depth image and depth information are obtained. The core steps of SGBM algorithm are as follows: (1) selecting matching primitive; (2) Pixel-by-pixel matching calculation: (3) Around point P, eight paths are set at 45° interval to calculate the minimum cost path; (4) Eliminate mismatching.

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3 3D Object Following Method 3.1 2D Planar Target Tracking Algorithm In order to realize three-dimensional spatial target tracking, 2D (two-dimensional) image tracking is first needed, and then three-dimensional tracking is carried out by combining depth information. Two-dimensional image tracking, there are many classical target tracking algorithms, such as: TLD [12], Struck [13], CT and KCF [14]. However, in many target tracking algorithms, the performance of KCF in all aspects is amazing. In terms of average accuracy, the accuracy of KCF was 73.2%, while that of Struck was 65.6%, that of TLD was 60.8%, and that of CT was only 40.6%. KCF is far ahead of the FPS, and the FPS of KCF is 172, while the FPS of the CT, TLD and Struck is 64, 28, 20, respectively. The choice of KCF as the target tracking algorithm can make the system more efficient and meet the needs of people. The steps of the KCF algorithm are as follows: The method of ridge regression is used in training [15, 16]. If the training sample set is (xi , yi ), the linear regression function is as follows: f (xi ) = ω T xi

(6)

Then the optimization of the algorithm can be solved by the least square method. min ω



2

[ f (xi ) − yi ]2 + λω

(7)

i

The matrix form is as follows: minX ω − y2 + λω2 ω

(8)

Where each row of X represents a vector and y is a column vector. Let the derivative be 0, and we can get:  −1 T ω = X T X + λI X y

(9)

In Formula (9), I is the unit matrix. All the training samples in KCF are based on the cyclic displacement of the target sample. The displacement of the sampling window shown in Fig. 2. Assuming the original graph matrix x = [x1 , x2 , . . . , xn ]T , the cyclic shift T  Q 1 = xn , x1 , x2 , . . . , xn−1 can be obtained. For a two-dimensional image, the x and y axes may be cycled respectively in order to achieve movement of the various orientations. Therefore, the cyclic matrix C(x) generated by x is obtained by multiplying the permutation matrix.

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(a) Artwork master

(b) Displacement once

(c) Displacement twice

Fig. 2 Displacement of the sampling window

C(x) matrix has the property of diagonalization in Fourier space. If the following Fourier diagonalization equation is substituted for ridge regression, there is the following formula: X = Fdiag(x)F ˆ H

(10)

In Formula 10: the value of x corresponding to√the Fourier change of the generated X vector (that is, the first-row matrix of X); xˆ = n F x, F is discrete Fourier matrix; F H is the Hermitian conjugation of F. After a series of transformations, the following ω can be obtained:





ω=

xˆ  yˆ xˆ  xˆ + λ

(11)

According to the Fourier space transformation, there is the following formula: ω = F −1 (ω)

(12)

In Formula (12), F −1 is an inverse transformation.

3.2 3D Space Object Tracking Method The depth information is obtained by SGBM algorithm, and the position coordinates in the two-dimensional image are obtained by KCF algorithm. Therefore, the fusion of KCF and SGBM algorithm is used to realize 3D spatial target tracking. After the target is tracked by using the KCF algorithm, the image coordinates of the center point of the target are obtained, and then the three-dimensional coordinates of the target in the environment are obtained according to the SGBM algorithm to realize the tracking and location of the moving object. The algorithm flow chart is shown in Fig. 3. Firstly, the target region is selected with the mouse and the real-

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Binocular image acquisition

Target selection

SGBM gets target depth information

KCF tracks the position of the target in the image

3D coordinates in camera coordinate system

Fig. 3 Target location and tracking of binocular camera

time tracking of the target is carried out by KCF algorithm to solve the problem of target loss. The image coordinates of the center point of the target are calculated by using the tracked target region. Then the 3D coordinates of the target in the camera coordinate system are obtained according to the SGBM algorithm.

3.3 3D Space Object Following Method On the basis of Sect. 3.2, we have obtained the three-dimensional coordinates of the object, which can be combined with the motion control of the robot chassis to follow and ensure that the target object is always in the center of the image. The process of following the specific objectives is as follows: First, the image is captured by the camera, then the following target is selected in the image, and then the two adjacent frames of the image are matched. Then the KCF and SGBM algorithm are fused to obtain the depth information zc of the target and the pixel offset s, which is relative to the center point of the image. The velocity information v of the robot chassis is calculated by depth information zc , and the angular velocity information ω of the robot chassis is calculated by pixel offset s. The distance between the robot and the target object is set to be zc . The maximum value is z max and the minimum value is z min . The speed of the robot is set to v, the maximum value is vmax , and the minimum value is vmin . The pixel offset of the target relative to the center point of the image is set to s (with the right offset as an example), the maximum value is smax , and the minimum value is smin . The angular velocity of the robot is set to ω, the maximum value is ωmax , and the minimum value is ωmin . Considering the actual motion of the robot, in order to make the motion control of the robot smooth and stable, we distribute the motion state of the robot evenly through

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theoretical analysis and practical testing. The following expressions for the motion state of the robot are given: ⎧ −vmax + z max × zc × k, 0 < z c < z min ⎪ ⎪ ⎨ 0, z c = z min v= ⎪ z c × k + h, z min < z c < z max ⎪ ⎩ vmax , z c > z max

(13)

In Formula (13), k = (vmax − vmin )/(z max − z min ), h = vmin − k × z min . ⎧ ωmin , 0 < s < smin ⎪ ⎪ ⎨ s × m + n, smin < s < smax ω= ⎪ ω , s > smax ⎪ ⎩ max 0, s = 0

(14)

In Formula (14), m = (ωmax − ωmin )/(smax − smin ), n = ωmin − m × smin . The motion of the robot is controlled by velocity information and angular velocity information. The motion control of the robot is smooth and stable through the uniform distribution of velocity information and angular velocity information. The algorithm diagram is shown in Fig. 4.

4 Experiment and Analysis In order to show the effectiveness and feasibility of the proposed follow-up method, we compare the actual experiments in different scenarios and analyze the experimental results in detail.

4.1 Experimental Installation The hardware portion of the system consists of the following devices: (1) Binocular camera: the binocular camera splits together two JA-100 monocular cameras, then calibrates them for their own binocular calibration. (2) Upper computer: Acer V5-471G notebook computer. The ubutun14.04 operating system is installed in the upper computer, and ROS system is run. (3) Omni-directional mobile platform: the omni-directional mobile platform CAonimar, consists of four omni-wheel, four drivers, four motors, inertial navigation module mpu6050 and an arduino master board. The overall system real-time diagram is shown in Fig. 5.

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Select a follow Target in an image

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Obtaining Pixel offset s by KCF algorithm

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Calculating robot speed v and angular velocity w Robot following response

Fig. 5 Physical diagram of whole experimental equipment

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4.2 Experimental and Analysis In this paper, the experiments of two scenarios are designed and tested for many times. The experimental diagram in different scenarios is shown in Fig. 6. The schematic of the different scenarios shown in Fig. 7. In order to analyze the real effect of the algorithm, we define the positioning error as follows: (15) εe = (xˆt − xt )2 + ( yˆt − yt )2   Where xˆt , yˆt is the ideal position calculated under a certain path, and (xt , yt ) is the real position of the robot. The (a) of scene is a 10-m-long straight line, which mainly tests the positioning accuracy of the follow-up method in a single environment. From the experimental results of the running trajectory, it can be seen that the maximum horizontal offset of

(a) Straight path

(b) Broken line path

Fig. 6 Experimental diagrams in different scenarios

Fig. 7 Schematics of different scenarios experiments

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the robot is 0.2 m. According to the error analysis, it can be seen that the maximum error of the real position and the ideal position of the robot is 0.8 m at the same time, and the final error converges to 0.2 m. The experimental results and error analysis are shown in Figs. 8 and 9. The (b) of the scene is a broken line of 15 m. This paper mainly tests the positioning accuracy of the following method in the changing environment. From the experimental results of the running trajectory, it can be seen that the maximum horizontal offset of the robot is 0.2 m, and the maximum vertical offset is 0.2 m. According to the error analysis, it can be seen that the maximum error of the real position and the ideal position of the robot is 0.9 m at the same time, and the final error converges to 0.2 m. The experimental results and error analysis are shown in Figs. 10 and 11. Fig. 8 Straight line following path diagram

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According to the experimental results of the above two groups of different indoor scenes and the comparison of the errors, it can be seen that the following algorithm proposed in this paper has an ideal follow-up effect, and the error fluctuation range is more stable and the positioning accuracy is better in all kinds of scenes. However, there are still some problems in the stability of follow-up, and some of the time errors are large.

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5 Conclusion This paper presents a 3D object tracking method for mobile robots based on binocular vision. The KCF algorithm and the SGBM algorithm are coupled together with the mobile platform to achieve 3D spatial target tracking. Compared with other methods, it is simpler and more convenient. Practical experiments also show that the proposed method has high precision, low hardware requirements, and low computational complexity, but there are still some problems. For example, there is a slight drift at a corner point or as the following distance increases. Therefore, in the future, we need to further improve and optimize this. Acknowledgements This work is supported by four Projects from National Natural Science Foundation of China under grant No. 60705035, No. 61075087, No. 61573263, No. 61273188, National Key Research and Development Program of China under Grant No. 2017YFC08065035-05, Hubei Province Science and Technology Support Project under Grant 2015BAA018, Scientific Research Plan Key Project of Hubei Provincial Department of Education (D20131105), and Zhejiang Open Foundation of the Most Important Subjects, also supported by Zhejiang Provincial Natural Science Foundation under Grant LY16F030007.

References 1. Wu, J., Abdulla, H.M.D., Snasel, V.: Application of binocular vision and diamond search technology in computer vision navigation. In: 2009 International Conference on Intelligent Networking and Collaborative Systems, pp. 87–92 (2009) 2. Lulio, L.C., Tronco, M.L., Porto, A.J.V.: ANN statistical image recognition method for computer vision in agricultural mobile robot navigation. In: 2010 IEEE International Conference on Mechatronics and Automation, pp. 1771–1776 (2010) 3. David, S.B., Beveridge, J.R., Bruce, A.D., Lui, Y.M.: Visual object tracking using adaptive correlation filters. In: Computer Society Conference on Computer Vision and Pattern Recognition, pp. 171–173 (2010) 4. Qi, M.B., Yang, L.B., Jiang, J.G.: MRF segmentation and tracking method for adaptive weights. Chin. J. Image Graph. 16(4), 572–578 (2011) 5. Mur-Artal, R., Tardós, J.D.: ORB-SLAM2: an open-source SLAM system for monocular, stereo, and RGB-D cameras. IEEE Trans. Rob. 33(5), 1255–1262 (2016) 6. Faten, C., Chokri, R., Nabil, D.: Mobile robot navigation based on tangent circle algorithm. Int. J. Comput. Appl. Technol. 59(1), 31–42 (2019) 7. Deng, W., Zhang, H., Li, Y.B., Gao, F.: Research on target recognition and path planning for EOD robot. Int. J. Comput. Appl. Technol. 57(1), 325–333 (2018) 8. Danelljan, M., Robinson, A., Khan, F.S., et al.: Beyond correlation filters: learning continuous convolution operators for visual tracking. In: 14th European Conference on Computer Vision, pp. 472–488 (2016) 9. Nam, H., Han, B.: Learning multi-domain convolutional neural networks for visual tracking. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition, pp. 4293–4302 (2016) 10. Ding, D.J., Wang, C.G., Zhao, X.L.: Robot autonomous positioning and obstacle detection based on vision. J. Comput. Appl. 1–8 (2019) 11. Ma, L., Sun, M.Z., Huang, C., et al.: Fast binocular stereo matching algorithm based on strong similarity detection. J. Comput. Eng. Appl. 6, 193–197 (2018)

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12. Zhang, J., Xiong, X.Y., Bao, Y.B.: TLD target tracking algorithm based on KCF similarity. J. Comput. Eng. Sci. 41(02), 293–301 (2019) 13. Xiao, E.L., Han, C.: An improved struck algorithm for automatic real-time facial tracking. J. Electron. Technol. 29(03), 42–47 (2016) 14. Wang, D.P., Xie, Y.: Target occlusion detection algorithm based on KCF. J. Inf. Technol. Netw. Secur. 37(12), 39–43 (2018) 15. Wang, J.P., Lu, H.C., Li, X.H., Tong, N., Liu, W.: Saliency detection via background and foreground seed selection. Neurocomputing 152, 359–368 (2015) 16. Kim, J., Han, D., Tai, Y.W., Kim, J.: Salient region detection via high-dimensional color transform. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 883–890 (2014)

Control Allocation Reconstruction of Launch Vehicle Based on Neural Network Zhu Li, Yaokun Zhang, Zhaowei Liang, Zhongtao Cheng, Lei Liu and Ye Yang

Abstract After the single engine thrust reduction fault of the launch vehicle, if the conventional fixed control allocation method is used, the actual control torque generated by the engine is difficult to meet the expected torque generated by the basic controller. Therefore, this paper proposes a neural network based control allocation method. The method learns the pseudo-inverse allocation method, so that the actual control torque can well track the desired control torque. Finally, the proposed neural network control allocation method is simulated and verified. The results show the feasibility and effectiveness of the proposed method. Keywords Launch vehicle · Thrust reduction fault · Neural network control allocation · Pseudo-inverse method

1 Introduction Control allocation is a key method to solve the redundant control of aircraft with multiple actuators. When control surfaces or actuators are fault or actuator efficiency changes, it can be done redistributing the control instruction to reconfigure the control system, which no longer need to readjust the complex flight control law, and greatly reduces the difficulty of the design of the control system comparing with the traditional reconfiguration control methods [1]. The main methods of control allocation include: generalized inverse method, Daisy Chaining method, direct allocation method, mathematical programming method and adaptive method. Among them, there are many studies on generalized inverse method, mathematical programming method and adaptive method [2]. For Z. Li · Y. Zhang · Z. Liang · Z. Cheng · L. Liu (B) National Key Laboratory of Science and Technology on Multispectral Information Processing School of Artificial Intelligence and Automation, HUST, Wuhan 430074, China e-mail: [email protected] Y. Yang Science and Technology on Aerospace Intelligent Control Laboratory, Beijing Aerospace Automatic Control Institute, Beijing 100854, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_97

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example, literature [3] compares the performance of the control allocation method based on generalized inverse, direct allocation method and fixed point method applied to the flight control system with uncertainty. Literature [4] studies the input constraint problem of control allocation method based on pseudo inverse. The literature [5] proposed a composited integrated guidance and control (IGC) algorithm to tackle the problem of inaccuracy information. The literature [6] proposed a disturbance observer-based gain adaptation high-order sliding mode control method. For the launch vehicle control system with multiple engines, when the engine thrust reduction fault occurs, using fixed allocation method to allocate the equivalent oscillation angle instruction, the actual control torque generated by the engine cannot well meet the desired control torque. Aiming at this problem, use the methods of control allocation to reconfigure the control system. In this paper, the control allocation method based on BP neural network is used to solve the reconfiguration control problem of launch vehicle with thrust reduction fault. Compared with the mathematical programming method, the neural networkbased control allocation has the advantages of fast distribution speed and small calculation amount. Compared with the pseudo-inverse method, the pseudo-inverse method can not consider the physical constraints of the actuator. When the learning object of the neural network control allocation method is the control allocation method considering the actuator constraint, the neural network control allocation method will consider the actuator constraints. This paper mainly explores the learning ability of neural networks, so the pseudo-inverse control allocation method is used as the learning object of neural network.

2 Description of the Problem This paper takes a certain type of launch vehicle as the research object. As shown in Fig. 1, the first stage engine of the launch vehicle consists of four strap-on engines and two core engines, each with its longitudinal axis parallel to the longitudinal axis Fig. 1 Rear view of the rocket’s primary engine layout

x1

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of the rocket. Two of the core engines are in a diagonal layout, and both can be used for two-way cross swing, and the oscillation angles in different directions are respectively recorded as δxj1 , δxj2 , δxj3 , δxj4 . The four strap-on engines are distributed symmetrically around the rocket and can be tangentially oscillated. The oscillation angles in different directions are recorded as δzt1 , δzt2 , δzt3 , δzt4 . The direction of the arrow shown in the figure is the positive direction of each engine swing [7]. The rocket forms a control torque through each engine oscillation angle, that is, the control of the flight attitude is finally achieved by adjusting the eight oscillation angles of the engine. Generally, in the case of a rocket without failure, the oscillation angle control of each rocket engine is obtained by a fixed control allocation method. The total equivalent control oscillation angle of the pitch channel, the yaw channel and the roll channel is δφ , δ , δγ ; The equivalent control oscillation angle of the three channels of the strap-on engine is δφzt , δzt , δγzt ; The equivalent control oscillation angle of the three channels of the core engine is δφxj , δxj , δγxj . If the relationship between the total equivalent control oscillation angle command and the equivalent control oscillation angle command of the core engine and the strap-on engine is λ and 1. In general, set λ = 2. then: ⎧ ⎨ λδϕx j = δϕzt = δϕ λδ = δψ zt = δψ ⎩ ψxj λδγ x j = δγ zt = δγ

(1)

When using the fixed control allocation method, the oscillation angle control amount of each engine is obtained by: ⎧ ⎪ ⎪ δzt I = −δψ zt + δγ zt ⎨ δzt I I = −δϕzt + δγ zt ⎪ δ = δψ zt + δγ zt ⎪ ⎩ zt I I I δzt I V = δϕzt + δγ zt

⎧ ⎪ ⎪ δx j I = (−δψ x j + δγ x j ) ⎨ δx j I I = (−δϕx j + δγ x j ) , ⎪ = (δψ x j + δγ x j ) δ ⎪ ⎩ xjI I I δx j I V = (δϕx j + δγ x j )

(2)

When studying the influence of the engine thrust reduction fault on the rocket motion, the actual thrust of the engine under the thrust reduction fault is the partial value of the rated thrust, then: ⎧ Pzt1 ⎪ ⎪ ⎨ Pzt2 ⎪ P ⎪ ⎩ zt3 Pzt4

= k zt1 Pzt  = k zt2 Pzt Px j1 = k x j1 Px j , = k zt3 Pzt Px j2 = k x j2 Px j = k zt4 Pzt

(3)

Among them, Pzt , Pxj is the current rated thrust of the strap-on and core engine, Pzt1 ~ Pzt4 , Pxj1 , Pxj2 are the actual thrust values of each engine output after the failure; k zt1 ~ k zt4 , k xj1 , k xj2 are scale factors that reflect the magnitude of thrust reduction after engine failure. Taking the No. 1 strap-on engine as an example, as shown in Fig. 2,

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Fig. 2 Schematic diagram of thrust under engine thrust reduction failure

at the time t 0 , the engine has a thrust reduction failure, and the actual thrust rapidly drops to a certain fixed value [8]. Considering the engine thrust reduction failure, the actual control torque generated by the engine is:   MC X = −Pzt r zt k zt1 δzt I + k zt2 δzt I I + k zt3 δzt I I I + k zt4 δzt I V 1   − Px j r x j k x j1 δx j I + k x j2 δx j I I + k x j2 δx j I I I + k x j4 δx j I V     MCY = Pzt (X R − X Z ) k zt1 δzt I − k zt2 δzt I I I + Px j (X R − X Z ) k x j1 δx jt I − k x j2 δx j I I I 1     MC Z = Pzt (X R − X Z ) k zt2 δzt I I − k zt4 δzt I V + Px j (X R − X Z ) k x j2 δx j I I − k x j1 δx j I V 1

(4)

Among them, XR is the distance from the engine’s swing point to the theoretical tip of the rocket; XZ is the distance from the rocket’s centroid to the theoretical tip of the rocket; rzt is the distance from the rocker strap-on engine swing point to the longitudinal axis of the rocket; rxj is the distance from the rocker core engine swing point to the longitudinal axis of the rocket. When the thrust reduction fault occurs in a single engine of a launch vehicle, if the fixed control allocation method is used, the actual control torque generated by the launch vehicle engine will not meet the desired control torque generated by the basic controller. Therefore, control allocation reconstruction is required so that the actual control torque can track the desired control torque.

3 Neural Network Control Allocation Reconstruction Design The neural network can approximate continuous nonlinear functions with arbitrary precision and have the ability to adapt and self-learn for complex uncertain problems. Neural networks are widely used in system identification, system control, optimization calculation, and fault diagnosis and fault-tolerant control of control systems [9–13]. Therefore, the powerful data fitting ability of the neural network can be utilized to control the allocation of the launch vehicle under the condition of the thrust drop failure.

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3.1 Construction of Neural Networks In this paper, BP neural network is used to learn the control allocation data generated by pseudo-inverse method. The input-output mapping relationship is [14]: yi =

N2 j=1

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+ θωi , i = 1, . . . , N3

(5)

k=1

where k = 1, 2,…, N1 . Here, N1 , N2 , and N3 represent the number of neural network inputs, the number of hidden layer neurons, and the number of outputs. xk is the i-th element of the network input, and yi is the i-th element of the network output. σ(x) as a sigmoid excitation function is given by: 2  −1 σ (x) =  1 + e−2x

(6)

Designed neural network input:   x = δϕ δψ δγ k zt1 k zt2 k zt3 k zt4 k x j1 k x j2

(7)

Among them, δφ , δ , δγ are control commands generated by the PID controller. kzt1 , kzt2 , kzt3 , kzt4 , kxj1 , kxj2 are the degrees of thrust reduction of each engine. Neural network output:   y = δzt I δzt I I δzt I I I δzt I V δx j I δx j I I δx j I I I δx j I V

(8)

Among them, δztI , δztII , δztIII , δztIV , δxjI , δxjII , δxjIII , δxjIV are the oscillation angles of the respective engines. The number of hidden layer neurons in the designed neural network is 10, so the number of weights of the entire neural network is 188, including the threshold of neurons.

3.2 Learning of Neural Networks Because the main purpose of this paper is to verify the feasibility of neural network control allocation in the case of single engine thrust reduction of the launch vehicle, so just select a feasible control allocation method for learning. Therefore, the learning object of the neural network designed in this paper is based on the pseudo-inverse method. In order to realize the neural network control allocation under the single engine thrust fault, it is necessary to first obtain the control input and output data based on the pseudo-inverse method, that is, the control command generated by the PID controller and the oscillation angle of each engine under different fault

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conditions. In order to simplify the training process, only the data of the No. 1 core engine and the No. 2 core engine under different thrust reduction were selected, The choice is that the thrust of the No. 1 core engine is reduced by 0, 20, 40, 60, 80, 100% at 50 s, and the thrust of the No. 2 core engine is reduced by 0, 20% at 50 s, 40, 60, 80, 100%.

4 Simulation Results and Analysis The simulation process is as follows: the initial rocket pitch angle command is 90°, then gradually changes to 25° in 0–160 s, and maintains 25° to 165 s. During this time, the yaw angle, the roll angle command remains at 0°. Rocket strap-on engine oscillation angle range is −8° to 8°, core engine oscillation angle range is −6° to 6°. Based on the neural network learning data, the BP neural network control allocation reconstruction is simulated and verified. In order to verify the learning ability of neural network control allocation, the simulation situation needs to be different from the neural network training situation. Therefore, the simulation situation is that the thrust of the No. 1 core engine is reduced by 70%, and the thrust of the No. 2 core engine is reduced by 90%. 1. The Thrust of the No. 1 Core Engine is Reduced by 70% at 60 s Figure 3 shows the flight attitude angle of the launch vehicle generated by fixed allocation, pseudo-inverse allocation, and neural network allocation. Figure 4 shows the Z-axis desired control torque generated by the PID controller under different allocation methods, the Z-axis actual control torque generated by different allocation methods, and the difference between the desired torque and the actual control torque. 2. The Thrust of the No. 2 Core Engine is Reduced by 90% at 60 s Figure 5 shows the flight attitude angle of the launch vehicle generated by fixed allocation, pseudo-inverse allocation, and neural network allocation. Figure 6 shows

(a) Pitch angle error

(b) Yaw angle error

Fig. 3 Rocket attitude angle error diagram with 70% thrust reduction

(c) Roll angle error

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Fig. 4 Z-axis torque comparison diagram with 70% thrust reduction

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Fig. 6 Z-axis torque comparison diagram with 90% thrust reduction

the Z-axis desired control torque generated by the PID controller under different allocation methods, the Z-axis actual control torque generated by different allocation methods, and the difference between the desired torque and the actual control torque. It can be seen from Figs. 3 and 5 that the more severe the degree of the fault has an greater influence on the attitude angle. When using fixed allocation, the error of the attitude angle is greater than the error of using the neural network to control the allocation. It can be seen that the use of a neural network for control allocation is feasible and enables the launch vehicle to maintain a good flight state in the event of a fault. Moreover, the difference between the attitude angle error generated by

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the neural network control allocation and the attitude angle error generated by the pseudo-inverse control allocation is small, and it can be seen that the neural network has well learned the pseudo-inverse allocation method. It can be seen from Figs. 4 and 6 that after the failure occurs, if the fixed allocation is used, the actual torque generated by the engine cannot satisfy the desired torque generated by the control law, and the neural network allocation can better track the desired torque. Moreover, the difference between the torque error generated by the neural network allocation and the torque error generated by the pseudo-inverse allocation is small.

5 Conclusion The simulation results show that the control allocation based on neural network has better instruction tracking performance than the fixed allocation. And the neural network has a certain learning ability, and can learn the pseudo-inverse control allocation method. At the same time, after learning, it has good command tracking performance for unlearned fault conditions. It is foreseeable that the neural network will exhibit better instruction tracking performance when learning using a control allocation method that takes into account more factors. Acknowledgements This work was supported in part by the National Nature Science Foundation of China (Grant Nos. 61873319, 61803162 and 61573161).

References 1. Oppenheimer, M.W., Doman, D.B., Bolender, M.A.: Control allocation for over-actuated systems. In: Mediterranean Conference on Control & Automation (2006) 2. Johansen, T.A., Fossen, T.I.: Control allocation—a survey. J. Automatica. 49(5), 1087–1103 (2013) 3. Ma, J., Li, P., Li, W., et al.: Performance comparison of control allocation for aircraft with control effectiveness uncertainties. In: Asia Simulation conference 2008/the 7th International Conference on System Simulation and Scientific Computing (2008) 4. Hang, X., Duan, G.: A developed constrained control allocation approach based on pseudo inverse. In: Chinese Automation Congress. IEEE, New York (2018) 5. Ping, M., Denghui, Z., Songyan, W., et al.: Integrated guidance and control design method based on finite-time state observer. J. Syst. Eng. Electron. 29(6), 1251–1262 (2018) 6. Yin, X., Wang, B., Liu, L., Wang, Y.: Disturbance observer-based gain adaptation high-order sliding mode control of hypersonic vehicles. J. Aerosp. Sci. Technol. 89, 19–30 (2019) 7. Yanshen, W.: Attitude control technology of new-generation launch vehicles. J. Beijing Univ. Aeronaut. Astronaut. (2009) 8. Zhi-Xiang, W., Jia-wen, L., Dao-Kui, L.: Failure: simulation of thrust decline of launch vehicle based on six DOF model. J. Manned. Spaceflight. 23(5), 650–657 (2017)

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9. Huang, J., Qian, J., Liu, L., Wang, Y., Xiong, C., Ria, S.: Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator. J. Franklin Inst. 353, 2761–2782 (2016) 10. Wu, Y.C., Feng, J.W.: Development and application of artificial neural network (2018) 11. Yao, L., Wang, H.: Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model. Int. J. Model. Ident. Control 29(1), 22–30 (2018) 12. Han, Y., Yu, J., Liu, Z., et al.: Command filter-based adaptive neural control for permanent magnet synchronous motor stochastic nonlinear systems with input saturation. Int. J. Model. Ident. Control 30(1), 38–47 (2018) 13. Rahoui, A., Seddiki, H., Bechouche, A., et al.: Adaptive neural networks for AC voltage sensorless control of three-phase PWM rectifiers. Int. J. Model. Ident. Control 31(2), 139– 151 (2019) 14. Basheer, I.: Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Methods 43(1), 3–31 (2000)

An EEC Dual Channel Switching Algorithm Based on Engine Thrust Sensitivity Xiuqi Wang, Jie Shen and Zhongzhi Hu

Abstract In order to select the active control channel when the dual channel electronic engine controller (EEC) of aero-engine is faulty, a method to analyze the engine thrust sensitivity to input parameters based on the inverse model is proposed to compute a channel health level. Based on the health level, the channel switching logic under the conditions of “hard fault” and “soft fault” is designed and verified in a simulation platform. The simulation results show that under different faults, the EEC can perform channel switching based on the proposed method, which shall help to improve the safety and performance of the engine control system. Keywords Aero-engine · EEC · Dual channel switching · Inverse model

1 Introduction The operating environment of the aero-engine control system is harsh, and the reliability of a digital EEC is critical for the safety and performance of an aero-engine control system [1]. In addition to use of high-quality EEC components to improve the basic reliability of the system [2], fault-tolerant technology is often used in engineering to improve the system reliability [3]. The dual channel EEC, one in active control and the other in standby, is implemented by means of hardware redundancy. However, when an EEC channel fails, especially when both channels fail, it is necessary to establish a mechanism to evaluate the health level of the channels, based on which the active control channel is selected. At present, the commonly used method is to compare the measured residual value of the two channels with the set threshold. When the residual exceeds the threshold, X. Wang · J. Shen · Z. Hu (B) College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yu Dao Street, Qin Huai District, Nanjing, Jiangsu 210016, China e-mail: [email protected] X. Wang e-mail: [email protected] J. Shen e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_98

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the Kalman filter and other analytical methods are used to detect and isolate the fault and perform channel switching [4]. But if the residuals of both channels are within the specified threshold, it is impossible to judge which channel is better. Another method is to add another channel (Channel C) on the basis of two control channels (Channels A and B). The reliability of each channel is obtained by probability calculation method, and Channel C is used as a third-party analytical channel to provide a reference value for fault decision-making, and the channel with the least deviation from the reference value is chosen as the active control channel [5], but this method obviously increases system weight and cost. In fact, the main function of the aero-engine control system is to control the engine thrust. The effect of the thrust control directly affects the flight safety and performance of the aircraft. Therefore, the concept of thrust sensitivity is introduced to evaluate the influence of different sensor signals on the thrust control and therefore to compute the channel health level. Based on this, the EEC channels are evaluated and the channel switching logic is designed. The structure of this paper is as follows: Sect. 2 calculates and analyzes the thrust sensitivity to each parameter based on the inverse model; Sect. 3 introduces the proposed channel switching algorithm; Sect. 4 verifies the switching algorithm by simulation; Sect. 5 gives the conclusion. Definition of thrust sensitivity: The relative deviation of the thrust caused by the unit relative deviation of the closed-loop feedback sensor signal of the control system.

2 Model-Based Thrust Sensitivity Analysis 2.1 Inverse Engine Model JT9D engine model, as an illustrative example, is used for analysis and simulation and the related introduction can be referred to [6]. A typical control loop under the steady state conditions of an aero-engine is shown in Fig. 1. The steady state control law, whose input is the converted speed error and output is the converted fuel value, in the control loop, is designed based on a similar normalized linearization model. The

Fig. 1 Steady state control loop of aero-engine

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T2 and P2 sensor signals are used for the similar normalization of the fan speed and the calculation of real main fuel, the normalization formulas are shown in Eqs. (1) and (2). The sensor signals for engine feedback required by the steady state control law include N1, T2 and P2 , so the calculation and analysis of thrust sensitivity to the above three signals is needed.    N1 N1 / √ ∗ 100% PN1 = √ T2 T2 ds     Wf Wf / ∗ 100% PWf = √ √ P2 T2 P2 T2 ds 

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In this paper, the inverse engine model is used to estimate the deviation of the closed-loop feedback sensor signals, then the calculation deviation of main fuel and engine thrust are calculated, and the thrust sensitivity to each closed-loop feedback sensor signal is obtained. The so-called inverse model is to exchange the closedloop controlled parameters of the open-loop model with the corresponding control parameters of the open-loop model. For commercial turbofan engines, the inverse model controls the main fuel through fan speed or engine pressure ratio. The solving principle of the inverse model is shown in Eqs. (3)–(5) [7]:  Open-loop model:

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2.2 Calculation of the Engine Thrust Sensitivity The simulation structure for calculating thrust sensitivity using the JT9D inverse model is shown in Fig. 2. The input and output of the inverse model are similarly

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Fig. 2 Simulation structure for calculating thrust sensitivity by JT9D inverse model

normalized, and the speed normalization and fuel calculation process are added before and after the normalized JT9D inverse model. When calculating the thrust sensitivity to N1, T2 and P2 , the disturbance positions and the feedback positions of the three sensor signals in steady state control loop are same. Therefore, the normalized inverse model can be used to replace the steady state controller in the steady state control loop, and finally the engine thrust deviation and the thrust sensitivity are obtained. The deviation of N1 in the steady state control loop indicates that the actual speed signal is deviated. If it is not isolated, the thrust control will produce a steady state deviation. Because T2 and P2 are only used for conversion, the thrust will not be affected if the deviation of T2 and P2 is unchanged in the steady state of the engine. However, when deviation of T2 and P2 changes, it will disturb the calculated main fuel, and eventually disturb the thrust, resulting in dynamic deviation. In summary, it is necessary to separately analyze the steady state sensitivity and dynamic sensitivity when using the inverse model to calculate thrust sensitivity. In order to rank the sensitivity of thrust dynamic deviation of N1, T2 and P2 , the thrust dynamic deviation is calculated and analyzed separately. Firstly, in the steady state of N1 = 1441, the disturbances of N1, T2 and P2 with different amplitudes are made separately. Secondly, the disturbances of N1, T2 and P2 with 0.1% are made separately in the different engine operating conditions. The results are shown in Fig. 3. It can be seen from Fig. 3a that the dynamic thrust sensitivity to different parameters are constant when the engine operating conditions are constant, but the order is N1 > P2 > T2 . In Fig. 3b, it can also be concluded that the order of dynamic thrust sensitivity to each parameter under different engine operating conditions is N1 > P2 > T2 .

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3 Design of Channel Switching Algorithms 3.1 Simplified System Assumptions When sensor signal fails, the control system has a variety of fault-tolerant means to ensure the safe operation of the system. In order to facilitate channel switching simulation, the control system and its fault-tolerant system are simplified appropriately, including: a. Fault diagnosis is realized by BIT self-test. Sensor signal faults include signal failure “hard fault” and signal small amplitude shift “soft fault”. b. Consider the redundant signal voting. c. The control logic only considers the steady state control law with the fan speed as the control parameter. d. Circuit hardware disturbances are not considered when channel switching occurs. e. Analytical reconstruction and control law reconstruction are not considered.

3.2 Channel Switching Logic In order to simulate channel switching under EEC channel failure, the control loop needs to have the function of fault diagnosis and isolation, so it is necessary to design simple fault diagnosis and redundant signal voting logic. For channel switching logic, the active control channel is selected according to the thrust sensitivity to each sensor signal when the sensor signal has “hard fault”or “soft fault”. Channel Switching Logic under Hard Fault. “Hard fault” means that sensor signal failure occurs in EEC channel. In this case, the channel switching logic is as follows:

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a. First, the existence of a fault-free channel is judged. If so, the fault-free channel is chosen as the active control channel. b. If there are faults in both channels, it is judged whether the N1 fault states in the two channels are consistent. If they are inconsistent, the channel with no fault of N1 signal is selected as the active control channel. c. If the fault states of N1 signal in the two channels are consistent, the sum of the dynamic thrust sensitivity to T2 and P2 fault signals is calculated separately, and the channel with the smaller one is taken as the active control channel. Channel Switching Logic under Soft Fault. “Soft Fault” means that the EEC channel has a small amplitude shift of the sensor signal that the BIT cannot detect. N1 is the control target, whose sensor signal deviation will cause the steady state deviation of the thrust. Therefore, the steady state thrust deviation caused by the N1 deviation should be used as a main judgment indicator of the thrust control effect. In addition, the moment when the deviation of the parameters N1, T2 and P2 changes will cause dynamic thrust disturbance, so the dynamic thrust deviation can be used as the secondary judgment indicator of the thrust control effect. The absolute values of the thrust steady state deviations of Channels A and B are respectively defined as FAs and FBs ; the sum of the absolute values of the thrust dynamic deviations of T2 and P2 fault signals of Channels A and B are respectively defined as FAd and FBd . The channel switching logic is as follows: a. If |(FAs − FBs )/FAs | > ε, then compare the size of FAs and FBs , and take the channel with the smaller one as the active control channel. Reasonable selection of the value of ε can avoid repeated switching when judging steady state deviation. b. If |(FAs − FBs )/FAs | < ε, switch to the dynamic deviation judgment logic. c. If |(FAd − FBd )/FAd | > θ, then compare the size of FAd and FBd , and take the channel with the small one as the active control channel. Reasonable selection of the value of θ can avoid repeated switching when judging dynamic deviation. d. If |(FAd − FBd )/FAd | < θ, no switching is performed. Computing Flow for Channel Switching Logic. The calculation structure of the channel switching logic is shown in Fig. 4. The input of the airborne model is the fuel Fig. 4 Computing flow for dual channel EEC channel switching logic

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supply for output of the active control channel. The output N10 , T20 and P20 of the airborne model are used as reference values to calculate the signal deviation of the two channels. The inverse model calculates the thrust sensitivity to each parameter in this state according to N10 , T20 and P20 . The thrust online estimation modules of Channels A and B estimate the thrust control deviation of each channel according to the sensor signal deviation and thrust sensitivity. Finally, channel switching logic performs channel switching based on the “hard fault” information of the two channels and estimated thrust deviation.

4 Verification of the Switching Algorithms In order to simplify the problem, the fault condition of the sensor signal conditioning module in EEC is only be considered. In order to simulate a real system, a random error is superimposed on the sensor signal. Figure 5 shows the error band of the speed signal when the target speed is given as N1_dem = 2500 r/min, which is set to −0.1 to 0.1% [1]. The simulation in this paper is carried out on the CONTROL SYSTEM simulation platform built in reference [6], many other advanced control algorithms [8–10] can also be carried out on this platform.

4.1 Switching Without Fault When the sensor signal faults are not injected into the EEC channels, the N1 sensor signal and the active control channel selected are as shown in Fig. 6. The sign of the active control channel is “1” indicating that Channel A is the active control channel, and “2” indicating that Channel B is the active control channel. Fig. 5 Speed sensor signal diagram after superimposing errors

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It can be seen from Fig. 6 that in the case of “no fault”, the sensor error bands of Channels A and B are same, which is a normal error. The channel does not need to be switched, and the channel switching logic always takes Channel A as the active control channel.

4.2 Switching with Hard Faults Hard faults are injected into T2 signal of Channel A at 20 s, P2 signal of Channel B at 25 s, N1 signal of Channel A at 30 s, and N1 signal of Channel B at 35 s, respectively. The simulation results are shown in Fig. 7. It can be seen from Fig. 7 that at 20 s, the T2 signal of Channel A fails, and the Channel B becomes the active control channel; at 25 s, the P2 signal of Channel B fails, and both channels have faults, but the order of dynamic thrust sensitivity (T2 < P2 ) indicates that the more critical signal fault occurs in Channel B, then the active control channel becomes Channel A; at 30 s, the N1 signal of Channel A fails, which is the key signal for thrust control, so the active control channel becomes Channel B; at 35 s, the N1 signal of Channel B also fails, the N1 fault states of Channels A and B are consistent, the switching algorithm selects A as the active control channel according to the order of dynamic thrust sensitivity (T2 < P2 ). The above channel switching process is consistent with the design.

4.3 Switching with Soft Faults Switching verification under steady state deviation. The steady state deviation is caused by the “soft fault” of N1 sensor signal, so a 4% deviation is injected into the N1 signal of Channel A at 20 s, and a 4% deviation is injected into T2 and P2 of Channel B at 25 s, respectively. The simulation results are shown in Fig. 8. It can

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be seen from Fig. 8 that at 20 s, N1 signal of Channel A is shifted, the steady state thrust deviation of Channel A is greater than that of Channel B, so the active channel changes from Channel A to Channel B at this moment; at 25 s, the T2 and P2 signals of Channel B are shifted, the steady state thrust deviation of Channel A is larger than that of Channel B although the dynamic thrust deviation of Channel B is larger than that of Channel A, so the active control channel is Channel B. Switching verification under dynamic deviation. Dynamic thrust deviation judgment is only performed when the steady state thrust deviation of the two channels are similar, so only soft faults are injected into Channels A and B: 2% deviation is injected into T2 signal of Channel A at 20 s, 2% deviation is injected into P2 signal of Channel B at 25 s, 4% deviation is injected into P2 signal of Channel A at 30 s and 4% deviation is injected into T2 signal of Channel B, respectively. The simulation results are shown in Fig. 9. It can be seen from Fig. 9 that at 20 s, the T2 signal of Channel A is 2% shifted, the dynamic thrust deviation of Channel A is greater than that of Channel B, so the active control channel is changed from Channel A to Channel B; at 25 s, the P2 signal of Channel B is shifted by 2%, the dynamic thrust deviation of Channel B is greater than that of Channel A, so the active control channel is changed from Channel B to

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5 Conclusions In this paper, a new method for evaluating channel health level is proposed. Without increasing system redundancy, the EEC dual channel switching algorithm is designed by the concept of thrust sensitivity and the method of inverse model. The steady state and dynamic deviations of thrust caused by the deviations of three sensor signals are considered. The simulation results show that the switching algorithm can select the active control channel with the least impact on engine thrust under different fault conditions, which can minimize the channel health risk and improve the safety and reliability of an aero-engine control system. Considering that the channel switching logic in this paper is aimed at a steady state of the engine, it is necessary to further analyze the transient state conditions and evaluate the switching method under different engine operating conditions.

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References 1. Yao, H.: Full Authority Digital Electricity Control System for Aero-Engine. Aviation Industry Press, Beijing (2014) 2. Xu, W., Niu, D.C.: Design of electronic controller for dual-duration aero-engine. Comput. Knowl. Technol. 12(06), 253–254 (2016) 3. Lu, J., Zhang, Y.G., Wang, C.L.: Overview of residual technology of electric actuator. J. Mech. Trans. 34(03), 92–95 (2010) 4. Xu, X.: Research on Fault Tolerant Control Technology of Micro Turbojet Engine. Nanjing University of Aeronautics and Astronautics (2013) 5. Ma, T.T., Guo, Y.Q., Lu, J.: Study on the online fault diagnosis system of aero-engine based on dual-channel sensor. Comput. Measure. Control 19(07), 1533–1537 (2011) 6. Shen, J.: Fully Digital FADEC System Simulation Platform Development. Master’s Thesis, Nanjing University of Aeronautics and Astronautics, Nanjing, China (2018) 7. Brown, H., Elgin, J.A.: Aircraft engine control mode analysis. J. Eng. Gas Turbines Power 107(4), 838–844 (1984) 8. Onyeka, A.E., Yan, X.G., Mao, Z.H., Mu, J.Q.: Stabilization of Time delay systems with nonlinear disturbances using sliding mode control. Int. J. Model. Ident. Control 31(3), 259– 267 (2019) 9. Lin, L., Ma, Y., Chen, W.M.: Modelling and attitude control of novel multi-ducted-fan aerial vehicle in forward flight. Int. J. Model. Ident. Control 31(1), 81–93 (2019) 10. Kang, Y.F., Zhao, L., Yao, L.: Fault diagnosis and model predictive fault tolerant control for stochastic distribution collaborative systems. Int. J. Model. Ident. Control 30(1), 30–37 (2018)

A U-Model Sliding Mode Control Design for Discrete Nonlinear Systems Jianhua Zhang, Yang Li, Xiaoyun Xu, Xinling Dou, Xueli Wu and Feng Zhu

Abstract For discrete time systems, a design method of linear sliding mode controller is proposed depend on U model. The surface of sliding mode and controller are designed to solve the problem of signal tracking in discrete nonlinear systems. Eventually, a simulation example is given to verify the effectiveness of the designed controller. This method can effectively track the ideal output and the control effect is better and verified by an example. Keywords Discrete time · U model · Sliding mode control · Uncertain system

1 Introduction Sliding mode control is a method of using the controller to make the system state switch from the hyperplane to the superplane. The system switches the hyperplane according to the expected dynamic characteristics. When the switching hyperplane is reached, it slides along the switching hyperplane to the origin of the system.

J. Zhang (B) · Y. Li · X. Xu · X. Dou · X. Wu Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China e-mail: [email protected] Y. Li e-mail: [email protected] X. Xu e-mail: [email protected] X. Dou e-mail: [email protected] X. Wu e-mail: [email protected] F. Zhu CCCC-FHDI Engineering Co., Ltd., Guangzhou, Guangdong 510230, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_99

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Generally speaking, the design process about that control achieves the expected value of the system by designing a suitable sliding surface along the appropriate sliding mode surface. Then design the control law according to the system requirements, so that the system state trajectory moves to the sliding surface. This control method is robust and can achieve fast and robust dynamic response by fast switching of control quantities. It can resist the uncertainty of system parameters and is insensitive to external disturbances. These features make sliding mode control Object parameters and disturbances can be ignored when designing the controller. With the widespread use of computer control systems, it is becoming more and more important to study sliding mode control problems in some situation (in discrete domains e.g.). It is an effective robust control method for solving nonlinear or uncertain systems [1]. In the literature [2], The trajectory is tracked by sliding mode control method. And for nonlinear system, in article [3] designed a time-varying sliding mode controller to track trajectories. In reference [4], the model tracking and tracking problems for uncertain linear systems are studied. The method described herein is to make the tracking error are bounded arbitrarily small or the tracking error is reduced to zero asymptotically. Linearization of nonlinear systems has been widely concerned, as described in [5]. In the literature [6], a method based on repeated scalar linear systems for designing sliding mode controllers is proposed for nonlinear systems using Lyapunov theorem. Under certain conditions, the nonlinear system for uncertainty in [7] uses the integral sliding mode control method to mediate the output to reduce the tracking error [8–10]. Because the specific conditions need to be met, the system requirements are slightly higher. In this paper, based on the U mode linear sliding mode method, the controller is designed to solve the signal tracking problem in discrete nonlinear systems, and the stability of the system is proved by Lyapunov stability theory.

2 Description of the Problem Consider a discrete time system that can be described as a dynamic equation as follows: z 1 (k + 1) = (a11 + a11 )z 1 (k) + (a12 + a12 )z 2 (k) z 2 (k + 1) = (a21 + a21 )z 1 (k) + (a22 + a22 )z 2 (k) + f (u) +  f y(k) = z 1 (k)

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3.1 Sliding Surface Design Select the sliding surface s(k) = a11 x1 (k) + a12 x2 (k) − yd (k + 1)

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4 Simulation The verification process is as follows: z 1 (k + 1) = (a11 + a11 )z 1 (k) + (a12 + a12 )z 2 (k) z 2 (k + 1) = (a21 + a21 )z 1 (k) + (a22 + a22 )z 2 (k) + u + u 2 + u 3 +  f

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5 Conclusion Aiming at the signal tracking problem in discrete nonlinear systems, this paper proposes a design method based on U-model linear sliding mode controller. Under the U model, the linear method is used to perform signal tracking on discrete nonlinear systems. The design of linear sliding mode controller based on U model is a new design method. Through example simulation, it is possible to effectively track a given output. Reduce the error in tracking a given signal.

References 1. Nana, S., Yugang, N., Bei, C.: Optimal integral sliding mode for uncertain discrete time systems. In: Proceedings of the 31st Chinese Control Conference, Hefei, pp. 3155–3159 (2012) 2. Aydi, A., Djemel, M., Chtourou, M.: Robust sliding mode control for nonlinear uncertain discrete-time systems. In: 2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Sousse, pp. 657–662 (2016) 3. Mutoh, Y., Kogure, N.: Sliding mode control of linear time-varying systems application to trajectory tracking control of nonlinear systems. In: 2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO), Vienna, pp. 492–498 (2014) 4. Feng, Y., Xue, C., Yu, X., Han, F.: On a discrete-time quasi-sliding mode control. In: 2018 15th International Workshop on Variable Structure Systems (VSS), Graz, pp. 251–254 (2018) 5. Zhu, Q.M., Zhao, D.Y., Zhang, J.: A General U-Block Model-Based Design Procedure for Nonlinear Polynomial Control Systems. Taylor & Francis, Inc. (2016) 6. Liu, X., Hu, F., Su, X.: Sliding mode control of a class of nonlinear systems. In: 2018 IEEE 7th Data Driven Control and Learning Systems Conference (DDCLS), Enshi, pp. 1069–1072 (2018) 7. Guizhi, M., Kemao, M.: Output regulation for nonlinear systems via integral sliding mode. In: Proceedings of the 33rd Chinese Control Conference, Nanjing, pp. 2331–2335 (2014) 8. Aloqaily, A., Al-Nawayseh, M.K., Baarah, A.H., Salah, Z., Al-Hassan, M., Al-Ghuwairi, A.-R.: A neural network analytical model for predicting determinants of mobile learning acceptance. Int. J. Comput. Appl. Technol. 60(1), 73–85 (2019) 9. Pham, H.V., Lam, T.N.: A new method using knowledge reasoning techniques for improving robot performance in coverage path planning. Int. J. Comput. Appl. Technol. 60(1), 57–64 (2019) 10. Zhang, J., Yang, S., Li, Y., Wu, X.: A flight conflict detection model for UAV based on fourdimensional coordinates. Int. J. Comput. Appl. Technol. 60(1), 51–56 (2019) 11. Chen, J., San, H., Wu, X., Na, J.: Stability discrimination of quadruped robots by using tetrahedral method. Int. J. Appl. Math. Control Eng. 1(2), 55–61 (2018) 12. Wang, Y., Gou, Y., Liu, Q., Li, B., Li, S., Liang, K.: Design of control system for water quality monitor in irrigating Farmland. Int. J. Appl. Math. Control Eng. 1(2), 26–32 (2018) 13. Wen, S., Liu, D., Wang, X.: Finite-time stability of fractional order neural networks with proportional delays. Int. J. Appl. Math. Control Eng. 1(2), 1–8 (2018)

Adaptive Fast Finite-Time Consensus for Second-Order Multi-agent Systems Jiabo Ren, Baofang Wang and Mingjie Cai

Abstract We will study the adaptive fast finite-time consensus (FTC) control problem of second-order multi-agent systems (MASs) with unknown dynamics and external disturbances in this paper. Based on the basis of radial basis function neural networks theories, we use it to approximate the unknown functions. According to the consensus protocols and adaptive laws, we will prove that velocity errors of arbitrary two agents reach a small region of zero in finite time as well as position errors. Ultimately, the effectiveness of the designed method is tested through a numerical example. Keywords MASs · fast FTC · Adaptive control

1 Introduction In the past few decades, some researchers have paid more attention to the consensus of MASs owing to its great potential in various areas. For instance formation control [1], smart grids [2] and unmanned vehicles [3]. Consensus of MAS is to design control algorithms to deal with the states of any two agents reach a desired region [4]. Convergence rate is of great significance for the consensus control algorithms of MASs owing to its enormous advantages. Such as faster convergence rate, better disturbance rejection and robustness against uncertainties [5, 6]. Consequently, FTC of MASs has caused widespread concern in some practical systems. In [7, 8], FTC control algorithms for first-order and second-order MASs were designed. By using the Barrier Lyapunov function and double-integrator dynamics, FTC protocols were designed for second-order MASs with output constraint and unknown nonlinear perturbations in [9]. In addition, Ranjbar, Ghasemi and Akramizadeh proposed timevarying leader-following consensus of MASs [10]. In [11], a control system with delayed states and nonlinear disturbances were proposed by employing the terminal J. Ren · B. Wang · M. Cai (B) School of Automation, Qingdao University, Qingdao 266071, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_100

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sliding-mode control technique. By employing the fast terminal sliding-mode control technique, the adaptive second-order non-singular control approach for nonlinear uncertain systems was designed in [12]. Recently, [13] addressed the consensus problems of fractional-order MASs via the fast sliding-mode control technique. In [14], fast convergence consensus problem of MASs with switching topology was studied, it can be seen as a time-optimal control algorithm problem of unknown weight parameters and switching times. Therefore, our motivation is to address the problem of adaptive fast FTC for second-order MASs. By using the propose method, a novel fast FTC algorithm was developed. Consider uncertain dynamics are unknown, a novel control algorithm is developed via the Lyapunov’s relevant theory.

2 Preliminaries 2.1 Problem Formulation Consider the second-order MASs: x˙ i = vi v˙i = ui + fi (xi , vi ) + di (t) , i ∈ M = {1, . . . , m} ,

(1)

where xi ∈ R represents the position, vi ∈ R represents the velocity, di (t) is the external disturbance, fi (xi , vi ) is an unknown continuous function contenting fi (0, 0) = 0, ui ∈ R is the control input to be designed. Then, some lemmas and assumptions need to be introduced. Assumption 1 For any i ∈ M , there exists a known constant ζ , namely, |di (t)| ≤ ζ < +∞. Definition 1 The FTC of MAS (1) can be achieved if for arbitrary initial condition P0 = [x0 , v0 ]T , there exists ε1 > 0, ε2 > 0and T (P  0 , ε1 , ε2 ) < ∞, so that position and velocity errors content xi − xj  < ε1 , vi − vj  < ε2 , for all t ≥ T , i ∈ M , j ∈ M , i = j. Lemma 1 [15] If there exists a continuous differentiable function V (x) for a nonlinear system x˙ = f (x), scalars ι > 0, 0 < γ < 1, l > 0 and 0 < κ < ∞ ensure that V˙ (x) ≤ −ιV γ (x) − lV (x) + κ, thus nonlinear system x˙ = f (x) trajectory is practical finite-time stable.

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2.2 Graph Theory We will introduce a lot of knowledge about graph theory in this section. An undirected graph is described by G = {V, E, A}, which consists of M agents, where V = {v1 , v2 , ..., vM } represents the set of vertices, E ⊆ V × V represents the set of edges, A represents the weighted adjacency matrix of graph G. When there exists an edge between agent i and agent j, i.e., (vi , vj ) ∈ E, then aij = aji > 0 and aij = aji = 0 otherwise. In addition, take care that self edges (vi , vi ) are not permitted, / E, aii = 0. The set of neighbors of node vi is defined therefore (vi , vi ) ∈ mas Ni = m×m } ∈ R ∈ V : (v , v ) ∈ E . Denote D = diag{d , . . . , d with d = v j i j 1 m i j=1 aij =  a for i ∈ M as a degree matrix of graph G, then the Laplacian of the weighted ij j∈Ni G is defined as L = D − A. A path from vi to vj in graph G is a sequence of different vertices beginning with vi and ending with vj , so that the continuous vertices are adjacent. Consequently, there exists a path of arbitrary two agents vi , vj ∈ V if G is connected. Assumption 2 For second-order MAS (1), graph G is connected. In this paper, an adaptive FTC protocol for second-order MAS (1) will be designed. By the proposed approach, the fast FTC of MAS (1) can be achieved.

3 Main Results 3.1 Consensus Algorithms Design We will design adaptive FTC protocols for second-order MASs in this section. Firstly, virtual velocities are designed. Secondly, we will design control protocols and control laws.  Step 1: Define ρi = j∈Ni aij (xi − xj ), i ∈ M , ρ = [ρ1 , . . . , ρm ]T . By considering the following function 2 1   aij xi − xj . 4 i=1 j∈N m

V1 =

(2)

i

The time derivative of V1 is ⎤ ⎡ m m m         ⎣ aij xi − xj ⎦ vi = ρi vi∗ + ρi vi − vi∗ , V˙1 = i=1

j∈Ni

where vi∗ represents virtual velocity.

i=1

i=1

(3)

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Next, vi∗ is designed as    vi∗ = −ρir k1 + k2 1 + ρi2 , i ∈ M ,

(4)

where k1 > 0 and k2 > 0 are constants to be designed, 0.5 < r < 1 , V˙1 ≤

m 

m m     ρi vi − vi∗ − k1 ρi1+r − k2 ρi2 .

i=1

i=1

(5)

i=1

Step 2: Define a new variable ηi = vi1/r − vi∗1/r , i ∈ M . From Lemma 2 in [16], it yields   vi − vi∗ ≤ vi − vi∗  ≤ 21−r |ηi |r .

(6)

Then according to Lemma 4 in [17] yields   21−r 1+r 21−r 1+r ρi + η . ρi vi − vi∗ ≤ 21−r |ρi | |ηi |r ≤ 1+r 1+r i

(7)

Combining (5) and (7), we have  m

m m  21−r  1+r 21−r r  1+r ρi − k2 ρi2 + η . V˙1 ≤ − k1 − 1 + r i=1 1 + r i=1 i i=1

(8)

Choose the next Lyapunov function V2 = V1 +

m  i=1

Wi , Wi =

1 (2 − r) 21−r



vi vi∗

(s1/r − vi∗1/r )

2−r

ds.

(9)

Combining (8) and (9), the time derivative of V2 is m m m m  21−r  1+r 21−r r  1+r  ˙ 2 ˙ ) V2 ≤ −(k1 − ρ − k2 ρi + η + Wi , 1 + r i=1 i 1 + r i=1 i i=1 i=1

(10)

where W˙ i =

ηi2−r ui ηi2−r fi (xi , vi ) ηi2−r di (t) + + (2 − r)21−r (2 − r)21−r (2 − r)21−r ∗1/ r  vi 1 dv 1−r − 1−r i (s1/r − vi∗1/r ) ds. 2 dt vi∗

(11)

Adaptive Fast Finite-Time Consensus …

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i According to the RBFNNs in [4], we consider the term (2−r)2 1−r fi (xi , vi ). Since fi (xi , vi ) is an unknown function, we can use a RBFNN to approximate it on the compact set Ξi as follows:

fi (xi , vi ) = θi∗T ωi (xi , vi ) + δi (xi , vi ), ∀(xi , vi ) ∈ Ξi ,

(12)

where θi∗ ∈ Rgi represents optimal parameter vector, ωi (xi , vi ) ∈ Rgi represents basis function vector, δi (xi , vi ) ∈ R represents approximation error, |δi (xi , vi )| ≤ εiN , gi > 1 is the node number of neural network.   T T Let θ¯i∗T = θi∗T , εiN , i (xi , vi ) = ωi∗T (xi , vi ), 1 . In fact, basis function vector ωi (xi , vi ) contents 0 < ωiT (xi , vi )ωi (xi , vi ) < gi , we have   fi (xi , vi ) ≤ θ¯i∗T i (xi , vi ) ≤ θ¯i∗T i (xi , vi )      ≤ θ¯ ∗ 

i (xi , vi ) ≤ gi + 1 θ¯ ∗  . i

i

(13)

Then from Lemma 4 in [17], we obtain     ηi2−r fi (xi , vi ) ≤ ηi2−r  gi + 1 θ¯i∗  1+r 2−r 2r − 1 (r−2)/(2r−1) ≤ χi (gi + 1) 2(2−r) ηi1+r Θi∗ + χ , (14) 1+r 1+r i  (1+r)/(2−r) where χi > 0 is a constant and Θi∗ = θ¯i∗  is an unknown parameter. Hence, the term

ηi2−r f (x , vi ) (2−r)21−r i i

can be estimated as follows:

1+r 1 1 χi (gi + 1) 2(2−r) ηi1+r Θi∗ + χ¯ i , ηi2−r fi (xi , vi ) ≤ 1−r 1−r (2 − r)2 2 1+r

(15)

(r−2)/ (2r−1) 2r−1 is a constant. where χ¯ i = (2−r)2 1−r 1+r χi 2−r 1 Consider the term (2−r)21−r ηi di (t). According to Assumption 2 and Lemma 4 in [17],we have

1 1 2r − 1 . (16) η2−r di (t) ≤ ζ (1+r)/(2−r) ηi1+r + (2 − r)21−r i (1 + r)21−r (2 − r)21−r (1 + r) 1 Consider the term − 21−r Lemma 2 in [16], there has

d vi∗1/r  vi vi∗ dt

1 d v ∗1/r − 1−r i 2 dt



vi

vi∗

(s1/r − vi∗1/r )

(s

1/ r

−

1−r

ds. From the definition of ηi and

1−r vi∗1/r ) ds

   d v ∗1/r   i  ≤  |ηi | .  dt 

(17)

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Since ρi =



aij (xi − xj ), there has

j∈Ni

     d ρi    vj ,  dt  ≤ a |vi | + b j∈N

(18)

i

where a = maxi∈M

 j∈Ni

   aij , b = maxi,j∈M aij . Then from (4), we have

    d v ∗1/r   d ρ  2k2 2 1/ r (1−r)/ r  i  i    (k1 + k2 (1 + ρi2 )) + ρi (k1 + k2 (1 + ρi2 ))   = −   dt  dt r ⎛ ⎞   vj ⎠ , ≤ ψ(ρi ) ⎝a |vi | + b (19) j∈Ni 2k ρ 2

1−r

where ψ(ρi ) = (k1 + k2 (1 + ρi2 ))1/r + 2r i (k1 + k2 (1 + ρi2 )) r . Combining (19) and (18) and according to Lemma 4 in [17], we have 1 d v ∗1/r − 1−r i 2 dt



vi vi∗

(s1/r − vi∗1/r )

1−r

ds

 ≤ ψ(ρi ) a(|ηi | + |ρi |r (k1 + k2 (1 + ρi2 )))     r  +b (ηj  + ρj  (k1 + k2 (1 + ρj2 ))) |ηi | j∈Ni

ar 1+r ρ 1+r i  br ψ(ρi ) + ηj1+r , 1+r j∈N

≤ (ψ0 (ρi ) + ψ1 (ρi ))ηi1+r + +

br  1+r ρ 1 + r j∈N j i

(20)

i

where 1+r a  ψ(ρi )(k1 + k2 (1 + ρi2 )) , 1+r  1+r b  mbψ(ρi ) + ψ(ρi )(k1 + k2 (1 + ρj2 )) . ψ1 (ρi ) = 1+r 1 + r j∈N

ψ0 (ρi ) = aψ(ρi )+

i

Combining (11), (15), (16), and (20), we have V˙2 ≤ −ς1

m 

ρi1+r

− k2

m 

i=1

i=1

ρi2

m  1 + η2−r ui (2 − r)21−r i=1 i

  1+r 1 + 1−r χi (gi + 1) 2(2−r) ηi1+r Θi∗ + ψ2 (ρi )ηi1+r + ε, (21) 2 (1 + r) i=1 i=1 m

m

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where ar mbr 21−r − − > 0, 1+r 1+r 1+r ζ (1+r)/(2−r) 21−r r mbrψ(ρi ) ψ2 (ρi ) = + , +ψ0 (ρi ) + ψ1 (ρi ) + 1−r 1+r (1 + r)2 1+r  m  (r−2) (2r−1) 2r − 1 / ε= χ +1 . (2 − r)21−r (1 + r) i=1 i ς1 = k1 −

Choose the control input as follows:    ui = − (2 − r)21−r k3 + k4 (1 + ηi2 ) + ψ2 (ρi )  ! 1+r +χi (gi + 1) 2(2−r) 1 + Θˆ i2 ηi2r−1 ,

(22)

where k3 > 0 and k4 > 0 are constants, Θˆ i is the estimation of Θi∗ . Defining Θ˜ i = Θi∗ − Θˆ i as the estimation errors, substituting (22) into (21), we have m 

V˙2 ≤ −ς1

ρi1+r − k2

m 

i=1

+

ρi2 − k3

i=1

1 (1 + r)21−r

m 

m  i=1

ηi1+r − k4

m 

ηi2

i=1

χi (gi + 1) 2(2−r) ηi1+r Θ˜ i + ε. 1+r

(23)

i=1

Next, we will choose Lyapunov function candidate to acquire the update laws of Θˆ i . 1 2 Θ˜ , 2 i=1 i m

V (ξ ) = V2 +

(24)

T  where ξ = ρi , ηi , Θ˜ i . Choose the adaptive law as follow: Θ˙ˆ i =

1 21−r (1

χi (gi + 1) 2(2−r) ηi1+r − pi Θˆ i , 1+r

+ r)

(25)

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where pi > 0 is a design parameter. Then (23) becomes V˙ (ξ ) ≤ −ς1

m 

ρi1+r − k2

i=1

+

m 

ρi2 − k3

i=1

1 (2 − r)21−r

m 

m 

ηi1+r − k4

i=1

m 

ηi2

i=1

pi Θ˜ i Θˆ i + ε.

(26)

i=1

This completes the design procedure.

3.2 Consensus Analysis Theorem 1 Consider the second-order MAS (1), assume that Assumptions 1–2 are contented, with the aid of the FTC protocols (22) and the control laws (25), the practical FTC will be achieved. Proof From the proof of Theorem 9 in [18], we have m 

ρi2 ≥ λ2 xT Lx = 2λ2 V1 .

(27)

i=1

Then, from Wi and Lemma 2 in [16], we have Wi ≤

   1 vi − v ∗  s1/r − v ∗1/r 2−r ≤ 1 η2 . i i 1−r 2−r i (2 − r) 2

(28)

Combining (27) and (28), we have V2 ≤

m m m  1  2 1  2 ρi + ηi ≤ ς2 (ρi2 + ηi2 ), 2λ2 i=1 2 − r i=1 i=1

(29)

where ς2 = max {1/ (2λ), 1/ (2 − r)}. Then according to Lemma 3 in [19], we have V2 (1+r)/2 ≤ ς2(1+r)/2

m 

(ρi1+r + ηi1+r ).

(30)

i=1

Letting ς3 = min {ς1 , k3 } and ς4 = min {k2 , k4 }, combining (26), (29) and (30) we can obtain

Adaptive Fast Finite-Time Consensus … V˙ (ξ ) ≤ −ς3

m 

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(ρi1+r + ηi1+r ) − ς4

i=1

+

(ρi2 + ηi2 ) +

i=1

ς3 ≤ − (1+r) 2 V / ς2 m 

m 

ς3 (ξ ) + (1+r) 2 / ς2

1+r 2

m  1 pi Θ˜ i Θˆ i + ε 1+r (2 − r)2 i=1



1 2

m 

Θ˜ i2

i=1

1+r 2

−

m ς4 ς4  2 V (ξ ) + Θ˜ i ς2 2ς2 i=1

pi Θ˜ i Θˆ i + ε.

(31)

i=1

From Lemma 4 in [17], we have

1 2 Θ˜ 2 i

(1+r)/2

≤

1 2 1 − r 1 + r (1+r)/(1−r) Θ˜ + ( ) . 2 i 2 2

(32)

Note that Θ˜ i = Θi∗ − Θˆ i , i ∈ M . 1 1 pi Θ˜ i Θˆ i = pi Θ˜ i (−Θ˜ i + Θi∗ ) ≤ pi (− Θ˜ i2 + Θi∗2 ). 2 2 Choosing pi ≥

ς3 ς2(1+r)/2



ς3

+

ς4 ς2

and combining (30–33), we have (1+r)/ 2

1 2 Θ˜ 2 i=1 i m

ς2(1+r)/2

(33)

m m 1 ς4  2  ˜ Θ + + pi Θ˜ i Θˆ i 2 ς2 i=1 i i=1

1 ς3 1 ς4  2 mς3 1 − r 1 + r (1+r)/(1−r) ( ) Θ˜ i + (1+r)/2 + ) (1+r) 2 / 2 ς2 2 ς2 i=1 2 2 ς2 m

≤(

1  2 1  ∗2 Θ˜ + pi − pi Θ 2 i=1 i 2 i=1 i m

m

1  ∗2 mς3 1 − r 1 + r (1+r)/(1−r) pi ( ) Θi + (1+r)/2 . 2 i=1 2 2 ς2 m

≤

(34)

Substituting (34) into (33), we have V˙ (ξ ) ≤ −

where ε¯ = ε + 21 pi

m  i=1

ς3 V (1+r)/2 (ξ ) (1+r)/ 2 ς2

Θi∗2 +

−

ς4 V (ξ ) + ε¯ . ς2

(35)

1+r mς3 1−r 1+r 1−r ( 2 ) , ς2(1+r)/2 2

Therefore, from the Lemma 1, fast FTC for second-order MAS (1) can be achieved.

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4 Numerical Example Consider second-order MAS (1). We have designed a interconnected topology, it can be seen as in Fig. 1. Then, external disturbances are given as: d1 = 1.5 sin(t), d3 = 0.5 sin(t), d5 = 0.7 cos(t), d7 = 0.5 sin(t), d2 = sin(t), d4 = 0.8 cos t, d6 = 0.6 sin(t). which means ζ = 1.5. Herein, through the above protocols design procedure, we have the control protocols (22) and adaptive laws (25). From the Fig. 1, we have a = 2.7, b = 1 and λ2 = 0.22. Therefore, we can select the design parameters as follow: r = 3/5, k1 = 21−r + ar + mbr, k2 = k3 = k4 = 1, gi = 10, χi = 10, i ∈ M7 = {1, 2, 3, 4, 5, 6, 7} . It is easy to verify that ς1 > 0 and pi ≥ where

ς3 ς2(1+r)/2

+

ς4 ς2

are satisfied,

ς2 = max {1/ (2λ2 ), 1/ (2 − r)} = 1/ (2λ2 ), p1 = 40, p4 = 50, p6 = 50, ς3 = 1, p7 = 50ς4 = 1, p2 = 50, p3 = 60, p5 = 60. owing to Pi = [xi , vi ]T , i ∈ M7 , the initial condition is P1 (0) = [0.3, −0.2]T , P4 (0) = [−0.3, −0.2]T , P7 (0) = [−0.3, 0.2]T , P2 (0) = [−0.4, 0.3]T , P5 (0) = [0.4, −0.5]T , Θˆ i (0) = 0, P3 (0) = [0.5, −0.4]T , P6 (0) = [0.6, −0.4]T .

Fig. 1 Interconnected topology

Adaptive Fast Finite-Time Consensus … Fig. 2 Trajectory of position x

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1

x1 x2 x3 x4 x5 x6 x7

x

0.5

0

−0.5

0

0.1

0.2

0.3

0.4

0.5

Time (s)

Fig. 3 Trajectory of velocity v

v1 v2 v3 v4 v5 v6 v7

15

10

v

5

0

−5

−10 0

0.1

0.2

0.3

0.4

0.5

Time (s)

Through the above simulation, we can get the Figs. 2, 3 and 4. In Fig. 2, we can find that the trajectories of x can reach consensus in finite time. Meanwhile, in Fig. 3, the trajectories of v reach a desired region in finite time as well. The parameter estimations Θˆ i are given in Fig. 4, it is apparent that Θˆ i can reach a region of zero in finite time.

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Fig. 4 Trajectory of estimation Θˆ

ˆ1 Θ ˆ2 Θ ˆ3 Θ

0.2

ˆ4 Θ ˆ5 Θ

0.1

ˆ Θ

ˆ6 Θ ˆ7 Θ

0

−0.1 0

0.1

0.2

0.3

0.4

0.5

Time (s)

5 Conclusions In this paper, the adaptive fast FTC protocols for second-order MASs with unknown dynamics and external disturbances were presented. RBFNNs are adopted to approximate the unknown functions. Under FTC protocols and control laws, consensus could be achieved between arbitrary two agents in finite time. Finally, through the numerical results obtained, we illustrated the effectiveness of the proposed approach. Acknowledgements This work is supported by the National Natural Science Foundation (NNSF) of China (61803215), the Natural Science Foundation of Shandong Province (ZR2019BF038), and Qingdao Application Basic Research Project (18-2-2-40-jch).

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Industrial Robot Control Systems: A Review Li Xiao, Jin Gong and Jinbao Chen

Abstract Firstly, this paper introduces the industrial robot control system. Then, the development and research status of the open industrial robot control system are summarized, and this paper focuses on the hardware structure and software structure of the open industrial robot control system. And the application status of the typical multi-robot collaboration system is analyzed. Finally, the future development direction of the open robot control system is prospected. Keywords Industrial robots · Open control system · Hardware architecture · Software architecture · Multi-robot

1 Introduction In 2012, the United States proposed “Industrial Internet”; In 2013, Germany proposed “Industry 4.0”. In 2015, China proposed “Made in China 2025”. Many countries or organizations have made blueprints for the future industrial development, and these blueprints all point out the development trend of future manufacturing, that is, more emphasis on automation, informatization and intelligence. At present, the traditional manufacturing industry is faced with industrial transformation and upgrading, and the demand for manufacturing industry becomes increasingly urgent [1–3]. Modern industrial production and robot research for industrial robot has more flexible and more powerful programming capabilities. They can be connected to the same platform via bus or Ethernet to form a comprehensive control system with different devices in industrial production, and can adapt to different application and multivariety small batch production and processing tasks [4]. The Computer Integrated Manufacturing Systems (CIMS) require robots to be able to integrate with other automated devices to accomplish complex machining tasks. In order to improve the L. Xiao (B) · J. Gong · J. Chen The State Key Laboratory of High-Performance Complex Manufacturing, Central South University, Changsha 410012, China e-mail: [email protected] J. Gong Sunward Intelligent Equipment Co., Ltd, Changsha 410100, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_101

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overall operation level and intelligence level of the robot system, the robot controller is required to have a more open structure to integrate various external sensors and integrate various intelligent control algorithms [5]. Under certain circumstances, the improvement of industrial manufacturing level depends on the improvement of industrial robot technology, and the development of industrial robot control system is the cornerstone of the development of industrial robot technology. The level of automation and informatization of robots will directly affect the level of automation and informatization of industrial manufacturing [6]. Therefore, in order to improve the competitiveness of domestic industrial robots [7], it is necessary to develop a robot control system with excellent performance, which requires a deep understanding of industrial robot control system. This paper briefly introduces the development and current situation of industrial robot control system, and introduces several hardware and software implementation methods of industrial robot system, and prospects the future development trend.

2 Introduction of Industrial Robot Control System Industrial robot system usually consists of four parts: robot body, servo system, control system and sensor. Among them, the control system is equivalent to the brain of industrial robots, whose task is to drive the robot body to complete specific tasks according to the user’s instructions. As shown in Fig. 1, the structure block diagram of the robot control system [8] is mainly composed of the control part, the mechanical part and the sensing part. Among them, the control part is the core of the whole system, which is mainly responsible for the kinematics calculation, motion planning and interpolation calculation of the robot, and transmitting the user’s motion

Fig. 1 The structure block diagram of the robot control system

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Fig. 2 PUMA560 control system

control instructions to the actuator [9]. Therefore, to a large extent, the openness of the control system restricts the openness of the robot [10]. There are many classification methods for industrial robot control systems. According to the degree of system openness, robot control system can be divided into the following three categories [11]: the closed control system, the open control system and the hybrid control system. The closed robot control system is developed based on its own independent structure. It used a dedicated computer, a dedicated robot language, a dedicated operating system, and a dedicated microprocessor. The collection of new external hardware and software becomes very difficult or even impossible. Literature [12] introduces the control system of Puma560 industrial robot, as shown in Fig. 2. The Puma560 is the representative of this type of robot. The LSI-II is the heart of the robot controller. The robot uses the PDP-II as a hardware platform and uses the VAL, a specialized robot language. The openness of hybrid control system is between closed and open, that is, partially closed and partially open [13, 14]. In the hybrid controller, the control functions of the bottom layer are generally provided by the manufacturer, and its structure cannot be changed arbitrarily, but the interface with the function of the upper layer is reserved. In the specific practice, the hybrid controller generally adopts a modulebased implementation. The internal structure and implementation details of the module are generally not open to the user or limited to open, in order to protect intellectual property rights and related interests, but the interface module provides a variety of function. Users can customize the function and behavior of the module through the interface, and realize the interoperability and cooperation between multiple modules through the interface to form a complete controller. Among them, when the robot control system is closed or semi-closed, such robot control system is poor in

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openness, weak in network function and incompatible with the products of various manufacturers, which makes it difficult to meet the requirements of “Industry 4.0” for informatization.

3 Open Robot Control System According to IEEE standards, an open system is defined as: “A system to provide capabilities that enable properly implemented applications to run on a wide variety of platforms from multiple vendors, inter-operate with other system applications, and present a consistent style of interaction with the user” [1].

3.1 The Development of Open Robot Control System Since the concept of Open Control System has been proposed, many countries or enterprises have paid for the research and exploration. Three of them are the most influential. EU’s OSACA [15] (Open System Architecture for Control with Automation System), by Europe Research institutes and controller manufacturers jointly proposed to complete the development in 1996. As shown in Fig. 3, OSACA architecture is divided into two parts: application software and system platform. The core software of the system platform mainly includes three parts: operating system, communication system and configuration system. They serve applications through a unified API. Defining and using standard API enables system integrators and application developers to achieve portability of applications, interoperability between modules, and extensibility and interchangeability of functions. Since the life cycle of the system

Fig. 3 OSACA architecture

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hardware is much smaller than that of the software, the system software should be independent of the hardware and can be applied to any hardware. In 2003, Li [16] of Qingdao University and others used the SCARA operating machine to build a test platform, and proved that the open robot system based on OSACA has good operational performance and dynamic performance. However, in the actual operation process, it is found that the system still has certain reliability and other issues, which are subject to further research and improvement. In 2019, Zhunan [17] of Zhejiang university summarized and analyzed the shortcomings of the prototype system, combined the features of the SCARA manipulator, and aimed at the shortcomings of the prototype system, proposed the reference model of the open control system of the SCARA manipulator based on OSACA model, and passed the open verification experiment of the SCARA control system. Japan’s OSEC (Open System Environment Controller) program was initiated by an open CNC committee established by the Japan International Robotics and Factory Automation Research Center. It was proposed by some major Japanese machinery and electromechanical manufacturers in 1994, the purpose was to establish a national international FA (factory automation) control equipment of the standard, the research was focused on digital Controller itself and distributed control System, the development of a new generation based on PC platform, which has a high performance than the Open System of a new generation of numerical control System. In 1997, Sawada C. outlined in the literature [18] the architecture of the OSEC-II (the second version of the controller open system environment) released by the Alliance in August 1996. In late 1994, GM, Ford and Chrysler first proposed the concept of OMAC [19, 20] (Open Modular Architecture Controllers), arguing that openness is about allowing popular hardware and software to be integrated as Controllers’ infrastructure. In February 1997, the OMAC user group was established, and organizations interested in OMAC can join at any time to participate in relevant technology development. The main goal of OMAC is to clarify users’ application requirements for open architecture controllers. Develop a public API that meets this need; It provides common solutions to various problems in the development, implementation and commercialization of open controller technology. What distinguishes OMAC’s control system from the first two plans is that it has a standardized interface layer. At this time, it is convenient for users to develop a series of specific functional modules to meet their needs, namely “plug and play”, which is convenient to connect to the simple control system. The open robotic control system [21] emphasizes scalability, portability, tailorability and interoperability. Users and enterprises can extend and tailor system function modules to suit the functions and performance requirements of different applications; they can be ported to different operating systems and platforms, and maintain the original functions; they can interact with other external systems for data and even operations. Domestic research on open robot control systems is later than abroad, but due to the continuous efforts of domestic scholars’ research institutions in recent years, certain successes and progress have been achieved. In 2008, Xia [22] of Huazhong University of Science and Technology established the communication connection between PC and Motoman up-20 robot based on Ethernet, developed a robot control

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software, realized the host control of the robot by PC and the interaction of operation files and other functions. The MPI (Multi-Point Interface) network is used to connect the PC and the control core of the plasma spray equipment, Siemens PLC, to realize the open integration of the PC-based forming process monitoring, robotic spray path adaptive adjustment and robot real-time monitoring. And the open robot plasma spray forming system tests the system performance through process experiments. In 2018, literature [23] studied and developed an open 6R industrial robot control system based on Win CE, and proved that the control system achieved the expected design purpose in terms of motion accuracy, stability, maximum allowable speed and other aspects through experiments. At the same time as the rapid development of computers, robot control software [24] with platform versatility is also developing rapidly. CLARAty [25] (Coupled Layer Architecture for Robotic Autonomy) is a structure designed by the Jet Propulsion Laboratory for autonomous robot systems in 2001, and it is used on the Mars probe platform. In 2003, Player [19] was proposed, it is an open source robot software framework, and in 2005 launched its upgraded version, it is through the loose coupling between modules to improve the reusability of software. In the same year, the robot control software CARMEN [26] developed by Carnegie Mellon University made the experiment and simulation of the control algorithm easier. The open source software project Orca [27], which was proposed in 2006, uses commercial open source libraries in communication and interface definition based on software engineering methods to realize cross-platform development. In 2010, Willow Garage released the open source robot operating system ROS [28, 29], which is open source and has been used by a variety of robots. The advantage of the system is that it is not constrained by robot hardware, and the system itself has many robot control algorithms and instructions, which can be applied to different robots. For now, though not yet fully developed control system strictly, but with the development of computer hardware, sensors, etc. also with the development of the computer software theory, the robot control software mainly cross-platform, hierarchical control and modularization, distributed, and facilitate the development of software, easy to the characteristics of the composite and stable development, so the future of open control system of industrial robot research will be the focus of national development.

3.2 Implementation Strategy of Open Robot Control System In order to meet the requirement that the system can be modified, replaced or added by the user, the robot’s control system uses standard, open, and universal software and hardware platforms instead of dedicated, customized systems. The current control system development mostly uses the standard language such as C language, the software platform uses the standard operating system such as Windows. The most studied is the open robot control system based on PC [30], which utilizes the powerful hardware and software functions of PC to carry out real-time transformation on PC,

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and runs both robot control software and system management software on PC. This realization method is the full software control in common sense.

3.2.1

Hardware Implementation Method of Open Control System

From the perspective of hardware structure, the open control system [31] is mainly divided into two categories, the first is based on the PC bus system, and the second is based on the VME bus. PC has the advantages of low cost, openness, complete software development environment and good communication functions. At present, many robot manufacturers will mainly research and develop PC-based robot control systems. Therefore, there are already four hardware implementations. The first is “PC+ Motion Control Card”; the second is “IPC+ Motion Control Card”; the third is “PLC Control System”; the fourth is “General PC+ Industrial Real-Time Ethernet”. PC+ motion control card as the upper control can make full use of computer resources, for the robot control system with complex motion process and trajectory and strong flexibility. PC CPU can focus on human-machine interaction, real-time monitoring and sending instructions and other system management work; the dedicated CPU on the motion card handles all the details of motion control, such as speed calculation, travel control, multi-axis interpolation, etc., without occupying PC resources. At the same time, the motion cards also provide powerful motion control software library C language motion library, Windows DLL dynamic link library, etc., allowing users to solve the complex motion control problems more quickly and effectively. The research on this mode was carried out earlier. Keum-shik H et al. studied a modular and object-oriented method for an open robot control (PC-ORC) system based on PC. Huang [32], from the Institute of Robotics, Harbin Institute of Technology, developed the hardware control structure of PC + DSP + FPGA and applied it to the four degrees of freedom robotic arm of satellite remote operation. In 2015, literature [33] designed a set of open and good control system based on the control algorithm and system openness, and the control mode of PC+ motion control card was selected for industrial robots. The control system is proved to be in good working condition in the laboratory. The open robot control system composed of Industrial Personal Computer (IPC) and motion control card has the advantages of high reliability, strong information processing ability, high openness and accurate motion trajectory. The IPC can run Windows or Linux mainstream operating system, and can install Microsoft Visual C++, Qt and other software development environment based on this operating system, in order to have a simple, user-friendly robot control software development. In this mode, the division of labor between IPC and motion control card is clear. The software development based on IPC robot control system has the advantages of low cost, good system compatibility, strong system reliability and obvious computing power. Therefore, the use of computer platform and embedded real-time system provides the hardware guarantee for dynamic control algorithm and complex trajectory planning. At present, the domestic and foreign universities and research institutions have

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made corresponding research results in this mode. For example, Pan [9] of Huazhong University of Science and Technology in China has developed an open control system based on PC and PMAC. SIASUN-06B [34] robot controller based on PC bus and CAN bus has been developed by The China Automation Shenyang Institute of Automation. In 2018, Tian Shipeng from South China University of Technology in literature [35] designed an industrial robot system architecture of “EtherCAT bus +FPGA servo control + Yaskawa servo motor”, and realized the openness of the control system by EtherCAT communication feedback to IPC. Literature [36] adopts the hardware structure of PC + I/O control board to realize the control experiment of parallel robot in the open operating environment RTX + Windows. The experimental results show that the system has stability and reliability. Abroad, many big machine life manufacturers such as KUKA have also developed control systems based on IPC and Windows operating system. In the control system of KUKA, PC transfers the motion control instruction to the multi-function servo control card through PCI/ISA bus to drive the motor. The control system is characterized by good openness and flexibility, supporting a variety of common bus protocols such as PROFIBUS DeviceNet and Ethernet interface. ABB’s SIMATIC WinAC uses RTX real-time expansion. WinAC is open and can integrate logic control, motion control, video collection and other information into a PC [37]. The Programmable Logic Controller (PLC), a digital logic controller for automatic real-time control and designed for industrial control computer, meets the requirements of industrial environment. It is an automatic control product that combines automatic control technology with computer technology. The PLC-based robot control system [38] has mature technology and convenient programming. It has obvious advantages in reliability, expandability and adaptability to the environment, and has the advantages of small size, convenient installation and maintenance, strong interchangeability, etc. There are a whole set of technical solutions for reference, shorten the development cycle. In literature [39], Bian Hongyuan from southeast university designed and completed the industrial robot structure based on AB PLC controller, and realized the motion control of the robot with the AB PLC ControlLogix control system. Literature [40] designed a set of PLC controlled industrial manipulator sorting robot control system of different colors and materials, which can be seamlessly connected with other logistics equipment to achieve the distribution and management of material objects, and has a good application prospect. In a word, PLC has a powerful networking function, so it can realize the monitoring of multiple robots through the network. Many large companies such as ABB, Rockwell PLC can support the control and management of industrial robots, their controller internal motion control function, and support a variety of protocols, which is conducive to achieve highly integrated operation and motor position loop closed-loop control. At present, the robot based on PLC controller has been successfully applied in stacking, handling and welding. Another development direction of industrial robot open control system is networking [41]. Ken Goldberge proposed the concept of web-based robots in 1994. The high speed and high efficiency of industrial Ethernet has a natural advantage in data transmission, which makes the automatic control network become an inevitable

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development trend. Traditional fieldbus technology adopts all-digital communication. Although it is convenient and open, the maximum communication bandwidth is no more than 20 Mbps, which cannot meet the requirements of modern motion control system for high speed and high precision. Industrial Ethernet [42], with its remarkable speed and stability, has been applied in motion control, replacing the traditional fieldbus in many occasions and becoming a new generation of network standard. Literature [43] proposes a cps-based industrial robot system, which is divided into physical layer, network layer, control layer and application layer, realizing the integration of information world and physical world. The system can realize data acquisition, communication and control of equipment, robot task extraction, simulation, optimization and monitoring, and has been verified on ER3A-C60 industrial robot. DCOM (Distributed Component Object Model) technology is adopted to facilitate the communication between different robots in the distributed control network, and the monitoring of all robots in the distributed control network is successfully realized on ABB S4 robot.

3.2.2

Software Implementation Method of Open Control System

The robot operating system is a software platform for standardized robot design, which enables every robot designer to use the same platform for robot software development. The standard robot operating system includes hardware abstraction, bottom device control, common function realization, inter-process message and packet management, etc. Generally speaking, it can be divided into bottom device operating system layer and various software packages of different functions realized by robots contributed by user groups. Literature [24] introduces a variety of robot control software platforms and their applications in various occasions. The Robot Operating System (ROS) is an open-source Operating System designed specifically for robots. ROS was developed in 2007 by the Stanford Artificial Intelligence Laboratory (SAIL) and the robotics company (Willow Garage) for its personal robotics program. After more than a decade of development, ROS has gone from a niche operating system that nobody wanted to use to becoming one of the mainstream robot operating systems. At present, many robot companies have adopted ROS system to develop some products that are applied to the new market, such as ClearPath, Rethink, Unbounded, Neurala, Blue River. The most typical one is PR2 robot of Willow Garage. Like Android, ROS is open source and has similar functions. It can provide hardware abstraction, bottom device control, common function implementation, inter-process message and packet management. What makes it unique is the ability to support multiple languages, such as C++, Python, Octave, LISP, and even supports multiple languages, which simplifies the developer’s work. Because it is a Linux-based system, its reliability will also be higher, the volume can be done smaller, suitable for embedded devices. Literature [44] proposes a ROS based development platform for easily extensible robot system, which provides convenience for developers to develop intelligent industrial robot system. In 2017, Liu Feng from the University of Chinese Academy of Sciences designed and developed the JPB06

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Series six-DOF intelligent industrial robot system based on this platform. There are ROS-based robots designed by other research institutions, such as Fraunhofer institute Care-O-bot mobile manipulator, Nao of Aldebaran Robotics, Kawada HRP2-V [45], Shadow’s robotic hand [46], etc. Herman Bruyninckx [47] initiated the OROCOS (Open robot control Software) research project and developed a generic software package for robot control, which can be applied to different robots, and the program is open source and can be download from the website. Orocos is a C++ framework for building real-time control software for developing robot or machine control software. The Orocos Real-Time Toolkit provides a basic framework for quickly developing applications that can run on real-time operating systems such as RTAI and Xenomai, and of course it also supports Linux. The goal of this project plan is to develop a universal, free modular architecture for robot control. Orocos [48, 49] plans to use four C++ libraries: a real-time toolset, a kinematics and dynamics algorithm set, a Bayesian filter library, and an Orocos component library. On November 6, 2015, Turing robot, a domestic artificial intelligence entrepreneurial team, released an artificial intelligence robot operating system, Turing OS [50], at the National Convention Center. It is also basically the first intelligent robot operating system in China. This robot operating system can not only imitate human’s feelings and thoughts, but more importantly, it can realize self-learning and upgrade, truly practicing “artificial intelligence”. Currently, Turing OS has been used in existing robot products, and more robots that build this system are being developed, and will gradually face the market. There are a variety of robot system development platforms abroad, including non-commercial development platforms (Microsoft Robotics Studio [51], Robotics Developer Studio (MRDS), OpenJAUS, etc.) and commercial development platforms (iRobot AWARE [52], Evolution Robotics ERSP, URBI, Webots). As well as open source software projects from universities (Player/Stage [53]), and XBotCore [54]. With the development of industrial robot control technology, the development of “modular and standardized industrial robot controller with open structure” is a development direction of industrial robot controller. At present, the control systems of several famous robot companies at home and abroad: ABB industrial robot control system—IRC5, KUKA industrial robot control system—KRC4, KEBA industrial robot control system—Keba, FANUC industrial robot control system—FANUCRobotR30iA, Xinsong industrial robot control system—SIASUN-GRC, etc.

4 Multi-robot Collaborative Control System Since the late 1980s, multi-robot systems [55, 56] have received the attention of a large number of scholars and have developed rapidly. Compared with the traditional multiple single robot system, multi-robot systems have more advantages. The sensor information of a single robot in a distributed multi-robot system can be effectively complementary, so the whole robot system has higher data redundancy,

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stronger adaptability and robustness. In particular, when completing complex tasks, the advantages of multi-robot are more prominent. In general, multi-robot system [57] can complete complex tasks that are difficult for a single robot to achieve with the help of advanced cooperation architecture and coordination strategy. The control of multi-robot cooperative system is a hot research topic in the field of robotics. At present, the industrial production system is developing towards the large, complex, dynamic and open direction, and the traditional industrial control system and the production equipment based on a single robot have been difficult to meet the needs of production tasks. In the field of industrial production, the tasks of simultaneous operation of multi-robot system include collaborative welding with or without fixtures, assembly and collaborative handling of large and heavy workpieces [58]. In abroad, the new generation robot controller IRC5 produced by ABB can control four ABB industrial robots at the same time [59], and its MultiMove function can realize multi-robot handling, welding and other tasks with high accuracy. The Motoman robot produced by Yaskawa can coordinate the movement of 8 robots at the same time, and it is convenient to realize a special fixtureless welding system. In addition, Motoman robot also offer multiple types of dual-arm robot systems such as SDA10, SDA20 and DA20 for complex assembly tasks. KUKA offers industrial robots with RobotTeam functionality to facilitate the construction of multi-robot collaboration systems. In domestic, the MRCAS [60] (multi-robots Cooperative Assembly System) was established by Shenyang Institute of Automation based on the assembly of multirobots in the manufacturing environment. By adopting a layered architecture combining centralization and decentralization, the system can complete the functions of self-formed formation, formation transformation, autonomous obstacle avoidance, etc., and further complete the assembly task by multi-robot coordination and cooperation.

5 Development Trend of Open Control System (1) Network. Networking refers to connecting the motion controllers arranged in different positions through the network by means of fieldbus or Ethernet, depending on the existing communication and information technology. It is convenient to build a distributed motion control system and multi-axis expansion of the motion controller to realize a more powerful and flexible motion control system. (2) Modular. Under the open structure, the robot control system can be modularized, which also facilitates the structuralization and reconstruction of industrial robots. Modular design, which not only facilitates installation and maintenance, but also improves system reliability and system structure. (3) Intelligent. With the continuous development of the theory of artificial intelligence (AI) and the continuous test and innovation of practical application, fuzzy

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control, neural network and other optimization algorithms have been widely used in the motion control system. While improving the control performance, it is necessary to improve the system’s self-learning, self-diagnosis and fault tolerance. At present, the domestic and foreign manufacturers of motion control have taken the intelligent level of motion controller as a new technical point and are deepening its application. (4) Other development trends. With the development of robotics, how to effectively apply the research results of other fields (such as image processing, voice recognition, optimal control, artificial intelligence, etc.) to the real-time operation of the robot control system is a challenging research work, which requires a lot of scientific research and experiments.

6 Conclusion In summary, the control system, as a vital component of industrial robots, plays a decisive and restrictive role in the development of robotics. This paper summarizes the research results related to industrial robot control systems, hoping to provide a theoretical basis for related research.

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13. Jerry, D., Jeremy, H.G., et al.: Hybrid systems in robotics. IEEE Robot. Autom. Mag. 18, 33–43 (2011) 14. Kilyen, A.O., Letia, T.S.: Hybrid robot controller synthesis with GP and UETPN. In: 2018 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR), Cluj-Napoca, pp. 1–6 (2018) 15. Lutz, P., Sperling, W.: OSACA-the vendor neutral control architecture. In: Proceedings of the European Conference on Integration in Manufacturing, Dresden, Germany, pp. 247–256 (1997) 16. Li, Z., Liu, B.: Research on open robot control architecture based on OSACA. Combined Mach. Tool Autom. Process. Technol. 03, 70–72+74 (2003) 17. Zhunan, F.: Research on SCARA manipulator open control system based on OSACA model. Zhejiang University (2019) 18. Chihiro, S., Okano, A.: Open controller architecture OSEC-II: architecture overview and prototype systems. In: Proceedings of IEEE 6th International Conference on Emerging Technologies and Factory Automation, pp. 543–550 (2017) 19. Ma, X., Han, Z., Wang, Y., et al.: Development of a PC-based open architecture software-CNC system. Chin. J. Aeronaut. 03, 272–281 (2007) 20. https://omac.org/ 21. Tang, F., Geng, S.R., Qiang, C., et al.: Open robot control platform based on LSOA. Appl. Mech. Mater. (2013) 22. Xia, J., Zhang, H., Wang, G., et al.: Study on open robotic plasma spray forming system based on ethernet. Robot 01, 17–21 (2008) 23. Zhenhua, W., Xu, L., et al.: Research and development of Open 6R industrial robot control system based on Win CE. Combined Mach. Tool Autom. Process. Technol. 6, 76–80 (2018) 24. Abdelfetah, H., Abderraouf, M., et al.: A survey of development frameworks for robotics. In: 8th International Conference on Modelling, Identification and Control (ICMIC-2016), pp. 67–72 25. Ding, L., Wang, D., Li, T., Yang, Y.: A brief introduction to CLARAty software system. Mach. Tool Hydraul. 40(17), 118–122 (2012) 26. Montemerlom, R., Thrun, S.: Perspectives on standardization in mobile robot programming: the Carnegie Mellon navigation (CARMEN) toolkit. In: 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003. Proceedings, vol. 3. IEEE, New York, pp. 2436–2441 (2003) 27. Brooks, A., Kaupp, T., Makarenko, A., et al.: Orca: components for robotics. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Workshop on Robotic Standardization, pp. 163–168 (2006) 28. Panagiota, T., Sotiris, M., George, M., et al.: ROS based coordination of human robot cooperative assembly tasks-an industrial case study. Proc. CIRP 37(1), 254–259 (2015) 29. Liu, F.: Design and implementation of ROS-based intelligent industrial robot system. University of Chinese Academy of Sciences (Institute of Computing Technology, Chinese Academy of Sciences) (2017) 30. Maosheng, T., Tang, X., Zhang, Y.: Implementation and design of open control system for industrial robot based on double CPU. In: 2011 IEEE 2nd International Conference on Computing Control and Industrial Engineering (2011) 31. Mou, H.: Analysis and research on motion control of industrial robots. Electr. Technol. Softw. Eng. 23, 115–117 (2018) 32. Huang, J.: Research on Cartesian impedance control system of manipulator in human-machine collision environment. Harbin: Harbin Institute of Technology (2009) 33. Zhongzhong, H.: Design of open industrial robot control system based on multi-axis motion control card. Hefei University of Technology (2015) 34. Wang, T., Qu, D.: The open architecture of industrial robot control system. Robot 24(3), 256– 261 (2002) 35. Tian, S.: Development of six-axis robot control system based on EtherCAT bus. South China University of Technology (2018) 36. Hu, G.: Research on open networked robot communication platform and control method. Southeast University (2005)

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The Research on Aircraft Anti-skid Braking Switching Control with Road Online Identification Based on Fuzzy Algorithm Jie Gao and Bing Gao

Abstract Aircraft anti-skid brake determines the safety, efficiency and comfort of braking directly. Under the same road condition, different slip rates will lead to different adhesion coefficients between tires and roads, and the optimal slip rates of different road conditions are different. In this paper an aircraft anti-skid switching control system with road identification based on fuzzy algorithm was proposed. Nonlinear model of aircraft all-electric brake system was established, and according to typical road conditions, the optimal slip rate of road surface was identified online through fuzzy reasoning, then the anti-skid braking control is carried out by using fuzzy and PID switching control algorithm. The MATLAB simulation results show that the system can identify road conditions online and adjust braking force in real time, which can keep the optimal slip rate, shorten the braking distance and achieve smooth braking. Keywords Aircraft anti-skid braking · Optimal slip rate · Fuzzy · PID · Switching control · Identify · Real time

1 Introduction The anti-skid braking system is important airborne equipment for aircraft, which is of great significance to the safety during the take-off and landing. With the development toward large tonnage, high speed and high comfort of aircraft, the landing process of aircraft requires higher performance of braking system. In recent years, multi-electric technology has been widely used in aircraft. Because the advantages of replacing traditional hydraulic pressure, reducing aircraft weight and improving safety, allelectric brake system has also been widely concerned and studied. J. Gao (B) School of Electronic Information and Automation, Civil Aviation University of China, 2898 Jinbei Road, Dongli District, Tianjin 300300, China e-mail: [email protected] B. Gao Engineering Techniques Training Center, Civil Aviation University of China, 2898 Jinbei Road, Dongli District, Tianjin 300300, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_102

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From the view of controlled variables, the commonly control algorithms used in aircraft anti-skid braking system are mainly divided into slip rate control, deceleration rate control and slip speed control. Slip rate control mode has high braking efficiency and strong ability to adapt to harsh ground conditions, but the calculation of slip rate depends on accurate aircraft speed and is sensitive to speed errors, so it is limited to use. Deceleration rate control mode and slip speed control mode are not sensitive to measurement errors. However, these two control modes slip deeper at low speed and have poor ability to adapt to runway changes, so braking is limited. Vehicle efficiency is low. Generally speaking, the current anti-skid control strategy has its limitations in principle. Therefore, the anti-skid control algorithm with high efficiency and strong robustness is a research hotspot in the field of aircraft brake control. For this reason, many scholars have done a lot of research on anti-skid control algorithm. Among them, the most common one is to adopt multi-threshold PID control, which is also called pressure offset [1]. In order to improve the robustness of the system, intelligent algorithm is more used in aircraft anti-skid control. Fuzzy control algorithm, neural network control and hybrid intelligent control are used to control aircraft anti-skid braking, which overcomes the influence of uncertain factors and achieves braking target tracking [2–4]. In order to improve the accuracy of antiskid control, Kalman filter algorithm is often used to accurately estimate the relevant aircraft parameters [5]. Immune evolutionary algorithm is introduced to improve the efficiency of optimization, which further optimizes the control system [6]. Reference [7] applies model-free adaptive control method to aircraft anti-skid control, and achieves stable slip rate in a relatively short time. Reference [8] uses iterative learning combined with compensation control method to track the optimal slip rate of antiskid system. Reference [9] designs an adaptive sliding film controller, which opens up a new idea for the control of slip rate. For road identification, Reference [10] estimates the maximum adhesion coefficient of target road by analogy based on the same non-linear trend of adhesion coefficient-slip curve with slip rate which is more suitable for identifying two similar road types. Reference [11, 12] identifies road conditions based on wheel deceleration and achieves good result. Because the aircraft anti-skid brake is a multi-variable non-linear system, the control algorithm must have good response and tracking ability. Intelligent algorithm is good at strong robustness and dynamic response, but weak system tracking precision, and higher requirements for hardware performance from the practical point of view. Considering the types of airport road conditions and the restrictions of aircraft landing and taxiing, in this paper fuzzy algorithm is introduced based on traditional PID control, which uses fuzzy reasoning to identify the airport road conditions online, and revises the corresponding optimal slip rate. The whole anti-skid braking system is made in Fuzzy and PID switching control mode as to adjust the all-electric brake which keeps the aircraft near the optimal slip rate and the maximum attachment coefficient in the braking process. So the system braking takes into account the good dynamic response performance, but also has high precision tracking capability which can improve the efficiency of anti-skid braking and shorten the braking distance.

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2 Mathematical Model of All-Electric Braking System The key of aircraft anti-skid control is to ensure the maximum adhesion between the wheel and ground. The attachment coefficient is the most critical parameter to the adhesion, and the relationship between them is proportional. The slip rate is the most important factor affecting the attachment coefficient [1]. σ =

va − vw va

(1)

Then, va is the speed of aircraft, vw is the speed of wheel. And the relationship between slip rate and attachment coefficient is non-linear. Aircraft antiskid braking system model mainly includes airframe dynamics, wheel model, slip ratio and attachment coefficient model, electric actuator and brake device model. Ignoring the existence of crosswind effect in aircraft anti-skid control process, assume that the main landing gear wheel on both sides in the braking process is completely symmetrical. The airframe model only considers transverse, vertical and pitch, as follow: ⎧ ⎨ m v˙ x = T0 − Fz − Fx − μgd (mg − Fy ) F + N1 + N2 − mg = 0 ⎩ y N2 b − (Fx2 + n Fx1 )h c − n N1 a − T0 h t = 0

(2)

Symbols See Reference [8], the aircraft wheel model and the attachment coefficient model are respectively: ω˙ j =

μN1 Rg − Ms M j − Ms = I I

(3)

Fx N

(4)

μgd =

ω˙ j is wheel angular acceleration, M j is ground binding moment, M s is braking torque, I is the wheel inertia braked, μ is ground attachment coefficient, N 1 is wheel load, Rg as the tire rolling radius。 Electromechanical actuator converts electrical signal into motor speed, and then converts it into mechanical signal of linear motion of ball screw. Finally, brake torque is provided by brake pressure disc. Brushless DC Motor is selected for motor model [9], Mathematical relationships among motor speed, torque T, screw displacement x and pressure P are as follows: ⎧ ω ⎪ ⎨ x˙ = 2πi0 L P = Kl x ⎪ ⎩ T0 = J ω0 + Tm +

(5) P x˙ ω0

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J is the moment of inertia converted from the whole electromechanical actuator to the motor shaft, i is the motor transmission ratio, K l is the coefficient of displacement and thrust, T m is the total resistance moment of the motor. L is the length of the lead screw.

3 Road Identification Based on Fuzzy Algorithm 3.1 Fuzzy Control Fuzzy controller is a kind of language controller, which is mainly composed of fuzzification, fuzzy logic reasoning, clarification and knowledge base. Fuzzy reasoning is realized by fuzzy conditional statements based on fuzzy set theory. The control process is to change the precise input of the system into fuzzy input by fuzzification. Next, the corresponding linguistic variables of the fuzzy input are inferred according to the fuzzy rules to get the fuzzy output. Finally, the fuzzy output is converted into clarity.

3.2 Road Identification Aircraft runway surface conditions are basically the same, all of them are asphalt concrete. The difference of anti-skid control is mainly reflected in the difference of the max attachment coefficient of the road caused by the change of weather, which affects the target input of the optimal slip rate. Because the μ-σ curve has great nonlinearity, it is difficult to establish an accurate model, so in this paper Burckhardt model is selected, as shown below. μ = C1 (1 − e−C2 s ) − C3 s

(6)

Taking four typical μ-σ curves of road as reference standard, the specific values of fitting parameters for various road types are shown in Table 1. The μ − σ curve is obtained by substituting the parameters in the table into Formula (6) as shown in Fig. 1. Table 1 The specific values of fitting parameters

Road

C1

C2

C3

Ice

0.0500

306.3900

0.0010

Snow

0.1946

94.1290

0.0646

Wet

0.8570

33.8220

0.3470

Dry

1.2801

23.9900

0.5200

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1.4 ice snow wet dry

Attachment coefficient

1.2

1

0.8

0.6

0.4

0.2

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

slide-rate

Fig. 1 Four typical pavement μ-σ curves

Table 2 The optimal slip rate and attachment coefficient

Road

sopt

μmax

Ice

0.03

0.05

Snow

0.06

0.19

Wet

0.13

0.80

Dry

0.16

1.17

The extreme values of burckhardt model under the above typical road conditions can be obtained:  sopt = C12 ln CC1 C3 2 (7) μmax = C1 − CC23 (1 + ln CC1 C3 2 ) Finally, the optimal slip rate and attachment coefficient under four typical road conditions are obtained, as shown in Table 2. As the optimal slip rates of different roads are quite different, so it is necessary to establish four kinds of fuzzy reasoning rules for typical roads. The input of the fuzzy reasoning is μ and μ, ˙ the range of which is [0, 1.2] and [−1, inf]. The output variables are similar to four typical pavements in the range of [0, 1]. The membership functions are shown in Fig. 2. Fuzzy rules are established as shown in Table 3. The process of fuzzy reasoning is shown in Fig. 3.

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Table 3 Fuzzy rules Num

μ

μ˙

Ice

Snow

Wet

Dry

1

S

S

VS

DS

DS

DS

2

S

M

VS

MS

SS

DS

3

S

L

DS

VS

SS

DS

4

M

S

DS

VS

DS

DS

5

M

M

SS

VS

SS

DS

6

M

L

DS

SS

VS

MS

7

ML

S

DS

DS

VS

MS

8

ML

M

DS

SS

VS

SS

9

ML

L

DS

DS

SS

VS

10

L

S

DS

DS

SS

VS

11

L

M

DS

DS

DS

VS

12

L

L

DS

DS

DS

VS

After empowering according to the similarity degree derived from reasoning, the final result of pavement recognition is obtained: 

2max +ω3 μ3max +ω4 μ4max μmax = ω1 μ1max +ωω2 μ1 +ω 2 +ω3 +ω4 ω1 σ1opt +ω2 σ2opt +ω3 σ3opt +ω4 σ4opt σopt = ω1 +ω2 +ω3 +ω4

(8)

3.3 Anti-skid Control System Based on Fuzzy-PID Switching The anti-skid system based on the fuzzy-PID switching control mainly relies on the fuzzy algorithm to identify the road surface and control system rapid response in the early stage. When the identification results are very similar and the target slip error does not exceed the limit value, it automatically switches to the traditional PID control to achieve accurate system response. The control system structure is shown in Fig. 4.

4 Simulation Research Taking the data of a certain type of civil aviation airliner as reference object, the simulation model of control system is established under the environment of M ATLAB/Simulink, and the control logic of the system is compiled with M language. The initial landing speed of the aircraft is set at 70 m/s, and the road condition is a typical Dry-running road surface. After 5 s, the aircraft enters the wet-running

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Membership Function of Adhesion Coefficient Change Rate

Membership function of Adhesion coefficient

Membership function of output Fig. 2 Membership function of input and output Attachment change rate Attachment coefficient

Fuzzy weight

Weighted

determination

calculation

Fig. 3 The process of fuzzy reasoning

σopt μmax

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Fig. 4 Anti-skid system based on fuzzy pavement identification switching control

0.2 Fuzzy PID switching control PID

0.18 0.16

Slide-rate

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0

5

10

15

Time s

Fig. 5 Slip rate dynamic response of switching control PID

road surface. When the speed of the aircraft decreases to 5 m/s, the simulation stops (Figs. 5, 6, 7 and 8). From the simulation results, it is easy to know that in the dynamic response of the system, the road surface identification and early control of the fuzzy algorithm make the system achieve or approach the optimal slip rate in a short time, and then the system can basically complete the accurate tracking of the optimal slip rate

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70 Without identify Fuzzy identify

Aircraft velocity m/s

60

50

40

30

20

10 0

2

4

6

8

10

12

14

16

18

Time s

Fig. 6 Aircraft speed comparison 70 Wheel velocity with fuzzy identify Aircraft velocity with fuzzy identify 60

Velocity m/s

50

40

30

20

10

0

0

10

5

Time s

Fig. 7 Comparison of aircraft and wheel speed

15

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J. Gao and B. Gao 800 Without identification With fuzzy identification

700

Distance m

600 500 400 300 200 100 0

0

2

4

6

8

10

12

14

16

18

Time s

Fig. 8 Braking distance

in 2 s through the later PID adjustment. Compared with the system without road identification, the system can adjust the optimal slip rate and shorten the braking distance in time after the change of road conditions. At the same time, the speed of aircraft and engine wheel is relatively smooth, which ensures comfort on the premise of improving braking efficiency.

5 Conclusion Based on the model of all-electric brake anti-skid system, this paper designs a switching control system with the online identification of roads by the fuzzy algorithm. The knowledge base of fuzzy reasoning is established by the fuzzy algorithm, which can identify road conditions in real time. Combining with the traditional PID control, the switching control of fuzzy PID for different road environments not only has good rapid system response ability, but also takes into account the advantages of PID. Acknowledgements This work is supported by National Nature Science Foundation under Grant 51707195 and basic research business fee of the Civil Aviation University of China under Grant 3122014C009.

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References 1. Jiao, Z., Liu, X.: Aircraft antiskid braking control method based on tire–runway friction Model. J. Aircraft 54(1), 75–84 (2017) 2. Wei, X., Yin, Q., Nie, H.: Aircraft electric anti-skid braking system based on fuzzy-PID controller with parameter self-adjustment feature. J. Nanjing Univ. Aeronaut. Astronaut. 31(1), 111–118 (2014) 3. He, H., Wu, R.: Improved BP neural network in design of aircraft antiskid brake system. J. Beijing Univ. Aeronaut. Astronaut. 30(6), 561–564 (2004) 4. Yuren, L., Zhihui, Z., Jianlong, X.: Study on fuzzy sliding-mode variable structure control for aircraft anti-skid braking. J. Northwestern Polytech. Univ. 33(1), 45–49 (2015) 5. Huang, Y.: LQ optimal simulation for aircraft anti-skid brake control system. J. Beijing Univ. Aeronaut. Astronaut. 29(12), 1119–1122 (2003) 6. Liu, Z., LI, Z., Airong, J.: Study on aircraft anti-skid brake system based on immune fuzzy control algorithm. Comput. Measure. Control 17(8), 1562–1565 (2009) 7. Shi, W., Liu, W., Chen, J.: Application of model free control technology on the aircraft anti-skid brake systems. Comput. Measure. Control 20(6), 1552–1554 (2012) 8. Gao, J., Gao, B.: Research on feedback compensation control for aircraft electric antiskid brake system based on IL. J. Syst. Simul. 29(7), 1625–1630 (2017) 9. Li, F., Jia, Z.: Adaptive control for aircraft anti-skid braking system based on friction force model. J. Beijing Univ. Aeronaut. Astronaut. 39(4), 447–452 (2013) 10. Yuan, C., Zhang, L., Chen, L., He, Y., Shen, J., Bei, S.: A research on the algorithm for identifying the peak adhesion coefficient of road surface. Autom. Eng. 11(39), 1268–1273 (2017) 11. Li, R., Zheng, T., Feng, H., Li, Y., Chen, W.: Road automatic identification of automobile ABS via fuzzy adaptive method. J. Chongqing Univ. Posts Telecommun. 2(19), 201–205 (2007) (Natural Science) 12. Jones, L.P.: Modeling braking friction between an aircraft tire and the runway. In: Proceedings of AIAA Modeling and Simulation Technologies Conference, pp. 66–74 (2011)

Automatic Sleep Staging Based on XGBOOST Physiological Signals Xiangfa Zhao, Panxiang Rong, Guobing Sun and Bin Zhang

Abstract The sleep staging can provide a feasible method for sleep medicine treatment, and the artificial sleep staging is becoming outdated, although there is still room for the improvement of accuracy of automatic sleep staging, an automatic sleep staging method is proposed based on XGBOOST and physiological signals. Firstly, the EEG signals and heart rate signals with high availability are selected from a database containing physiological signals, and then the physiological signals are newly sampled and the features are extracted in the time domain, the frequency domain and the nonlinear domain. Secondly, Successive Projections Algorithm (SPA) is applied to select features extracted above, and the redundant features are removed away. Finally, the selected feature sets are put into the XGBOOST model for automatic sleep staging, and the accuracy can reach 92.35%. Keywords Sleep staging · Physiological signals · SPA · XGBOOST

1 Introduction Sleep is a very important part of human life. It is a complex physiological process and an important part of the body’s functional recovery [1, 2]. Especially in such an era of rapid development, everyone is under pressure from all walks of life, which has seriously affected our sleep quality, and sleep-related diseases have gradually come into people’s life [3, 4]. Sleep stage is an important means to solve our sleep problems. Sleep staging can not only accurately describe the state switch during sleep and complete the sleep quality assessment, but also understand the related principles of sleep related diseases such as breathing or heartbeat through continuous X. Zhao · P. Rong (B) · G. Sun (B) · B. Zhang College of Electronic Engineering, Heilongjiang University, Harbin, China e-mail: [email protected] G. Sun e-mail: [email protected] X. Zhao · P. Rong · G. Sun Key Laboratory of Information Fusion Estimation and Detection, Harbin, Heilongjiang Province, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_103

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monitoring of the sleep process. Therefore, sleep staging is of great significance for the diagnosis and treatment of diseases [5, 6]. Sleep staging refers to the analysis of sleep quality by dividing sleep into different phases. Currently in the sleep staging field, sleep scores are performed by professional sleep technologists based on visual observations of the signals. In 1968, Rechtschaffen and Kates [7] proposed the famous R&K golden staging criterion. Sleep is divided into six stages according to the electroencephalogram (EEG), muscle signal (EMG) and ophthalmic signal (EEG) during sleep, namely, awakening stage, Rapid eye movement (REM) and Non-rapid eye movement. The non-rem stage is divided into light sleep stage 1 (S1), light sleep stage 2 (S2), deep sleep stage 3 (S3) and deep sleep stage 4 (S4). The sleep stages S4 and S3 are collectively known as slow-wave sleep because of the dominance of slow oscillations from the neocortex. Sleep stages S2 and S1 together are called light sleep According to the study, the human sleep process is not fixed, but the cycle of transformation. The order is as follows: S1-S2-S3-S4-S3-S2-S1-REM. After REM sleep, individuals return to light sleep stage S1 and begin a new cycle. As the sleep cycle was carried out, the individual spent more and more time in rem sleep, and the depth of sleep was reduced accordingly. Also, the sleep cycle takes about 90 min. Generally, normal people experience 4 to 6 sleep cycles every night [8]. At present, the R&K Sleep staging criteria modified by the American Academy of Sleep Medicine (AASM) in 2007 are generally adopted internationally, and S3 and S4 in the R&K Sleep staging criteria are combined into one phase, and each phase is represented by W, R, N1, N2 and N3 respectively [9]. Early sleep staging work is all done manually, which is not only very complicated and requires experts with relevant experience, but also involves a large amount of work [10]. Therefore, in recent years, a large number of researchers have devoted themselves to the automatic sleep staging method and applied the pattern recognition method to the automatic sleep staging [11]. The commonly used pattern recognition methods include support vector machine, random forest, ANN, KNN, SVM, etc. [12]. These models were also more than 85% accurate in sleep staging. With the rapid development of the field of artificial intelligence, many new algorithms appear. This makes automatic sleep staging increasingly accurate. This paper summarizes the common feature extraction methods in recent years, and extracts features from multiple domains, including time domain, frequency domain and nonlinear domain. Successive projections algorithm (SPA) is used in the feature selection section. SPA is a forward variable selection algorithm that minimizes the collinlinearity of vector space. Its advantage lies in the extraction of several characteristic wavelengths of the whole band and the elimination of redundant information in the original spectral matrix. SPA is mainly used in the direction of spectral pretreatment, but it is very helpful in the selection of physiological signal features. Finally, this article USES the algorithm XGBOOST, which has been extremely popular in mathematical analysis competitions in recent years. XGBOOST in traditional Boosting, on the basis of introducing the regularization item, to join the pruning, control the complexity of the model. XGBOOST borrows from the RF to support column sampling, which

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not only prevents overfitting, but also reduces computational complexity. This paper improves the accuracy of sleep staging and speeds up the sleep staging.

2 Data and Methods 2.1 Data Sources In this study, Sleep-EDF database available at Physionet Subjects database have been utilized to conduct the experiments. Data in this paper refers to the CAP sleep database of PHYSIONET [13, 14]. The CAP sleep database is a collection of 108 polysomnogram records registered with the sleep disorders center. The waveforms include at least 3 EEG channels, EOG, EMG of the submentalis muscle, bilateral anterior tibial EMG, respiration signals and EKG. In this study, 28 groups of subjects were selected from the database, including 6 subjects with REM behavior disorder, 10 subjects with nocturnal frontal lobe epilepsy, 6 subjects with insomnia and 6 subjects without pathology, including 13 males and 15 females, aged from 16 to 67 years old. The 28 groups of sleep data used in this paper were measured under the condition of fully satisfying the sleep test, and were marked by sleep experts according to the R&K rules. These notes are used as a reference standard to test the staging accuracy of the proposed method.

2.2 EEG and Sleep The amplitude, frequency and phase of EEG signal are continuously changing, so it is difficult to find the periodic rule. It is usually composed of α, β, θ, δ, Spindle, Sawtooth and k-complex, and different sleep stages show different rhythm waves [15]. See Table 1.

2.3 ECG Signals and Sleep Heart rate variability (HRV) refers to the tiny change in the time it takes for the heart to beat twice, reflecting the degree of the fluctuation of heart rate in sinus rhythm mediated by autonomic nerves [16]. In the process that human body undertakes morpheus, can have a lot of neuromodulatory system to participate in. Different sleep states are bound to produce different changes in the neuromodulatory system. Physiological parameters regulated by the nervous system include heart rate, blood pressure, ECG, and heartbeat. In the early 1970s, some scholars proposed to use the R-R interval of ECG for sleep staging. The continuous efforts of many researchers

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Table 1 Description of various rhythm waves Characteristic wave

Amplitude

Frequency

Characteristics

Physiological response (health)

Sleep state

α

20–100 μV

8–13 Hz

The frequency is faster, the amplitude changes in a shuttle shape, and each shuttle type lasts for 1–2 s

Appeared when awake and quiet, disappeared by outside interference

REM Awake

β

5–20 μV

13–30 Hz

The fastest frequency

Mentally nervous, emotional, representing the brain awakening

REM Awake

δ

20–200 μV

0.5–4 Hz

Slowest frequency

It does not appear in awake state, only in extreme fatigue, deep sleep appears

S3 S4

θ

20–150 μV

4–8 Hz

Slower frequency

Unconsciousness is not monitored, and sleepiness and depression occur

REM S1

k-complex

0.5–1.5 Hz

Negative phase spike initial, then connect a positive phase spike for more than 0.5 s

Light sleep

S2

Sawtooth

2–6 Hz

Sawtooth triangle wave

Dream related

REM

Spindle

12–14

The amplitude increases first and then decreases

Light sleep

S2

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have proved this hypothesis: heart rate variability has a good correlation in the study of sleep stages. Therefore, single channel electroencephalogram (EEG) and electrocardiogram (ECG) were selected as physiological signals in this paper.

2.4 Pretreatment Feature extraction is an important part of sleep staging process, but before feature extraction, EEG signals and ECG selected from the database should be preprocessed to eliminate inconsistency and reduce noise and human influence. To ensure the consistency of different recorded data, all subjects’ EEG and ECG signals were resampled at 128 Hz sampling frequency. The physiological signal data was divided into a sleep stage every 30 s as a sample point, that is, each sample point had a total of 3840 data points. The sleep duration was 214 h 45 min, with a total of 25,770 physiological signal sample points. Then the pre-processed data are extracted from time domain, frequency domain and nonlinear domain. We chose to extract common characteristic parameters such as standard deviation, median, arithmetic mean, skewness, variance value and zero crossover value. For ECG signals, the extracted features are r-r interval features: the time interval between two adjacent heartbeat R wave peaks of ECG. During feature extraction in frequency domain, EEG rhythm waves of different frequencies will be generated according to different sleep stages. The energy and energy ratio in frequency domain are extracted. The corresponding frequency band ranges of the four kinds of rhythm waves are shown in Table 2. The specific steps are shown below. (1) FFT is applied to EEG signal x(n) time series to obtain x(n) spectrum P (ω), as Formula (1)

P(ω) =

N−1 

x(n)e−j N ωn , ω = 0, 1, . . . , N − 1 2π

(1)

n=0

(2) δ, θ, α, β, Rhythmic wave band energy as Formulas (2), (3), (4) and (5).

Table 2 Rhythm wave corresponding frequency table Rhythm wave

δ

θ

α

β

Frequency range (Hz)

0.5–4

4–8

8–13

13–30

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4 E(δ) =

p(ω)2 dw

(2)

p(ω)2 dw

(3)

p(ω)2 dw

(4)

p(ω)2 dw

(5)

0.5

8 E(θ) = 4

13 E(α) = 8

30 E(β) = 13

(3) Band energy ratio as Formulas (6), (7), (8), (9), (10) and (11). Eall = E(δ) + E(θ) + E(α) + E(β)

ER(δ) = E(δ)/Eall

(6)

ER(θ) = E(θ)/Eall

(7)

ER(α) = E(α)/Eall

(8)

ER(β) = E(β)/Eall

(9)

ER(δ/θ) = E(δ)/E(θ)

(10)

ER(α/θ) = E(α)/E(θ)

(11)

Since 1980, the nonlinear theory has been rapidly developed and widely applied in many fields.

2.5 Feature Selection SPA is a forward variable selection algorithm that minimizes the collinearity of vector space. It has the advantage of extracting several characteristic wavelengths of the whole band. Although it is mainly used for the optimal band selection of spectral images, it is also operable for other multidimensional matrices and can eliminate

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the redundant information in the original feature matrix. It can also be used for feature screening to minimize the collinearity between variables, reduce the number of variables used in modeling, and improve the speed and efficiency of modeling. The algorithm is described as follows. Let xk(0) be the initial iteration vector, and N be the number of variables to be extracted. The spectral matrix is j column. Before the iteration, select column 1 j of the spectral matrix, Assign the jth column of the modeling set to xj , denoted as xk(0) . The set of unselected column vector positions is denoted as s, as shown in Formula (12) s = { j, 1 ≤ j ≤ J, j ∈ / {k(0), . . . , k(n − 1)}}

(12)

The projection of x and j on the remaining column vectors is calculated respectively, as shown in Eq. (13)   T xk(n−1) )−1 , j ∈ s P x j = x j − x Tj xk(n−1) xk(n−1) (xk(n−1)

(13)

  k(n) = arg(max( P x j ), j ∈ s, x j = P x j , j ∈ s, n = n + 1, If n is less than, we go back to finally, the extracted variable is {x_(k(n) = 0,…, N − 1}. Corresponding to each k(0) and N, multiple linear regression analysis (MLR) was carried out after one cycle, and the prediction standard deviation (RMSEV) of the verification set was obtained, and the k(0) and N corresponding to the smallest RMSEV value were the optimal values [17].

2.6 Model Selection Sleep stages can be realized by automatic classification of extracted features by pattern recognition method. Common pattern recognition methods include Fisher linear discrimination, Bayesian method, artificial neural network (ANN), support vector machine (SVM), k-nearest neighbor (KNN), XGBOOST, etc. In this experiment, XGBOOST pattern recognition method commonly used to process a large amount of data is selected. XGBOOST is a kind of pattern recognition classification method that has been widely used in recent years. XGBOOST integrates the advantages of gradient promotion, random forest and other algorithms, and innovatively proposes the model’s discrete consciousness and off-core calculation method, which not only improves the prediction effect of the algorithm model on the distributed database but also greatly improves the speed of model training [18]. It is one of the most commonly used models in the competition at home and abroad.

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XGBOOST is a lifting tree model, and the tree model used is the CART regression tree model. The idea of this algorithm is to add trees continuously, that is, to split features continuously to generate a tree. It is essentially learning a new function to fit the residuals of the previous prediction. The fitting process is then repeated until the requirements are met. When the training is over, we can get k trees, and the predicted value we need is to add up the node scores of each tree. The general function of prediction is shown in Eq. (14). f(t) i =

t 

fk (xi ) = f(t−1) + ft (xi ) i

(14)

k=1 (t−1) are the predictions at steps t and t − where ft (xi ) is the learner at step t, f(t) i and fi 1, and xi is the input variable. At the same time, in order to prevent overfitting of the model, XGBOOST derives the analytical formula as shown in (15) from the original model. It will not affect the calculation speed of the model, and can evaluate the quality of the model.

Obj

(t)

n t     = l yi , yi + (fi) k=1

(15)

k=1

In which l is loss function, n is the use of the number of observations,  is the regularization item.

3 Results and Discussion 3.1 Pretreatment Results After preprocessing, physiological signal data with consistent frequency were obtained, and feature extraction was performed on the processed signals. The extraction results are shown in Table 3. On this basis, the extracted features are extracted Table 3 Multiple domain feature tables Area

Feature

Time domain

Standard deviation, median, arithmetic mean,Skewness, variance value, zero crossing value R-R gap

Frequency domain

E(δ), E(θ), E(α), E(β), ER(δ), ER(θ), ER(α), ER(β), ER(δ/θ) ER(α/θ)

Nonlinear domain

Multi-scale entropy

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again to generate new features. The methods used include the first derivative, second derivative, time domain plus window for 4 min, etc. A total of 99 features are generated.

3.2 Feature Selection Results In the preprocessing of the previous chapter, we extracted the 99-dimensional feature set from the original signal. But too high dimension of the feature set is easy to produce dimension disaster problem for our experiment. At the same time, there are too many features for us to be sure that the correlation of each feature is available. In the process of modeling and classification, the calculation amount is too large and the calculation time is too high. Therefore, feature selection processing is required for feature extraction results. There are many methods for feature selection, such as principal component analysis (PC) and correlation coefficient method. SPA was used in this experiment. SPA is a forward variable selection algorithm that minimizes the collinearity of vector space and can eliminate redundant information in the original spectral matrix. SPA is mainly used for the selection of characteristic bands in spectral experiments. However, through experiments, it can also greatly improve the accuracy of training in the study of physiological signal processing. First, the 99-dimensional feature set is imported into the SPA model. Then, the parameters of SPA model are set. Finally, 16 features with the largest weight of classification information are selected from 99 features. The 16 features were selected for the following modeling classification. See Fig. 1.

Fig. 1 The number of selected characteristics and the numbered graph of selected characteristics

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90.22 100

95.84

74.07

81.51

80 60 40

S4 S2

20 W

0 W

S1

S2 W

S3 S1

S2

S4 S3

REM S4

REM

Fig. 2 Classification accuracy of each sleep state

3.3 Modeling Classification Results After preprocessing and feature selection, we finally obtained a 16-dimensional data set of 25,770 samples. First, we randomly divide the data into three sets of the training set, correction set and test set according to the proportion of 60, 20 and 20%. The training set is mainly used to train the model, learn the sample data set, and set up a classifier by matching some parameters. The correction set is mainly used to adjust the parameters of the classifier for the learned model, such as selecting the number of hidden elements in the neural network. Calibration sets are also used to determine parameters for network structure or control model complexity. The test set mainly tests the discrimination ability (recognition rate, etc.) of the trained model. Then, 60% of the classified data was put into the model for training, and 20% of the data was used for correction and parameter adjustment. The classification accuracy of the corrected set was 92.16%. Finally, the remaining 20% data was used for testing, and the final accuracy was 92.35%. The classification of the six sleep stages is shown in Fig. 2.

4 Conclusions Data from the CAP sleep database of PHYSIONET were used in this study. Firstly, the signals to be preprocessed, namely EEG signal and heart rate signal, are determined. All signals were formatted and resampled at a 128 Hz frequency. On the basis of the above, feature extraction is carried out from frequency domain, time domain and nonlinear domain. Then we use the continuous projection method to select the features of the extracted data. Finally, the selected feature data is divided into training

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set, calibration set and test set, and the training set is sent to XGBOOST model for training, and the calibration set is used for parameter adjustment, and the test set is used for final verification. The conclusion is consistent with the expert decision in the database. Experiments show that the new algorithm XGBOOST model has a high classification ability for sleep staging, which can be used for monitoring and medical treatment. Acknowledgements This research was supported by the Basic Institution Scientific Research Operating Foundation of Heilongjiang Province in 2018 (Guobing Sun).

References 1. Hassan, A.R., Bhuiyan, M.I.H.: Automatic sleep scoring using statistical features in the EMD domain and ensemble methods. Biocybern. Biomed. Eng. 36(1), 248–255 (2016) 2. Khalighi, S., Sousa, T., Nunes, U.: Adaptive automatic sleep stage classification under covariate shift. In: 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, New York, pp. 2259–2262 (2012) 3. Hassan, A.R., Bhuiyan, M.I.H.: Computer-aided sleep staging using complete ensemble empirical mode decomposition with adaptive noise and bootstrap aggregating. Biomed. Signal Process. Control 24, 1–10 (2016) 4. Huang, C.S,. Lin, C.L., Yang, W.Y., et al.: Applying the fuzzy c-means based dimension reduction to improve the sleep classification system. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ). IEEE, New York, pp. 1–5 (2013) 5. Khalighi, S., Sousa, T., Pires, G., et al.: Automatic sleep staging: a computer assisted approach for optimal combination of features and polysomnographic channels. Exp. Syst. Appl. 40(17), 7046–7059 (2013) 6. Sen, ¸ B., Peker, M., Çavu¸so˘glu, A., et al.: A comparative study on classification of sleep stage based on EEG signals using feature selection and classification algorithms. J. Med. Syst. 38(3), 18 (2014) 7. Rechtschaffen, A., Kales, A.: A manual of standardized terminology, techniques and scoring system for sleep stages of human subjects. Washington, D.C. (1968) 8. Krishnan, G.P., Chauvette, S., Shamie, I., et al.: Cellular and neurochemical basis of sleep stages in the thalamocortical network. Elife 5 (2016) 9. American Academy of Sleep Medicine. The AASM manual for the scoring of sleep and associated events: Rules. Terminology and Technical Specifications, pp. 48–49 (2007) 10. Radha, M., Garcia-Molina, G., Poel, M., et al.: Comparison of feature and classifier algorithms for online automatic sleep staging based on a single EEG signal. In: 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1876–1880. IEEE, New York (2014) 11. Ouali, M.A., Ghanai, M., Chafaa, K.: A new type-2 fuzzy modelling and identification for electrophysiological signals: a comparison between PSO, BBO, FA and GA approaches. Int. J. Model. Ident. Control 29(2), 163–184 (2018) 12. Gao, K., Su, S., Li, D.Y., et al.: A sentiment analysis approach based on exploiting Chinese linguistic features and classification. Int. J. Model. Ident. Control 29(3), 226–232 (2018) 13. Terzano, M.G., Parrino, L., Sherieri, A., Chervin, R., Chokroverty, S., Guilleminault, C., Hirshkowitz, M., Mahowald, M., Moldofsky, H., Rosa, A., Thomas, R., Walters, A.: Atlas, rules, and recording techniques for the scoring of cyclic alternating pattern (CAP) in human sleep. Sleep Med. 2(6), 537–553 (2001)

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14. Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.Ch., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.-K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (Circulation Electronic Pages http://circ.ahajournals.org/cgi/content/full/ 101/23/e215) (2000) (June 13) 15. Abdullah, H., Maddage, N.C., Cosic, I., et al.: Cross-correlation of EEG frequency bands and heart rate variability for sleep apnoea classification. Med. Biol. Eng. Compu. 48(12), 1261– 1269 (2010) 16. Estrada, E., Nazeran, H.: EEG and HRV signal features for automatic sleep staging and apnea detection. In: 2010 20th International Conference on Electronics, Communications and Computer (CONIELECOMP). IEEE, New York, pp. 142–147 (2010) 17. Wang, J.H.: Combining recursive projection and dynamic programming technique in multi UAVs formation anomaly detection. Int. J. Model. Ident. Control 31(1), 53–61 (2019) 18. Chen, T., Guestrin, C.: XGBOOST: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, New York (2016)

Research on Unmanned Aerial Vehicle Water Combined Quality Detection and Early-Warning System Han Cao, Lei Cheng, Bei Wu and GuoQiang Gao

Abstract Many lands in China are close to rivers and oceans and they are very suitable for developing fisheries. Water quality monitoring is indispensable to the development of fisheries. Therefore, a method of detecting fishery water quality by using unmanned aerial vehicle (UAV) electrode sensor array, evaluating and predicting the data transmission back to the background, and feeding back the evaluation and prediction results in time is proposed. The results show that this method can timely monitor fishery water quality and predict the future trend of water quality, and improve the detection efficiency. Keywords Fishery water · Prediction · Electrode sensor array · UAV

1 Introduction Among the standards for measuring fishery water quality [1], the pH value of fishery water, ammonia nitrogen content, temperature, dissolved oxygen are important data indicators for traditional fish farming, which have a direct impact on fish farming. In the traditional analysis and prediction of fishery water quality, it takes a long time to sample fishery water and then carry out physical and chemical analysis, which will greatly delay the timely management of fishery water and resulting in irreversible losses. Therefore, it is necessary to find a faster, more convenient and reliable method. As far as we know, the electrode electrochemical sensors have the characteristics of fast equivalent circuit network, high selectivity of measurement, the excellent waterproof performance and corrosion resistance. It is an excellent choice for fishery water quality monitoring. At the same time, due to the strong mobility and flexibility of UAV [2], excellent performance, and the rapid development of the Internet of Things, it has gradually spread over the entire fishery and aquaculture area, and can be connected to the Internet of Things anytime and anywhere. Unmanned aerial vehicle H. Cao · L. Cheng (B) · B. Wu · G. Gao School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_104

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(UAV) and Internet of Things (IOT) have expanded our application ideas in the fishery field, and found a real-time monitoring system of UAV fishery water quality through the Internet of Things. The application of UAV and Internet of Things technology in water quality monitoring can reduce the labor cost of monitoring work, improve the accuracy of water quality detection, effectively combine the measured water quality information with digitization, and improve the effect of online water quality detection. This paper focuses on the application of electrodes chemical water quality sensor in fishery production practice [3], and carries it on the UAV platform, transfers data to the cloud database through GPRS network for LSTM [4]. Finally, the data on the cloud database is fed back in real time through the access of Android system application by Internet of Things technology, and processed and predicted synchronously in the background. Results the method presented in the form of visualization was used to evaluate and predict the water quality of modern aquaculture more accurately and quickly.

2 Methods 2.1 Overall Architecture The whole UAV fishery water quality monitoring system includes UAV, electrochemical sensor array and real-time feedback data application. UAV carries electrochemical sensor array to monitor activities in a large area of fishery and aquaculture area. The monitoring data are used in the feedback and response of the Internet of Things, and timely analysis and processing are carried out to achieve the purpose of monitoring.

2.2 UAV Suitable for Water Surface Firstly, in order to ensure long-term monitoring of fishery water quality, UAVs can choose long-term six-rotor UAVs, and six-rotor UAVs can also provide more powerful load capacity. Secondly, In order to ensure UAV to float smoothly on the water surface and leave the water quickly, the floating structure can be made of ethylenevinyl acetate copolymer (EVA). EVA [5] is a polymeric material whose molecular formula is (C2 H4 ) x. (C4 H6 O2 ) y, which is made of foam after foaming. It has the characteristics of closed cell structure, no water absorption, good water resistance, corrosion resistance, high resilience and high tensile resistance, EVA material has a good process in and is easy to process floating structure. The structure of a six-rotor long-range floating UAV is shown in Fig. 1.

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Fig. 1 Six-rotor long-range floating UAV

2.3 Electrode Chemical Sensor Array Most of the electrode chemical sensors are based on chemical electrolyte as the medium, belonging to the primary battery system. After contacting fishery water, the substances to be measured are exchanged through the thin film, and the electrolyte inside can take place electrolytic reaction to produce corresponding electrical signals. For different detection components, the electrolyte inside the electrode chemical sensor is different, and the film material is selective, so the electrode chemical sensor has the characteristics of high selectivity and reliability. Although the temperature will affect the sampling results of multiple electrode chemical sensors. However, by integrating the electrode chemical sensor with the temperature sensor, the data measured by the electrode chemical sensor can be corrected by the temperature sensor. Through long-term study on the impact of water quality indicators on fisheries and fishery water quality standards, we found that temperature, dissolved oxygen, ammonia nitrogen content and pH value are the most important factors affecting the survival rate of fish. Therefore, we chose these four electrode chemical sensors as monitoring sensors of UAV fisheries water quality monitoring system. Four electrode chemical sensors are shown in Fig. 2.

2.4 Application of Real-Time Feedback Data In the application design, the specific design of the Internet of Things is divided into three parts: the design of the network layer software subsystem, the design of the perception layer wireless gateway software subsystem and the design of the application layer water quality monitoring information management system.

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Fig. 2 Four electrode sensors

In the design of network layer software subsystem, star network with selforganizing function is adopted. Among them, the main frame types are node access, network parameters acquisition, sensor parameters acquisition, water quality parameters adjustment, etc. As long as the instruction of specified format is sent down in the downlink, the data can be obtained through the upstream link and the required parameters can be obtained. In the design of the software subsystem of the perception layer wireless gateway, the wireless gateway is used to complete the functions of management control, protocol conversion and data forwarding. It can support data collaboration and aggregation in WSN network, GPRS access and Internet connection. In the design of management system for water quality information monitoring at application level, the management system of water quality information for application level monitoring is designed with B/S architecture and provides gateway-oriented and user-oriented services through Web Service. The main subsystems include water quality and environment monitoring subsystem, expert decision-making and knowledge query subsystem, system configuration subsystem and online technical support subsystem.

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3 Data Acquisition System We use remote controllers, computer terminal ground stations and GPS satellite positioning to allow UAV to fly on planned routes and land accurately in the water quality area to be measured. After the UAV is parked on the water surface, sensors hidden in EVA materials begin to monitor the water quality. Each group of data contains temperature and content. There are three groups of data. After average processing, the date upload to TLINK Internet of Things platform, during floating sampling, data is only transmitted to TLINK Internet of Things platform. After floating sampling, the application of real-time feedback data transfers the data collected by the sensor to the mobile terminal in real time by analyzing the user account and device number provided by TLINK platform and calling the interface provided by TLINK platform for developers. Firstly, the device interface provided by TLINK Internet of Things platform is imported into Android Studio project background system, and the background environment of data transmission is configured. The user ID, API key applied in TLINK Internet of Things and device number created by TLINK Internet of Things data monitoring platform are transmitted to Android Studio background program to connect the Internet of Things with Android platform. Then, OkHttpUtils is used to request the network and JSON is used to parse the data. The data in the sensor array is pulled out and loaded dynamically into the text document corresponding to the UI. For example, in a test, the measurement data displays as follows (Fig. 3). After reading the data, the collected data are extracted and analyzed from the array through the algorithm set in the background. The analysis process displays as follows (Fig. 4). Pictures taken in the field display as follows (Fig. 5). The specific data acquisition process displays as follows (Fig. 6). By recording the data transmitted by the cloud database platform within a week, processing and sorting it into tables and applying the feedback image (Fig. 7).

4 Data Processing and Algorithms Through the use of the Internet of Things, our means of water quality monitoring and assurance have been better expanded. By using the Internet of Things technology to identify by identification equipment, and then through processing and transmission equipment to transmit data and information, the characteristics of communication between different equipment can be realized, and the four indicators measured by sensors after each water quality monitoring can be read, and the data of the indicator layer in the sensor array are pulled to the variables for storage. The standard fluctuation range is set up in the background, and the evaluation variables are assigned according to the deviation degree between the measured data and the standard range. The sum of the variables is used as the evaluation basis to set the water quality grade.

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Fig. 3 Display of measurement data

Therefore, the long-term water quality monitoring will record every data in a period of time, and process and forecast the recorded data. The predicted experimental data are compared with fishery water quality measurement standards, and the possible results are analyzed, and the corresponding solutions are given. LSTM algorithm is mainly used for long-term water quality monitoring data processing. LSTM differs from RNN in that it adds a “processor” to the algorithm to judge whether information is useful or not. The structure of the processor is called cell. LSTM can perform better in a longer sequence than ordinary RNN. The original working data obtained in the evaluation operation are processed by MATLAB as follows (Fig. 8). According to the fishery water quality measurement standard, the standard range of dissolved oxygen concentration is 4–10 mg/L, the standard range of ammonia nitrogen concentration is less than or equal to 0.2 mg/L, and the standard range of acid and alkali is 6.5–8.5. The evaluation results of water quality in fish ponds are

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Pull data from sensor data list

Y If dissolved oxygen is concentraƟon within the standard range (4mg/L~10mg/L) ?

If dissolved ammonia is concentraƟon within the standard range (0.2 mg/L)?

a=1

N

a=0

Y

b=1

N

b=0

Y If pH value is concentraƟon within the standard range (0.2 mg/L)?

N c=1

Sum

Sum=a+b+c

c=0

1

Sum=2

Sum=3

Water quality grade:

Water quality grade:

Water quality grade:

Bad

Good

Excellent

Fig. 4 Flow chart of water quality analysis

divided into three grades: 1, 2 and 3. According to the deviation degree of dissolved oxygen, ammonia nitrogen and ph, different click events are set for buttons to show different bullet windows. The contents of bullet windows are different adjustment suggestions for users according to the actual situation of water quality measured. Water quality grade is divided into Table 1. The latest measured data in the background pull-out sensor array are stored in the corresponding variables, and the data in these variables are extracted for analysis. The following conclusions can be drawn:The pH value is basically stable between

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Fig. 5 Pictures taken at the scene of data acquisition Fig. 6 Data acquisition process

Unmanned Aerial Vehicle Entering Test Site

Sensors begin to detect

Data transmission to the Internet of Things

Application downloads data and process it

N Detect whether the data is abnormal

Y Display the predicted results

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Fig. 7 History data

7.7 and 7.9, NO2 is between 0.09 and 0.1, NH4 + is between 0.1 and 0.11. It will remain stable for a period of time in the future, and will not have a great impact on the water quality of fish ponds. Dissolved oxygen is about 3.8–3.9, which is much lower than the fishery water quality monitoring standard. It will greatly reduce the survival probability of fish. If not treated, the dissolved oxygen will continue to decrease, resulting in irreparable loss, thus judging the water quality grade of 2. The experimental results after treatment are as follows (Table 2). It can be seen from the table that the predicted value of pH is between 7.7 and 7.9, the predicted value of NO2 is between 0.09 and 0.1, and the predicted value of NH4 + is between 0.1 and 0.11. However, the predicted value of dissolved oxygen is greatly reduced and the water quality grade score is 2, which indicates that the predicted experimental results are basically consistent with the analysis results.

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Fig. 8 The original data measured by the sensor

Tables 1 Classification pH

NO2 −

DO

NH4 +

1 (100)

6.5–8.5

5–8

split]dom_elt[p_search->split]) 9. p_search=p_search->left 10. else 11. p_search=p_search->right 12. Nearest=last node of search_path} 13. Distance=distache(target, nearest) 14. p_back=last_node of search_path 15. while(search_path!=NULL)

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16. {if(p_back->left=NULL &&p_back->right=NULL 17. {if(distance(nearest,target)>distance(p_back->dom_elt,target)) 18. Nearest=p_back->dom_elt 19. Distance= distance(p_back->dom_elt,target)} 20. else 21. {s=p_back->split 22. if(abs(p_back->dom_elt[s]-target60

∞

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Fig. 6 Flowchart of euclidean clustering

condition has too many points so it is abandoned. In Fig. 7c, the radius is undersize and it caused points of classes are less than the threshold. From the test that variable radius is more appropriate for the actual circumstances.

4 Conclusions In this paper, we present an improved segmentation method based on Euclidean. In order to achieve more efficient accurate effect, we use several methods to improve the existing segmentation algorithm. First, we use k-d tree data structure to establish the index structure of point cloud data to speed up the retrieval speed. Second, we

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Fig. 7 Clustering results

use voxel grid to reduce useless points while keeping the point cloud data details not lost. Then, we use random sample consensus (RANSAC) method to separate ground and object. Finally, we use Euclidean clustering to get the result by setting different thresholds as the distance increases. At the end of this paper, we verify the validity of the algorithm by an experiment and the result shows that this algorithm can meets the requirements for real-time performance. In the next study, we will try to solve the problem by deep learning and tensorflow.

References 1. Hu, Z., Bai, D.: Planar object detection form 3D points clouds based on pyramid voxel representation. Multimedia Tools Appl. 76(22), 24343–24357 (2017) 2. Sveier, A., Kleppe, A.L., Tingelstad, L., et al.: Object detection in point clouds using conformal geometric algebra. In: Advances in Applied Clifford Algebras, pp. 1–16 (2017) 3. Yuan, Z., Lu, T., Tan, C.L.: Learning discriminated and correlated patches for multi-view object detection using sparse coding. Pattern Recogn. 69, 26–38 (2017) 4. Fangchao, H., Zhen, T., Yinguo, L., Shuai, H., Mingchi, F.: A combined clustering and image mapping based point cloud segmentation for 3D object detection. In: The 30th Chinese Control and Decision Conference, Shenyang, China (2018) 5. Sharma, A., Singh, P.K., Khurana, P.: Analytical review on object segmentation and recognition. In: Proceedings of 6th International Conference on Cloud System and Big Data Engineering, pp. 524–530. IEEE, New York (2016) 6. Buch, N., Velastin, S.A., Orwell, J.: A review of computer vision techniques for the analysis of urban traffic. IEEE Trans. Intell. Transp. Syst. 12(3), 920–939 (2011) 7. Zhu, H., Yuen, K.V., Mihaylova, L., et al.: Overview of environment perception for intelligent vehicles. IEEE Trans. Intell. Transp. Syst. 18(10), 2584–2601 (2017)

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8. Shuning, F., Na, H., Pengfei, F., Junjie, Z.: A 3D point cloud segmentation method based on local convexity and dimension features. In: The 30th Chinese Control and Decision Conference, Shenyang, China (2018) 9. Grilli, E., Menna, F., Remondino, F.: A review of point clouds segmentation and classification algorithms. ISPRS—Int. Arch. Photogrammetry Remote Sens. Spat. Inf. Sci. 2017, 339–344 (2017) 10. Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509 (1975). https://doi.org/10.1145/361002.361007 11. Altman, N.S.: An introduction to kernel and nearest-neighbor nonparametric regression. Am. Stat. 46(3), 175–185. https://doi.org/10.1080/00031305.1992.10475879. hdl:1813/31637 (1992) 12. Fischler, M.A., Martin, A., Bolles, R.C.: A paradigm for model fitting with applications to image analysis and automated cartography. Read. Comput. Vis. 24(6), 726–740 (1987) 13. Li, L., Yang, F., Zhu, H., Li, D., Li, Y., Tang, L.: An improved RANSAC for 3D point cloud plane segmentation based on normal distribution transformation cells. Remote Sens. 9(5), 433 (2017) 14. Wenlong, Y., Junguo, L., Weihang, Z., Yubin, M.: A new plane segmentation method of point cloud based on mean shift and RANSAN. In: The 30th Chinese Control and Decision Conference, Shenyang, China (2018) 15. Anton, H.: Elementary Linear Algebra, 7th ed., pp. 170–171. Wiley, Hoboken, ISBN 978-0471-58742-2 (1994)

RLV Guidance and Control System Design for Terminal Area Energy Management Phase Lingxia Mu, Xiang Yu and Youmin Zhang

Abstract Reusable launch vehicle (RLV) is designed as one kind of the second generation launch vehicles, which can launch payloads to outer space frequently and return back to the earth like an aircraft. A reliable guidance and control system for terminal area energy management (TAEM) phase is of paramount importance to ensure a safe return. This paper presents a TAEM guidance and control (TAEM G&C) approach. Within the proposed scheme, off-line trajectory, task management, guidance law, control law, and 6-DOF RLV model are included. The developed TAEM G&C system is able to ensure the RLV safely return to the terminal end point from an arbitrary entry point in a specific range. Numerical simulation is conducted to evaluate the efficiency of the performance of the TAEM G&C system. Keywords Reusable launch vehicle (RLV) · Terminal area energy management (TAEM) · Guidance and control system

1 Introduction As the increased demand of frequent exploration to the outer space, it is a need to improve the space transportation ability. Reusable launch vehicle (RLV) becomes a viable solution, which can launch payloads more frequently in comparison to the traditional one-time launch vehicle such as disposable rocket. As a new-generation launch vehicle, it is expected to reentry the earth atmosphere after finishing the space task and land on the earth surface elegantly like an aircraft [1–3]. L. Mu Department of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China X. Yu School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China Y. Zhang (B) Department of Mechanical, Industrial & Aerospace Engineering, Concordia University, Montreal, QC H3G 1M8, Canada e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_106

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The terminal area energy management (TAEM) phase is critical phase for the accomplishment of the re-entry and recovery. It is after the hypersonic re-entry phase and followed by the approach and landing phase. Recently, the intention on the TAEM guidance and control (TAEM G&C) method has been significantly increased. In [4], a three-dimensional trajectory planning algorithm is constructed using an iteration method. In [5], numerical optimization method is used to generate the TAEM trajectory. In [6], an on-board guidance method is designed by considering uncertainty resulting from terminal entry condition and system model. In [7], constrained longitudinal trajectory planning method is investigated. In [8], sliding mode guidance method is studied for the TAEM flight phase. Mostly, the guidance and control method are separately studied with consideration of the point-mass 3-DOF motion dynamics and 6-DOF dynamic model, respectively. This paper is dedicated to integrate the guidance and control system and analyze the behavior of the RLV terminal flight.

2 TAEM Guidance and Control System Design The proposed TAEM G&C system is designed based on the idea of distributed guidance and control. As shown in Fig. 1, a trajectory generator is firstly constructed where a set of reference trajectories are optimized with consideration of the RLV kinemics, TAEM task, and possible uncertainties. It follows by a guidance law module, where the reference trajectory can be tracked, leading to guidance commands [α, γ , Nz ]T . Subsequently, the control law module generates the actuator commands [δa , δr , δe , δsb ]T by considering the RLV dynamics. It is assumed that the actuators and sensors can provide the needed signals accurately.

Task management Guidance commands Reference trajectory

Guidance law

Control surface Control law

Actuator

6DOF RLV model

RLV attitudes Trajectory states

Fig. 1 The block scheme of the proposed TAEM G&C system

Sensor

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3 Modules of the TAEM G&C System As depicted in Fig. 1, four modules are mainly designed to construct the proposed TAEM G&C system. In this section three of them will be discussed including task management, guidance law, and control law, respectively. The function of the task management is shown in Fig. 2. The module of task management firstly selects the flight phase according to the current energy and states of the RLV. Then the corresponding trajectory to be tracked is determined and trajectory states are extracted, by which guidance commands can be calculated for the following guidance law module. Figure 3 illustrates the working principle of the task management module. The detailed trajectory method and guidance law can be found in authors’ previous paper [5]. The control law is designed on the basis of the traditional decoupled PID strategy. The working principle of the control law are depicted in Fig. 4. The guidance commands are received from the abovementioned guidance loop. The generated control Task Management Flight phase selection Trajectory states extraction Guidance command calculation Fig. 2 The function of task management module

Trajectory states extraction

Trajectory states

Flight phase

Inputs of flight states

Flight phase switching, and rang-to-go calculation

The position of heading align cone

Range -to-go

Longitudinal guidance commands calculation

Lateral guidance commands calculation

Fig. 3 The principle of task management module

Longitudinal commands

Lateral commands

Outputs for longitudinal guidance law

Outputs for lateral guidance law

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Constraint control (AOA and Nz constraints)

Logic decision

Pitch angular rate control

Nz control

Guidance law

Guidance commands

Roll angle control Dutch-roll unstable

Flight states

Actuator commands

Longitudinal control loop

Dutch-roll control

Lateral control loop

Fig. 4 The design principle of control law module

commands are sent to the actuator module in terms of the control surface deflection. The longitudinal control and lateral control are designed separately and integrated afterwards. Note that in longitudinal control loop the constraints of angle of attack (AOA) and normal loads (Nz) are considered. In lateral control, roll angle control and Dutch-roll control are designed by accounting for the characteristics of the TAEM flight.

4 Numerical Simulation In the numerical simulation, the initial altitude of the RLV is set as 85 kft, the initial velocity is 2456 ft/s, the Mach number is Ma2.5, the range-to-go is around 424, 264 ft, and the dynamic pressure is 200 psf. The terminal states constraints are approaching the RLV to the altitude of 10 kft with Mach number Ma0.5. The terminal dynamic pressure is 255 psf. These parameters are all presented in Table 1. On the basis of the provided initial conditions and terminal constraints, using the proposed TAEM G&C system, simulation results are presented in Figs. 5, 6, 7, 8 and 9. The whole TAEM flight time is around 420 s. During this process, the RLV has been through a large range of velocity from supersonic speed, transonic speed, and subsonic speed. The time history of the RLV trajectory and attitudes varies a lot. Figure 5 shows the three-dimensional TAEM trajectories and two-dimensional ground-track. As can be observed, the RLV starts from an approximate straight-line, followed by a small turn maneuver, and then a straight-line until the terminal point. Figure 6 presents the time history of the RLV trajectory states. During the entire TAEM flight phase, the dynamic pressure always below 400 psf, and the normal load (Nz) is below 1, which satisfies the constraints condition the RLV usually subject to. But, as can be seen from Fig. 7, the profiles of flight path angle and AOA show

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Table 1 The simulation task setting

Initial conditions Terminal constraints

Downtrack X(ft)

Crosstrack Y(ft)

Altitude H(ft)

−30e4

−30e4

8.5e4

0

0

1e4

Mach

Flight path angle γ (◦ )

Heading angle χ(◦ )

Dynamic pressure q(psf) ¯

2.5

−4

60

200

0.5

/

/

255

Fig. 5 TAEM trajectory in three-dimensional and two-dimensional

oscillations, which might be not well-constructed from the perspective of control tracking possibility. The guidance command tracking performance of the control law is shown in Fig. 8. The red dot line denotes the time history of guidance commands and the blue solid one represents the flight states. The commands are well tracked even in the oscillation situation. This indicates the performance of the TAEM guidance and control are mainly depended on the performance of the guidance loop. The deflections of the control surface are displayed in Fig. 9.

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Fig. 6 Time histories of RLV trajectory states

5 Conclusions Currently, we construct a G&C system for the RLV’s TAEM entry flight, using the distributed structure, where the trajectory, guidance law, and control law are separately designed as independent modules. The G&C system is tested and results show the efficiency of the proposed TAEM G&C system. Generally, the system is feasible to complete the specific task. But, as can be observed from the simulation results, the performance of the TAEM guidance and control are mainly depended on the guidance loop. Hence, in our future work, we will focus on enhancing the guidance performance by studying more precision and robust guidance method. Acknowledgements The authors would like to acknowledge the financial supports from National Natural Science Foundation of China (under Grants Nos. 61573282 and 61833013) and Natural Science Foundation of Shaanxi Province under (under Grant No. 19JK0569) for the work reported in this paper.

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Fig. 7 Time histories of RLV attitudes

Fig. 8 Guidance commands tracking performance

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Fig. 9 Time histories of control inputs

References 1. Hanson, J.M.: A plan for advanced guidance and control technology for 2nd generation reusable launch vehicles. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, pp. 4557– 4577 (2002) 2. Kluever, C.A.: Terminal guidance for an unpowered reusable launch vehicle with bank constraints. J. Guid. Control Dyn. 30(1), 162–168 (2007) 3. Mu, L.X., Wang, X.M., Xie, R., et al.: A survey of the hypersonic flight vehicle and its guidance and control technology. J. Harbin Inst. Technol. 51(03), 1–14 (2019) 4. Mu, L.X., Yu, X., Zhang, Y.M., et al.: Trajectory planning for terminal area energy management phase of reusable launch vehicles. In: The 20th IFAC Symposium on Automatic Control in Aerospace, Sherbrooke, Canada, August 21–25 (2016) 5. Lan, X.J., Liu, L., Wang, Y.J.: Online trajectory planning and guidance for reusable launch vehicles in the terminal area. Acta Astronaut. 118, 237–245 (2016) 6. Mu, L.X., Yu, X., Zhang, Y.M., et al.: Onboard guidance system design for reusable launch vehicles in the terminal area energy management phase. Acta Astronaut. 143(2), 62–75 (2018) 7. Liang, Z.X., Li, Q.D., Ren, Z.: Onboard planning of constrained longitudinal trajectory for reusable launch vehicles in terminal area. Adv. Space Res. 57(3), 742–753 (2016) 8. Mu, L.X., Yu, X., Wang, B., et al.: 3D gliding guidance for an unpowered RLV in the TAEM phase. In: The 33rd Youth Academic Annual Conference of Chinese Association of Automation, Nanjing, China, May 18–20 (2018)

A Compound Attitude Control System for a High Coupling Reentry Vehicle Jiaping Zhang, Xu Li, Qianwei He, Zihao Huang, Ye Yang and Lei Liu

Abstract A compound attitude control system is designed for a reentry vehicle with highly coupling effect of reaction control system (RCS). RCS and aerodynamic surfaces are two kinds of vehicle actuators. A task-driven control allocation strategy based on the change of dynamic pressure is proposed. In low dynamic pressure area, only RCS is available. Faced with the high coupling effect of RCS, the linear programming is adopted to generate RCS switching schedule. The effectiveness of the proposed compound attitude control system is verified by simulation. Keywords RCS · Attitude control · Allocation strategy · Compound control

1 Introduction Aerodynamic surfaces of a reentry vehicle cannot provide sufficient attitude control torque when atmospheric density is low. Reaction control system (RCS) is an effective complement [1]. Due to the discrete characteristic, it is a challenge for the design of RCS allocation strategy. Compound control of RCS and aerodynamic surfaces has gradually become a research hotspot. Recently, much research on attitude control has been carried out. In [2], based on the change of dynamic pressure, the reentry process is divided into three stages, and PID control laws are designed respectively. Fang introduces three logical allocation methods of RCS, i.e. axle control, graded control, and table lookup, besides analyzes their advantages and disadvantages [3]. Zhai et al. propose a fuzzy rulebased allocation strategy [4]. T-S model-based fuzzy control may be also used [5]. Besides, when the actuator fails, a diagnosis algorithm based on RBF neural network J. Zhang · X. Li · Q. He · Z. Huang · L. Liu (B) National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, HUST, Wuhan 430074, China e-mail: [email protected] Y. Yang Beijing Aerospace Automatic Control Institute, Science and Technology on Aerospace Intelligent Control Laboratory, Beijing 100854, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_107

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can be used for fault detection [6]. The pulse width modulation (PWM) modulation method is widely used in the RCS allocation. Then, Zhou et al. analyze the stability of PWM modulation algorithm [7]. As for compound allocation strategy, Xu et al. comprehensively analyze composite control strategies in reentry [8]. In [9], a compound distribution strategy based on dynamic pressure changes is proposed. In [10], a compound allocation method based on chain allocation method is proposed. In [11–13], the control allocation problem is formulated into a programming problem. By selecting appropriate cost function and constraints, the control allocation is well solved. In [14], the robust stability of the attitude control system of the hypersonic gliding vehicle is discussed. The reentry vehicle attitude control problem is investigated in this paper. In early reentry, only RCS is available. Due to the high coupling effect of RCS, it is difficult to allocate RCS switching schedule. The linear programming method is adopted to solve this problem. And the design process of a compound control system is discussed systematically. A composite control strategy based on weighted coefficient is proposed. Finally, the effectiveness of RCS allocation strategy and compound control system is verified by simulation.

2 Vehicle Model 2.1 Model Overview In this paper, a vehicle in reentry phase is taken as the research object. The aerodynamic surfaces consist of a pair of flaps at the bottom, a pair of flaps on either side and a vertical tail on the leeward side. The RCS is mounted at the rear of the vehicle and produces three channels of the moment.

2.2 Reaction Control System Modeling The RCS is a set of reverse thrusters mounted in the same plane as the tail of the vehicle. In this paper, the RCS contains 8 reverse thrust thrusters, which are distributed on the tail plane according to the position shown in Fig. 1. In Fig. 1, the installation angles of thruster 1 and 2 are 135°; 3 and 4 are 45°; 5 and 6 are −45°; 7 and 8 are −135°. The thruster mounting position is symmetrical from left to right. According to the mounting position, it can be seen that the eight thrusters are of high coupling. Therefore, in the following thruster logic allocation section, the methods of axle control and graded control are not suitable for this RCS model.   Assuming that L i = X i Yi Z i is the position vector of the trust force relative to the center of mass of the thruster i, and F i is the force provided by thruster i.

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Fig. 1 RCS thruster layout map

2

3

1

4

Yb Zb

8

5 7

6

Therefore, we can get the control moment provided by thruster i: T  M i = F i × L i = M xi M yi M z i (i = 1, 2, . . . , 8)

(1)

The total control moment provided by RCS is formulation (2): 



M = M1 M2 M3 M4 M5 M6 M7 M8 =



8  i=1

M xi

8 

M yi

i=1

8 

T M zi

(2)

i=1

8 8 8 where, i=1 M xi , i=1 M yi and i=1 M z i are the components of the total moment of eight thrusters on the x, y and z axes of the centroid coordinate system, i.e. the moment corresponding to the three channels of roll, yaw, and pitch. Table 1 shows the calculated control moment provided by every RCS thruster. It can be seen from Table 1: (1) Every RCS thruster provides control moments of three axes. Thus it is difficult to implement the specific control. (2) As for thruster logic allocation, axle control and graded control have difficulties. The question will be solved using linear programming in detail. Table 1 Control moment provided by RCS thrusters

Number 1

Mx /N · m 34

M y /N · m 48

Mz /N · m −48

2

34

48

−48

3

−34

−48

−48

4

−34

−48

−48

5

34

−48

48

6

34

−48

48

7

−34

48

48

8

−34

48

48

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2.3 Reentry Attitude Model The angular velocity and angular velocity of three channels in flight are determined by the reentry attitude model. It consists of six equations [15]. (1) kinematic model ⎧ ⎪ ⎨ γ˙ = secβ(ωx cosα + ωz sinα) + f 1 α˙ = ω y − tanβ(ωx cosα + ωz sinα) + f 2 ⎪ ⎩ ˙ β = −ωz cosα + ωx sinα + f 3

(3)

where ⎧ q Sr e f C L q Sr e f CY g ⎪ ⎪ f1 = (tanθ sinγ + tanβ) + tanθ cosγ − cosθ cosγ tanβ ⎪ ⎪ mV mV V ⎪ ⎪ ⎨  1 mgcosθ cosγ − q Sr e f C L f2 = ⎪ mV cosβ ⎪ ⎪ ⎪ ⎪  ⎪ ⎩ f 3 = 1 q Sr e f CY cosβ + mgcosθ sinγ mV (4) where, γ , α, β, θ is the bank angle, the angle of attack, the sideslip angle and the heading angle, respectively. ωx , ω y , ωz are the angle velocity of roll, pitch and yaw, respectively. g, m are the gravitational constant and the mass of the vehicle. q, Sr e f is the dynamic pressure and the reference area. C L , C D , CY are the coefficients with respect to lift, drag, and side force, respectively. (2) dynamic model ⎧ ⎪ ⎨ ω˙ x = (Mx + (I yy − Izz )ω y ωz )/Ix x ω˙ y = (M y + (Izz − Ix x )ωz ωx )/I yy ⎪ ⎩ ω˙ z = (M y + (Ix x − I yy )ωx ω y )/Izz

(5)

where, Mx , M y , Mz are the control moment of roll, pitch and yaw, respectively. Ii j (i = x, y, z, j = x, y, z) is the rotary inertia matrix.

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3 RCS Allocation Strategy The attitude control system based on RCS can be designed as Fig. 2. In the diagram, the control moment Mr can be calculated by three-channel control law through the attitude deviation. Mr is a continuous moment, while the RCS is the discrete control actuator. Therefore, it must be modulated to a series of discrete control times T through PWM part. Next, thruster logic allocation part will determine the switching commands R for different RCS thrusters. The discrete control moment M RC S will be produced by RCS. Overall, the three-channel control law, the PWM and the thruster logic allocation are the most important three parts of the overall control system.

3.1 Design of Three-Channel RCS Controller Due to the high nonlinearity and strong coupling, it is a challenge for the design of reentry vehicle control design [16]. On pure RCS control stage, three-channel control law can be independently designed to maintain the longitudinal and lateral attitude stability. PID controller is a reliable and widely used method [17]. Although, some researchers point out that a PID controller is difficult to carry out a high-precision trajectory tracking task [18]. In the PID controller designed in this paper, the integral part can improve the control accuracy, but at the cost of more fuel. Therefore, PD controller can meet the control requirements. (1) RCS controller of pitch channel The RCS controller of pitch channel consists of two loops. The inner loop is differential control, and the pitch angular velocity is used for feedback to increase damping. While the outer loop is proportional control, and the angle of attack is used for feedback to track the command angle. The RCS control structure of the pitch channel is shown in Fig. 3. The RCS controller of pitch channel is shown in Eq. (10): M pitch = K ωRz · (K αR · (αc − α) − ωz )

(6)

where, M pitch is the required control moment. K ωRz and K αR are the controller parameters.

Fig. 2 Overall allocation strategy block diagram

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Fig. 3 The RCS control structure of the pitch channel

(2) The RCS controller of yaw and roll channel The RCS controllers of yaw and roll channel are similar to that of pitch channel. Generally, the sideslip angle is zero, so the task of yaw and roll controller is to eliminate the derivation. The control laws are given below. M yaw = K ωRy · (K βR · β − ω y )

(7)

Mr oll = K ωRx · (K γR · (γc − γ ) − ωx )

(8)

where, M yaw and Mr oll are the required control moments of yaw and roll channel.

3.2 RCS Pulse Width Modulation Algorithm In this section, PWM algorithm was introduced to convert the continuous moments to RCS switching command. The basic theory of PWM is impulse equivalence principle: in a control cycle, if the impulse of a continuous input and a discrete input are equal, the control effects they produced are the same. If Mc is the continuous moment calculated by the control law, M RC S is the discrete moment provided by RCS, and the width τi is the opening time of RCS in ith control cycle T. The impulse equivalence can be expressed by the following Eq. (9): M c · T = M RC S · τi

(9)

Therefore, the RCS opening time in ith control cycle can be expressed by Eq. (10): τi = (M c · T )/M RC S

(10)

In each control cycle, the required control moment can be calculated by the Eqs. (6)–(8), then the opening time of every RCS thruster can be obtained by Eq. (10).

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3.3 RCS Thruster Logical Distribution The opening duration calculated by the PWM algorithm actually contains the ignition command information. The function of logical distribution is to distribute ignition commands to eight thrusters. Due to the high coupling effect of RCS, here the method of linear programming is introduced. Assuming that in a control cycle, the continuous three channel control moment matrix obtained by RCS control laws is as follows: T  M c = M x M y Mz

(11)

Besides assuming that the opening duration matrix of eight RCS thrusters is: T  S = t 1 t2 t3 t4 t5 t6 t7 t8

(12)

where, t j ( j = 1, 2, . . . , 8) is the opening duration of jth RCS thruster, i.e. eight unknown variables to be solved. The control moments in Table 1 are written as a matrix R: ⎡ ⎤ 34 34 −34 −34 34 34 −34 −34 R = ⎣ 48 48 −48 −48 −48 −48 48 48 ⎦ (13) −48 −48 −48 −48 48 48 48 48 According to the impulse equivalence theorem, the following equation can be obtained: Mc · T = R · S

(14)

Define the moment impulse in a control cycle: T T   B = b1 b2 b3 = M c · T = Mx · T M y · T Mz · T

(15)

Then the Eq. (14) can be rewritten as follows: R·S= B

(16)

The objective function consists of two parts. To meet the control requirements, the first objective is to lead the moment impulse produced by RCS close to the desired moment impulse. Considering that the propellant is limited, the second objective function is the sum of all RCS thrusters’ opening duration. The overall objective function is: min J = R · S − B + ω1 · ST S subject to: 0 < t j ≤ T, j = 1, 2, . . . , 8

(17)

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where, ω1 is weight coefficient. Meeting control requirements is prior to propellant saving, thus ω1 should be less than 1 and can be valued at 0.1. Combining Formulas (16)–(17), it can be seen that it is a typical linear programming problem which can be easily solved.

4 Compound Control Allocation Strategy In reentry, as the altitude decreases, the aerodynamic surfaces effect increases. The vehicle enters the compound control stage.

4.1 Control Allocation Strategy The task in this section is to distribute the attitude deviation into two parts. One part is eliminated by RCS and the other part is eliminated by aerodynamic surfaces. The overall block diagram of compound control is shown in Fig. 4. Assume that the deviation between the actual attitude angle and the command attitude angle is ξ , then the above allocation problem can be expressed by Eq. (18). ξr and ξa are the attitude angle deviation distributed to RCS and aerodynamic surfaces, respectively. ξr + ξa = ξ

(18)

As the altitude decreases, the proportion of RCS control performance decreases, while the proportion of aerodynamic surfaces increases. A weight coefficient 0 ≤ k ≤ 1 is introduced to distribute the attitude angle deviation: 

ξr = k · ξ

(19)

ξa = (1 − k) · ξ

Δξ r RCS control

Δξ

Attitude command -

Compound allocation strategy

Attitude model

Δξ a Fig. 4 The overall block diagram of compound control

Aerodynamic rudder control

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The value of k is related to dynamic pressure as following: k = (q − q2 )/(q1 − q2 )

(20)

where, q1 and q2 are the start and end dynamic pressure.

5 Simulation Results First, the initial conditions of the simulation are given: (1) The aircraft reenters at an altitude of 100 km at a speed of 20 Ma. The initial dynamic pressure is 0, angle of attack is −7.9°, sideslip angle and rolling angle is 0°; (2) Only RCS is available in the process of height from 100 to 85 km; (3) The aerodynamic surfaces control is introduced at an altitude of 85 km. When the dynamic pressure is 120 Pa, the compound control begins which ends at the 59 km. The overall simulation time is 120 s. The attitude angle tracking curve is shown in Figs. 5, 6 and 7. α, β, γ are the actual angle of attack, sideslip angle, and bank angle, respectively. αcom , βcom , γcom are the corresponding command angles. When only RCS is available, attitude tracking can be realized quickly. The effectiveness of RCS allocation strategy is proved. There is no obvious jitter on the tracking curve and the attitude errors are all within the allowed range. The RCS allocation strategy and composite allocation strategy designed in this paper are reasonable and effective. The output curves of the three-channel RCS are shown in Figs. 8, 9 and 10. respectively. The discrete characteristics of RCS can be clearly seen in the diagram. It can be found that in early reentry, the aerodynamic surfaces fail and only RCS is available. The RCS is activated more frequently. As the height drops, the aerodynamic surfaces Fig. 5 Angle of attack curve

40

Angle of attack(∞)

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com

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Time(s)

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Fig. 6 Sideslip angle curve

0.1

Sideslip angle(∞ )

0.05

com

0

-0.05

-0.1 0

20

40

60

80

100

120

Time(s)

Fig. 7 Bank angle curve

0.6

0.4

Bank angle(∞)

com 0.2

0

-0.2 0

20

40

60

80

100

120

8

10

12

Time(s)

Fig. 8 Roll RCS moment

100

M r (Nm)

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-50

-100 0

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M (Nm) y

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Control cycle

Fig. 10 Pitch RCS moment

12

10 10

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Mp (N m)

50

0

-50

-100 0

2

4

6

Control cycle

8

12

10 10

4

gradually participate in control, and the switching frequency of RCS decreases. It illustrates the effectiveness of the compound control strategy.

6 Conclusion In this paper, a compound control system has been proposed for a reentry vehicle with high coupling effect of RCS. A dual-loop PD controller has been designed to obtain the desired control torque. Considering the high coupling effect, linear programming is used in the design of the thruster logical distribution. A task-driven

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compound control strategy based on the linear change of dynamic pressure is proposed. The simulation results evaluate the effectiveness of the designed compound control system and RCS allocation strategy. Acknowledgements This work was supported in part by the National Nature Science Foundation of China (Grant Nos. 61873319, 61803162 and 61573161).

References 1. Mu, R., Zhang, X.: Control allocation design of reaction control system for reusable launch vehicle. Abstr. Appl. Anal. 1, 1–13 (2014) 2. Bennett, D.E.: Space shuttle entry flight control overview. In: Bauman, E.J., Emsley, Z.W. (eds.) Proceedings of the Annual Rocky Mountain Guidance and Control Conference, vol. 51, pp. 393–403 (1983) 3. Yuanpeng, F.: Reaction control system control method for reusable launch vehicle. J. Acta Aeronautica Et Astronautica Sinica B05, 97–101 (2008) 4. Zhai, R., Qi, R., Zhang, J.: Compound fault-tolerant attitude control for hypersonic vehicle with reaction control systems in reentry phase. J. ISA Trans. (2019) 5. Li, P.W., Zhang, W.C.: Towards a unified stability analysis of continuous-time T-S model-based fuzzy control systems. Int. J. Modell. Ident. Control (2019) 6. Yao, L.N., Wang, H.R.: Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model. Int. J. Modell. Ident. Control (2019) 7. Zhou, Y., Huang, Y.M., Sun, C.Z.: Control technology based on pulse width modulation of RCS. Inf. Electron. Eng. 10(4), 446–450 (2012) 8. Zhi, X.U., Shuo, T., Shu-Xing, Y.: Re-entry control strategy for reusable launch vehicle based on feedback linearization and model predictive control. J. Fire Control Command Control 36(2), 144–147 (2011) 9. Liu, Q.J.: Research on Attitude Control Technology of Reentry for Hypersonic Aircraft. Nanjing University of Aeronautics and Astronautics (2011) 10. Jung, D., Lowenberg, M.H., Jones, C.: Integration of control allocation methods in bifurcation analysis framework. J. Pract. Orthop. 35(1), 35–42 (2006) 11. Bolender, M.A., Doman, D.B.: Nonlinear control allocation using piecewise linear functions. J. Guid. Control Dyn. 27(6), 1017–1027 (2004) 12. Doman, D., Gamble, B., Ngo, A.: Quantized control allocation of reaction control jets and aerodynamic control surfaces. J. Guid. Control Dyn. 32(1), 13–24 (2009) 13. He, J., Qi, R., Jiang, B., Zhai, R.: Fault-tolerant control with mixed aerodynamic surfaces and RCS jets for hypersonic reentry vehicles. Chin J Aeronaut. 30(2), 780–795 (2017) 14. Liu, L., Dong, S., Wang, Y.J., Ou, L.L.: Clearance of flight control law based on structural singular value theory. IEEE Trans. Aerosp. Electron. Syst. 51(3), 2138–2147 (2015) 15. Yu, X., Li, P., Zhang, Y.: The design of fixed-time observer and finite-time fault-tolerant control for hypersonic gliding vehicles. IEEE Trans. Ind. Electron. 65(5), 4135–4144 (2018) 16. Yin, X.M., Wang, B., Liu, L., Wang, Y.J.: Disturbance observer-based gain adaptation highorder sliding mode control of hypersonic vehicles. Aerosp. Sci. Technol. 89, 19–30 (2019) 17. Li, K., Li, S.Y., Wu, Y.L.: Enhanced receding horizon optimal performance for online tuning of PID controller parameters. Int. J. Modell. Ident. Control (2018) 18. Huang, J., Qian, J., Liu, L., Wang, Y.J., Xiong, C.H., Ri, S.: Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator. J. Franklin Inst. 353, 2761–2782 (2016)

An Improved FCM Algorithm Based on the Firework Algorithm for Liquid Rocket Engine Fault Detection Liang Zhaowei, Huang Zihao, Li Zhu, Zhang Jiaping and Lei Liu

Abstract A novel fault detection method based on fuzzy C-means (FCM) clustering algorithm is proposed for a liquid engine of a launching rocket. However, the FCM algorithm is sensitive to the initial cluster center, and the search process suffers from local optimums. Therefore, this paper proposes an improved FCM based on the firework algorithm. The improved FCM utilizes the explosion and mutation mechanism of the firework algorithm to initialize the number of cluster center for FCM iteration, which makes up for the deficiency of the FCM clustering algorithm. Finally, the effectiveness and validation of the algorithm are verified by simulation. Keywords Fault detection · Fuzzy C-means clustering · The firework algorithm · Rocket engine

1 Introduction A liquid rocket engine is a very complex fluid-thermal power system. It not only works in harsh environments such as high temperature, high pressure, strong vibration and strong corrosion, but also release quantity of energy when working. Thus, an engine frequently suffers malfunction. Once a rocket engine fails, it not only affects the performance of the engine, but even destroys the whole space mission [1]. Therefore, engine fault detection is the key to improve the reliability and safety of rocket propulsion systems. There is a growing need for online supervision and fault diagnosis to increase the reliability of control systems [2–5]. Among the comprehensive investigations, two types of fault detection methods have been carried out. The first type is a modelbased fault detection method. The model-based method can accurately determine whether the engine is fail when an accurate model is available. However, the main shortcoming of this method is the reliability to high-fidelity mathematical model. On L. Zhaowei · H. Zihao · L. Zhu · Z. Jiaping · L. Liu (B) National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, HUST, Wuhan 430074, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_108

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the other hand, due to the nature of insensitivity to the accurate model, data-based fault detection method has been widely recognized. There are numerous data-driven methods applied in engine fault detection, such as neural networks [6], statistical analysis [7], and fuzzy logic [8]. In this paper, methods based on fuzzy logic is mainly used for the fault detection. Fuzzy logic theory is suitable to system with nonlinearity and uncertainty. It does not rely on accurate mathematical models and has high diagnostic efficiency. Fuzzy theory has many application directions. Among them, fuzzy C-means clustering algorithm (FCM) has been widely used in pattern recognition [9, 10], nonlinear system identification [11] and fault diagnosis [12]. Classification is the most commonly applied data mining technique, which employs a set of pre-classified examples to develop a model that can classify the population of records at large [13]. This paper proposes an improved FCM algorithm for liquid engine fault detection. By observing the typical parameters of the engine during normal operation, such as pressure of engine nozzle, turbo pump speed, combustion chamber pressure, and second consumption to generate residual signal. If the engine malfunction, a pre-alarm will be performed.

2 Improved Fuzzy C-Means Clustering Algorithm Fuzzy C-means clustering algorithm (FCM) is an improved method for C-means clustering based on fuzzy theory. Compared with the C-means clustering algorithm, the FCM is more flexible for data partitioning due to the introduction of the weighting exponent m. The higher degree of membership is, the greater similarity between the data is, while the lower degree is, the lower similarity is. However, the FCM still has certain disadvantages: Convergence is slow and the search process suffers from local optimums. In view of these above deficiencies, this paper proposes an improved FCM algorithm based on the firework algorithm [14]. The cluster center in the FCM can be initialized by the firework algorithm; meanwhile the explosion range of the spark will be adaptively updated. As a result, it will make the algorithm approximate a global optimal solution faster and the convergence effect is better. In the FCM, initial values of the cluster center are set randomly. Due to the sensitivity of the algorithm to the cluster center, the initial cluster center setting is of much importance, which will affect the efficiency and final effect of the iteration directly. In this paper, the idea of the firework algorithm is introduced in the initialization stage of cluster center, and the same objective function in the FCM is constructed, so that the best initial cluster center can be obtained. The specific steps of the improved algorithm are as follows:

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(1) Setting the clustering objective function:

JFC M (U, C) =

n c  

 2 u imj x j − vi 

(1)

i=1 j=1

Equation contains a number of variables: u i j (i = 1, 2, . . . , c, j = 1, 2, . . . , n) ∈ (0, 1) is the membership function. Cluster centers are C = {v1 , . . . , vc },   x j − vi 2 = (x j − vi )(x j − vi ) is the Euclidean distance from the j-th sample to the i-th cluster center. And take weighting exponent m ∈ [1.5, 3]. (2) Initialization After the firework population is randomly initialized according to the bounds of values and the dimension of the firework particles, the fitness of each firework is calculated based on the objective function. Among them, each firework represents a solution to the solution space. (3) Explosion Calculate the number and range of sparks generated by each firework explosion and explode to create sparks. Number of sparks:  ·  Ni = r ound N N

f max − f (xi ) + ε

i=1

( f max − f (xi )) + ε

 (2)

Range of spark explosion:  ·  f (xi − f min + ε) Ri = R N i=1 ( f (x i ) − f min ) + ε

(3)

 of the fireworks is set Among them, the maximum explosion radius coefficient R g , as shown in the following formula: to the simulated annealing factor R   Rg =R0 1 −

Gen Max Gen

(4)

Ni and Ri are the number of explosion sparks and the blast radius of the i-th  is the explosion spark coefficient, used to adjust the number of sparks fireworks. N generated by the explosion. f (xi ) indicates the fitness value of the fireworks xi . Fmax and Fmin represent the maximum and minimum firework values of fitness in the explosion. R0 is the initial maximum explosion radius. Gen is the current number of g is the maximum blast iterations. MaxGen is the maximum number of iterations. R g is more conducive radius coefficient of the g-th iteration. In the early algorithm, R

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g is gradually reduced to to global search. As the number of iterations increases, R facilitate search and accelerate the convergence of the algorithm. If the value of a spark generated by an explosion exceeds the feasible domain [xlower bound , xupper bound ], it is usually mapped to the feasible domain using a random mapping method. (4) Differential variation In this paper, the variation based on the differential evolution algorithm (DE) is used to replace the Gaussian mutation to generate the variation spark. The mutation operation is performed using the mutation strategy shown in (5), and the crossover operation is shown in (6): Ui = Q best + F · (Q 1 − Q 2 ) + F · (Q 3 − Q 4 )

Ui, j =

Ui, j , rand(0, 1) < C R Q i, j , else

(5) (6)

Among them, Q best is the best fitness for all fireworks and sparks, Q1, Q2, Q3, Q4 are four different individuals randomly selected within the population. F is the scaling factor. (5) Selection and judgment In the algorithm, the firework particles with the best fitness (the smallest fitness value) in this generation will be preserved first. The next iterative particle can be selected by the remaining ones according to the probability distribution, which is shown in (7).   N   j=1 x i − x j P(xi ) =  N  N     k=1 j=1 x k − x j

(7)

  N   between the i-th fireworks particle and j=1 x i − x j represents the distance   N  N  the rest of the particles. k=1 x − x j  represents the sum of the distances j=1 k between all the firework particles inside the population. Such a selection strategy can eliminate redundant fireworks particles and ensure the diversity of firework particles in the next iteration. Therefore, the final result will not fall into the local optimal solution. At the end of each selection, the particle fitness value obtained in the last selection is evaluated. If the termination condition is met, a set of initial cluster centers is output. If the condition is not met, back to the third step—the process of explosion. (6) Setting parameter According to the firework algorithm, the number of cluster centers c(2 ≤ c ≤ n) and cluster center V (b) = {v1 , v2 , . . . , vc } have been initialized. Besides, it is also

An Improved FCM Algorithm Based …

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necessary to set the threshold ε, the fuzzy weighting exponent m, and the iteration counter b. (7) Updating membership function and cluster center Calculate and update the membership function μi j using the following formula: For ∀i, j, if ∃di(b) j > 0, u i(b) j

⎧ ⎡ 2 ⎤⎫−1  m−1 c ⎨ ⎬ di(b) j ⎣ ⎦ = ⎩ ⎭ dl(b) j l=1

(8)

Di j represents the distance from the i-th cluster center to the training set sample points. Then update the cluster center matrix V (b+1) with the following formula:  m (b+1) u xj j=1 ij =   m (b+1) n j=1 u i j n

vi(b+1)

(9)

Minimize the objective function by continuously updating the position of the cluster center. b If JFC M takes the minimum value, it can stop the iterative update cluster center, and output the membership function U and the cluster center matrix V. Otherwise b = b + 1, turn to the previous step.

3 Detection Process Based on the Improved FCM Algorithm This process is a fault detection of the engine during starting work process, which is based on the improved FCM algorithm. Before the start of the detection process, it is necessary to determine the monitoring vector, preprocess data, initialize the cluster center, and determine the detection threshold.

3.1 Determining the Monitoring Vector Through the statistical analysis of the engine failure mode, the turbo pump and the combustion chamber are faulty multiple components, and the gas generator also plays an important role in the startup process. For the fault detection, the combustion chamber pressure Pc , the gas generator pressure Pg , the hydrogen pump outlet pressure Pe f and the oxygen pump outlet pressure Peo are determined as the monitoring

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parameters. In addition, the performance parameters change over time at a specific startup timing is also an important feature. Therefore, in the detection process, the time and monitoring parameters are combined as a monitoring vector.

3.2 Preprocessing Data Data preprocessing is the crucial step of machine learning which involves data wrangling and data munching to make data clean from null values, type errors, missing entries [15]. The units of the parameters in the monitoring vector are different, and the values differ greatly, even by several orders of magnitude. Therefore, when these data is used for clustering processing, the cluster center is more affected by the parameters with large values, and the parameters with small values have little effect on the clustering results. Therefore, data preprocessing must be performed first, and all parameters are converted to the same order of magnitude, so that the sensitivity of the parameter change is close.

3.3 Initializing the Cluster Center Firstly, we need to set the parameters of the firework algorithm, and randomly initialize the firework population X. Then, through evaluating all individual fitness f (xi ), the number of sparks and the explosion range are calculated by the Formulas (2) and (3); the final explosion produces spark matrix V and the differential variation produces the variation sparks U. After the explosion and mutation, it is necessary to evaluate the fitness of individuals again. Then select the next generation fireworks according to the roulette rules. If the objective function value at this time satisfies the set condition, the firework algorithm is terminated, and the initial cluster center of the FCM is output. If not satisfied, repeat the steps of exploding, mutating, and selecting the next generation of fireworks until the objection function value satisfies the condition.

3.4 Determining the Detection Threshold The initial cluster center and number obtained by the firework algorithm are used as the input of the improved FCM. The iterative update of the membership degree and the cluster center is performed according to Formula (8) and Formula (9) until the objective function satisfies the condition. Introducing a new concept, the minimum value of the average distance from training samples to each cluster center point, defined by dmin−mean , whose formula is:

An Improved FCM Algorithm Based … Table 1 Minimum value of average distance between the training data and the cluster center

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Test code

Minimum of average distance

TEST1-1

7.5965

TEST1-2

7.6028

TEST1-3

7.6046

TEST1-4

7.6001

dmin−mean = min ( mean (di j )) i=1,...,n j=1,...,m

(10)

  di j =  X i − C j  is the distance from i-th point in the training data to the cluster center C j , and X i is i-th group data in the training set. C j is the cluster center. By selecting dmin−mean as the width σ of the fuzzy membership function, the distance from each cluster center to training data center point is substantially within twice the range of σ . The detection of the test sample is actually to determine whether the minimum distance of the sample to each cluster center is greater than the set threshold. The threshold is determined mainly by calculating the training data. The detection threshold is:  (11) DT = −ln(μt ) × 2 × σ Table 1 shows the minimum distance between the training data and the cluster center. The average value is calculated to be 7.600, which is assigned to the membership function width σ . When the membership degree is greater than 0.92, the sample point belongs to this category. Take ut = 0.92 and calculate the detection threshold DT = 3.104.

3.5 Testing the Sample The minimum distance dmin is defined as the minimum Euclid distance between the detection parameter and each cluster center. dmin = min {X − C1 , . . . , X − Ci , . . . X − Cc } i=1,...,c

(12)

If the dmin of the sample point is greater than DT for three consecutive times, it is considered that a fault has occurred and a fault alarm should be issued.

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4 Analysis and Comparison of Test Results The fault detection algorithm was verified by using the test data of the first 2 s of the liquid hydrogen liquid oxygen rocket engine. By comparing the FCM with the improved FCM, the accuracy of fault detection and the effectiveness of optimization calculation time are confirmed.

4.1 Feasibility Analysis Figure 1a, b are the detection curves, which are obtained by the FCM and the improved one for the test data. The red line is the detection threshold, and the blue one is the minimum distance. From the Fig. 1a, b, during the first 1.2 s of engine startup ignition phase, the engine’s various detection parameters changed drastically, causing the minimum distance to fluctuate fiercely. After 1.2 s, the engine condition tends to be stable and the minimum distance gradually decreases. During the whole inspection process, the minimum distance did not exceed the detection threshold, and the detection result was normal. The result was consistent with the actual test of the engine, and no false alarm occurred. Both detection algorithms achieved the purpose of detection.

4.2 Comparison of the Accuracy Between the FCM and the Improved FCM The FCM is sensitive to the initial cluster center value, which is randomly set. Therefore, after several iterations, the final calculated output cluster center may deviate

(a) the FCM Fig. 1 Detection curves of the liquid engine

(b) the Improved FCM

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from the actual value or fall into the local optimal solution. Based on the shortcomings of appeal, this paper proposes an improved FCM algorithm combining the explosion and mutation mechanism. When the cluster center is initialized, the globality and diversity of the data are guaranteed, which makes the final output cluster center more accurate and avoids falling into local optimum. The following matrix Q 1 is the cluster center of the FCM, and Q 2 is the cluster center of the improved FCM. Comparing with the actual data, it’s suggested that Q2 is more consistent with the distribution law of test data. ⎤ ⎡ 10.9844 11.8899 10.9211 10.5734 ⎢ 18.9957 18.8097 19.3656 18.6412 ⎥ ⎥ ⎢ ⎢ 7.24652 8.34961 8.52018 8.28469 ⎥ ⎥ ⎢ ⎢ 5.03744 6.52218 7.25754 7.08108 ⎥ ⎥ ⎢ ⎥ ⎢ (13) Q 1 =⎢ 13.9804 14.8548 13.4424 12.9768 ⎥ ⎥ ⎢ ⎢ 0.714187 0.828674 2.50445 2.55018 ⎥ ⎥ ⎢ ⎢ 3.50359 4.46544 5.43208 5.34096 ⎥ ⎥ ⎢ ⎣ 17.6653 18.2476 17.3478 16.6997 ⎦ 16.1334 16.7581 15.5268 14.9638 ⎡

10.8226 ⎢ 17.204 ⎢ ⎢ 2.69078 ⎢ ⎢ 12.7883 ⎢ ⎢ Q 2 =⎢ 8.13027 ⎢ ⎢ 0.137022 ⎢ ⎢ 18.9928 ⎢ ⎣ 4.33332 14.722

11.7986 17.7713 3.12365 13.7682 8.96327 0.200158 18.8132 5.71807 15.5127

10.8586 16.7595 4.24907 12.4319 8.87356 1.84718 19.3608 6.5796 14.1174

⎤ 10.5138 16.1388 ⎥ ⎥ 4.21325 ⎥ ⎥ 12.0135 ⎥ ⎥ ⎥ 8.62155 ⎥ ⎥ 1.92364 ⎥ ⎥ 18.6365 ⎥ ⎥ 6.43483 ⎦ 13.6202

(14)

4.3 Comparison of the Speed Between the FCM and the Improved FCM Figure 2 shows the failure test curve of the test data in the TEST-2 engine startup process. (a) is the detection result graph of the FCM, and (b) is the detection result graph of the improved FCM. The red line is the detection threshold, and the blue line is the minimum distance. It can be seen from the Fig. 2a, b that the minimum distance dmin significantly exceeds the detection threshold DT. If the curve satisfies the continuity rule of the abnormal point, the engine is proved to be malfunctioned. The improved FCM algorithm has a more accurate cluster center than the FCM algorithm, so that a better detection threshold can be calculated. The detection threshold of the FCM detection algorithm is 3.263, and the improved detection threshold becomes 3.104.

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(a) the FCM

(b) the Improved FCM

Fig. 2 Detection curve of start-up process TEST-2

Due to the difference in detection thresholds, the alarm times of the two detection algorithms are different. The alarm time of the FCM algorithm is 0.96 s, and the alarm time of improved FCM algorithm is 0.92 s. which suggests that the improved algorithm advances by 0.04 s. The appeal results demonstrate that the improved FCM detection algorithm has faster efficiency in fault detection. Figure 3 shows the comparison results of the two algorithms when calculating the cluster center. The termination conditions of the two algorithms are the same—reaching the equal function value. The improved FCM algorithm proposed in this paper will approach convergence after six iterations, while the FCM algorithm requires fifteen iterations. It proves the efficiency of the algorithm. Table 2 shows the specific values of the comparison results. Fig. 3 Comparison of results

An Improved FCM Algorithm Based … Table 2 Values of the comparison results

1161 Objective function value

Iterations

Average time (s)

The FCM

46.863

15

1.723

Improved FCM

46.862

6

0.631

5 Conclusion Aiming at the shortcomings of the FCM algorithm, such as sensitivity to initial value, local optimum problem and low computational efficiency, an improved FCM algorithm based on the firework algorithm is proposed. The improved FCM algorithm introduces explosion and mutation mechanisms. Before iteration, the initial cluster center is calculated by the firework algorithm, so that the final clustering effect is better. When calculating the blast radius, the smaller the fitness of the firework particles is, the larger the blast radius is. Thus, the search range becomes wider. It’s presented that the mutation mechanism increases the diversity of the population and avoids falling into local optimum. During fault detection of the rocket engine, the simulation shows that the improved FCM algorithm can perform fault pre-alarming more effectively and accurately. Acknowledgements This work was supported in part by the National Nature Science Foundation of China (Grant Nos. 61873319, 61803162 and 61573161).

References 1. Li, J.: Study on fault detection and isolation methods for LOX/methane rocket engines (2015) 2. Wang, M., Sun, X., Xing, H., Zheng, H.: Online fault detection for networked control system with unknown network-induced delays. Int. J. Modell. Ident. Control 30(4), 293 (2018) 3. Hou, Z., Liu, L., Wang, Y.: Time-to-go estimation for terminal sliding mode based impact angle constrained guidance. Aerosp. Sci. Technol. 71, 685–694 (2017) 4. Cheng, Z., Wang, B., Liu, L., Wang, Y.: A composite impact-time-control guidance law and simultaneous arrival. Aerosp. Sci. Technol. 80, 403–412 (2018) 5. Liu, L., Dong, S., Wang, Y., Liuli, O.: Clearance of flight control law based on structural singular value theory. IEEE Trans. Aerosp. Electron. Syst. 51(3), 2138–2147 (2015) 6. Tayarani-Bathaie, S.S., Vanini, Z.S., Khorasani, K.: Dynamic neural network-based fault diagnosis of gas turbine engines. Neurocomputing 125, 153–165 (2014) (Advances in Neural Network Research and Applications Advances in Bio-Inspired Computing: Techniques and Applications Selected papers from the 9th International Symposium of Neural Networks, July 2012) 7. Sarkar, S., Jin, X., Ray, A.: Data-driven fault detection in aircraft engines with noisy sensor measurements. J. Eng. Gas Turbines Power 133(8), 081602 (2011) 8. Ogaji, S., Marinai, L., Sampath, S., Singh, R., Prober, S.: Gas-turbine fault diagnostics: a fuzzy-logic approach. Appl. Energy 82(1), 81–89 (2005) 9. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms, pp. 95–107. Plenum Press, New York (1981)

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10. Yang, M.S.: A survey of fuzzy clustering. Math. Comput. Modell. 18, 1–16 (1993) 11. Jianzhong, S.: Identification of Nonlinear Systems Based on Fuzzy Clustering. North China Electric Power University (2012) 12. Han, D.: Fuzzy cluster analysis and its application to fault diagnosis of power transformer. Xi’an University of technology (2008) 13. Sathiyapriya, S., Kanagaraj, A.: Basics of data mining techniques and its application. Int. J. Comput. Technol. 5(4), 44–47 (2018) 14. Tan, Y., Zheng, S.: Recent advances in fireworks algorithm. CAAI Trans. Intell. Syst. 9(5), 515–528 (2014) 15. Murali, V., Chatrapathy, K.: BuyerPlyGround: Agriculture trade market using blockchain with machine learning. Int. J. Comput. Technol. 31–36 (2019)

Two-Stage Least Squares Based Iterative Parameter Identification Method for Time-Delay Systems Ya Gu, Huigang Xu, Yongxin Chou, Jicheng Liu and Peiyi Zhu

Abstract This study focuses on a two-stage least squares based iterative algorithm for state space system with unmeasurable time delay sequence. Obtaining unknown parameters of interest is a major challenge to deal with: synthesizing input-output data for parameter estimation. This paper uses the linear transformation to transform the time-varying state space model to the least squares identification model. Keywords Iterative identification · State space model · Time-delay

1 Introduction The state space models have wide range of applications in adaptive control, system analysis and parameter estimation [1–3]. Various state estimation methods have been presented for linear systems and nonlinear systems. Zhang et al. reported the parameter and state estimation problem for a bilinear state space system with moving average noise [4]; Ding proposed the adaptive modified input and state estimation for the unknown inputs linear discrete-time system [5]; Liu studied the state estimation for discrete-time Markov jump linear systems with time-correlated and mode-dependent measurement noise [6]. Y. Gu · H. Xu · Y. Chou · J. Liu (B) · P. Zhu School of Electric and Automatic Engineering, Changshu Institute of Technology, Changshu 215500, People’s Republic of China e-mail: [email protected] Y. Gu e-mail: [email protected] H. Xu e-mail: [email protected] Y. Chou e-mail: [email protected] P. Zhu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_109

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The ultimate purpose of the system identification is to find a model that is very close to a real system basic to the given input-output data [7–9]. The general optimization method can be used to get the parameters and a signal model from the observation data [10–12]. For system analysis and system identification, the basic is to get the parameters of a system [13–15]. There exist a large quantity of parameter estimation algorithms: Ding et al. presented a hierarchical least squares identification method for Hammerstein nonlinear systems with key item separation [16]. In this paper, based on the principle of iterative identification and the idea of least squares identification, a least square iterative method for two-stage state space model with time-delay is proposed. To solve the problem of information matrices containing unmeasurable items, unmeasurable items are substituted for their iterative resizes, which are calculated by previous parameter estimates.

2 Problem Description Consider the state space system with multi-step time-delays, ξ (ι + 1) = A1 ξ (ι) + A2 ξ (ι − 1) + A3 ξ (ι − 2) + · · · +Ar ξ (ι − r + 1) + f u(ι), ς (ι) = cξ (ι) + v(ι),

(1) (2)

where ξ (ι) = [ξ1 (ι), ξ2 (ι), . . . , ξn (ι)]T ∈ Rn represents the state vector, u(ι) ∈ R represents the system input, ς (ι) ∈ R stands for the system output, v(ι) ∈ R denotes random noise with zero mean. This paper is to develop a two-stage least squares based iterative parameter estimation method. Without loss of generality, assume that the order rn is given and u(ι) = 0, ς (ι) = 0 and v(ι) = 0 for ι  0. Lemma 1 The transfer function of (1) and (2) having the form G(o) :=

c adj[or I − or−1 A1 − or−2 A2 − · · · − Ar ]f or−1 . det[or I − or−1 A1 − or−2 A2 − · · · − Ar ]

Proof The first method is to prove this lemma by using the property of the shift operator o. Writing for the sake of convenience, Eq. (1) can be represented by oξ (ι) = A1 ξ (ι) + o−1 A2 ξ (ι) + o−2 A3 ξ (ι) + · · · + o−r+1 Ar ξ (ι) + f u(ι).

(3)

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1165

Multiplying both sides by or−1 gives or ξ (ι) = or−1 A1 ξ (ι) + or−2 A2 ξ (ι) + or−3 A3 ξ (ι) + · · · + Ar ξ (ι) + or−1 f u(ι), or

(4)

ξ (ι) = (or I − or−1 A1 − or−2 A2 − · · · − Ar )−1 f or−1 u(ι).

Substituting ξ (ι) into Eq. (2) gives ς (ι) = c(or I − or−1 A1 − or−2 A2 − · · · − Ar )−1 f or−1 u(ι) + v(ι) =: G(o)u(ι) + v(ι). Thus, we have the transfer function: G(o) = c(or I − or−1 A1 − or−2 A2 − · · · − Ar )−1 f or−1 c adj[or I − or−1 A1 − or−2 A2 − · · · − Ar ]f or−1 = det[or I − or−1 A1 − or−2 A2 − · · · − Ar ] β(o) , =: α(o) where α(o) and β(o) are polynomials in a unit backward shift operator o−1 [o−1 ς (ι) = ς (ι − 1)], and α(o) := o−rn det[or I − A1 or−1 − A2 or−2 − · · · − Ar ] = o−rn (orn + α1 orn−1 + α2 orn−2 + · · · + αrn ) = 1 + α1 o−1 + α2 o−2 + · · · + αrn o−rn , β(o) := o−rn c adj[or I − A1 or−1 − A2 or−2 − · · · − Ar ]f or−1 = β1 o−1 + β2 o−2 + · · · + βrn o−rn .

(5) (6)

Define the parameter vector χ , χ 1 and χ 2 and the information vectors ϕ(ι), ϕ 1 (ι) and ϕ 2 (ι) as χ := [χ T1 , χ T2 ]T ∈ R2rn , χ 1 := [α1 , α2 , . . . , αrn ]T ∈ Rrn , χ 2 := [β1 , β2 , . . . , βrn ]T ∈ Rrn , ϕ(ι) := [ϕ T1 (ι), ϕ T2 (ι)]T ∈ R2rn , ϕ 1 (ι) := [−ξ(ι − 1), −ξ(ι − 2), . . . , −ξ(ι − rn)]T ∈ Rrn , ϕ 2 (ι) := [u(ι − 1), u(ι − 2), . . . , u(ι − rn)]T ∈ Rrn .

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Define an intermediate variable: ξ(ι) :=

β(o) u(ι). α(o)

(7)

Substituting (5) and (6) into (7) can be described by ξ(ι) =

β1 o−1 + β2 o−2 + · · · + βrn o−rn u(ι), 1 + α1 o−1 + α2 o−2 + · · · + αrn o−rn

or ξ(ι) = −α1 ξ(ι − 1) − α2 ξ(ι − 2) − · · · − αrn ξ(ι − rn) +β1 u(ι − 1) + β2 u(ι − 2) + · · · + βrn u(ι − rn) = ϕ T1 (ι)χ 1 + ϕ T2 (ι)χ 2 = ϕ T (ι)χ. Thus, the identification model of the state space system with time-delays in (1) and (2) is of the form (8) ς (ι) = ϕ T (ι)χ + v(ι).

3 The Two-Stage Least Squares Based Iterative Algorithm This section derives a two-stage least squares based iterative parameter estimation method using the decomposition technique. The basic method is to decompose the model in (8) into two subsystems. Define two intermediate variables, ς1 (ι) := ς (ι) − ϕ T2 (ι)χ 2 , ς2 (ι) := ς (ι) − ϕ T1 (ι)χ 1 .

(9) (10)

The identification model in (8) can be decomposed into two fictitious subsystems, ς1 (ι) = ϕ T1 (ι)χ 1 + v(ι), ς2 (ι) = ϕ T2 (ι)χ 2 + v(ι).

(11) (12)

Consider the data from ι = 1 to ι = L (L  2rn) and define the stacked output vectors ς (L), ς 1 (L) and ς 2 (L), the stacked information matrices Φ1 (L), Φ2 (L) and the stacked white noise vector V (L) as

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⎤ ⎤ ⎤ ⎡ ⎡ ς(1) v(1) ς1 (1) ⎢ ς(2) ⎥ ⎢ v(2) ⎥ ⎢ ς1 (2) ⎥ ⎥ ⎥ ⎥ ⎢ ⎢ ⎢ ς(L) := ⎢ . ⎥ ∈ RL , V (L) := ⎢ . ⎥ ∈ RL , ς 1 (L) := ⎢ . ⎥ ∈ RL , ⎣ .. ⎦ ⎣ .. ⎦ ⎣ .. ⎦ ς(L) v(L) ς1 (L) ⎤ ⎤ ⎡ ⎡ T ς2 (1) ϕ 1 (1) ⎢ ς2 (2) ⎥ ⎢ ϕ T1 (2) ⎥ ⎥ ⎥ ⎢ ⎢ ς 2 (L) := ⎢ . ⎥ ∈ RL , Φ1 (L) := ⎢ . ⎥ ∈ RL×rn , ⎣ .. ⎦ ⎣ .. ⎦ ς2 (L) ϕ T1 (L) ⎤ ⎡ T ϕ 2 (1) ⎢ ϕ T2 (2) ⎥ ⎥ ⎢ Φ2 (L) := ⎢ . ⎥ ∈ RL×rn . ⎣ .. ⎦ ϕ T2 (L) ⎡

Define two criterion functions, J1 (χ 1 ) := ς 1 (L) − Φ1 (L)χ 1 2 , J2 (χ 2 ) := ς 2 (L) − Φ2 (L)χ 2 2 . Letting the partial derivatives of J1 (χ 1 ) and J2 (χ 2 ) with regard to χ 1 and χ 2 be zero becomes ∂J1 (χ 1 ) = −2Φ1T (L)[ς 1 (L) − Φ1 (L)χ 1 ] = 0, ∂χ 1 ∂J2 (χ 2 ) = −2Φ2T (L)[ς 2 (L) − Φ2 (L)χ 2 ] = 0. ∂χ 2 We can acquire the following least squares estimates of the parameter vectors χ 1 and χ 2: χˆ 1 = [Φ1T (L)Φ1 (L)]−1 Φ1T (L)ς 1 (L) = [Φ1T (L)Φ1 (L)]−1 Φ1T (L)[ς (L) − Φ2 (L)χ 2 ], χˆ 2 = [Φ2T (L)Φ2 (L)]−1 Φ2T (L)ς 2 (L) = [Φ2T (L)Φ2 (L)]−1 Φ2T (L)[ς (L) − Φ1 (L)χ 1 ]. ˆ Let k = 1, 2, 3, . . . be an iterative variable, χ(k) := [χˆ T1 (k), χˆ T2 (k)]T be the iterative estimate of χ = [χ T1 (k), χ T2 (k)]T at iteration k, and ξˆk (ι − i) be the estimate of ξ(ι − i) at iteration k, and define

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 ϕˆ k (ι) :=

ϕˆ 1k (ι) ∈ R2rn , ϕ 2 (ι)

ϕˆ 1k (ι) := [−ξˆk−1 (ι − 1), −ξˆk−1 (ι − 2), . . . , −ξˆk−1 (ι − rn)]T ∈ Rrn , Φˆ 1 (L) := [ϕˆ 1k (1), ϕˆ 1k (2), . . . , ϕˆ 1k (L)] ∈ RL×rn . Thus, we can summarize the two-stage least squares based iterative (TS-LSI) identification algorithm for estimating χ i as follows: χˆ 1k = [Φˆ 1T (L)Φˆ 1 (L)]−1 Φˆ 1T (L)[ς (L) − Φ2 (L)χˆ 2,k−1 ], χˆ 2k

k = 1, 2, 3, . . . , = [Φ2T (L)Φ2 (L)]−1 Φ2T (L)[ς (L) − Φˆ 1 (L)χˆ 1k ],

(13) (14)

ς (L) = [ς (1), ς (2), . . . , ς (L)]T , Φˆ 1 (L) = [ϕˆ 1k (1), ϕˆ 1k (2), . . . , ϕˆ 1k (L)]T ,

(15) (16)

Φ2 (L) = [ϕ 2 (1), ϕ 2 (2), . . . , ϕ 2 (L)]T , ϕˆ 1k (t) = [−ξˆk−1 (ι − 1), . . . , −ξˆk−1 (ι − rn)]T , ϕ 2 (ι) = [u(ι − 1), u(ι − 2), . . . , u(ι − rn)]T , ϕˆ k (ι) = [ϕˆ T1k (ι), ϕ T2 (ι)]T , χˆ k = [χˆ T1k , χˆ T2k ]T , ξˆk (ι) = ϕˆ T1k (ι)χˆ 1k + ϕ T2 (ι)χˆ 2k .

(17) (18) (19) (20) (21) (22)

4 Example Consider the state space system with time delay: 

 0 1 −0.02 ξ (ι + 1) = ξ (ι) + −1 0.07 0 y(ι) = [1, 0]ξ (ι) + v(ι).

−0.03 1.15



 ξ (ι − 1) +

1.00 −1.00

u(ι),

The input–output representation is expressed as β(o) u(ι) + v(ι) α(o) o−1 − 1.07o−2 − 1.12o−3 = u(ι) + v(ι), 1 − 0.07o−1 − 0.13o−2 − 0.0314o−3 − 0.023o−4 χ = [−0.07, −0.13, −0.0314, −0.023, 1, −1.07, −1.12]T .

y(ι) =

In simulation, the input {u(ι)} is taken as an uncorrelated persistent excitation signal sequence with zero mean and unit variance, and {v(ι)} as a white noise sequence

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0.2 0.18 0.16 0.14

δ

0.12 0.1 0.08 σ2=0.202

0.06 0.04

σ2=0.502

0.02 0

1

2

3

4

5

6

7

8

9

10

k

Fig. 1 The two-stage LSI estimation errors δ versus k with different σ 2 (L = 3000)

with zero mean and variance σ 2 = 0.202 and σ 2 = 0.502 . Applying the TS-LSI method in (13)–(22) to estimate the parameters of this example system. The parameter estimation errors versus k is shown in Fig. 1. From Fig. 1, the following conclusion can be drawn: the parameter estimation errors given by the TS-LSI method become smaller along with the iteration k increases.

5 Conclusions This paper presents an iterative parameter estimation method based on two-stage least squares linear systems based on state space models with time delays. The given algorithm performs a hierarchical computation process at each iteration and provides accurate parameter estimates. Simulation results show that the method has fast convergence rate and high precision parameter estimation can be obtained after several iterations. Acknowledgements This work was supported by the Natural Science Fundamental Research Project of Colleges and Universities in Jiangsu Province (18KJB120001), the Natural Science Foundation of Jiangsu Province (BK20181033), the National Natural Science Foundation of China (61903050) and Changshu Scientific and Technology Development Plan Project (CQ201701).

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References 1. Kim, J., Tong, L., et al.: Subspace methods for data attack on state estimation: a data driven approach. IEEE Trans. Sig. Process. 63(5), 1102–1114 (2015) 2. Ahmed, A., Moinuddin, M., et al.: q-state space least mean family of algorithms. Circuits Syst. Sig. Process. 37(2), 729–751 (2018) 3. Guo, Z.Y., Shi, D.W., et al.: Worst-case stealthy innovation-based linear attack on remote state estimation. Automatica 89, 117–124 (2018) 4. Zhang, X., Xu, L., et al.: Combined state and parameter estimation for a bilinear state space system with moving average noise. J. Franklin Inst. 355(6), 3079–3103 (2018) 5. Ding, B., Fang, H.J.: Adaptive modified input and state estimation for linear discrete-time system with unknown inputs. Circuits Syst. Sig. Process. 36(9), 3630–3649 (2017) 6. Liu, W., Shi, P., et al.: State estimation for discrete-time Markov jump linear systems with time-correlated and mode-dependent measurement noise. Automatica 85, 9–21 (2017) 7. Blanchard, E., Sandu, A., et al.: Parameter estimation for mechanical systems via an explicit representation of uncertainty. Eng. Comput. 26(5), 541–569 (2009) 8. Jalaleddini, K., Kearney, R.: Subspace identification of SISO Hammerstein systems: application to stretch reflex identification. IEEE Trans. Biomed. Eng. 60(10), 2725–2734 (2013) 9. Wills, A., Ninness, B.: On gradient-based search for multivariable system estimates. IEEE Trans. Autom. Control 53(1), 298–306 (2008) 10. Phillip, F.: Pulse signal and source identification using fuzzy-neural techniques. IEEE Aerosp. Electron. Syst. Mag. 28(1), 22–33 (2013) 11. Gu, Y., Ding, F., et al.: State filtering and parameter estimation for linear systems with d-step state-delay. IET Sig. Process. 8(6), 639–646 (2014) 12. Dong, S.J., Liu, T., et al.: Identification of dual-rate sampled systems with time delay subject to load disturbance. IET Control Theory Appl. 11(9), 1404–1413 (2017) 13. Zhang, Y., Wang, Z.D., et al.: Event-based finite-time filtering for multirate systems with fading measurements. IEEE Trans. Aerosp. Electron. Syst. 53(3), 1431–1441 (2017) 14. Cerone, V., Razza, V., et al.: Set-membership errors-in-variables identification of MIMO linear systems. Automatica 90, 25–37 (2018) 15. Levitt, M., Guta, M., et al.: Power spectrum identification for quantum linear systems. Automatica 90, 255–262 (2018) 16. Ding, F., Chen, H.B., et al.: A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation. J. Franklin Inst. 355, 3737–3752 (2018)

Trajectory Tracking of Unmanned Ground Vehicle Based on Iterative Learning Model Predictive Control Chaofang Hu, Lingxue Zhao and Na Wang

Abstract In this paper, an iterative learning model predictive control (ILMPC) strategy is introduced for the trajectory tracking of Unmanned Ground Vehicle (UGV). First, a linear time-varying (LTV) system of UGV is derived from the simplified dynamic vehicle model of UGV by Taylors formula. Second, the constrained ILMPC controller is introduced to solve the trajectory tracking problem, which is described as a QP problem. Finally, a simulation about trajectory tracking of batch process is presented to show the effectiveness of the proposed controller. Keywords UGV · Iterative learning · MPC · LTV system

1 Introduction Many military and civil applications require unmanned ground vehicles (UGVs), and trajectory tracking is the key part of controlling UGV [1]. Variable strategies have been applied for trajectory tracking of UGV. For example, PID controller is widely used for trajectory tracking [2]. Besides, some other methods such as fuzzy control [3], adaptive control [4–6], neural network control [7] and model predictive control [8, 9] have been gradually used. When UGV works for a certain application which requires high security or accurate tracking, the repetitive control process is necessary. Iterative learning control (ILC) is a control method for batch or iterative processes. It doesn’t require an accurate mathematical model, and is suitable for objects with C. Hu (B) · L. Zhao School of Electrical and Information Engineering, Tianjin University, Tianjin, China e-mail: [email protected] Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, China N. Wang School of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_110

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repetitive operation characteristics for a finite time interval [10, 11]. ILC method learns through the historical control experience and generates a new control input which can track the reference trajectory accurately. Model predictive control (MPC) is an advanced control algorithm. Since MPC is easy to solve multivariate and constrained optimization problems, it is widely used in many control processes [8]. However, MPC can’t make good use of prior knowledge, so some studies about MPC combined with ILC have come out, called iterative learning model predictive control (ILMPC). ILMPC has combined the advantages of MPC and ILC. For one thing, ILMPC can utilize the prior knowledge to correct the control input repeatedly; for another, ILMPC uses the method of receding horizon optimization and feedback correction to improve the ability of disturbance rejection. In this paper, the ILMPC method [12] is introduced for trajectory tracking of UGV. A simplified dynamic vehicle model is established, and the linearization around the reference trajectory points is applied to derive the linear time-varying (LTV) system. Based on the LTV system, an incremental state-space model is used in ILMPC. In order to guarantee the feasible solution will always be found, the slack variable is used. Simulation shows the effectiveness of the proposed ILMPC.

2 UGV Model for Iterative Learning Model Predictive Control 2.1 UGV Model Considering the longitudinal, lateral and yaw dynamics of UGV, ignoring the pitch and roll dynamics, a bicycle model simplified from four-wheel dynamics is used in this paper, shown in Fig. 1. The UGV is a front wheel drive vehicle, so the steering angles of the rear tires remain unchanged.

Fig. 1 The bicycle dynamic model of UGV

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In Fig. 1, XOY is the inertial coordinate system, xoy is the vehicle body coordinate system. x˙ and y˙ are the longitudinal and lateral velocities of UGV, respectively; ϕ is the yaw angle of UGV over the center of mass; δ f is the steering angle of the front tire; a and b are the wheelbases. The model is described as:   m y¨ = −m x˙ ϕ˙ + 2 Fl f sin δ f + Fc f cos δf + 2Fcr m x¨ = m y˙ϕ˙ + 2 Fl f cos δ f − Fc f sin δ f + 2Flr (1) Iz ϕ¨ = 2a Fl f sin δ f + Fc f cos δ f − 2bFcr where m is the mass of UGV, Iz is the moment of inertia of UGV, Fl f and Flr are longitudinal tire forces of the front and rear tires respectively; Fc f and Fcr are lateral tire forces of the front and rear tire forces respectively. In order to simplify the model, we use linear functions to rewrite the longitudinal and lateral tire forces: Fl f = Cl f s f , Flr =Clr sr   ϕ˙ Fc f = Cc f α f = Cc f δ f − tan−1 y˙ +a   x˙ ϕ˙ Fcr = Ccr αr = Ccr −tan−1 y˙ −b x˙

(2)

where Cl f and Cc f are the longitudinal and lateral cornering stiffness of the front tire respectively; Clr and Ccr are the longitudinal and lateral cornering stiffness of the rear tire respectively; s f and sr are the slip rates of the front and rear tires; α f and αr are the side slip angles of the front and rear tires, which are related to ϕ, ˙ x, ˙ y˙ and δ f . Assuming that δ f and side slip angles are small enough, α f and αr are simplified as: y˙ + a ϕ˙ y˙ − bϕ˙ , αr = − (3) αf = δf − x˙ x˙ Similarly, model (1) can also be simplified. Considering the transformation of coordinate system X OY and xoy, the UGV model is described as follows: ⎧

   y˙ +a ϕ˙ y˙ −bϕ˙ 2 ⎪ − x ˙ ϕ ˙ + C δ − C − ⎪ c f f cr ⎪ m ⎪

 x˙  x˙  ⎪ ⎪ ⎪ y˙ ϕ˙ + 2 Cl f s f + Cc f δ f − y˙ +a ϕ˙ δ f + Clr sr ⎪ ⎪ m x˙ ⎨ ˙ξ = ϕ˙

   ⎪ y˙ +a ϕ˙ y˙ −bϕ˙ 2 ⎪ aC δ + bC − ⎪ c f f cr ⎪ Iz x˙ x˙ ⎪ ⎪ ⎪ x˙ sin ϕ + y˙ cos ϕ ⎪ ⎪ ⎩ x˙ cos ϕ − y˙ sin ϕ

(4)



T where ξ = y˙ x˙ ϕ ϕ˙ Y X is the state variables, u = δ f is the control input, and the output is   001000 h (ξ ) = Cξ, C = (5) 000010

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The nonlinear vehicle dynamic model can be described as follows: ξ˙ = f (ξ, u) , y = h (ξ )

(6)

2.2 Linear Time-Variant Model Due to the complexity of the nonlinear differential equations (6), linearization method is required. Suppose that the states and input of the reference trajectory have obtained in advance. The relationship between the states and input of the reference trajectory at each point is described as: ξ˙r = f (ξr , u r ) (7) where ξr and u r are the states and inputs of the reference trajectory, ξr =

T y˙r x˙r ϕr ϕ˙r Yr X r , u r = δ f r . Expand the right side of Eq. (6) in Taylor series around the point (ξr , u r ), and neglect the high order terms, then Eq. (6) can be rewritten as: ξ˙ = f (ξr , u r ) +

∂ f (ξ, u) ∂ f (ξ, u) | ξ =ξr (ξ − ξr ) + | ξ =ξr (u − u r ) u=u r u=u r ∂ξ ∂u

(8)

Subtract Eq. (7) from Eq. (8):   ∂ f (ξ, u)  ˙ξ˜ = ∂ f (ξ, u)  (ξ − ξr ) + (u − u r ) ∂ξ  ξ =ξr ∂u  ξ =ξr u=u r

Define At =



∂ f (ξ,u)  ∂ξ  ξ =ξr u=u r

and Bt =

(9)

u=u r



∂ f (ξ,u)  ∂u  ξ =ξr u=u r

, and discrete the system with

time interval of T . The discrete-time LTV system of UGV is described as: ξ˜ (w + 1) = Aw,t ξ˜ (w) + Bw,t u˜ (w)

(10)

where t is the time index, ξ˜ = ξ − ξr , u˜ = u − u r , Aw,t = I + T At , Bw,t = T Bt , where ⎡ ⎤ −2(Cc f +Ccr ) 2(bCcr −aCc f ) ∂ f y˙ 0 − x ˙ + 0 0 r m x˙r ∂ x˙ m x˙r ⎢ ⎥ 2aC δ ∂ f x˙ ⎢ ϕ˙r − 2Cc f δ f r 0 y˙r − mcx˙fr f r 0 0⎥ ⎢ ⎥ m x˙r ∂ x˙ ⎢ 0 0 0 1 0 0⎥ ⎢ ⎥ At = ⎢ 2 bC −aC ⎥ −2(a 2 Cc f +b2 Ccr ) ⎢ ( crI x˙ c f ) ∂∂ fx˙ϕ˙ ⎥ 0 0 0 Iz x˙r z r ⎢ ⎥ ⎣ cos (ϕr ) sin (ϕr ) x˙r cos (ϕr ) − y˙r sin (ϕr ) 0 0 0⎦ − sin (ϕr ) cos (ϕr ) − y˙r cos (ϕr ) − x˙r sin (ϕr ) 0 00

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  y˙r +a ϕ˙r 2Cc f 2Cc f 2δ f r − x˙r m m

 0

2aCc f Iz

00

2 Cc f ( y˙r + a ϕ˙r ) + Ccr ( y˙r − bϕ˙r ) ∂ f y˙ − ϕ˙r = ∂ x˙ m x˙r2

where

2Cc f δ f r ( y˙r + a ϕ˙r ) ∂ f x˙ = ∂ x˙ m x˙r2

2 aCc f ( y˙r + a ϕ˙r ) − bCcr ( y˙r − bϕ˙r ) ∂ f ϕ˙ = ∂ x˙ Iz x˙r2

3 Iterative Learning Model Predictive Controller 3.1 Incremental State-Space Model The incremental state-space model is obtained by model (10). Assume that the model operates on t ∈ [0, T ]. Different from model (10), the control input of the model is the control increment δu. The model is described as: A¯

ξ¯k (t)

B¯

         Aw,t Bw,t B ξ˜k (t) ξ˜k (t + 1) = + δu k (t) 0 I I − 1) u˜ k (t) u ˜ (t k  

ξ˜k (t) yk (t) = Cw,t 0    u˜ k (t − 1)





 

(11)

C¯

where k represents the batch index, δu k (t) = u˜ k (t) − u˜ k (t − 1).

3.2 Prediction Model Define the prediction horizon as N p , the control horizon as Nc . In order to simplify the computation, assume that A¯ w,t = A¯ t , B¯ w,t = B¯ t , C¯ w,t = C¯ t , w = 1, . . . , t + N p − 1. In prediction horizon, the state and output variables are expressed as:   Np N p−1 ¯ N p−Nc −1 ¯ Bt δu (t|t) + · · · + A¯ t Bt δu (t + Nc |t) ξ¯k t + N p |t = A¯ t ξ¯k (t|t) + A¯ t (12)

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  N N −1 yk t + N p |t = C¯ t A¯ t p ξ¯k (t|t) + C¯ t A¯ t p B¯ t δu (t|t) N p−Nc −1 ¯ + · · · + C¯ t A¯ t Bt δu (t + Nc |t)

(13)

Expanding the output equation into the whole prediction horizon, yield the following equation: (14) Yk (t) = Ψt ξ¯k (t|t) + Θt δu k (t) where ⎡ ⎤ ⎤ C¯ t A¯ t yk (t + 1|t) ⎢ C¯ A¯ 2 ⎥ ⎡ ⎤ ⎢ yk (t + 2|t) ⎥ ⎢ t t ⎥ δu k (t|t) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ .. ⎢ ... ⎥ ⎢ δu k (t + 1|t) ⎥ ⎢ ⎥ . ⎥ ⎢ ⎥ ⎥ , Ψt = ⎢ Yk (t) = ⎢ ⎢ ¯ ¯ Nc ⎥ , δu k (t) = ⎢ ⎥ .. ⎢ yk (t + Nc |t) ⎥ C A ⎢ ⎥ ⎣ ⎦ t t . ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ .. ⎥ .. ⎢ δu k (t + Nc |t) ⎣ ⎦ ⎣ . ⎦  .  Np ¯ ¯ yk t + N p |t C t At ⎡

⎡ ⎢ ⎢ Θt = ⎢ ⎣

C¯ t B¯ t ¯ Ct A¯ t B¯ t .. .

0 C¯ t B¯ t .. .

··· ··· .. .

0 0 .. .

N p −Nc N −1 N −2 B¯ t C¯ t A¯ t p B¯ t C¯ t A¯ t p B¯ t · · · C¯ t A¯ t

⎤ ⎥ ⎥ ⎥ ⎦

The relationship between two adjacent batches is: Yˆk (t) = Yk−1 (t) + Ψt Δξ¯k (t) + Θt Δδu k

(15)

where ‘hat’ means the predictive value, Δ is the batch-increment index, which indicates Δδu k (t) = {u˜ k (t) − u˜ k (t − 1)} − {u˜ k−1 (t) − u˜ k−1 (t − 1)} and Δξ¯k (t) = ξ¯k (t) − ξ¯k−1 (t). The differences between the real outputs and reference trajectory is: eˆk (t) = ek−1 (t) − Ψt Δξ¯k (t) − Θt Δδu k

(16)

3.3 Constrained ILMPC Controller In this paper, constraints are established for tracking trajectories safely and smoothly. In ILMPC controller [12], constraints include the maximum and minimum limits on input values u˜ kNc (t), the rate of steering angle change between two adjacent moments δu kNc (t), the rate of steering angle change between two adjacent batches Δu kNc (t) N and output values yˆk p (t + 1|t).

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Each constraint should be defined with respect to Δδu kNc as follows: Nc u˜ kNc = Im u˜ k (t − 1) + I L δu k−1 (t) + I L Δδu kNc (t) Nc δu kNc (t) = δu k−1 (t) + Δδu kNc (t) Nc Δu k (t) = Im Δu k (t − 1) + I L Δδu kNc (t) N Np Yk p (t + 1|t) = Yk−1 (t + 1) + Φt ξ¯k (t|t) + Θt Δδu kNc (t)

⎡ ⎤ ⎡ I I ⎢I⎥ ⎢I ⎢ ⎥ ⎢ Im = ⎢ . ⎥ , I L = ⎢ . ⎣ .. ⎦ ⎣ .. I I

where

(17)

⎤ 0 ··· 0 I ··· 0⎥ ⎥ .. . . .. ⎥ . . .⎦ I ··· I

To ensure the difference between the real trajectory and the reference trajectory is small enough, the objective function is designed as follows: min J =

Δδu kNc (t)

 1 Np N eˆk (t + 1|t)T Q eˆk p (t + 1|t) + Δδu kNc (t)T RΔδu kNc (t) 2

(18)

N

where Q is the weight of the difference eˆk p , R is the weight of input variable. Substituting Eq. (16) into Eq. (18), yield T    Nc Nc T Δδu Δδu (t) (t) QΘ + R 0 Θ t k t min J = 21 N p k N Np 0 S εk (t + 1) εk p (t + 1) Δδu kNc (t),εk (t+1)     T  Np Δδu kNc (t) ΘtT Q Φt Δξˆ¯ k (t|t) − ek−1 (t + 1) + N εk p (t + 1) 0 

⎡ ⎤ Nc ⎤ −u˜ min Nc + Im u˜ k (t − 1) + I L δu k−1 (t) 0 ⎢ u˜ Nc − I u˜ (t − 1) − I δu Nc (t) ⎥ m k L ⎢ max ⎥ k−1 0 ⎥ ⎢ ⎥ ⎥ Nc −δu min Nc + δu k−1 (t) ⎢ ⎥ 0 ⎥ ⎢ ⎥ ⎥ Nc  ⎢ ⎥ Nc − δu δu (t) max 0 ⎥ k−1 ⎢ ⎥ ⎥ Δδu kNc (t) Nc ⎢ ⎥ Nc + Δu −Δu (t) 0 ⎥ ≤ min k−1 ⎢ ⎥ ⎥ ε N p (t + 1) Nc ⎢ ⎥ k N 0 ⎥ − Δu Δu (t) max c k−1 ⎢ ⎥ ⎥ Np ⎢ ⎥ ˆ −I ⎥ ⎢ −ymin N p + yk−1 (t + 1) + Φt Δξ¯ (t|t) ⎥ ⎥ ⎢ ⎥ −I ⎦ ⎣ ymax N p − y N p (t + 1) − Φt Δξˆ¯ (t|t) ⎦ k−1 −I 0 (19) N where εk p (t + 1) is slack variable used to soften the constraints of output values. ⎡

−I L ⎢ IL ⎢ ⎢ −I ⎢ ⎢ I ⎢ s.t. ⎢ ⎢ −I L ⎢ IL ⎢ ⎢ −Θt ⎢ ⎣ Θt 0

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3.4 Learning Algorithm Step 1. Step 2. Step 3. Step 4. Step 5.

Let iteration number k = 0. Initialize tracking starting time t. In iteration k, update matrix Θt and Φt . Use MPC method to obtain control sequence and apply the control input to UGV. If the trajectory tracking in this iteration is completed, go to next step, else save the current motion information of vehicle and return step 3. Let k = k + 1 and go back to step 2.

4 Simulation In this section, we consider an application of trajectory tracking of UGV with a batch process. Consider the UGVs which are used for a certain kind of military or civil applications such as transportation work of a certain section of the mountain road. Since the condition of mountain road is complicated, the accurate tracking of trajectory is necessary in order to ensure safety. All physical parameters of the UGV for the simulation are given in Table 1. In the designed trajectory tracking controller, the sampling time is 0.02 s. The parameters and constraints are listed as follows:  N p = 5, Nc = 5, R = 900, S = 10,000, Q =

12,000 0 0 10



−0.3 ≤ u k (t) ≤ 0.3 −0.08 ≤ δu k (t) ≤ 0.08 −0.08 ≤ Δu k (t) ≤ 0.08 −0.08 ≤ Δδu k (t) ≤ 0.08 The tracking results are shown in Figs. 2 and 3. The black solid line represents the reference trajectory, the red, green and blue dotted lines represent the first, fifth

Table 1 Dynamic parameters of UGV Dynamic parameters m Iz a, b Cc f , Ccr Cl f , Clr s f , sr

Value 1723 kg 4175 kg m2 1.232 m, 1.468 m 66,900 N rad−1 62,700 N rad−1 0.2

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4

Fig. 2 The results of trajectory tracking of UGV using ILMPC

y1 y5 y7 yr

3 2 −1.62

y/m

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−1.64 −1.66

0

−1.68 −1

−1.7

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Fig. 3 The yaw angle of UGV in trajectory tracking

0

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and seventh batch, respectively. In Fig. 2, the result of trajectory tracking using the ILMPC method is shown. After being stable, compared with the first batch, the error of reference and real trajectory in the seventh batch decreases by 0.002 m. Figure 3 shows the relationship between the longitude position and the yaw angle. The yaw angle is close to zero finally and the error is less than 0.48%.

5 Conclusion In this paper, an iterative learning model predictive control strategy is proposed for the trajectory tracking of UGV. The proposed strategy makes good use of the prior knowledge and by using the method of receding horizon optimization, the dynamic performance of the system is improved. An linear time-varying system is applied,

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and the incremental state-space model is established for ILMPC. Simulation shows the effectiveness of ILMPC, which can decrease the error of reference states and real states and have a better performance in trajectory tracking. Acknowledgements This work is supported by National Natural Science Foundation of China under Grant (No. 61773279) and Research Foundation of Key Laboratory of System Control and Information Processing, Ministry of Education (No. Scip201608).

References 1. Yoon, Y., Shin, J., Kim, H.J., Park, Y., Sastry, S.: Model-predictive active steering and obstacle avoidance for autonomous ground vehicles. Control Eng. Pract. 17(7), 741–750 (2016) 2. Marino, R., Scalzi, S., Netto, M.: Nested PID steering control for lane keeping in autonomous vehicles. Control Eng. Pract. 19(12), 1459–1467 (2011) 3. Zhang, C., Hu, J., Qiu, J., Yang, W., Sun, H., Chen, Q.: A novel fuzzy observer-based steering control approach for path tracking in autonomous vehicles. IEEE Trans. Fuzzy Syst. 27(2), 278–290 (2019) 4. Guo, J., Luo, Y., Li, K.: An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles. IEEE Trans. Intell. Transp. Syst. 19(8), 2482–2492 (2018) 5. Shirazi, M.M., Rad, A.B.: L1 adaptive control of vehicle lateral dynamics. IEEE Trans. Intell. Veh. 3(1), 92–101 (2018) 6. Hu, C.F., Cao, L., Zhao, L.X., Wang, N.: Model predictive control-based steering control of unmanned ground vehicle with tire blowout. J. Tianjin Univ. (Sci. Technol.) 52(5), 468–474 (2019) 7. Chu, Z., Zhu, D., Yang, S.X.: Observer-based adaptive neural network trajectory tracking control for remotely operated vehicle. IEEE Trans. Neural Netw. Learn. Syst. 28(7), 1633– 1645 (2017) 8. Kayacan, E., Ramon, H., Saeys, W.: Robust trajectory tracking error model-based predictive control for unmanned ground vehicles. IEEE/ASME Trans. Mechatron. 21(2), 806–814 (2016) 9. Zhou, H., Jia, F., Jing, H., Liu Z. and Guvenç, ¨ L.: Coordinated longitudinal and lateral motion control for four wheel independent motor-drive electric vehicle. IEEE Trans. Veh. Technol. 67(5), 3782–3790 (2018) 10. Oh, S.K., Park, B.J., Lee, J.M.: Point-to-point iterative learning model predictive control. Automatica 89, 135–143 (2018) 11. Bu, X., Hou, Z.: Adaptive iterative learning control for linear systems with binary-valued observations. IEEE Trans. Neural Netw. Learn. Syst. 29(1), 232–237 (2018) 12. Oh, S.K., Lee, J.M.: Iterative learning model predictive control for constrained multivariable control of batch processes. Comput. Chem. Eng. 93, 284–292 (2016)

Attack-Time Cooperative Guidance of Multi-missile System Based on Bessel Curve Yiwen Liu, Xuejing Lan and Wenbiao Xu

Abstract In this paper, an attack-time cooperative guidance scheme is proposed to improve the penetration ability of the guided missiles, which aim at realizing the saturated attack on a single target and it has a specified angle of attack. The guidance scheme consists of three stages. In the first stage, a time coordination method based on paranoid proportional navigation method for tracking guided missile is designed. In the second stage, the missiles are adjusted to achieve the coordination of attack angle. In the third stage, Bessel curve is used to design the trajectory with large climb and dive to improve the penetration ability during the attacking. Finally, the feasibility of the guidance law is verified by simulation. Keywords Multi-missile system · Attack-time coordination · Bessel curve · Inverse dynamics

1 Introduction Abundant achievements have been achieved in the past 40 years, such as classical proportional navigation (PN) and augmented proportional navigation (APN). With the emergence of more and more sophisticated instruments, many modern control theories are used in the field of guidance, for example, optimal control theory [1–5] and adaptive sliding mode control theory [6–8]. Nowadays, the improvement and development of anti-missile system make the missile guidance technology face severe challenges. It is necessary to improve the penetration capability of missiles. Reference [9] presented a guidance law for constant velocity interception. Reference [10] studied the interception and participation of maneuvering targets. The penetration capability of the missile can be enhanced by Y. Liu · X. Lan (B) School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, People’s Republic of China e-mail: [email protected] W. Xu Guangdong Institute of Metrology, Guangzhou 510405, People’s Republic of China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_111

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planning a path with large climb and dive angles while giving the missile high maneuverability. In Ref. [11], an innovative method for determining the optimal trajectory based on third-order Bessel curve and genetic algorithm is proposed. Reference [12] studied a guidance method with specific attack angle based on third-order Bessel curve and inverse dynamics, which improves the penetration and damage capability of missiles. Multi-missile cooperative guidance is one of the key technologies. The challenge is to design a guidance law with short time and suitable range to achieve missile collaboration. Many articles have done relevant research [13–15]. Reference [16] proposed a distributed coordination algorithm considering obstacle avoidance. Reference [17] studied the cooperative guidance problem of distributed group of multiple missiles with fixed and switched directional communication topology. Reference [18] proposed a novel second-order sliding mode control (NSOSMC) scheme. In this paper, an attack-time cooperative guidance law based on Bessel curve and inverse dynamics is proposed. The aim is to achieve multi-missile time coordinated saturation attack and improve missile penetration capability. By using the Bessel curve, the missile can obtain the trajectory with large climb and dive. Thus, the penetration ability is improved, and the multi-missile cooperative attack is realized with fewer parameters. Finally, the feasibility of this method is verified by simulation, and the cooperative saturation attack of missile is realized.

2 Cooperative Guidance Law of Time and Angle When the missile is guided by the third-order Bessel curve design, if the targetrelative distance, initial velocity, and initial trajectory angles are not the same, it will lead to a large attack-time error to the target. Therefore, the initial conditions of the missiles should be coordinated before they are guided by the Bessel curve.

2.1 Time Cooperative Phase Guidance A leader-follower mode is used in the cooperative guidance scheme of the multimissiles. In the first and second stages, it is assumed that the following missiles and the leading missile have the same constant velocity, but different trajectory angles. The dynamics of missiles are defined as follows: d Ri = −v cos(ϕi ) dt

(1)

dqi = v sin(ϕi ) dt

(2)

Ri

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qi = θi + ϕi

(3)

dθi ani = dt v

(4)

d xi = v cos θi dt

(5)

dyi = v sin θi dt

(6)

where, v represents the velocity. Ri is the target distance. qi represents the lineof-sight (LOS) angle. θi represents the flight path angle. ϕi is the angle between the missile’s velocity vector and the target line of sight, and represents the prefixed angle. ani represents the guidance command. xi and yi are the horizontal displacement and vertical displacement, respectively. The subscript i denotes the identity of the missiles. i = 0 denotes the leading missile, and i = 1, 2, 3, . . . denote the following missiles. The sketch of the guidance geometry relation is shown in Fig. 1. Generally, the missile farthest from the target is chosen as the leading missile. The guidance law of the leading missile in the first stage is designed based on the biased proportional guidance [19]. an0 = N v

K v2 cos(ϕ0 )β0 dq0 − dt R0

(7)

where, N ≥ 2 and K > 0 are constant parameters. β0 is the generalized attack angle error defined as follows: dθ0 dq0 dβ0 = −N dt dt dt

Fig. 1 Guidance geometry relation

(8)

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The initial value of β0 can be determined as follows: β0 = θ0 − N q0 + (N − 1)θt

(9)

The first term of (7) is the classical proportional navigation law to ensure the hitting of target. The biased term of (7) is the feedback term of angle attack error to control the attack angle. The guidance law of the following missiles in the first stage consists of two parts. ani = ani1 + ani2

(10)

where, ani1 is the biased proportional guidance item for hitting the target as (11). ani2 is an additional control item for the time coordination. ani1 = N v

K v2 cos(ϕi )βi dqi − dt Ri

(11)

The dynamics of the prefix angle for the leading missile and the following missiles are derived with the guidance law: dϕ0 K v cos(ϕ0 )β0 v sin(ϕ0 ) + = (1 − N ) dt R0 R0

(12)

v sin(ϕi ) dϕi K v cos(ϕi )βi ani2 = (1 − N ) + − dt Ri Ri v

(13)

The purpose of designing ani2 is that ϕi should approach ϕ0 or −ϕ0 , when Ri approaches R0 . i = R0 − Ri ,  (1) ϕi follow ϕ0 guidance law: We define R ϕi = ϕ0 − ϕi . Then, it is derived that:

i dR = v[cos(ϕ0 −  ϕi ) − cos(ϕ0 )] (14) dt     d ϕi cos(ϕ0 )β0 ani2 cos(ϕi )βi sin(ϕ0 ) sin(ϕi ) + Kv + − − = (1 − N )v dt R0 Ri R0 Ri v (15) i by controlling  It is known that ani2 indirectly controls R ϕi . Equation (14) can be regarded as a non-linear slow subsystem and (15) is a non-linear fast subsystem. Let the desired dynamics of the slow subsystem be: i dR i = −k R R dt

(16)

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where, k R is the bandwidth of the expected slow subsystem defined as follows: kR =

c1 c2 +

(17)

i R v

Then, based on (14) and (16), we can obtain the desired command of  ϕi , which is denoted as  ϕic : ⎧  i  kR R ⎪ ⎪ ⎪ ; [0 ≤ ϕi ≤ π ] ⎨ ϕ0 − arccos cos(ϕ0 ) − v  ϕic =   i ⎪ kR R ⎪ ⎪ ; [−π ≤ ϕi ≤ 0] ⎩ ϕ0 + arccos cos(ϕ0 ) − v

(18)

In order to obtain the desired dynamics of the designed slow subsystem, the  ϕi should converge to the  ϕic rapidly. For this reason, the dynamics of the fast subsystem is designed as follows: d ϕic d ϕi = − kϕ ( ϕic ) ϕi −  dt dt

(19)

where, kϕ represents the bandwidth of fast subsystem. The derivation of (18) yields: ⎧ dϕ 0 ⎪ + ηi ; [0 ≤ ϕi ≤ π ] ⎨ d ϕic dt = ⎪ dt ⎩ dϕ0 − η ; [−π ≤ ϕ ≤ 0] i i dt

(20)

where,  k2 R

− dϕ0 sin(ϕ0 ) + Rv i ηi = dt

  2 1 − cos(ϕ0 ) − k RvRi

(21)

By combining (15), (18) and (19), it can be obtained that:



sin(ϕ0 −  ϕi ) sin(ϕ0 )2 ani2 = (1 − N )v2 − i R0 ξ1 R0 − R

ani2 = (1 − N )v2

sin(ϕ0 −  ϕi ) sin(ϕ0 )2 +  R0 ξ R 0 − Ri

i   k2 R − kϕ  ϕi − ϕ0 + ξ3 ; + K v2 ξ2 + R ξ1 [0 ≤ ϕi0 (0) ≤ π ], and [0 ≤ ϕ0 ]

(22)

i   k2 R − kϕ  ϕi − ϕ0 − ξ3 ; + K v2 ξ2 − R ξ [−π ≤ ϕi0 (0) ≤ 0], and [ϕ0 < 0]

(23)

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where,  ξ1 =

 i 2 kR R 1 − cos(ϕ0 ) − v

ϕi )βi cos(ϕ0 −  cos(ϕ0 )β0 −  R0 R 0 − Ri  i  kR R ξ3 = arccos cos(ϕ0 ) − v

ξ2 =

(24) (25) (26)

(2) ϕi follow −ϕ0 guidance law: In this situation,  ϕi = −ϕ0 − ϕi is defined. The derivation of ani2 is the same as above, and will not be repeated here.

2.2 Attack Angle Constrained Phase Guidance The missile achieves the same position and the same speed after time coordination. At this time, the lead missile makes a large maneuver, which results in certain angle error after reaching the first designated target. Now, by assigning the second target position in a short distance and adjusting the angle, the lead missile and the lead missile can have the same speed, angle and missile-target distance within a small time error. At this time, all missiles only use biased proportional guidance to a specified target in a short distance to achieve the same angle. an = N v

K v2 cos(ϕi )βi dqi − dt Ri

(27)

3 Inverse Dynamic Guidance Design Based on Bessel Curve In the third stage of long-range guidance, each missile has its own guidance instructions. Different missiles have different third-order Bessel curves.

3.1 Inverse Dynamic Guidance of Bessel Curve In this paper, the third-order Bessel curve shown in Fig. 2 is used to design the trajectory of the missile. The expression of the third-order Bessel curve is as follows:

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Fig. 2 Third-order bessel curve

B(λ) = (1 − λ)3 Sinit + 3λ(1 − λ)2 Smid1 + 3λ2 (1 − λ)Smid2 + λ3 S f inal

(28)

where, λ ∈ [0, 1] is the parameter of the curve. Sinit (xinit , yinit ) is the initial point of the curve, Smid1 (xmid1 , ymid1 ) and Smid2 (xmid2 , ymid2 ) are the control points of the curve trajectory that is used to control the climb and dive of the trajectory curve. S f inal (x f inal , y f inal ) is the location of the target. θinit is the initial flight path angle and θ f inal is the final attack angle constraint. In order to solve the coordinates of Smid1 and Smid2 to determine the trajectory of the curve. Now we introduce two parameters b1 and b2 with the following definitions: xmid1 − xinit x f inal − xinit xmid2 − xinit b2 = x f inal − xinit ymid1 − yinit tan θinit = xmid1 − xinit y f inal − ymid2 tan θ f inal = x f inal − xmid2

b1 =

(29)

So the coordinates of the two points can be obtained as follows: xmid1 = b1 (x f inal − xinit ) + xinit ymid1 = tan θinit (xmid1 − xinit ) + yinit xmid2 = b2 (x f inal − xinit ) + xinit ymid2 = tan θ f inal (x f inal − xmid2 ) + y f inal

(30)

Since ani is obtained from the reference trajectory of Bessel curve, coordinates x and y should be introduced into the missile motion model. It can be obtained that:

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  ani dy dθ = 2 ; θ = arctan ; dx v cos θ dx

dθ = dx



d2 y dx2

 cos2 θ

(31)

Therefore, the expression of guidance command ani can be expressed in the following form:  ani =

 2   dθ 2 d y 2 v cos3 θ v cos θ = dx dx2

(32)

According to (28), it can be obtained that: dx = −3x0 (1 − λ)2 + 3x1 (3λ2 − 4λ + 1) + 3x2 (−3λ2 + 2λ) + 3λ2 x3 dλ d2x = 6x0 (1 − λ) + 6x1 (3λ − 2) + 6x2 (−3λ + 1) + 6λx3 (33) dλ2 The expression of y is the same as that of x. Then, we can obtain: dy dy/dλ = dx d x/dλ d2 y = dx2

d2 y dλ2

2

− ddλx2 ddy/dλ x/dλ  d x 2

(34)

dλ

Thus, the desired ani can be obtained by substituting (34) into (32) with λ = 0.

4 Numerical Simulation Results One leading missile and two following missiles are considered in the simulation. The initial conditions of missiles are set as: x0 , y0 = [0, 0] m, x1 , y1 = [100, 200] m, x2 , y2 = [0, 300] m, v = 100 m/s, θ0 = 10°, θ1 = 20°, and θ2 = 30°. The target position is set to [xt, yt ] = [12000, 2200] m. The terminal angle is set to θt = −30°. In the first time coordination phase and the second attack angle control phase, we set the parameters as: N = 3, K = 3, kϕ = 5, c1 = 0.4, c2 = 0.7. The simulation results are shown in Figs. 3 and 4. Figure 3 reflects the flight trajectory of the three missiles. The maneuver in the first time-coordination stage is large and tends to be consistent in the third stage. It can be seen from Fig. 4 that the flight path angles of the three missiles are eventually consistent. The simulation results show that after the first stage, the leading and the following missiles achieve the unified goal at the same time and complete the task of time coordination. There are still some errors in flight path angle.

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Fig. 3 Trajectories of three missiles

Fig. 4 Flight path angle profiles

After the second stage, the leading missile and the following missiles achieve the same flight path angle, the same velocity and the smaller error of the missiletarget distance after short distance flight. Based on the guidance of the third stage, the leading missile and the following missiles have similar trajectories. The error of attack time is limited within 0.01 s. The missiles can hit the target quickly at a specified attack angle with high maneuverability.

5 Conclusions An attack-time cooperative guidance scheme of the multi-missile system is presented in this paper. The Bessel curve and inverse dynamics are used to design the guidance command. The effectiveness of the proposed guidance scheme has been successfully

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verified by realizing the cooperative attack of multiple missiles at specified angles in the simulation. However, further improvements of the guidance scheme are necessary. For example, the time cooperative guidance in the first stage is in ideal condition, which limits the adaptability of the method. The coordination time is relatively long, which needs further optimization. Acknowledgements This work was supported by National Natural Science Foundation of China (Grant No. 61803111), and Scientific Research Projects of Guangzhou Education Bureau (Grant No. 201831805).

References 1. He, S., Lee, C.H.: Optimal proportional-integral guidance with reduced sensitivity to target maneuvers. IEEE Trans. Aerosp. Electron. Syst. 54(5), 2568–2579 (2018) 2. Farooq, A., Limebeer, D.J.N.: Trajectory optimization for air-to-surface missiles with imaging radars. J. Guidance Control Dyn. 25(5), 876–887 (2002) 3. Yanushevsky, R., Boord, W.: Lyapunov approach to guidance laws design. Nonlinear Anal. Theory Methods Appl. 63(5–7), 743–749 (2005) 4. Song, E.J., Tahk, M.J.: Real-time neural-network midcourse guidance. Control Eng. Pract. 9(10), 1145–1154 (2001) 5. Chwa, D., Choi, J.Y.: Adaptive nonlinear guidance law considering control loop dynamics. IEEE Trans. Aero. Electr. Syst. 39(4), 1134–1143 (2003) 6. Shen, G., et al.: Adaptive sliding-mode control for mars entry trajectory tracking with finitetime convergence. Int. J. Robust Nonlinear Control 29(5), 1249–1264 (2019) 7. Zong, Q., et al.: Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty. Nonlinear Dyn. 78(1), 289–315 (2014) 8. Chen, T., Zhu, M., Zheng, Z.: Asymmetric error-constrained path-following control of a stratospheric airship with disturbances and actuator saturation. Mech. Syst. Sig. Process. 119, 501– 522 (2019) 9. Kumar, S.R., Rao, S., Ghose, D.: Nonsingular terminal sliding mode guidance with impact angle constraints. J. Guidance Control Dyn. 37(4), 1114–1130 (2014) 10. Weiss, M., Shima, T.: Linear quadratic optimal control-based missile guidance law with obstacle avoidance. IEEE Trans. Aerosp. Electron. Syst. 55(1), 205–214 (2019) 11. Esmaelzadeh, R., Naghash, A., Mortazavi, M.: Near optimal re-entry guidance law using inverse problem approach. Inverse Probl. Sci. Eng. 16(2), 187–198 (2008) 12. Qin, Z., Qi, X., Yongling, F.: Terminal guidance based on bézier curve for climb-and-dive maneuvering trajectory with impact angle constraint. IEEE Access 7, 2969–2977 (2019) 13. Shaferman, V., Shima, T.: Cooperative multiple model adaptive guidance for an aircraft defending missile. In: AIAA Guidance, Navigation, and Control Conference, vol. 33, issue 6, pp. 1801– 1813 (2010) 14. Yang, B., Liu, H.H.T., Yao, Y.: Cooperative interception guidance for multiple vehicles: a receding horizon optimization approach. In: Guidance Navigation Control Conference, pp. 827–831 (2014) 15. Xingling, S., Honglun, W.: Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO. ISA Trans. 57, 10–22 (2015) 16. Zhao, J., Zhou, R.: Obstacle avoidance for multi-missile network via distributed coordination algorithm. Chin. J. Aeronaut. 29(2), 441–447 (2016)

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17. Zhao, Q., et al.: Distributed group cooperative guidance for multiple missiles with fixed and switching directed communication topologies. Nonlinear Dyn. 90(4), 2507–2523 (2017) 18. Han, T., Hu, Q.: Robust autopilot design for STT missiles with multiple disturbances using twisting control. Aerosp. Sci. Technol. 70, 428–434 (2017) 19. Kim, T.H., Park, B.G., Tahk, M.J.: Bias-shaping method for biased proportional navigation with terminal-angle constraint. J. Guidance Control Dyn. 36(6), 1810–1816 (2013)

Flight Control Experimental Platform of Transport Aircraft Based on FlightGear/Matlab Yue Wang, Shuguang Zhang, Pengqi Yin and Shiguang Guo

Abstract A flight control experimental platform of Transport Aircraft based on FlightGear and Matlab is presented in this paper. Based on NASA aerodynamic data, the flight simulation model of transport aircraft Boeing 747 is established and validated first. Then, an example of stability Augmentation control Law is designed. Flight simulation data are transmitted through using the interface technology of FlightGear and Matlab software in order to implement the real-time 3D visual flight. Additionally, the experimental platform is synthetically validated by the straightin approach automatic flight mission. Teaching practice has shown the significant practicality of the experimental platform for its application in developing control experiment to improve the students’ understanding of the linking theory with practical. Keywords Flightgear · Matlab · Transport aircraft · Flight control platform

1 Introduction Flight dynamics and control is an important specialty curriculum for graduate students majoring in flight technology and safety. This curriculum appears to be both systematic and theoretical, and has a strong background in practice. However, as the theory is a kind of description that is so abstract, it is difficult for students to improve the understanding of linking theory with practice on the teaching practice Y. Wang (B) · S. Zhang School of Transportation Science and Engineering, Beihang University, Beijing 100191, People’s Republic of China e-mail: [email protected] Y. Wang · S. Guo Flight Technology College, Civil Aviation University of China, Tianjin 300300, People’s Republic of China P. Yin School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_112

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of this course [1]. Therefore, in order to cultivate innovative and applied professional talents, it is necessary for the curriculum to develop teaching experiments corresponding to a series of curriculum knowledge points. At present, Flight visualization simulation technology has been applied in flight technology training and flight safety research by many domestic and foreign research institutes and universities. FlightGear is one of the popular flight simulation software, which attracts many users to modify and redevelop conveniently due to its open source characteristics and the external data interface reserved for development [2–5]. For example, FlightGear is applied in research on smart icing systems in Illinois University [6] and flight intelligent robot in University of Wales in the United Kingdom [7].

2 Flight Simulation Method Based on the pre-developed teaching experiment system [8], a typical transport aircraft Boeing 747 is selected as an example first. Second, the six-degree-of-freedom non-linear simulation model of 747 aircraft and the corresponding stability augment and flight control law are developed and validated by using Matlab code and Simulink. Finally, using the interface technology of FlightGear and Matlab software, the dynamic module runs independently outside, and the flight simulation data are transmitted in real time. Then the flight simulation experimental platform using FlightGear as the visual engine is realized.

2.1 Aircraft Modeling and Validation The dynamic model of Boeing 747, which is the basis of simulation, is established based on NASA aerodynamic data [9]. And on the basis of this 747 model, a secondorder actuator model is added, parameters of which are shown in Table 1. Another document, NASA CR-2144 [10], provides the transfer functions of each channel responses of Boeing 747 aircraft in multiple states, which can be applied Table 1 Actuator and control surface

Control surface name

Positive limit (°)

Negative limit (°)

Deflection rate limit (°/s)

Elevator

23

−17

37

Aileron

25

−25

45

Rudder

25

−25

50

3

−12

0.4

Horizontal stabilizer

Flight Control Experimental Platform of Transport Aircraft … Table 2 Trim condition in model comparison

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Parameter

Nonlinear model trim data

Linear model trim data

Gross weight (kg)

255,840

255,840

Altitude (m)

0

0

Mach number (Ma)

0.198

0.198

Flight path angle (°)

0

0

Trimmed angle of attack (°)

8.6

8.5

in a typical comparison with the non-linear model used in this paper. Moreover, it is necessary to trim and linearize the non-linear aircraft model in the corresponding state. The trim condition is shown in Table 2.

2.1.1

Comparison of Longitudinal Characteristics

The transfer function of pitch angle and climb rate of elevator deflection is obtained by linearizing the original model of non-linearity, which is compared with reference [11]. The Bode diagram is shown in Figs. 1 and 2. From the Byrd diagram, it can be seen that the response characteristics of the elevator input instructions are very close to each other in the bandwidth (rad/s) concerned, except that there is a slight deviation in the short period frequency. The response characteristics of climbing rate (altitude change rate) in low frequency band are quite different, which is a common error distribution characteristic in flight dynamics modeling, because a series of “weak” items work together. Regardless of manual flying or automatic flying, the low-frequency error of altitude response can easily be “masked” by the feedback mechanism, which will not have a significant impact on the simulation results.

2.1.2

Comparison of Lateral-Directional Characteristics

By linearizing the original non-linear model, the transfer functions of roll rate and yaw rate for aileron and rudder deflection are obtained, which are compared with those in reference [11]. It can be seen that the coincidence between the lateral-directional channels is high.

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Fig. 1 Pitch attitude response to elevator deflection

Fig. 2 Altitude change rate response to elevator deflection

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2.2 Stability Augmentation Control Law Design In the simulation experiments, flight parameters such as pitch angle and roll angle of the aircraft need to be precisely controlled, so the control law of the aircraft is designed in this section. Linear control theory is used in the design of aircraft control law. It is said that, according small perturbation theory, when the flight condition of an aircraft is perturbed slightly, the nonlinear dynamic equation can be simplified to Taylor series containing only linear term. The first-order state space equation is obtained after sorting out. According to the state space equation, the control law can be designed. According to the objectives of the simulation experiment, for example, when simulating the influence of wind shear on transport aircraft and recovery strategy, the pitch axis of the aircraft should have the normal response of attitude pose holding of pitch attitude command. For this purpose, the control law is designed. Firstly, the aircraft model is trimmed and linearized. The trimmed state is determined in the approach and landing phase based on the objective of control experiments. And then, the total state space model of aircraft is obtained, and the longitudinal state space model is obtained after decoupling. The control block diagram of the longitudinal control law is shown in Fig. 3. The pitch angle rate feedback is selected in the longitudinal inner loop to increase the system damping. The pitch angle feedback is used in the outer loop to realize the command control of the pitch angle. The feedback of pitch rate signal in Fig. 3 is only used to increase the damping. In order not to affect the pilot’s steady-state control, the signal is fed back to the forward channel through a high-pass filter. Because of the good characteristics of B747 aircraft, no excessive pitch rate feedback gain is needed. The pitch attitude angle loop is controlled by proportional integral control, and the PI controller is designed as shown in Formula (1).

Theta Command

PI Controller

Boeing747

Actuator

θ

Dynamic Model q

-KK_q

Sensor

Fig. 3 Pitch control law design block diagram

s s+wq HighPass

Sensor

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Fig. 4 Pitch angle command tracking simulation

G(s) =

0.2(s + 0.15) s

(1)

Then, the attitude angle command controller designed can be applied to the nonlinear model to preliminarily verify the controller. The aircraft is trimmed to a constant level flight state at Ma = 0.2 and 200 m. The simulation results are shown in Fig. 4. In the simulation process, the system receives an elevation angle square wave command signal with an amplitude of 4° at 10 s, and the signal lasts for 10 s. After that, the system recovers to the trimmed attitude angle. At 50 s, a square wave command signal with opposite elevation angle was received, and the signal lasted for 10 s, and then remained as a trimmed attitude angle. From the simulation results, the elevation angle can track the command signal well and realize the command control function of the elevation angle. Lateral-directional control law is still designed based on small-perturbation theory. The design goal of the control law is to make the response characteristics of the roll axis similar to the attitude holding type of conventional roll rate control, and the rudder can coordinate the turning with roll control to eliminate the sideslip angle. Secondly, the yaw control response should have the command type of sideslip angle, and the roll response induced by sideslip should be eliminated by coordinated deflection of aileron, so that the lateral and directional control can be fully decoupled. In addition, it is necessary to consider the elimination of the possible impact of Dutch roll mode in the design process of the control of lateral-directional control. The structure diagram of the lateral-directional controller is shown in Fig. 5, which includes both roll axis and yaw axis control. Because the control structure contains two decoupling control laws, the two channels cannot be separated. The inner loop of the roll axis increases the damping for P feedback, while the outer loop uses the roll

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phi_sensor

K_p

p_sensor

p phi Command

PID Controller

φ

Aileron

B747 Dynamics Model

K_ari

beta Command

PID Controller

β α

Rudder

r

High Pass

r_sensor

K_alpha

K_beta

alpha_sensor

beta_sensor

Fig. 5 Lateral-directional control block diagram

angle feedback to form the roll angle command control mode. The inner loop of yaw axis is yaw rate feedback, while the outer loop uses side slip angle feedback to realize the control command mode of side slip angle. When the aircraft is maneuvering at a higher angle of attack, aileron input can only stimulate rotation along the body axis, and angle of attack and sideslip angle alternately occur. This flight characteristic is not expected by pilots. Rolling control should be designed to rotate around the velocity vector, which is realized by crosslinking the rudder and aileron. This loop and yaw damper loop together form the yaw axis control inner loop. The crosslinking control parameters can be expressed as shown in Formula (2). K AR =

N δa − L δa tan α N δr − L δr tan α

(2)

The parametric adjustment process of the lateral and directional control law is similar to that of the longitudinal control law, which is no longer described in detail. The controller can be preliminarily validated by applying the designed control law

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parameters to the non-linear model. The aircraft is trimmed at the altitude of 200 m with Ma = 0.2 as the steady level flight state. In the simulation process, the controller sends out 15° roll angle instruction at 15 s, the aircraft starts to execute coordinated turning. At 52 s, the controller sends out 0° roll angle instruction, and the aircraft finishes coordinated turning. In the coordinated turning process shown in Fig. 6, the speed and angle of attack of the aircraft fluctuate slightly. At the beginning of roll, a certain sideslip occurs, but soon the sideslip angle is eliminated. The roll angle follows the command fast, while the yaw angle increases slowly to 90°. During the period, the maximum deflection of aileron control surface is 8°, the maximum deflection of rudder is about 6°, and the amount of rudder used in the steady-state for anti-sideslip stage is −3°. During steady-state coordinated turning, the aircraft maintains yaw angle rate of 2°/s and completes 90° coordinated turning in 45 s. The simulation results verify the availability of the lateral-directional control law.

Fig. 6 Roll angle command coordinated turning simulation

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2.3 Connection with FlightGear FlightGear-based virtual display scheme is used for external operation. The simulation module transmits 747 flight status parameters to FlightGear to drive threedimensional animation display in real time through communication module in MATLAB. In external mode, because FlightGear is only a display terminal, the default settings should be changed in the advanced options in FlightGear’s Startup Wizard. The FDM option is set to external or null, indicating that the aircraft dynamics model comes from the outside. In addition, it should be noted that the FlightGear software aircraft parameters folder contains the corresponding aircraft data parameters. Moreover, Generate Run Script module is used to create a running script, setting the initial conditions such as weather, time, place, etc., so as to achieve satisfactory results at startup.

3 Verification of Experimental Platform In this section, through the simulation of the automatic flight in approach and landing phase, the longitudinal and lateral-directional control and trajectory design of the experimental platform are comprehensively validated.

3.1 Definition of Automatic Navigation Function Automated flight simulation needs to control many parameters such as aircraft altitude, track angle, attitude, lateral offset, heading, yaw angle and so on. Different control modes are selected according to different mission stages. Therefore, it is necessary to design a navigation algorithm based on the existing control law to control the aircraft trajectory. Automatic flight mission simulates Capital Airport standard instrument approach procedure [12]. Two simple procedures named ILS instrument approach are shown in the Chart. One of them is straight-in approach procedure which is from the southern side of the airport directly to the runway. In this section, the experimental platform is validated by the simulation of straight-in approach.

3.2 Straight-in Approach To facilitate the expression, a coordinate system based on airport location is established, in which the origin coordinates are defined at the starting point of the runway, the runway direction is X-axis forward, the vertical direction is Z-axis forward, and

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Table 3 Straight-in approach task decomposition Navigation point coordinates (km)

Task definition

Longitudinal command

Lateral-directional command

(−26.0, 0)

Complete course offset correction and align with runway direction

900 m altitude hold command mode, maintain 900 m (QFE)

Offset command mode, eliminate offset value to 0

(−23.0, 0)

Descend to 550 m (QFE)

Track command mode, slowly down to 550 m (QFE)

Offset command mode, eliminate offset value to 0

(-20.0, 0)

Maintain 550 m (QFE) and Level flight

Altitude command mode,maintain 550 m (QFE)

Offset command mode, eliminate offset value to 0

(−10.5, 0)

Intercept the glide slope and fly along the glide slope at −3°

Track angle command mode,down to 75 m (QFE)

Offset command mode, eliminate offset value to 0

(−1.4, 0)

Fly along the glide slope at −2°

Track angle command mode

Offset command mode, eliminate offset value to 0

the Y-axis direction is determined according to the right-hand rule. The tasks to be accomplished in different flight stages of the straight-in approach are analyzed according to the IAP chart as shown in Table 3. After the flight mission is realized in the simulation program, the automatic flight on route can be simulated. The initial condition of the simulation is that the aircraft flying at a constant speed and level fight at 900 m (QFE) 30 km from the runway threshold, and the aircraft had aligned with the runway. On this basis, the initial data of the aircraft are added with appropriate deviation, vertical deviation dH = 100 m (positive upward), horizontal deviation dy = 200 m, roll angle deviation dϕ = 10° and yaw angle deviation dψ = 20°. Under such initial conditions, the simulation results are shown in Fig. 7. The initial deviation can be corrected in about 50 s and will not affect the subsequent approach phase. In the process of correcting the initial deviation, the maximum lateral deviation is 360 m because the initial heading deviates from the runway in the same direction as the initial lateral deviation. In the course of correcting the lateral offset, the maximum roll angle reaches 22°, the aileron reaches limit position 10° in a short time, and the maximum rudder deflection reaches 11°. Lateral offset correction is fast without overshoot. The initial height deviation is corrected within 20 s. The maximum elevator deflection is 15°. Throughout the whole process, the effect of altitude tracking is good.

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Fig. 7 Straight-in approach simulation

4 Conclusions Firstly, Using FlightGear/Matlab, the flight simulation model of transport aircraft Boeing 747 is established and validated based on NASA aerodynamic data. Secondly, an example of stability Augmentation control Law is given. Then, flight simulation data are transmitted through using the interface technology of FlightGear and Matlab software in order to implement the real-time 3D visual flight. Finally, through the simulation of the automatic flight in approach phase, the experimental platform is comprehensively validated. In the future, a series of flight control experiments can be developed using this experimental platform. By modifying the parameters of the dynamic model of the aircraft, letting the students adjust the parameters of the controller by themselves, or letting the students operate the flight manually in FlightGear, the students can feel the influence of the changes of the relevant parameters on the flight and integrate theory with practice. For teachers, this way is conducive to their timely and convenient updating and improvement of teaching resources. Acknowledgements This paper is supported by Beihang University of China and Civil Aviation University of China. We also appreciate the support of this work from the National Natural

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Science Foundation of China (No. U1733117), the Thirteenth Five-Year Plan of Educational Science of Tianjin (No. HE3072) and Fundamental Research Funds for the Central Universities (No. 3122014X002).

References 1. Weigang, G., Wei, H., Xiuxia, W.: Visual simulation system of flight performance based on matlab/flightgear. J. Exp. Technol. Manag. 10, 110–112 (2010) 2. Huang, H., Youping, X., Ziwu, D.: Real-time visual flight simulation system based on flightgear simulator. J. Syst. Simul. 19, 72–74 (2007) 3. Lu, L., Yue, M., Wanming, C.: Modelling and attitude control of novel multi-ducted-fan aerial vehicle in forward flight. Int. J. Model. Ident. Control 31, 81–93 (2019) 4. Rajani, S.H., Krishna, B.M., Nair, U.: Adaptive and modified adaptive control for pressure regulation in a hypersonic wind tunnel. Int. J. Model. Ident. Control 29(1), 78–87 (2018) 5. Jianhong, W.: Combining recursive projection and dynamic programming technique in multi UAVs formation anomaly detection. Int. J. Model. Ident. Control 31, 53–61 (2019) 6. Michael, B.B, Tamer, B.: Smart icing systems for aircraft icing safety. In: 40th AIAA Aerospace Sciences Meeting and Exhibit, pp. 151–156. AIAA Press, Reno (2002) 7. Shaw, A., Barnes, D.P., Summers, P.: Landmark recognition for localisation and navigation of aerial vehicles. In: 40th 7th ESA Workshop on Advanced Space Technologies for Robotics and Automation, pp. 113–119. ESA Press, Netherlands (2002) 8. Yue, W., Yihang, C.: Design of flight simulation teaching experiments based on flightgear. J. Exp. Technol. Manag. 10, 130–134 (2016) 9. Hanke, C.R., Nordwall, D.R.: The Simulation of a Jumbo Jet Transport Aircraft Modeling Data. Technical report, Boeing Commercial Airplane Company (1970) 10. Heffley, R.K., Jewell, W.F.: Aircraft Handling Qualities Data. Technical report, National Aeronautics and Space Administration (1972) 11. Hinton, D. A.: Flight-Management Strategies for Escape From Microburst Encounters. Technical report, National Aeronautics and Space Administration (1988) 12. Zelong, Z.: Commercial Pilot Tutorial. Southwest Jiaotong University Press, Chengdu (1999)

A Dynamic Buffer Reservation Method Based on Markov Chain to Solve Deadlock Problem in Scheduling Zhonghua Han, Yuehan Liu, Haibo Shi and Xutian Tian

Abstract In order to solve the problem of the deadlock situation which usually happens in the process of Re-entrant Flexible Flow-shop with Limited Buffer Scheduling (RFFLBS), this paper focuses on the study of Dynamic Buffer Reservation Method Based on Markov Chain, DBRM-MC. The occurrence of the deadlock situation will be reduced by actively reserving buffer capacity for reentry jobs to reduce the competition for other buffer resources from non-reentrant processes. The mathematical model of RFFLBS is established and the simulation test is carried out. The test results show that the dynamic buffer reservation method based on Markov Chain can effectively decreases the deadlock situation. Keywords Flexible flow shop · Reentrant process · Limited buffer · Deadlock situation · Markov Chain

1 Introduction The limited buffer flexible flow shop [1] with reentrant process scheduling exists in semiconductor production, bus manufacturing, steel smelting and other industries [2]. Due to the constraints of the actual production workshop space and storage equipment, the flexible flow shop can only set a buffer with limited capacity [3]. If there is a production task with reentrant process [4] at the same time, the flexible flow shop Z. Han · Y. Liu (B) · X. Tian Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, China e-mail: [email protected] Z. Han · H. Shi Department of Digital Factory, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China Key Laboratory of Network Control System, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China Z. Han Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_113

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may be deadlocked [5]. If we can find a way to overcome the deadlock situation and ensure the smooth progress of the scheduling process [6], it has important theoretical and practical value [7]. The deadlock situation is a production stagnation caused by severe production blockage during the production process. It severely restricts the production process and increases the difficulty of production control. Research on the causes and solutions of the deadlock situation has received more and more attention from scholars in recent years. Xing et al. [8] and others put forward the deadlock-free improved particle swarm optimization by embedding the avoided deadlock strategy to the particle algorithm, dislodge the job sequence which might cause the deadlock situation for no deadlock situation. Xing et al. [9] and others put forward the optimal deadlock avoidance policy and embeds this algorithm into the genetic algorithm, checking and amending the DAP feasibility of chromosome in the genetic algorithm for suitable scheduling. They also make a Deadlock-free genetic scheduling algorithm. Although the above method can solve the deadlock problem, these methods will not be able to obtain a feasible solution under certain data scale conditions. And these methods will bring high computational time cost due to the iterative process of the population evolution algorithm, which is not easy to apply in practical engineering projects. Aiming at the deadlock problem in the limited buffer flexible flow shop with reentrant process scheduling, a dynamic capacity reservation method based on Markov Chain [10] is proposed. By predicting the use of buffer resources at a future time, the buffer resources are reserved for the jobs that perform the reentrant operation, thereby reducing the probability of occurrence of deadlock in the RFFLBS process.

2 Finite Buffer Flexible Flow Shop Model with Reentrant Process The Limited Buffer Re-entrant Flexible Flow-shop Scheduling Problem can be described that the processing sequence of n job is produced by the m operation that can be fixed in the non-reentrant and re-entrant section. The non-reentrant operation section is composed of the nrm non-reentrant manufacturing operation. Every operation is made of a group of same models but different number parallel machine {M1 , . . . , Mnr m }. The re-entrant operation section is composed of the rm re-entrant operation. Every operation is made up of a group of same models but different number parallel machine {Mnr m+1 , . . . , Mnr m+r m }. Every parallel machine represents a station that can product one job every time. Affected by the production resource, the buffer area can accommodate the limited job. The job manufactures according to the designated operation sequence of the process flow. Every job has different re-entrant times r tsi based on the process flow. Every job Ji totally be processed nr m + r m × r tsi time. The job in the parallel station must choose one station to manufacture. The finished job continues to the corresponding buffer of the operation. If the next station in the operation is available, the job can be chosen to process

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Oper1

Opernrm Bunrm

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WSnrm,1

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Opernrm+rm

Opernrm+1 Bunrm+1

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WSnrm,2

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WSnrm+rm,2

WS1,M1

WSnrm,Mnrm

WSnrm+1,Mnrm+1

WSnrm+rm,Mnrm+rm

Non-reentrant operation section

Reentrant operation section

Fig. 1 Limited buffer flexible flow shop with reentrant process

depending on the local assignment method. The job process flow must include one operation featured by the re-entrant at least. The job to be used the re-entrant operation should insert the designated waiting process queue again after all re-entrant process flow. The scheduling results should confirm the station allocation, processing sequence, the start time and completion time of every job in the process flow (Fig. 1).

2.1 Model Parameter n Ji Jnr m JU JD rm nrm m O per j Mj W S j,k Bu j bs tj Bc j b j, p F Li

The largest job number. The ith job i ∈ {1, . . . , n}. The first finished job from the non-reentrant operation section and being on the re-entrant operation section. The first finished job in the O perr u operation at the t time. The first finished job in the O perr d operation at the t time. The re-entrant operation number in the production line. The non-reentrant operation number in the production line. The whole operation number in the shop m = nr m + r m. The jth operation j ∈ {1, . . . , m}. The largest parallel machine station number of the O per j operation. The k station in the O per j operation j ∈ {1, . . . , m}. The buffer in the O per j operation j ∈ {2, . . . , m}. The job number in the Bu j buffer at the t time j ∈ {2, . . . , m}. The largest buffer capacity in the buffer Bu j j ∈ {2, . . . , m}.  The buffer station in the buffer Bu j j ∈ {2, . . . , m} p ∈ 1, 2, . . . , Bc j . The process flow of the Ji job, it is the job collection according to the process flow during the production i ∈ {1, . . . , n}.

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r tsi f mi li Si,l j,k Ci,l j,k W Ti,l j,k

The re-entrant operation time of the Ji job i ∈ {1, . . . , n}. The total operation number in the process flow F L i . The processing sequence number F L i of the Ji job in the process flow. The Ji ’s starting time in the W S j,k , the lth O per j operation in F L i . The Ji ’s completion time in W S j,k station, the lth O per j operation in F L i . The job Ji ’s processing time in the W S j,k station, the lth O per j operation in F L i ’s process flow.

2.2 Hypothetical Variable ⎧ At time t, the job Ji is not on the parking space b j, p ⎪ ⎪ ⎨0 of the buffer Bu j corresponding to the process O per j O Ai, j, p (t) = At time t, the job Ji is on the parking space b j, p ⎪ ⎪ ⎩1 of the buffer Bu j corresponding to the process O per j (1) The constraint of the re-entrant flexible flow shop.

Ci,l j,k = Si,l j,k + W Ti,l j,k , i ∈ {1, . . . , n}, j ∈ {1, . . . , m}, l ∈ {1, . . . , f m}, l ∈ {1, . . . , f m}

(1)

Ci,l j,k ≥ Si,l j,k , i ∈ {1, . . . , n}, j ∈ {1, . . . , m}, l ∈ {1, . . . , f m}

(2)

f m i = nr m + r m × r tsi

(3)

Under the condition of the re-entrant operation, Eq. (1) proves the relationship among the starting time, processing time and the completion time in its process flow. Equation (2) demonstrates the relationship between the starting time and the completion time in the continuous operation of the same job. As for the implement of the re-entrant operation of the process flow, Eq. (3) proves that the total number of the Ji job in the F L i process flow is equal to the total number of the Ji job’s non-reentrant and re-entrant operation times. (2) The constraint of flexible flow shop with limited buffer.

T ai,l j−1,k = T ei,l j, p ≥ Ci,l j−1,k , i ∈ {1, . . . , n}, j ∈ {2, 3, . . . , m},     p ∈ 1, 2, . . . , Bc j , k ∈ 1, 2, . . . , M j

(4)

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T oli, j, p = Si,l j,k , i ∈ {1, . . . , n}, j ∈ {2, 3, . . . , m},     p ∈ 1, 2, . . . , Bc j , k ∈ 1, 2, . . . , M j

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(5)

Equation (8) demonstrates that the job Ji ’s releasing time from the former operation is equal to the job’s completion time in the former operation. If there is blocking situation in the limited buffer, the job finishing the former operation will be left in the processing station. Equation (5) proves that the job Ji from the buffer processing queue into the processing operation O per j will be produced instantly.

3 Dynamic Buffer Reservation Method Based on Markov Chain In order to solve the deadlock situation caused by the limited buffer capacity with the re-entrant flexible flow shop, the Dynamic Buffer Reservation Method Based on Markov Chain, (DBRM-MC) is in this paper. The concrete steps are showed as the following. Step 1: Analyze the production history data of the flexible flow shop, and establish the transfer matrix Py (y = 1, . . . , Bcr u ) of each station of the reentrant process.  Py =

Py1 , Py2 Py3 , Py4

(6)

Py1 and Py3 indicates that at the beginning of the unit time t  , no matter whether the job processed at this station has not occurred or changed, after the unit time t  , the job processed at the station does not change.Py2 and Py4 indicates that at the beginning of the unit time t  , no matter whether the job processed at this station has not occurred or changed, after the unit time t  , the job processed at the station has changed. Buffer resources are also released, which can be regarded as the probability of buffer resource release per unit time t  in different situations. Step 2: When the flexible flow shop production process proceeds to time t, if the following conditions are met, step 3 is performed and the buffer resource release probability is calculated. At time t, the finished job Jnr m from the non-returnable process segment is to enter the buffer Bu r u of the process O perr u : At time t, The buffer number Bu r u of the process O perr u stores the number of job Jnr m is smaller than the upper limit of the buffer Bu r u capacity Bcr u , bsrt u = Bcr u − 1, the remaining capacity of the buffer in operation O perr u can only store one job. At time t, all stations of the reentrant production process O perr u for job reentry are occupied. At time t, There is a need to folded back the job that can be reentrant in the re-entry process O perr d . Meet the above conditions, If the completion time C ljU ,r u,k of the first completed job JU at the station W of the re-entry process O perr u is less than or equal to the completion

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time t2 of the job J D which can be re-entered into the production process O perr d , the limited buffer capacity reservation is performed. Subsequent operation of the method, otherwise, buffer B directly reserves the buffer capacity for the folded back job. Step 3: Calculate the probability that the job will be changed when the job is folded back to perform the processing of the job in the reentrant process, and the probability of the buffer Bu r u resource release at the future t2 time is obtained. S0 = (a1 , a2 ), (a1 + a2 = 1)

(7)

Equation (7), a1 indicates the production process data from the start of production to the time t, and the number of unit times t  in which the job is not changed on the station W Sr u,ku during the time period from 0 to t is statistically obtained. The ratio of the total number of unit time t  in the time from 0 to t, in other words, it indicates the probability that the station in the unit time t is occupied by the same job. a2 indicates the probability of being occupied by different jobs. S0 indicates the probability vector of the jobs change at this station in unit time t  at time t. Calculate the Sv probability vector of the job change processed at the station t at the future t2 time according to Eq. (8), According to the obtained result, the probability P1 that the station W Sr u,ku where the job JU which is the first to be completed in the process O perr u is always occupied is obtained, and the probability P2 that is not always occupied. (P1 , P2 ) = Sv = S0 × Pyv = (a1 , a2 ) × Pyv

(8)

In the Eq. (8), v indicates the total number of unit times t  in the time from t to t2 . Step 4: Determine whether to reserve buffer capacity based on the calculated transfer vector. By step 3, the buffer resource release probability is determined to determine whether the buffer corresponding to the reentrant operation in which the job will be folded back reserves the remaining capacity for the job. When P2 ≤ P1 , the probability of W Sr u,ku processing different jobs at time t2 is lower, and the buffer resources are difficult to release. If buffer Bu r u allows job Jnr m to enter, preempting buffer Bu r u ‘s unique resource, causing reentrant job J D to compete with job Jnr m from non-reentrant operation segment for buffer resource failure and stay at its current station, all the jobs processed by other stations in the re-entry process O perr d of J D need to be folded back to perform the reentrant process, and deadlock can happen. Therefore, in order to avoid the deadlock, remaining capacity of the buffer Bu r u is reserved for the job J D at time t. Step 5: According to the judgment result of step 4, it is determined whether the capacity operation is reserved for the reentrant job. If it is determined in step 4 that the process O perr u is reserved for the reentrant job, the job Jnr m from the non-reentrant process does not enter the reentrant process. Job J D does not occupy the remaining capacity of the limited buffer and continues

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Jnrm

bru,2 (J)

Non-reentrant operaƟon

t2

bru,Bcru (JD)

Operru WSru,1 (J )

WSru,kru (Ju)

WSru,Mru (J)

Burd brd,1 (J) brd,2 (J)

brd,Bcrd (J)

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WSrd,kru ( )

t2

WSrd,Mrd (J)

Fig. 2 The job that executes reentrant process into the reserved buffer

to stay at the current station. When the production process proceeds to time t2 , the job J D from the process O perr d can enter the reentrant process O perr u (Fig. 2).

4 Simulation Verification and Result Analysis The welding shop of a bus manufacturing can be simplified into one production process, the process in the painting workshop is simplified to 2 processes, and the simulation data contains 3 processes {O per1 , O per2 , O per3 }, where {O per2 , O per3 } is a reentrant process. Each of the three processes has a corresponding buffer {Bu 1 , Bu 2 , Bu 3 }, where {Bu 1 } is an infinite buffer and {Bu 2 , Bu 3 } is a finite buffer, the number of buffer parking spaces corresponding to the buffer is Bc2 = 2, Bc3 = 3. Total number of jobs n = 15, local assignment method using FCFS rules, number of jobs reentry {r ts1 , r ts2 , . . . , r ts15 } = {5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 1}, the green color in the figure indicates the bus staying time in the buffer, and the red color indicates the blocking time. From Fig. 3, when t = 128, both the jobs J2 and J7 have completed the processing of the process O per2 , ready to enter the buffer Bu 2 . There is only one free buffer parking space in the buffer Bu 2 . In the reentrant process O per3 , there are jobs J3 , J6 and J12 that need to enter the reentrant process again. The estimated completion time of the first completed job in the reentrant process O per2 is C5,2,3 = 130 less than the estimated completion time of the first completed job O per3 in the reentrant process C3,3,3 = 140. At t = 128, the finished job in the non-reentrant process will enter the buffer of the reentrant process, and the job in the reentrant process will enter the same buffer, and only one buffer parking space remains in this buffer. At the same time, the processing stations are occupied. Satisfying the conditions for starting the Markov Chain prediction operation and performing the subsequent steps in step 2 of the DBRM-MC method. If the prediction operation in the DBRM-MC method is not started at time t = 128, at this time, the job J7 has a residence time of 28 at the station

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Fig. 3 Gantt chart of deadlock without DBRM-MC

W S1,1 , and the job J2 has a residence time of 23 at the station W S1,3 . Assigning job J7 into parking space b2,3 according to a local assignment method based on FCFS rules, job J3 will remain in its finished station W S3,3 , as shown in Fig. 3, at time t = 140, all buffer parking spaces and processing stations can be re-entered, and jobs J2 and J6 will remain in the station over time. At t = 153, all the jobs are blocked at the station, and the entire production process is stagnant and deadlock occurs. As can be seen from the above analysis, at t = 128, the conditions for starting the Markov Chain prediction operation in step 2 of the DBRM-MC method are satisfied. Transfer vector is obtained by Markov Chain prediction operation, S = [0.67382353, 0.32617647]. Probability of change of job processed by station W S2,2 (probability of buffer O1 resource release) P2 = 0.67382353 is larger than the job being processed (the probability that the buffer is always occupied) P1 = 0.32617647. According to the DBRM-MC method step 3 discriminates the buffer reservation condition, assign job J7 to continue waiting in the current processing station W S1,1 , reserve the parking space b2,3 of buffer O per2 for job J3 . When the machine reaches t = 140, the job J3 enters the reserved buffer parking space b2,3 . As shown in Fig. 4, the production process continues and all production tasks are successfully completed. Therefore,

Fig. 4 Gantt chart of output result after adding DBRM-MC

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it can be seen that the DBRM-MC method can interfere with the local assignment process of the job, which can reduce the occurrence of deadlock.

5 Conclusion In this paper, the deadlock problem in the re-entrant flexible flow-shop with limited buffer scheduling in a bus manufacturing enterprise is taken as the research object, and a dynamic buffer reservation method based on Markov Chain is proposed. The reservation method reserves buffer resources in advance for reentrant jobs, reduces the probability of deadlock situations, ensures the smooth progress of the scheduling process, and obtains better scheduling results. The research results of this problem can provide effective guidance and help for the production operation process of related enterprises, and improve the utilization rate of existing resources of enterprises. Acknowledgements This work was supported by Liaoning Provincial Science Foundation, China (No. 2018106008), Project of Liaoning Province Education Department (No. LJZ2017015) and Shenyang Municipal Science and Technology Project, China (No. Z18-5-015).

References 1. Tran, T.H., Ng, K.M.: A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems. Eng. Optim. 4(4), 83–502 (2013) 2. Chu, F., Liu, M., Liu, X.: Reentrant flow shop scheduling considering multiresource qualification matching. Sci. Program. 10(1), 95–96 (2018) 3. Han, Z., Zhu, Y., Ma, X., Chen, Z.: Multiple rules with game theoretic analysis for flexible flow shop scheduling problem with component altering times. Int. J. Model. Ident. Control 26(1), 1–18 (2016) 4. Hekmatfar, M., Fatemi Ghomi, S.M.T., Karimi, B.: Two stage reentrant hybrid flow shop with setup times and the criterion of minimizing makespan. Appl. Soft Comput. J. 12(11), 4530– 4539 (2011) 5. Fan, G., Lu, Y., Xu, Z., Yang, J.: Resource allocation model and deadlock-free optimization scheduling for underground locomotive transportation. Syst. Eng. Theory Pract. 8(33), 2087– 2096 (2013) 6. Zhang, C., Shi, Z., Huang, Z.: Flow shop scheduling with a batch processor and limited buffer. Int. J. Prod. Res. 6(11), 3217–3233 (2017) 7. Pan, Q., Wang, L., Gao, L.: A chaotic harmony search algorithm for the flow shop scheduling problem with limited buffers. Appl. Soft Comput. J. 12(11), 5270–5280 (2011) 8. Xing, K., Kang, M., Gao, Z.: Deadlock-free modified particle swarm optimization scheduling algorithm for flexible manufacturing systems. Control Decis. 29(08), 1345–1353 (2014) 9. Xing, K., Han, L., Zhou, M.: Deadlock-free genetic scheduling algorithm for automated manufacturing systems based on deadlock control policy. IEEE Trans. Syst. Man Cybern. Part B Cybern. 3(42), 603–615 (2012) 10. Li, J., Munehisa, T.: Genetic algorithm using the inhomogeneous Markov Chain for job shop scheduling problem. ICIC Express Lett. 1(9), 501–509 (2015)

Robust Adaptive Position/Force Control for Flexible-Link with Flexible-Joint Manipulator Baigeng Wang, Shurong Li and Zhe Liu

Abstract In this paper, a robust adaptive position/force control strategy based on a terminal sliding-mode was designed for the constrained flexible-link and flexiblejoint manipulator. At first, the dimensional reduced dynamic model of flexible link with flexible joint is obtained by coordinate transformation. Then, in order to guarantee the stability of the system, the controller design process is divided into three steps. Furthermore, by using the theory of finite-time, the controller can guarantee that the position error and force error asymptotic converge to zero in finite time. Finally, the simulation results illustrate the validity and the feasibility of the proposed method in this paper. Keywords Flexible link · Flexible joint · Adaptive control · Sliding mode

1 Introduction In recent years, industrial robots gradually replace human beings as the main body of labor force. Scientists are also beginning to study more and more kinds of robotic arms [1–5]. Flexible manipulator has the characteristics of light weight, flexibility and low energy consumption, which has been widely used in various field. Considerable achievements have been made due to the in-depth study of the control algorithm of flexible manipulator. In order to alleviate the effects of nonlinearities and uncertainties, a neural network control strategy based on sliding mode was proposed [3]. In [4], Fabian Schnelle proposed an adaptive nonlinear model predictive controller to solve the problem of uncertain parameters. In [5], considering the contact force between the robot end-effector and the constrained surface, Matsuno, F. designed a hybrid position/force control scheme based on two-link manipulator. In [6], Shuzhi S. Ge proposed an adaptive neural network controller for the weak flexible manipulator, but the controller was unable to guarantee the stability for the B. Wang (B) · S. Li · Z. Liu College of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_114

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strong flexible system. In [7], an adaptive controller for a strong flexible joint manipulator based on backstepping is proposed, which can guarantee the stability of the system and the asymptotic convergence of the position error. In this paper, a robust adaptive position/force control strategy based on the terminal sliding-mode was designed for flexible-link with flexible-joint. Firstly, the model of the flexible-link with flexible-joint was built, and for this model, dimensionality reduction is processed by transformation matrix. Secondly, the sliding mode function is established, which can guarantee both position error and force error to converge to zero asymptotically. Thirdly, by using the theory of finite-time, the designed controller can guarantee both position error and force error to converge to zero in finite time and guarantee the stability of flexible link in finite time. Finally, the simulation results show the feasibility of the given method.

2 Dynamic Model The dynamic model in the joint space of flexible-link with flexible-joint manipulator can be described as [9]: 

M11 M12 M21 M22

           θ¨ K s θe f C11 C12 θ˙ G1 = + + + C21 C22 q˙ G2 0 q¨ 0

(1)

Jm θ¨m + K s θe = τm

(2)

θe = θm − θ

(3)

where θ ∈ R n and θm ∈ R n are the vector of joint positions and the motor shafts respectively; q ∈ R N are the generalized coordinates of flexible-link; f ∈ R n donates the constraint force; τm ∈ R n is the vector of the motor torques; Jm = diag[ jmi ] ∈ R n×n donates the symmetric positive-definite inertia matrix of the actuator; K s = diag[ksi ] ∈ R n×n is the joint stiffness matrix (Fig. 1). Fig. 1 The model of the flexible-link constrained manipulator

Y φ (θ ) = 0

θ2

θ1

X

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Assume that the first link is a rigid link and the end link is a flexible link and the constraints imposed are described by a holonomic smooth manifold as: (θ ) = 0 ∈ R m

(4)

The constraint force is described as: f = J Tλ

(5)

∂ ∈ R m×n ∂θ

(6)

J=

where λ ∈ R m is the associated Lagrange multiplier; φ(θ ) is the constraint on the manipulator; m is the dimension of the constraint surface. Due to the presence of m dimension constraint, the manipulator is left only n − m degrees of freedom. The positions of the manipulator can be described by: T  θ = θ1T θ2T

(7)

where θ1 ∈ R n−m , θ2 ∈ R m . Assume that w(xn , t) is the lateral deformation of the flexible-link at time t in the point of (0 ≤ xn ≤ L n ), where can be expressed by: w(xn , t) =

n  i=1

qi (t) sin

i xn π Ln

(8)

where qi (t), (i = 1, 2, . . . , n) is the generalized coordinates of flexible-link. The dynamic model (1) of the manipulator can be expressed as: M11 θ¨ + M12 q¨ + C11 θ˙ + C12 q˙ + G 1 = K s θe + J T λ

(9)

M21 θ¨ + M22 q¨ + C21 θ˙ + G 2 = 0

(10)

Then, we can obtained from (10):   −1 M21 θ¨ + C21 θ˙ + G 2 q¨ = −M22

(11)

Substituting (11) into (9), then we can obtained as: 

 −1 T ¨ M12 θ + C11 θ˙ + C12 q˙ + G 1 M11 − M12 M22   −1 C12 θ˙ + G 2 = K s θe + J T λ − M12 M22

Define the matrix:

(12)

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  −1 C12 θ˙ + G 2 M = M11 − M12 M22−1 M12T , C = C11 θ˙ + C12 q˙ + G 1 − M12 M22 (13) Then, (10) can be rewritten as: M θ¨ + C = K s θe + J T λ

(14)

Substituting (15) into (11), then we can obtained as:   M22 q¨ + h = −N τ + J T λ

(15)

    −1 T −1 where N (θ, q) = M21 M11 − M12 M22 M12 , h θ, q, θ˙ , q˙ = C21 θ˙ + G 2 − N C. Define the matric as follow:     In−m 0 (16) E 1 = In−m 0 ∈ R (n−m)×n , A = ∂ /θ1 Im Then, ˙ 1T θ˙1 θ˙ = AE 1T θ˙1 , θ¨ = AE 1T θ¨1 + AE

(17)

Substituting (17) into (14), the dynamic model can be express as:   ˙ 1T θ˙1 + C = K s θe + J T λ M AE 1T θ¨1 + AE

(18)

Multiply (18) by AT : D E 1T θ¨1 + B = AT K s θe + AT J T λ

(19)

˙ 1T θ˙1 + AT C = B. where AT M A = D, A T M AE The dynamic model of the manipulator has the following properties: Property 1 If θ, θ˙ , q, q˙ are uniformly bounded and continuous, then M(θ, q), ˙ q) are uniformly bounded and continuous. C(θ, q), ˙ G(θ, q), A(θ, q), A(θ, Property 2 Define an intermediate variable x ∈ R n , the dynamic equation of the manipulator is linearized as follows:   ˙ 1T x + C = Y1 θ1 , θ˙1 , x, x˙ P1 M AE 1T x˙ + M AE   where Y1 θ1 , θ˙1 , x, x˙ ∈ R n×l is systematic regression matrix; p1 ∈ R l is the vector of the dynamic parameters.   Property 3 If the regression matrix Y1 θ1 , θ˙1 , x, x˙ and the vector of the dynamical parameters P1 can be described as:

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 T  T    T T T , diag Y12 , . . . , diag Y1n ∈ R n×l , P1 = [ p11 Y1 = diag Y11 , p12 , · · · , p1lT ] ∈ R l Then, K s Y1 P1 = Y1 Ps where T T , ks2 p12 , . . . , ksl p1lT ]T = 1 P1 ∈ R l , K s P1 = [ks1 p11

For the controller design, the following assumptions and lemmas are made: Assumption 1 K s and Jm are unknown but bounded, and their estimates  K˜ s  ≤ ρ1 and  J˜m  ≤ ρ2 , where ρ1 and ρ2 are known positive constants. Lemma 1 If V (t) which is a positive function satisfies the following differential inequalities: V (t) ≤ −αV κ (t), ∀t ≥ t0 , ∀(t0 ) ≥ 0 where α > 0, 0 < κ < 1. For any time t0 , if V (t) satisfies: V 1−κ (t) ≤ V 1−κ (t0 ) − α(1 − κ)(t − t0 ), t0 ≤ t ≤ t1 Therefore, V (t) = 0, ∀t ≥ t1 , t1 = t1 +

V 1−κ (t0 ) α(1 − κ)

Lemma 2 If x: [0, ∞) → R is square-integrable

lim

t

t→∞ 0

 x 2 (τ )dτ < ∞ , and

x(t), ˙ t ∈ [0 , ∞) exists and is bounded, then lim x(t) = 0. t→∞

3 Controller Design Define that desired joint trajectory, desired joint velocity and desired joint acceleration are denoted as θd , θ˙d , θ¨d . Step 1. Determination of θed : define the following variables which are related to the link position and the constraint force: em = θ1 − θ1d

(20)

e f = J T (λd − λ)

(21)

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z = θed − θe

(22)

where em ∈ R n−m , e f ∈ R n , z ∈ R n . The sliding mode control s is defined as: s1 = e˙m − 1 ema/b

(23)

  s = E 1T s1 + e f

(24)

θ1r = θ˙1d + 2 ea/b + e f

(25)

Define the auxiliary variable:

Therefore, there are the relationship between s and θ1r as:   s = E 1T θ1r − θ˙ 1

(26)

Considering Property 2 and (19), s˙ can be expressed as:   s˙ = E 1T θ˙1r − E 1T θ¨1 = D −1 AT Y P1 − AT K s θe − AT J T λ

(27)

Define the another auxiliary variable which will used in the next proof:   s = q, ˙ E 1+ = E 1 E 1T E 1 , ξ1T = s T D −1 , σ T = s T D −1 AT , ξ1 = E 1T s + μ

(28)

 −1 −1  −1 T The elements of diagonal matrices K s−1 = ks1 , ks2 , . . . , ksn , Kˆ s−1 =

T −1 ˆ −1 −1 kˆs1 , ks2 , . . . , kˆsn and K˜ s−1 = K s−1 − Kˆ s−1 . And define:

T −1 −1 −1 ϕ1 = K s K˜ s−1 = ks1 k˜s1 , ks2 k˜s2 , . . . , ksn k˜sn

(29)

Considering the generalized Lyapunov function: V1 =

T   1 1 T 1 1 s s + p − pˆ s 1 p − pˆ s + μT μ + ϕ1T 2 ϕ1 2 2 2 2

(30)

where pˆ s is the estimate of ps , 1 and 2 are positive definite diagonal matrices. The differentiation of V1 is: T  V˙1 = s T s˙ − p − pˆ s 1 p˙ˆ s + μT μ˙ + ϕ1T 2 ϕ˙1

(31)

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Substituting (27) into (31):  T   V˙1 = s T D −1 AT Y1 P1 − K s θe − J T λ − p1 − pˆ s 1 p˙ˆ s + μT μ˙ + ϕ1T 2 ϕ˙1 + s T D −1 AT K s z

(32)

Letting:  −1 θed = AT Ds r1 + Y1 Pˆ1 − Kˆ s−1 J T λd

(33)

Substituting θed into the (32), we can obtain:  V˙1 = s T D −1 AT Y1 P1 − K s Y1 Pˆ1 − s T K s s r1 + s T D −1 AT K s Kˆ s−1 J T λd T − s T D −1 AT J T λ − P1 − Pˆs 1 P˙ˆs + μT μ˙ + ϕ1T 2 ϕ˙ 1 + s T D −1 AT K s z (34) Then, we can obtain from (28): ξ1 AT J T λ = s T E 1 AT J T λ + μT AT J T λ

(35)

Using Property 3, we have: ξ1 AT J T λ = μT AT J T λ

(36)

μ˙ + K μ μ = −AT J T eλ

(37)

Letting:

where K μ ∈ R n×n is a positive definite constant matrix. Putting (36) and (37) into V˙1 :  T T  Y1 AD −T s − 1 p˙ˆ s − s T K s s r1 − σ T K s K˜ s−1 J T λd − μT K μ μ V˙1 = p1 − pˆ s + ϕ1T 2 ϕ˙1 + s T D −1 AT K s z

(38)

Letting: ϕ2 =



     T J T λd 1 σ1 , J T λd 2 σ2 , . . . , J T λd n σn

(39)

Substituting (39) into (38):  T T  Y1 AD −T s − 1 p˙ˆ s − s T K s s r1 − ϕ1T (ϕ2 − 2 ϕ˙1 ) V˙1 = p1 − pˆ s − μT K μ μ + s T D −1 AT K s z

(40)

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Letting: P˙ˆs = 1−1 Y1T AD −T s, ϕ˙1 = 2−1 ϕ2

(41)

From the definition of Pˆs and ϕ1 : P˙ˆ1 = 1 1−1 Y1T AD −T s,

K˙ˆ s−1 = 2−1 ϕ2

(42)

Substituting (41) into (40): V˙1 = −s T K s s r1 − μT K μ μ + s T D −1 AT K s z

(43)

Step 2. Determination of motor torque τm : considering the Lyapunov function 1 V2 = V1 + z T K s z 2

(44)

The differentiation of V2 is:  V˙2 = V˙1 + z˙ T K s z = −s T K s s r1 − μT K μ μ + s T D −1 AT + z˙ T (K s θed − τm + Jm q¨m )

(45) Letting:   τm = Kˆ s θed + Jˆm q¨m + ρ3 sgn s T D −1 AT + z˙ T

(46)

where ρ3 ≥ ρ1 θed  + ρ2 q¨m , ρ1 and ρ2 are the bounds of K˜ s and J˜m . Putting (46) into V˙2 and considering the definition of ρ3 :   V˙2 = −s T K s s r1 − μT K μ μ + s T D −1 AT + z˙ T η ≤ −s T K s s r1 − μT K μ μ

(47)

  where η = K˜ s θed + J˜m q¨m − ρ3 sgn s T D −1 AT + z˙ T . Therefore, we can obtain V˙2 ≤ −s T K s s r1 − μT K μ μ

(48)

Step 3. The stability of the q: considering Property 2 and (10), and then M21 θ¨ + M22 q¨ + C21 θ˙ + G 2 = Y2 P2

(49)

Defining a Lyapunov function: 1 1 V3 = V2 + s T s + P˜2T 3 P˜2 2 2

(50)

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where 3 ∈ R n×n is a positive definite constant matrix and Pˆ2 is the estimate of P2 , P˜2 = P2 − Pˆ2 . Substituting (11) into (50) and considering the definition of s:   −1 V˙3 = V˙2 + s T s˙ + P˜2T 3 P˙˜2 = V˙2 + s T −M22 Y2 P2 + P˜2T 3 P˙˜2

(51)

  P˜2 −1 Y2 P2 + 3−1 P˜2r2 P˙ˆ2 = − P˙˜2 = 3−1  2 s T −M22 ˜  P2 

(52)

Letting

Putting (52) into V˙3 : V˙3 = V˙2 + P˜2T 3 P˙˜2 ≤ −s T K s s r1 − μT K μ μ − P˜2T P˜2r2 ≤ −s T K s s r1 − P˜2T P˜2r2 (53) Next, discussing the asymptotic convergence in finite-time: −s T K s s r1 = −

n 

 ki |si |1+r1 ≤ −kmin 2u 1

i=1

1 2 s 2 i=1 i n

u 1 = −aV1u 1

(54)

where 0 < u 1 = (1 + r1 )/2 < 1, a = kmin 2u 1 > 0, kmin = min{ki } > 0. − P˜ T P˜ r2 = −α2

 n 1 i=1

2

  −1   ˜ λmax   Pi  ≤ −α2 V2u 2

(55)

 u    where 0 < u 2 = (1 + r2 )/2 < 1, α2 = 2/λmax  −1 2 , λmax  −1 is the maximum characteristic value of  −1 . Substituting (54) and (55) into (53): V˙ ≤ −α1 V1u 1 − α2 V2u 2 ≤ −αV u

(56)

where α = min{α1 , α1 }. Considering Lemma 1, V˙ can be guaranteed the asymptotic convergence in finitetime. It is obvious that s is bounded, and s˙ is also bounded from (27). Therefore, from Lemma 2, if t → ∞, s(t) will converge to zero and s(t) will also converge to zero in finite-time. Multiplying (24) by E 1 AT E 1+ : E 1 AT E 1+ s = E 1 AT s1 + E 1 AT e f From Property 3, E 1 A T e f = E 1 A T J T (λd − λ) = 0.

(57)

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Therefore, (57) can be expressed as: E 1 AT E 1+ s = E 1 AT s1

(58)

where E 1 AT E 1+ and E 1 AT are bounded. Thus, if s(t) converge to zero (t → ∞), then s1 (t) also converge to zero. Considering (24), e f = 0. Therefore, s1 = e˙m + ema/b = 0

(59)

According the terminal sliding mode theory, em , e˙m and e f will also converge to zero in finite-time. The specific process of proof is given as follows: Considering the Lyapunov function as follow: Vs = emT em

(60)

The differentiation of Vs is:  V˙s =

emT e˙m

=

−emT emr4

≤ −λmin ( )2

us

1 2 e 2 i=1 mi n

u s ≤ −2u s λmin ( )Vsu s

(61)

where 0 < u s = (1 + r4 )/2 < 1, considering Lemma 1 and (59), em , e˙m and e f will also converge to zero in finite-time. So, when t → ∞, θ(t) → θd (t), θ˙ (t) → θ˙d (t), e f → 0. s(t) converge to zero in finite-time, so q˙ converge to zero in finite-time. Therefore, q will converge to a constant in finite-time and the flexible-link is also stabilized.

4 Simulation and Analysis In this part, the improved method is applied to a two-link flexible manipulator with flexible joints. Suppose that the first link of the manipulator is rigid link and the end link is flexible link. The equation of dynamic model for this two-link flexible manipulator can be described in the following form:    1 a1 a2 b1 b2 T , M12 = , M21 = M12 = , M22 = ρ2 l2 I2×2 , a3 a4 b3 b4 2     ˙ 0 c1 θ2 c c T , C12 = 2 3 , C21 = C12 = , C22 = 0. −c1 θ˙1 0 c4 c5 

M11 C11

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Assuming that n = 2, and the parameters of the flexible manipulator are as follow: m 1 = m 2 = 1 kg; l1 = l2 = 1 m; ρ1 = ρ2 = 1 kg/m; J1 = J2 = 1 kgm2 . Assuming that the desired position and force are given as: θ1d =

π + sin(0.25π t), θ2d = π/3, λd = 8. 6

The simulation results are shown that θ1 asymptotically converge to θ1d in Fig. 2, and θ˙1 asymptotically converge to θ˙1 in Fig. 3. The position error and velocity error of joint 1 using linear sliding mode is shown in Fig. 4. The constraint force tracking and using conventional linear sliding mode is shown in Fig. 5. The simulation results show that the proposed method can make the position errors and force errors converge to zero The simulation results show the feasibility of the given the robust adaptive controller.

Fig. 2 Position tracking and position error of joint 1

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Fig. 3 Velocity tracking and velocity error of joint 1

Fig. 4 Position error and velocity error of joint 1 using linear sliding mode

B. Wang et al.

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5

Fig. 5 Contacting force error

elamd/N

0

-5

-10 0

2

4

t/s

6

8

10

References 1. Alshamasin, M.S., Ionescu, F., Kasasbeh, R.T.A.: Modelling and simulation of a SCARA robot using solid dynamics and verification by MATLAB/Simulink. Int. J. Model. Ident. Control 15(1), 28–37 (2012) 2. Xiao, B., Su, H., Zhao, Y., et al.: Ant colony optimisation algorithm-based multi-robot exploration. Int. J. Model. Ident. Control 18(1), 41–46 (2013) 3. Tang, Y., Sun, F., Sun, Z.: Neural network control of flexible-link manipulators using sliding mode. Neurocomputing 70(1), 288–295 (2006) 4. Schnelle, F., Eberhard, P.: Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters. Acta Mech. 33, 529–542 (2017) 5. Matsuno, F., Asano, T., Sakawa, Y.: Modeling and quasi-static hybrid position/force control of constrained planar two-link flexible manipulators. IEEE Trans. Robot. Autom. 10(3), 287–297 (1994) 6. Ge, S.S., Postlethwaite, I.: Adaptive neural network controller design for flexible joint robots using singular perturbation technique. Trans. Inst. Meas. Control 17(3), 120–131 (1995) 7. Huang, L., Ge, S.S., Lee, T.H.: Position/force control of uncertain constrained flexible joint robots. Mechatronics 16(2), 111–120 (2006)

Identification of Flowrates and Pressures in HVAC Distribution Network Based on Collective Intelligence System Zhen Yu

and Huai Li

Abstract This paper introduced a new method for the identification of flowrates and pressures in HVAC distribution network based on a novel collective intelligence system. The proposed method implements the identification of pressures and flowrates by solving basic energy and flowrate balance functions locally, and exchanging information with neighbor nodes. The proposed method is applied to two typical distribution networks. The convergence time and identified pressure distributions are discussed. The potential of using the collective intelligence system for the HVAC system control is further explored, and the benefits are discussed. Without central configuration and calculation, the proposed method is more feasible in building level control practice than traditional methods. Keywords Identification · HVAC · Distribution network

1 Introduction Heating Ventilation and Air Conditioning (HVAC) system consumes more than 40% of the energy in many types of buildings [1, 2]. The HVAC system is composed of cold and heat source, distribution system and HVAC terminal devices. The distribution system circulates the cold and heat to the HVAC terminal devices, where it is transferred to the building spaces through heat exchange between the HVAC devices and the indoor air. The proper hydraunic and heat balancing of the distribution system is essential for the optimal control of the HVAC system to avoid over supply or insufficient supply of heat or cold to the building spaces. However, surveys reveal that the distribution system often causes low energy efficiency of HVAC system. The HVAC distributions system is seldom commissioned appropriately according to its design conditions before the operation [3, 4]. During the operation, the heating and cooling load varied according to the weather conditions and internal loads, which required the adjustment Z. Yu (B) · H. Li China Academy of Building Research, Beijing, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_115

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of the flowrates in the distribution system. The mechanism of pressure interference between different HVAC devices in the distribution system is complex. For large scale district heating applications, a centralized mathematical model of the distribution network is often established by experienced specialists to assist the optimal control of distribution system. Due to the complexity and high requirement of the expertise, this approach is not feasible for building-level control practice. This paper proposes a decentralized identification method to generate over-all description of the HVAC distribution system and calculate the pressures and flowrates with only local information. The approach is based on a flat-structured building automation system that using distributed smart nodes as collective intelligent system [5]. Each smart node contains linkage, flow resistance and flowrate information of itself and its neighbor nodes. By exchanging information and updating previous knowledge, the CIS evolves to reach the agreement about the pressures and flowrates in the distribution network. Comparing to traditional centralized approach, the proposed method is easy to implement, robust and more feasible for building level control of HVAC distribution system. In this paper, the concept and structure of the collective intelligence system (CIS) is introduced firstly. A description of the distribution system is then given and the proposed identification and calculation method is proposed. The simulation results of using the proposed method in different distribution system are also provided. In the end, the benefit and potential of the proposed method is discussed.

2 Introduction of CIS Concept A decentralized, flat-structured building automation system controlled by smart nodes was proposed. The novel collective intelligence system (CIS) uses standard distributed smart nodes, called CPN, to manage the automation system. Each CPN controls a subspace in the building, and all CPNs have identical structure, hardware and software. A CPN has a limited number of communication ports that connect to the neighboring CPNs. Unlike the traditional centralized system, all CPNs have equal relations to one another. Each CPN represents a smart zone or a smart device. A smart zone includes a building subspace, HVAC equipment sensors, and actuators in the space. A smart device represents a chiller, a boiler or other building devices. The CPNs can only exchange information with their neighboring nodes. There is no central computer that works as a higher-level coordinator or controller. Using the proposed control architecture, the CIS can decentralize the building automation system into a flat-structured system, which enables the new system to self-identify, self-integrate, self-adapt and self-program [6, 7] (Fig. 1). The decentralized architecture of the building automation system uses distributed smart nodes working together to achieve overall optimum. For the identification of pressures and flowrates in the HVAC distribution system, the CPNs store local information such as the link information, local pressure and flow resistance. The

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Fig. 1 Structure of the CIS [8]

local information can be conveniently acquired from the local network and the setting information.

3 Identification of Flowrates and Pressures in the Distribution Network 3.1 Description of the Distribution Network of HVAC System A typical air distribution network of HVAC system is given in Fig. 2. Each node in the drawing represents a section of the air distribution network. The nodes are classified into three types: “N” represent the node has neither flow inward or outward, e.g. duct or space; “R” means the node has flow inward from outside, e.g. air intake; “D” means the node has flow outward to the outside, e.g. air outlet. The solid line between each node means the two nodes are connected. Each link has its properties such as the resistant (S) and the flowrate (Q). Each node also has its properties such as the pressure (P). Unlike the traditional system, the information about the distribution network is stored distributed in the CIS. As in Fig. 3, each node stores its own information. By exchanging information with each other, the nodes can also get information about their neighbor nodes. None of the nodes has the over-all information about the whole distribution network, and it does do not need to have this information. The governing functions of node N in Fig. 3 is: n  i=1

Qi = Q N

(1)

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N : CPN

D : Flow Drain

R : Flow Source

Fig. 2 Description of a typical air distribution network using CIS concept

Fig. 3 Standard unit of HVAC distribution network in CIS

Equation (1) describe the flow balance at node N. Q N is the flow intake or outlet flowrate to the ambient environment of node N; Q i is the flowrate from node Ni to node N; n is the number of neighbor nodes of node N. Pi − PN = si Q i2 , i = 1, . . . , n

(2)

Equation 2 describe the energy balance at node N. PN is the pressure of node N; Pi is the pressure of node Ni ; si is the flow resistance of the flow network link between node Ni and node N.

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Table 1 Identification process of pressures and flowrates in distribution network Step

Action

1

Each node in the distribution network acquire local information such as PN , QN , si …

2

As soon as the calculation is enabled, the calculation command spread in the network by exchanging information between neighbors

3

Each node solves the Eqs. (1) and (2) to get new PN and Qi , assuming the information from neighbor node is correct

4

Update local information about pressure and flowrate, using a learning: LF = 0.5 in the case study

5

Exchange information with its neighbor nodes, forward the new P, Q values

6

Compare the newly calculated pressure and flowrate and previous ones, if the difference is less than the give threshold, stop the iteration

7

When all the nodes stop the iteration, the identification finished

3.2 Identification Process In the CIS, each node has the local information about the distribution network. By exchanging the information with neighbor nodes, the new information will be used to update the previous information. The iteration continues until the newly updated information is the close enough to the previous information, which means the estimation of the pressures and flowrates is precise enough globally. This process is described in Table 1.

4 Results and Discussion The proposed method was firstly applied to a simple distribution network with 5 nodes given in Fig. 4. The node 1, 4 and 5 are boundary nodes which assumes to know its condition already. The node 1 is the flow inlet where the pressure is 100 Pa. The node 4 and node 5 are flow outlet where the pressure is set to 0. The conditions of node 2 and 3 are unknown. The learning factor about how much the new information will be used to update the previous knowledge was set to 0.5. The algorithm described in Table 1 was implemented in a CIS simulation environment developed by Python 2.7. The simulation results are given in Figs. 5 and 6. Fig. 4 A simplified air distribution network with 5 nodes using CIS concept

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Pressure (Pa)

60 40 Node 2 20 0

dP P2 0

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25

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iteration times Fig. 5 Simulation results of pressure at Node 2

pressure (Pa)

20 15 10

Node 3 dP

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P3 0

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25

30

iteration times Fig. 6 Simulation results of pressure at Node 3

Figure 5 gives the simulation results of pressure at Node 2. It can be seen that after about 10 iterations, the value of pressure (P2) at node 2 remains stable. The update value between each iteration (dP) reduced to 0 quickly. Similar results can be found in Fig. 6 about node 3. After a few iterations, the unknown pressure and flowrate at Node 2 and Node 3 were successfully found. The proposed method is then applied to a more complex distribution network with 13 nodes given in Fig. 7. Node 10 is the flow inlet with ambient pressure of 100 Pa; Node 12 is the flow outlet with ambient pressure of -100 Pa. Node 5, 7, 8, 9, 11 are nodes that only work as distribution network that do not exchange flow with outside; Node 1, 2, 3, 4, 6, 13 has opening to outside with ambient pressure of 0 Pa. Figure 8 gives the simulation results of the pressures of the 13 nodes. The pressure at each node converged to a stable value after about 10 iterations. Node 10 has the highest pressure as it is the main driving source of flow with ambient pressure of 100 Pa. Node 12 has the lowest pressure as it is the main flow drain with ambient pressure of −100 Pa. The pressures of other nodes scatter in the middle. It can be found that the update value between each iteration (dP) reduced to 0 quickly. The values at different nodes converge uniformly. It is because that the nodes belong to the same fluid network and the pressure change at any node will affect the values of others (Fig. 9).

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100 80 60 40 20 0 -20 -40 -60 -80

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Node 2

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Fig. 8 Simulation results of pressure at node 1–13

By applying the proposed identification method to two small scaled HVAC distribution networks, the effectiveness of the proposed was investigated. From the simulation, it can be seen that the proposed method is simple to implement and can be self-organizing without centralized configuration, which is very important for building-level control projects.

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5 Conclusion This paper introduced a new method for the identification of flowrates and pressures in HVAC distribution network. The method is based on a novel HVAC control architecture: collective intelligence system (CIS). The CIS can support the selfidentification, self-integration, self-programming and self-adaptation of the HVAC control system. The proposed method implements the identification of pressure of flowrate by solving basic energy and flowrate balance functions locally, exchanging the information with neighbour nodes for information updating and finally achieve global convergence. The proposed method was applied to two typical HVAC distribution networks. The convergence time and identified pressures are discussed. Compared with traditional centralized distribution network modelling and identification, the proposed method is simpler and more robust. The algorithm at each node is standard and can be pre-programmed. Only minimum local configuration is required which makes the real-world engineering practice more feasible compared to traditional method. The proposed method will be applied to more complex HVAC distribution networks and be put into practical applications for further study. Acknowledgements This work was supported by National Key Research and Development Project of China (No. 2017YFC0704100 entitled New Generation Intelligent Building Platform Techniques). We appreciate Dr. Ziyan Jiang for the helpful discussions.

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References 1. Lam, J.C.: Energy analysis of commercial buildings in subtropical climates. Build. Environ. 35(1), 19–26 (2000) 2. Abdelalim, A., O’Brien, W., Shi, Z.: Development of Sankey diagrams to visualize real HVAC performance. Energy Build. 149(Supplement C), 282–297 (2017) 3. Xiao, F., Wang, S.: Progress and methodologies of lifecycle commissioning of HVAC systems to enhance building sustainability. Renew. Sustain. Energy Rev. 13(5), 1144–1149 (2009) 4. Dalamagkidis, K., Kolokotsa, D., et al.: Reinforcement learning for energy conservation and comfort in buildings. Build. Environ. 42, 2686–2698 (2007) 5. Dai, Y., Jiang, Z., Shen, Q., Chen, P., Wang, S., Jiang, Y.: A decentralized algorithm for optimal distribution in HVAC systems. Build. Environ. 95(2016), 21–31 (2016) 6. Wang, S., Xing, J., et al.: A decentralized sensor fault detection and self-repair method for HVAC systems. Build. Serv. Eng. Res. Technol. 39(6), 667–678 (2018) 7. Zhang, Z., Zhao, Q., Yang, W.: A distributed algorithm for sensor fault detection. In: 14th IEEE International Conference on Automation Science and Engineering, Munich, Germany, pp. 756–761 (2018) 8. Zhao, Q., Xia, L., Jiang, Z.: Project report: new generation intelligent building platform techniques. Energy Inform. 1–2 (2018)

Neural Network Sliding Mode Control for Pneumatic Servo System Based on Particle Swarm Optimization Gang Liu, Guihai Li, Haoyue Song and Zhengyang Peng

Abstract Problems of pneumatic servo system, such as poor stability, non-linearity and uncertainty in the process of modeling, seriously affect the development of highperformance pneumatic controller. In this paper, a pneumatic servo system’s mathematical model is established at first and locally linearized to a third-order nonlinear system to simplify it. Then, to eliminate the chattering problem of sliding mode control, RBF neural network is applied to approximate the control law. Besides, particle swarm optimization (PSO) is come up to achieve the overall optimization effect of RBF neural network and further improve the control performance. Lyapunov function is defined to verify the system’s stability. The results of simulation show that the neural network sliding mode controller optimized by PSO overcomes the chattering problem of pneumatic actuator, ensuring the stability, robustness and rapidity of the pneumatic system. Keywords Pneumatic servo system · Particle swarm optimization · Neural network · Sliding mode control

1 Introduction Pneumatic servo system has the advantages of simple structure, clean use of energy, strong adaptability to the environment and easy maintenance. Using pneumatic control technology to realize production process automation is an important technical means of industrial automation. But the pneumatic servo system also faces many problems such as low stiffness, poor stability, non-linearity and uncertainty in the process of modeling [1]. Traditional control methods for pneumatic servo system, which is naturally unstable, cannot achieve ideal control effect. Since the sliding mode control has good

G. Liu (B) · G. Li · H. Song · Z. Peng Research Institute of Intelligent Systems and Control, Harbin Institute of Technology, Harbin 150001, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_116

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adaptability to system disturbance and parameter perturbation, especially it can construct variable structure control, so that disturbance cannot affect it [2]. That’s why we apply sliding mode control to uncertain controlled objects such as pneumatic servo system. One of its main drawbacks is chattering. Reference [3] replaced symbolic function with the saturation function, and the boundary layer was designed near the surface. Iwamura and Toda [4] took the difference of state as sliding mode gain, and designed a variable gain controller to suppress chattering. Fei [5] and others designed an integral sliding mode surface to eliminate chattering by integrating switching signals. References [6, 7] used fuzzy theory estimating the gain of controller to reduce chattering. Inspired by the above chattering suppression methods, we adopt an adaptive sliding mode control method with RBFNN. Since direct addition of them easily leads to slow control and single learning algorithm of RBFNN [8–10] and in order to adapt parameters of RBFNN on-line, we apply PSO to the network, which is proved high-performance. This paper’s main contributions are: Firstly, we established the actual system’s model with local linearization to make it simpler and more controllable. Secondly, aiming at the chattering problem, RBF neural network is used to approximate state variables and disturbances to effectively suppress chattering. Finally, we adopt particle swarm optimization to adapt the network on-line then the problem of slow control caused by RBF neural network is improved. The other parts are arranged as: Sect. 2 establishes the system’s mathematical model to obtain the control law reasonably. In the Sect. 3, the controller is designed. Then, in Sect. 4, Lyapunov function is defined to explain the system’s stability. Section 5 verifies the designed system through numerical simulation and experiments. Finally, the conclusion is given in the sixth section.

2 Mathematical Model of Pneumatic Actuator 2.1 Cylinder Flow Continuity Equation Assuming that the gas flow in the cylinder is continuous, the rate of change of gas mass flow is equal to the mass flow of the inflow gas minus the derivative of the mass of the outflow gas to time, and we have M = ρV, where ρ is the density of the gas medium. Then the gas flow equation in the cylinder is 

M˙ in −



dρ dV +V M˙ out = ρ dt dt

(1)

Since the whole process is adiabatic, the relationship between the initial temperature T0 of the cylinder chamber then the process temperature T would be:

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p p0

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 n−1 n (2)

The cylinder has two chambers, which are in series. We take S representing the cylinder’s effective cross-sectional area and assume two chambers’ initial state is S1 p10 = S2 p20 , T10 = T20 = T0 . We also set the initial position of the piston is in the middle of the cylinder. Since ρ = p/RT , where p is the pressure of the cylinder and R is a proportional constant. Above all, the mass flow rate of the two chambers of the cylinder can be written as: ⎧ ⎨ M˙ in = ⎩





1 V dp1 + nS1 p1 ddtV1 RT0 n  10 dt 2 + nk S1 p2 ddtV2 M˙ out = RT10 n lV10 dp dt

(3)

where k = S2 /S1 and l = V20 /V10 , which represents the initial volume ratio of the two chambers of the cylinder.

2.2 Modeling of Electronic Pressure Regulating Valve Since the process of gas flowing through the port of electronic pressure regulating valve is very complicated and there are many factors to be considered, the key of modeling is to select a suitable flow equation to describe this process. Similarly, the flow of gas through the valve is regarded as an isentropic adiabatic process. Then the flow formula of the pressure regulating valve can be written as follows:

M˙ i = pu ov ρ Tu /Te ψi ( pu , pe )

(4)

where ψi ( pu , pe ) =

⎧ ⎨ ⎩ 1−

1 

pu pe

−ζ

2

(1−ζ )2

pu pe

>ζ

pu pe

≤ζ

The equation shows that the mass flow through the valve is mainly affected by the opening ov of valve port and the ratio pu of outlet pressure pe to inlet pressure. Because the pressure pu of the gas source through the pressure regulator can be regarded as a constant, the mass flow rate can be approximated as a function of ov and pe . By linear expansion of Taylor series we can obtain:

M˙ 1 (ov , pe ) = f c1 ov + f p1 pe M˙ 2 (ov , pe ) = f c2 ov + f p2 pe

(5)

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Fig. 1 The photo and force sketch of the pneumatic actuator

where f ci =

∂ M˙ i ∂ov o =0 v

and f pi =

∂ M˙ i . ∂ pe p =0 e

2.3 Overall Force Acting on Actuator The sketch of the force acting on the actuator in its work is shown in Fig. 1. Based on this, we can carry out the force analysis of the actuator as follow. Suppose that the angle between the moving body and gravity direction is θ , the total mass of the actuator is m, the cylinder with rod cavity is cylinder 1 and the reaction force of the actuator by the workpiece during the working process is F R . We can obtain the reaction force of the actuator by the workpiece is as follows: (P1 S1 − P2 S2 ) − FR + G θ = m x¨

(6)

where G θ = mg sin θ , which is the component of the actuator’s gravity of in the direction of motion

2.4 Solution of Transfer Function From formulas above and set pl = p1 − kp2 , which represents the pressure acting on load, we can obtain     k k k M˙ 1 + M˙ 2 = f c1 + f c2 X V + f p1 ( p1 − kp2 ) − k f p1 + f p2 p2 j j j       dp1 dp2 k dx 1 V1 −k + 1+ k S1 p1 (7) = RT K dt dt j dt Laplace transformation of above formula is: S1 P1 (s) − S2 P2 (s) = ms 2 X (s) + FR (s) − G θ (s)

(8)

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After combining the two formulas above and substituting actual values, we get the transfer function between Fl (s) and X (s): Fl (s) 41,229 = 3 X (s) s + 968.7s 2 + 55,715s

(9)

The state space of the controlled object is described as: ⎧ x˙1 = x2 ⎪ ⎪ ⎨ x˙2 = x3 ⎪ x˙ = g(x) + ϕ(x)u + dt ⎪ ⎩ 3 y = x1

(10)

where y and u represent the input of control instruction and the output of the control system respectively. Functions g, ϕ are unclear and |ϕ(x)| ≤ . We set x = [x1 , x2 , x3 ]T .

3 Control Algorithm Design 3.1 Sliding Mode Controller with RBF Set the objective as x → xd , and xd = [yd , y˙d , y¨d ]T . Then the error is e = x − xd = [e, e, ˙ e¨]T and we can get the function as ... s = [s1 s2 s3 ] · e = s1 e + s2 e˙ + e

(11)

... where s1 , s2 > 0. Let w = s1 e˙ + s2 e¨ − x d , then we have: ... ... s˙ = s1 e˙ + s2 e¨ + x 1 − y d = g(x) + ϕ(x)u + w

(12)

Based on equations above, we can design the ideal sliding mode controller as:   1 1 1 ϕ˙ u = − (g + w) − s · − 2 + 2 + ϕ 2ϕ δϕ δϕ ∗

(13)

where δ > 0, so lim e(t) = 0. However, the control law above is unachievable t→∞ because g and ϕ are unknown and too complicate. From the expression we know that u ∗ is continuous function of x, s, δ and w, so it is appropriate to apply RBF neural network to approximate u ∗ . Then the network’s input can be z = [ x T , s, s/δ, w]T ∈ z ,where compact set

z is defined as

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z = {( x T , s, s/δ, w)| x ∈ ; xd ∈ d ;

... s = [s1 s2 s3 ] · e; w = s1 e˙ + s2 e¨ − y d }

(14)

When δ is very small, s and s/δ are of different orders of magnitude. In order to guarantee the neural network’s accuracy, the input should also contain s/δ. Define ideal network weights as V ∗ , then u ∗ = V ∗T f (z) + τ, ∀z ∈ z

(15)

where f (z) is Gauss basis function, τ is the approximation error of network and |τ | ≤ τ0 . The actual control law design is the network’s output, that is u = Vˆ T f (z), where ˆ V is V ∗ ’s approximation. The we have follows adaptive law  V˙ˆ = − f (z) · s + ξ Vˆ

(16)

where = T > 0 and ξ > 0.

3.2 Design of PSO Due to the change of system structure, the optimal parameters of RBF neural network need to be adjusted in real time. Compared with other evolutionary algorithms, PSO has a faster convergence speed because of its simple structure and fewer operating parameters [9], so we select it as the optimization algorithm in this paper. Suppose that in a D-dimensional space, there are N particles in the population, then the particles’ position as well as velocity can be written respectively as: ⎤ ⎡ ⎤ c11 · · · c1W z 11 · · · z 1W ⎢ .. ⎥, C = ⎢ .. .. ⎥ Z = ⎣ ... ⎣ . . ⎦ . ⎦ zN1 · · · zNW cN 1 · · · cN W ⎡

(17)

where W = k(n + 1), k is the nodes in hidden layer and n refers to dimension of input eigenvectors. z i j stands for the jth component of the position vector of the ith particle. Similarly, ci j means the jth component of the speed vector of the ith particle. During each iteration, position, velocity and fitness of the particle are updated according to the value of particles’ individual and global extreme as well as fitness. The specific equation is:

ct+1 = wct + τ1r1 ( pid − z t ) + τ2 r2 ( pgd − z t ) z t+1 = z t + ct+1

(18)

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where pid is the individual value, pgd is the global extremum, w represents the inertial weight, constants τ1 , τ2 are non-negative and r1 , r2 ∈ (0, 1). When iteration stops, the weights and thresholds of the neural network corresponding to the global extremum are the optimal solutions of the problem.

4 Proof of Control Algorithm Substituting u = Vˆ T f (z) and u ∗ into s˙ = g(x) + w + ϕ(x)u, we get  1 1 ϕ(x) ˙ T ˜ + − s s˙ = ϕ(x) V f (z) − τ − δ δϕ(x) 2ϕ(x) 

(19)

where V˜ = Vˆ − V ∗ .  We define Lyapunov function as L = 1/2 s 2 /ϕ(x) + V˜ T −1 V˙ˆ , then we have  ˙L = −

 ϕ(x) ˙ 1 + s 2 − τ s − ξ V˜ T Vˆ δϕ(x) ϕ 2 (x)

(20)

Since L ≥ s 2 /(2ϕ(x)), then we obtain s≤



2ϕ(x)L ≤



 2L ≤

   δ 2 ξ 2 − Et ∗ τ  + V  2 e L(0) + E 2 0 2

(21)

where E = max{δ, ξ }. According to basic inequalities, it can be obtained that |s| ≤ e− 2E t

 2L(0) +



   1/2 ¯ ¯ + ξ V ∗ 2 E δτ02  , ∀t ≥ 0

(22)

Above all, the system is stable.

5 Simulation In this paper, the sinusoidal signal yd1 = π/6 sin t and step signal yd2 = 1(t) are input as expected tracking instructions respectively, and the system state is initially as x0 = [0, 0, 0]. The initial values of the designed control law and the weight adaptive law of RBF neural network are set as = 15 · eye(13), ξ = 0.005 and δ = 0.25. In PSO, the number of iterations is 100 and c1 = c2 = 1.49445. The position, velocity and control input diagrams of controller before or after PSO optimization are obtained as shown in Figs. 2 and 3.

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Fig. 2 Simulation results without PSO optimization

Fig. 3 Simulation results after PSO optimization

According to the graphs, the sliding mode controller compensated by RBF neural network can track the control instructions quickly and achieve the control effect under the input of two different expected instructions. The controller optimized by particle swarm optimization achieves the desired effect in less time than that without particle swarm optimization, especially under sinusoidal signal input (about 5 s before optimization and 1.5 s after optimization). After particle swarm optimization, the chattering phenomena in the early stage of the actuator are further suppressed, which highlights the advantages of RBF neural network in suppressing sliding mode chattering.

6 Experiment Platform The control algorithm will be applied in a robot experiment shown as follow. A 6-DOF C60 robot is chosen to realize the algorithm. It mainly consists of active compliant flange, a workbench, a robot control cabinet and a PC-BASEO. Its basic structure is shown in the left of Fig. 4 as follow. And the actuator is installed at the

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Fig. 4 The actual robot arm system and the diagram of robot system

end of the control chain. Only slight adjustment is necessary during the progress of working. Among the system, the cylinder itself possesses one degree of freedom, which significantly simplifies the design of the terminal manipulator. In the diagram of robot system, the model of the item is first introduced in PCBASEO. The PC-BASEO then generate the trail point. The joints of the robot are then controlled by the robot controller. The whole construction of the control section is shown in the right of Fig. 4.

7 Conclusion In this paper, starting from the actual system, the mathematic model is established by locally linearization. Controller based on PSO is applied to approximate uncertainties in the model so as to eliminate the chattering problem of sliding mode control, so as to achieve the overall optimization effect of RBF neural network and further improve the control performance. The simulation results show that the control method designed in this paper overcomes chattering problem of actuator. We will take experiments in the future.

References 1. De Volder, M., Ceyssens, F., Reynaerts, D., Puers, R.: Microsized piston-cylinder pneumatic and hydraulic actuators fabricated by lithography. J. Microelectromech. Syst. 18(5), 1100–1104 (2009) 2. Chiang, C.-J., Chen, Y.-C.: Incremental fuzzy sliding mode control of pneumatic muscle actuators. J. Int. J. Adv. Rob. Syst. 14, 1917–1928 (2018) 3. Hu, X., Wu, L., Gao, H.: Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle. J. Franklin Inst. 349, 559–577 (2012) 4. Iwamura, T., Toda, M.: Motion control of an oscillatory-base manipulator using sliding mode control via rotating sliding surface with variable-gain integral control. In: Washington, DC, 2013. ACC, pp. 5742–5747 (2013)

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5. Fei, J.: A class of adaptive sliding mode controller with integral sliding surface. In: Changchun 2009. ICMA, pp. 1156–1161 (2009) 6. Aliasghary, M., Eksin, I., Guzelkaya, M.: Fuzzy-sliding mode reference learning control of inverted pendulum with big bang—big crunch optimization method. In: Cordoba 2011. IC ISDA, pp. 380–384 (2011) 7. Elmelhi, A.M.: Fuzzy sliding adaptive control. In: Qinhuangdao 2010. ICCDA, vol. 3, pp. 84– 88 (2010) 8. Zhang, Y.-J., Liu, Y.-D.: Application of an improved RBF neural network in sliding mode control system. In: Taiyuan 2010. ICCASM, vol. 12, pp. 489–492 (2010) 9. Chen, S., Hong, X., Luk, B.L., Harris, C.J.: Non-linear system identification using particle swarm optimization tuned radial basis function models. Int. J. Bio-Inspired Comput. 1(4), 246–258 (2009) 10. Lin, S.-C., Chen, Y.-Y.: RBF-network-based sliding mode control. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, vol. 2, pp. 1957–1961 (1994)

Delay Efficient D2D Communications over 5G Edge-Computing Mobile Networks Xiaohua Xu, Yuanfang Chen, Yanxiao Zhao, Shuibing He and Houbing Song

Abstract Device to Device (D2D) communication scheduling is fundamental for data offloading in fifth-generation (5G) edge-computing mobile networks. Suppose there are multiple users which aim to fetch cached popular contents locally via data offloading, and assume each device user has a demand, the objective is to seek an interference-aware schedule of transmission activities with minimum delay to satisfy all demands. We consider the problem with the duty-cycled constraint. We propose a combinatorial algorithm under the duty-cycled model. The approximation factor is independent of the cycling period length, while most existing methods for dutycycled scheduling are accompanied with large approximation bounds that increase linearly with the cycling period length of the duty-cycled model. Keywords D2D communication · Delay · Interference · Duty cycle · Combinatorial algorithm

X. Xu (B) Department of Computer Science, Kennesaw State University, Marietta, GA, USA e-mail: [email protected] Y. Chen School of Cyberspace, Hangzhou Dianzi University, Hangzhou, China Y. Zhao Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA, USA S. He College of Computer Science and Technology, Zhejiang University, Hangzhou, China H. Song Department of Electrical, Computer, Software, and Systems Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL, USA © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_117

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1 Introduction The rise in cellular data has motivated various means of increasing communication capability, such as Femtocell and multiple-input and multiple-output (MIMO). Traffic offloading via Device to Device (D2D) proximal communications is promising to boost spectral efficiency in the fifth generation (5G) architecture. In the pioneer work [5], Doppler et al. proposed to use D2D underlaying a Third Generation Partnership Project (3GPP) [16] Long Term Evolution Advanced (LTE-A) cellular network for local services with limited interference impact on the primary cellular network. In a D2D communication scenario, nearby devices communicate without the Evolved Node B (eNodeB) or any cellular infrastructure. If a neighboring device have the content that one user wants, it can send directly through D2D communication. Since then, D2D has been investigated extensively in the academia. On the other hand, AllJoyn [1], started by Qualcomm and now sponsored by Open Connectivity Foundation (OCF), is a collaborative open source software framework that allows devices to communicate with other devices around them. We aim to study single-hop D2D communication scheduling for data-offloading as most throughput-related activities can be reduced to this fundamental problem. For example, multi-hop network flow [17] essentially relies on a routing and onehop wireless link transmission schedule. Another application is the data aggregation scheduling [9]. At each time, we need to schedule as many single-hop communications as possible. The single-hop communication scheduling problem has also found applications in other areas. Two main branches dominate the literature on the general single-hop communication scheduling. One is capacity maximization or maximum weight independent set (MWIS) [17]. In the MWIS problem, there is a set of communication requests. A subset of transmissions is said to be independent if all the transmissions occur successfully without any conflict. The other branch is delay efficient or shortest scheduling. Given a collection of users, assume each user has a demand to transmit. The objective is to satisfy all demands within the shortest time-duration. This problem is critical for time sensitive applications. We study the delay efficient scheduling branch with several challenges. The first challenge is that the delay efficient D2D scheduling for data offloading is different from the traditional link scheduling problem. In the D2D scenario, each node with a demand has a flexibility to choose candidate neighboring nodes which contain the cached popular content locally. Some communication links may be redundant to satisfy this demand. Thus, the task contains joint scheduling of node-level activities and link-level scheduling. In other words, after we schedule some links, then some other links may be removed if the receiver node’s demand is already satisfied. However, this is not true in the traditional link scheduling scenario where we need to complete the transmissions of all links finally. The second challenge is the duty-cycle constraint. A user can transmit data whenever it wants while it is only allowed to retrieve data at some pre-defined time-slots. Thus, many problems under the duty-cycled model are much more challenging be-

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cause of the duty-cycled constraints. Most existing approximation algorithms on the duty-cycled model are accompanied with large approximation bounds which increase with the period length of the duty-cycled model such as [10, 12]. We observe that the above problems involve the routing structure design which may cause the large approximation ratio and the scaling of approximation ratios with the cycling period. Since the delay efficient D2D scheduling does not involve any routing structure, we aim to design an approximation algorithm for delay efficient D2D communication scheduling that has a ratio independent of the cycling period. Our main contributions are in the following. First, we propose an approximation algorithm for minimizing the delay for retrieving cached popular contents locally under the duty-cycled model. The approximation ratio is independent of the cycling period length. To the best of our knowledge, the only approximation algorithms on duty-cycled model that have approximation ratios independent of the cycling period are in [20, 25]. However, the results focus on beacon scheduling and multi-flow scheduling, respectively. In addition, their techniques can not be applied here. Second, the proposed algorithm is a combinatorial algorithm with duty-cycle aware communication activities. In other words, the method is much simple and fast. Third, we define the problem maximum weighted strongly independent set of retrieving nodes. The problem is a well-motivated problem itself. We organize the remaining sections of this paper in the following. Section 2 provides the system model. Section 3 presents the approximation algorithm. Section 4 provides the performance analysis. Section 5 presents the literature review. We conclude this paper in Sect. 6.

2 System Model In a scenario of LTE-A D2D communications in 3GPP, there are a collection of user devices and an eNodeB distributed within a two-dimensional plane. Under the protocol interference model [3], a receiver device node v can receive a message from a sender node u if we have |uv| ≤ 1, and for any other sender node w, we have |wv| > ρ. Assume each retrieving device node u has a demand d(u) to retrieve cached popular contents locally. For each requested piece of content, multiple devices may be possible to provide it. Thus, to satisfy a demand, the retrieving node may fetch data from any neighbor that contains the data. We assume that the union of all neighboring nodes’ cached data can satisfy the demand. In a duty-cycled network, assume the period is P. each node u has an active timeslot au ∈ [P]. Here [P] = {0, 1, 2, . . . , P − 1}. A node u is able to retrieve data at time t only if t ≡ au mod P. A fractional transmission schedule is a set S = {(I j , L j , γ j ) : 1 ≤ j ≤ k}

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such that I j is an independent set of retrieving nodes, and L j is the corresponding set of links and the receiver of each link in L j is a retrieving node in I j . We have γ j ∈ R+  for each 1 ≤ j ≤ k. The value kj=1 γ j is referred to as the length of the schedule S. V supported by the fractional schedule We define the retrieving load function c S ∈ R+ S as k  γ j · |I j ∩ {u}|, ∀u ∈ V. c S (u) = j=1

Given a set of retrieving nodes in a duty-cycled D2D wireless network, with a demand function on the node set, the problem D2D Shortest Scheduling (D2DShort) seeks a fractional transmission schedule such that the length is the shortest, each subset of links are interference-free with duty-cycled constraint satisfied, and for each node u, the demand d(u) ≤ c S (u).

3 Approximation Algorithm We first introduce a concept of strong independent set. Given a set of retrieving nodes, a subset of nodes are said to be a strong independent set if for any retrieving node u in this subset, no matter which arbitrary neighboring node serves as the sender to transmit cached popular contents locally to u, all the transmissions are interference-free. Maximum Weight Strongly Independent Set of Retrieving Nodes (MWISStrong): Given a set of nodes, assume each node is associated with a positive weight, the problem MWIS-Strong seeks a strongly independent set of minimum total weight.

3.1 Reducing D2D-Short to MWIS-Strong Our method for reducing D2D-Short to MWIS-Strong is based on the paradigm of adaptive zero-sum game with retirement used in [18, 19]. Let A be an algorithm for MWIS-Strong (to decide which node to choose and which not to choose), and  be a small parameter. We present a combinatorial approximation algorithm to reduce the problem D2D-Short to the problem MWIS-Strong. Given a demand function d on the retrieving nodes, we build up a fractional transmission schedule by successive augmentations in multiple rounds. At the beginning, each node u maintains a relative demand index π(u) which is initialized to φ. Based on the relative demand index of each node, each node is associated with a weight. Then, each round of scheduling consists of two phases, i.e., node-level and link-level scheduling.

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– [Phase I: node-level scheduling] The algorithm first finds a strongly independent set I of nodes by applying A to the subset of nodes using the weight associated. – [Phase II: link-level scheduling] For each node u in the strongly independent set I , select a neighboring node s which contains the data as a sender and form a → communication link − su , assume all corresponding links form a set L. After that, we set the length of this link set L. Then the relative demand index of each node is decreased accordingly. Note that each node’s relative demand index is decreased by at most one while there is exactly one node whose relative demand index is decreased by one. If the relative demand index of a node reaches zero or become not positive anymore after the update, the node is removed. For each round, we find a retrieving node set, a link set, and set the length correspondingly. The algorithm ends when each node’s relative demand index reaches negative or zero. Algorithm 1 presents the details. Here φ is a constant parameter. Algorithm 1: Reducing D2D-Short to MWIS-Strong Input : Set of nodes V , {d(u) : ∀u ∈ V }, {au : ∀u ∈ V }, cycling period P m ← |V |; ln m+ φ ← (1+)+ln(1−) ; p ← 0; while p < P do Let V p ⊆ {u : u ∈ V } be the subset of nodes with an active duty-cycle time-slot p; for each node u ∈ V p do π(u) ← φ; S p ← ∅; while V p = ∅ do Let A be an algorithm for MWIS-Strong; I ← the strongly independent set output by A applied to the subset V p with weight φ−π(u) function (1−) :u ∈Vp ; d(u) L ← ∅; for each node u ∈ I do select a neighboring node s of u which contains the cached data; → L ← L ∪ {− su };

x ← min{d(u) : u ∈ I };

S p ← S p ∪ {(I, L , φx )};

for each node u ∈ I do x π(u) ← π(u) − d(u) ; p if π(u) ≤ 0, V ← V p \{u} p ← p + 1; 

LS ←

p∈[P] LS

p;

return LS .

We summarize all notations in Table 1.

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Table 1 Notations V Set of nodes d Demand function on nodes π(u) Relative demand index of node u I Strongly independent set returned by A P Duty cycling period ω(u)

Weight of node u

m A

φ Vp Sp

L

Number of retrieving nodes Algorithm for MWIS-Strong Initial relative index of node u Subset of nodes with active time-slot p Transmission schedule for nodes with active time-slot p Corresponding link schedule for I

3.2 Divide and Conquer for MWIS-Strong We employ a cell partition and coloring to ensure that only nodes far apart could possibly be selected to the strongly independent set for retrieving cached data each time. We use vertical lines x = i ·  : i ∈ Z and horizontal lines y = h ·  : h ∈ Z to partition the plane into cells. Here the set Z consists of all integers. We set  = ρ + 1 to ensure that any two senders of a mutual distance  do not cause any interference under the protocol interference model. We color all cells such that every neighboring cells of the same color are separated apart by exactly one cell. Thus, the number of cell colors used is 4. After cell coloring, we select one retrieving node from each cell that contains node(s). For each color, all the nodes selected form a candidate solution for MWIS-Strong. We select a candidate solution of the maximum total weight.

4 Performance Analysis Theorem 1 The total number of rounds in Algorithm 1 is at most m · φ. Proof Let the set V p consist of all nodes with active time-slot p under the duty-cycled model. For each p, at the beginning, the summation of relative demand indices of all nodes in V p is |V p | · φ. In Algorithm 1, because exactly one node’s relative demand index is decreased by one, the total relative demand index is decreased by at least one at each round. Then, the total number of rounds for scheduling all nodes in V p is at most |V p | · φ. Combining all different V p together, the total number of rounds for scheduling all nodes in V is at most |V | · φ = m φ. Theorem 2 The proposed algorithm in Sect. 3.2 is a feasible solution for MWISStrong. Proof Each time only nodes far apart could possibly be selected to the set for retrieving cached data. For any pair of nodes selected, their mutual distance is at least

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ρ + 1. Thus, for each node u, no matter which neighboring node serves as the sender to transmit data to u, all the transmissions are still interference-free. Now we introduce a concept of maximum possible weight independent set of nodes (MWIS-Possible). Given a set of retrieving nodes, a subset of nodes is said to a possible independent set if we can find a corresponding sender for each retrieving node and all the transmissions are interference-free. Assume each node is associated with a positive weight, the objective is to select a possible independent set with maximum total weight. Clearly, the solution output by the method in Sect. 3.2 is a possible independent set and feasible for the problem MWIS-Possible. Lemma 1 The solution output by the method in Sect. 3.2 is feasible for the problem 2 MWIS-Possible, and achieves an approximation ratio of 64ρ 2 . π ρ−1

Proof For any pair of retrieving nodes, their mutual distance has to be at least ρ − 1. Thus, the maximum number of nodes that can be retrieving data concurrently in any 2 ρ−1 ρ−1 cell under the protocol interference model is

(ρ+1)+ π

2

+

 ρ−1 2

2

2

 = 16ρ 2 . In the π ρ−1

2

method in Sect. 3.2, we select at least one node from each cell of the same color and 2 there are total 4 colors, thus, the approximation ratio is 4 16ρ 2 . π ρ−1

 Theorem 3 The proposed algorithm achieves an approximation bound (8 + ε) · 2

64ρ 2  where ε is a small value. π ρ−1

Proof First, we only consider the nodes in V p with active time-slot p. Let ω(u) = (1 − )φ−π(u) : u ∈ V . p For each round t, let Vt , ωt (u), It , πt (u), xt be the corresponding values of p p p V , ω(u), I, π(u), x in Algorithm 1 at the t-th round. We have Vt+1 ⊆ Vt . πt (u)−πt+1 (u) . By using the inequalities We have ωt+1 (u) = ωt (u) · (1 − ) (1 − ) y ≤ 1 − y ≤ e−y , we have 

ωt+1 (u)

p

u∈Vt+1



u∈Vt

≤ 

p

u∈Vt

≤ 

ωt (u)

1 p

ωt (u)

1 u∈Vt

p

ωt (u)

·

 u∈Vt

·

 u∈Vt

ωt (u) · (1 − )πt (u)−πt+1 (u)

p

p

  ωt (u) · 1 −  πt (u) − πt+1 (u)

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 u∈Vt

=1− 

ωt (u)

p



·

u∈Vt

  ωt (u) · πt (u) − πt+1 (u)

p





xt ωt (u) · · ωt (u) d(u) u∈It  ωt (u)

u∈Vt

p

= 1 − xt · 

u∈It d(u)

u∈Vt

p

ωt (u)

Let It∗ be the optimal solution for the problem MWIS-Possible on the input 2 t (u) Vt with the weight function ωd(u) . Let μ = 4 64ρ 2 . By Lemma 1, we have π ρ−1  ωt (u) ωt (u) 1  ∗ ≥ · . Let χ (d) be the minimum length to schedule all nodes ∗ u∈It d(u) u∈It d(u) μ in V p with the demand function d. We have  ωt (u) p  ωt (u) 1 1 1 ωt (Vt ) u∈It d(u) ≥ = ≥ · · p p p ∗ ∗ d(u) μχ (d) ωt (Vt ) μ · ωt (Vt ) μ · ωt (Vt ) χ (d) ∗ p

u∈It

The second step holds because at any t-th round, we have χ∗ (d) · max

 ω(u)

d(u)  ω(u) x ∗j · max = I d(u) j u∈I ⎛ ⎞   ω(u) ⎝x ∗j · ⎠ ≥ d(u) ∗ j I

u∈I



u∈I j

≥ =

 ω(u)  · x ∗j d(u) ∗ u  ω(u) u

=



d(u)

u∈I j

· d(u)

ω(u)

u∈S

= ω(V p ) Thus, we have 

p

u∈Vt+1



u∈Vt

p

ωt+1 (u) ωt (u)

Therefore, we have

 ≤ 1 − xt · 

ωt (u) u∈It d(u)

u∈Vt

p

ωt (u)

≤1−

xt xt ≤ e− μχ∗ (d) μχ∗ (d)

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ωt+1 (u)

p u∈Vt+1




b + 1 is atmost (1 + )μa · P. If a ≥ 1, the  approximation ratio is (1 + 2

2

π ρ−1

π ρ−1

)μ(1 + a1 ) = (4 + ε) · (1 + a1 ) · 64ρ 2  ≤ (8 + ε) · 64ρ 2  . Here ε = 8.

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5 Related Work Delay efficient wireless communication scheduling [2, 17–19] has been studied in the literature. However, the above works do not consider the duty cycle constraint. There are extensive work on delay efficient duty-cycled wireless scheduling in multi-hop wireless networks. For example, [4, 7, 9, 22, 24, 26] studied data aggregation, [8, 12, 23] studied broadcast scheduling, [21] studied data gathering, and [10, 11] studied gossiping scheduling respectively. To the best of our knowledge, the only two results on delay efficient duty-cycled scheduling that have approximation ratios independent of the duty cycling period length are [20, 25]. Reference [20] studied delay efficient duty-cycled beacon scheduling. Reference [25] studied delay efficient duty-cycled multi-flow scheduling. To the best of our knowledge, existing works on deterministic and combinatorial algorithm design for delay efficient wireless scheduling do not consider a D2D communication with traffic offloading scenario. In [14], Lei et al. proposed an optimization framework and formulate a general queuing model for delay-aware resource control with bursty traffic. In [15], Sheng et al. investigated the trade-off between energy and delay trade-off. Regarding maximizing network capacity, in [13], Lee et al. studied maximizing the spatial reuse of radio resources by allowing the simultaneous transmission of D2D links on the same resources. In [27], Zhang et al. proposed an interference graph based resource sharing algorithm. In [6], Jiang et al. studied the problem of maximizing cellular traffic offloading via D2D communication.

6 Conclusion This paper presents an efficient algorithm for delay efficient D2D communication scheduling to satisfy each device’s demand in duty-cycled mobile networks. We analyze the efficiency of the proposed algorithms. As a future work, the problem of delay efficient D2D communication scheduling under the physical interference model is worth to be addressed. Acknowledgements The work of Yuanfang Chen is supported in part by the National Natural Science Foundation of China (Grant No. 61802097), and the Project of Qianjiang Talent (Grant No. QJD1802020). The work of Shuibing He is supported in part by the National Science Foundation of China (Grant No. 61572377), the Natural Science Foundation of Hubei Province of China (Grant No. 2017CFC889), and the Fundamental Research Funds for the Central Universities (Grant No. 2018QNA5015). However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

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Data Optimization for Spatial Data Mining and Classification in Marine Geochemical Exploration Haihong Wang, Li Liu, Jingjing Wang and Yanming Gao

Abstract In this paper, spatial big data mining is presented based on a new simplified data optimization and minimum bounding rectangle (MBR) methods. In order to speed up the spatial query and reduce the setup time of spatial index in marine geochemical exploration spatial database, a two-step data mining of objects method has been used. The spatial join queries such as the spatial relations between the objects can be transferred into the relative distance problem of points with their spatial characteristics. Then, support vector machines (SVMs) based on radial basis function (RBF) kernel classification have been used to those points and lines to get spatial targeting areas in order to evaluate the oil and gas resources. Comparison simulations of precision and spatial query speed of the method proposed have been conducted based on ArcGIS and Hadoop to verify the effectivness. Keywords Data optimization · Spatial data mining · Classification · MBR

H. Wang (B) · L. Liu · J. Wang College of Information Science and Technology, Qingdao University of Science and Technology, Qingdao 266061, China e-mail: [email protected] L. Liu e-mail: [email protected] J. Wang e-mail: [email protected] Y. Gao Key Laboratory of Marine Ecological Environment and Disaster Prevention and Reduction of Shandong Province, North China Sea Branch of the State Oceanic Administration, Qingdao 266033, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_118

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1 Introduction Marine Oil and gas geochemical exploration is the systematic detection of hydrocarbons and their associated organisms and alteration natural components into the ocean environment: soil, rock, water sediment, brine, gas, and other media by geochemical methods. Crude oil, petroleum or hydrocarbon reserves are usually located deep within the earth and even under the water. Massive spatial data has been collected from remote sensing, GIS data, computer graphics environmental assessment and planning. Geochemical explorations are likely to benefit from big data analytics techniques through spatial data mining and simulations. The search for crude oil and gas deposits is very expensive. How we acquire and leverage spatial information has dramatically significant implications [1]. Spatial data consists of spatial objects made up of points, lines, regions, rectangles, surfaces, volumes, rings, geospatial information, and even wide heterogeneous data [2]. A common way to deal with spatial data is to store it explicitly by parametrizing it and thereby obtaining a reduction to a point in a possibly higher-dimensional space [3]. However, if our query involves the space occupied by the data, then the situation is not so straightforward. There are two main problems for mining and querying massive spatial data to support spatial queries: the massive storage of spatial data, and the high computational complexity and complexity of processing of big data [4]. Especially the relation queries between objects. Recently, MapReduce based systems have emerged as a scalable and cost-effective solution for massively parallel data processing, but the system still suffers from a scalability issue [5, 6]. Reference [5] introduces HadoopGIS to solve the big data challenge and high computation complexity challenge. Reference [6] describes a full-fledged MapReduce framework with native support for spatial data. However, it still needs great time even we run such large-scale spatial queries. Thus, a next-step mining of the original data is necessary. In order to reduce the computation and simplified the spatial queries, Ref. [7] proposes a MBR method to find the relationship of two objects, thus lead an easy way to obtain the relative distances and relationships of objects [8, 9]. We proposed a data optimization method for spatial data mining in marine geochemical exploration. Firstly, we map and reconstruct the spatial objects problems with a set of points with original mining attributes based on MBRs method. Then the spatial information from the relative distance can be abstracted by a two-step procedure to obtain the relationship between two objects. It can easily be seen that the current spatial data mining mainly focuses on the calculation and mining of spatial point data. The complex spatial object types, such as lines, polygons and planes, which widely exist in spatial databases are mapping to the points with distance attribute, which means the general distance queries method could be used. A SVMs method is introduced into the data classification to obtain the target area needed. In the end, to compare the precision and the speed of the data optimization method, we use BP neural network (NN) trained the weights of the total 28 parameters. Comparison tests have been taken under ArcGis and Hadoop. The results are satisfied.

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2 Data Mining of Spatial Objects Although the spatial retrieval includes point, line, surface and buffer retrieval, there are only two cases in summary: Does the user-specified space range (line, surface, regions, 3D objects, including buffer surface) intersect with the data table space record? Are user-specified spatial points within the scope of data table space records?

2.1 MBR Data Optimization In this section we describe the topological relations between region objects without holes as defined by the model of [10]. If we distinguish the objects between boundaries and interiors, we can define the topological relationship between two objects by examining object intersections: For the simple case, if the MBRs of two objects are separated, they are also separated. However, for complex spatial constraint semantics, normal MBR strategy is not enough to support effective data mining. Therefore, in order to improve the efficiency of classification algorithm, the MBR relationship is used to construct the spatial relationship index between objects in advance, that is, to reconstruct the distance relationship between objects before they are trained into SVMs classifier. After the approximation of the MBRs, each extended object can be represented by a rectangle. If the distance between extended objects and their coverage are considered simultaneously, the distance between the MBRs as follows is called extended distance in (1). d(m, n) = dist(m, n) + ar ea(m, n)

(1)

 2 2 where dist(m, n) = (xm1 − xn1 )2 + (xm2 − xn2 )2 + (y √m1 − yn1 ) + (ym2 − yn2 ) is the distance of two MBR objects and ar ea(m, n) = |A(m) − A(n)| is the area effeteness of two MBR objects. MBR index optimization is based on the following principles: Let A and B be two MBRs. A, B are the boundaries of A, B respectively. A°, B° are the regions within the boundary of A, B respectively. A− , B− are the regions outside the boundary of A, B respectively. There are nine kinds of relations of the objects, which can form the following forms. 



⎤ A◦ ∩ B◦ A◦ ∩ B A◦ ∩ B− ⎥ ⎢ R(A, B) = ⎣ A ∩ B◦ A ∩ B A ∩ B◦ ⎦ A− ∩ B◦ A− ∩ B A− ∩ B− ⎡













(2)

Considering that the empty element is 0 and the non-empty element is 1, there is 29 = 512 spatial relationship in R(A, B). Table 1 illustrates only part of the mappings of A and B from actual objects relations to MBR relations. It actually contains the

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Table 1 Possible relationship and its relationship matrix Possible relationship

Relation to be test

Meet

d j (A, B) ∪ mt (A, B)

Cover

d j (A, B) ∪ mt (A, B) ∪ ol(A, B) ∪ ct (A, B) ∪ cv(A, B)

Contain

d j (A, B) ∪ mt (A, B) ∪ ol(A, B) ∪ ct (A, B) ∪ cv(A, B)

Inside

d j (A, B) ∪ mt (A, B) ∪ ol(A, B) ∪ in(A, B) ∪ cb(A, B)

Relationship matrix ⎡ ⎤ 0∗∗ ⎢ ⎥ ⎥ Rmt = ⎢ ⎣∗ 1 ∗⎦ ∗∗∗ ⎡ ⎤ ∗1∗ ⎢ ⎥ ⎥ Rcv = ⎢ ⎣0 1 ∗⎦ ∗∗∗ ⎡ ⎤ ∗1∗ ⎢ ⎥ ⎥ Rct = ⎢ ⎣∗ 0 ∗⎦ ∗∗∗

⎡

∗∗∗

⎤

⎢ ⎥ ⎥ Rin = ⎢ ⎣1 0 ∗⎦ ∗∗∗

eight spatial relations of objects: mt:meet, ol:overlap, cv:cover, eq:equal, dj:disjoint, cb:covered_by, in: inside,ct:contain [11]. The abstract spatial graphs can be arranged in a matrix. We illustrate this by examining the example shown in Table 1, which represents part relationship matrix, for a detailed information please refer to [11]. By the MBRs we can quickly judge whether an object satisfies a certain spatial relationship, based on the intrinsic relationship between MBR relationship and spatial geometry, as shown in Fig. 1. The spatial location index is calculated by spatial expansion information, and the converted data is stored in the spatial database.

Fig. 1 Relative distance of spatial object

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2.2 Index and Structure Optimazation In theory, the index of distance between spatial objects in database is a Cartesian product. If we removed the distance index between objects, a single spatial object table with n records can establish a N = n ∗ (n − 1) spatial index table of distance data. To trade space for time is also based on the following considerations: firstly, what we save is computing time by trading space for time, but the amount of I/O data exchange cost is also increases, so the balance between the amount of index and the amount of data analysis and calculation need to be taken into account when establishing the index; secondly, the searching speed of the spatial index depends not only on the amount of index, but also on the design and performance optimization of the database; lastly, the establishment of a complete index Spatial index of the relationship between all the objects is meaningless. The distance relationship between objects that are too far away will be discarded directly in the index database. The important feature vectors of the objects are inserted into a multidimensional index structure in order to obtain a new index system jointly. Only the distance relationship between the nearest point and the target point is preserved by setting parameters. When the distance between the two objects changes greatly, it can be considered that the distance between the two objects is large enough to be difficult to enter. The spatial objects will no longer be calculated. At the same time, we delete the duplicate index of the distance between two points.

3 Support Vector Classification Spatial classification is a process of grouping a set of spatial objects into clusters so that objects within a cluster have high similarity in comparison to one another, but are dissimilar to objects in other clusters [10, 12–15]. SVMs have been widely adopted for classification, regression and novelty detection. Reference [12] present a novel clustering method using the approach of support vector machines. Reference [14] proposed an efficient cluster assignment method to harvest cluster based by RBF kernel based SMVs through proximity graph modelling. The material to verified the method proposed in this paper is related to the investments of Bohai sea in 2006. The test area is divided into two blocks, located in the Bozhong sag, in the central part of the southwest Bohai Sea. There are 79 Columnar sampling points. At each point, we got the latitude, Longitude and 26 Chemical indicators such as Benzene, toluene, synchronous fluorescence 280 nm, synchronous fluorescence 300 nm, synchronous fluorescence 330 nm, pyrolytic hydrocarbon and propylene etc. There are 250,000 records corresponding to 79 subjects from the Marine Geochemical Exploration database are used to assess the performance on spatial classification using SVMs.

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3.1 SVMs Classifier Based on RBF In order to improve the accuracy of data mining, referring to Table 3, we divide the results of oil and gas evaluation index of regional ocean data into four categories, namely, oil and gas reservoir, oil and gas reservoir, gas reservoir and non-oil and gas reservoir. Where x ∈ R N is the input vector, · denotes the Euclidean norm, λi are real numbers. ϕ is a real valued function. {c p } Pp=1 ⊂ R N are the radial basis function centers. SVMs are supervised learning models with learning algorithms associated and the analyzing data are used for classification and regression analysis, the input x is first mapped into a m-dimensional feature space feature space by using kernel functions, and in this feature space the linear model  The linear model

is obtained. g(x, λ) in the feature space is given by g(x) = Pp=1 λ p ϕ h p , We could take the SVMs process as a neural network, there is N units

in the input layer and p units in the hidden layer. The pth imput is h p = x − c p , and the pth output is ϕ(h p ). In fact, the essence of our training using RBF is to determine the weight vector of the input layer to the hidden layer and the weight coefficient of the hidden layer to the output layer, such that g(x) =

P 

 λ p ϕ x − c p

(3)

p=1

Generally, the nonlinear basis functions used include Gaussian functions, exponential functions, trigonometric functions, thin-plate spline functions, multiquadratic functions, inverse multi-quadratic functions, etc. It is generally believed that the specific form of nonlinear

has little effect on performance.  functions

x − c p can be represented by concentric circles In fact, each basis function ϕ

  on a plane as rh : x ∈ R n | x − c p = h . The points on each group could form a set of contours by the same values. We take the 28 evaluation indicators as the input. According to the normalization method of the previous indicators, the data after preprocessing (smooth, interpolation, trend surface, normalization, etc.) are used as training samples. During the training process the accuracy of the sample set obtained after training is about 70%. This accuracy is not satisfied. The main reason may be that the presence of some unimportant factors have been introduced into the analysis of oil and gas geochemical analysis, which affects the accuracy and speed of the analysis. It is also confirmed through the training process that adding the main factor at the input will increase the accuracy, and adding non-primary or unrelated factors will reduce the accuracy. According to the experience of geochemical anomaly analysis and the data we have, we can get it by increasing or decreasing the dimension of the input set. Since the Specific characteristics of the data of marine oil and gas geochemical exploration, the more accurate data may not must lead to a more accurate result. By using compositions and ratios of the light hydrocarbons, methane, ethane, propane, and butane, one may predict whether oil or gas is more likely to be discovered in the

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Table 2 Part test results of the importance of chemical factors No.

Factor excluded

Accuracy rate (%)

Time (s)

1

All factors

70

6.57

Importance

2

Benzene

60

4.52

High

3

toluene

56

4.38

High

4

Synchronous fluorescence 280 nm

64

3.60

Medium

5

Synchronous fluorescence 300 nm

53

4.45

High

…

…

…

…

…

25

Pyrolytic hydrocarbon isopentane

74

5.36

Medium

26

Pyrolytic hydrocarbon ethylene

64

5.95

Medium

27

Pyrolytic hydrocarbon propylene

71

4.34

Medium

Table 3 Comparison of classification accuracy for using different factors No.

Operations

Accuracy rate (%)

Time (s)

1

All data (including spatial position)

75

6.57

2

Excluding all low relation factors

74

2.70

3

Excluding all low and medium relation factors without spatial position factors

87

2.76

4

Excluding all low and medium relation factors (including spatial position)

89

2.93

prospect area. Table 2 shows part of the test results of the importance of the Chemical factors. Table 3 shows the results of the comparison of classification accuracy for using different factors. From Tables 2 and 3 we can get the following conclusions: (1) Some factors are very important for the classification results. After excluding those factors, the accuracy will be greatly reduced, such as benzene and toluene; (2) Some factors have little effect and may bring a certain degree of accuracy decline. In order to evaluate the effectiveness of the SVMs, we randomly take 80% out of the data as training data, and the remaining 20% as test data, and repeat the test for the factors. Excluding some low relation factors and the training and analysis are carried out again. The detailed training methods are as follows.

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Table 4 Part comparison results of classification accuracy for BPNN, and SVMs No.

Dataset

SVMs

BP NN

Well

Distance (km)

Reservoir

Test result

Reservoir

Test result

1

Gas

0.43

Gas

Y

Oil and gas

Y

2

Oil

0.05

Oil

Y

Oil and gas

Y

3

None

0.00

None

Y

None

Y

4

Oil

0.29

Oil

Y

Oil

Y

…

…

…

…

…

…

…

18

Gas

0.29

Gas

Y

None

N

19

Oil

0.12

Oil

Y

Oil and gas

Y

20

Gas

0.47

Oil and gas

Y

Gas

Y

21

Accuracy rate

90%

85%

4 Main Results In this section, classification and comparison result will be propose. To compare the performance of BPNN and SVMs, we first use BPNN and SVMs based on all the compounds to all these two modeling methods. The detailed description is listed in Table 4. The classification results based on SVMs are shown on Fig. 2. The classification results based on BPNN are similar to that of the SVMs methods. We can see that between the two classification analysis results from Table 4, it is clear that SVMs method has the best effect and performance. Because of artificial intervention (expert database), BP NN algorithm can be adjusted in time, and the experience of analysts is added, and the result is also satisfied. From the perspective of the analysis results, SVMs can directly form the clustering of spatial information, and directly spatially cluster the spatial points according to the evaluation results. Because BP NN does not have real spatial analysis function, it needs to rely on the contour method of geochemical anomaly and geophysical anomaly to perform auxiliary analysis to get the final abnormal region. Table 5 shows the comparison of the database queries speed on the spatial objects with different relationships, the execution time efficiency of different retrieval statements with the same function changes greatly. Spatial retrieval speed can reach nearly 2000 times per second at most, and even the minimum one can reach 160 times per second after transferring the polygon relations to MBR relations.

5 Conclusion This paper contributes to the theory of spatial data mining by a new two-step data optimization method in order to reduce the spatial query to relative distance query. First, we introduce MBR measures into the spatial domain; Then applying index optimization method to reduce the spatial query cost. complex polygon-to-polygon

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Fig. 2 The clustering results of Mud Volcano and Pockmark of Med & Nile

Table 5 Comparison results on spatial queries on different relationship of spatial objects

Objects

Time (s)

Point to point

0.062

Point to line

0.265

Line to line

1.201

Point to polygon

122

Line to polygon

190.7

Polygon to polygon

329.6

problems are reduced to a simple point-to-point problem with little precision loss. RBF based SVMs has been used to evaluate the oil and gas reservoirs. Comparison tests have been conducted to show that developing spatial data optimization has great effect on spatial data mining. Acknowledgements The authors would like to thank for the support by National Natural Science Foundation of China under the Grant 61104004, 61170258, U1806201 and 61671261.

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References 1. Zhang, S., Su, J., Wang, X., et al.: Geochemistry of Palaeozoic marine petroleum from the Tarim Basin, NW China: Part 3. Thermal cracking of liquid hydrocarbons and gas washing as the major mechanisms for deep gas condensate accumulations. Org. Geochem. 42(11), 1394–1410 (2011) 2. Aji, A., Wang, F., Vo, H., et al.: Hadoop-GIS: a high performance spatial data warehousing system over MapReduce. Proc. VLDB Endowment 6(11), p1009 (2013) 3. Jones, V.T.: Overview of Geochemical Exploration Technology. Exploration Technologies, Incorporated (1984) 4. Zou, C., Dong, D., Wang, S., et al.: Geological characteristics and resource potential of shale gas in China. Pet. Explor. Dev. 37(6), 641–653 (2010) 5. Eldawy, A., Mokbel, M.F.: Spatialhadoop: a MapReduce framework for spatial data. In 31st IEEE International Conference on Data Engineering, ICDE 2015, Seoul, South Korea, 13–17 April 2015, pp. 1352–1363 (2015) 6. Papadias, D., Theodoridis, Y.: Spatial relations, minimum bounding rectangles, and spatial data structures. Int. J. Geogr. Inf. Sci. 11(2), 111–138 (1997) 7. Samet, H.: The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading, MA (1990) 8. Zheng, W.S., Gong, S., Xiang, T.: Reidentification by relative distance comparison. IEEE Trans. Pattern Anal. Mach. Intell. 35(3), 653–668 (2013) 9. Wu, Y., Xiong, W., Jing, N., et al.: Spatial distance join query estimation without data access. In: 2011 IEEE International Conference on Computer Science and Automation Engineering, vol. 2, pp. 228–232. IEEE (2011) 10. Elsawy, A., Selim, M.M., Sobhy, M.: A hybridised feature selection approach in molecular classification using CSO and GA. Int. J. Comput. Appl. Technol. 59(2), 165–174 (2019) 11. Safar, M.H.: Shape analysis and retrieval of multimedia objects. In: Intelligent Virtual World: Technologies and Applications in Distributed Virtual Environment, pp. 21–51(2004) 12. Ben-Hur, A., Horn, D., Siegelmann, H.T., et al.: Support vector clustering. J. Mach. Learn. Res. 2, 125–137 (2001) 13. Tarkhaneh, O., Isazadeh, A., Khamnei, H.J.: A new hybrid strategy for data clustering using cuckoo search based on Mantegna levy distribution, PSO and k-means. Int. J. Comput. Appl. Technol. 58(2), 137–149 (2018) 14. Liu, J.: Radial Basis Function (RBF) Neural Network Control for Mechanical Systems: Design, Analysis and Matlab Simulation. Springer Science & Business Media (2013) 15. Xing, H., Sun, X., Wang, M., et al.: Application of EEMD and neural network in stress prediction of anchor bolt. Int. J. Comput. Appl. Technol. 57(2), 157–166 (2018)

Single Machine Due Date Assignment Scheduling with Deterioration and Learning Effect Weiwei Liu and Chong Jiang

Abstract In this study, we consider single machine due date assignment scheduling problems with deterioration and learning effect. Under the common (CON) due date assignment method (and the slack (SLK) due date assignment method) and positiondependent weights, we prove that the weighted sum of the absolute value in lateness and a due date minimization can be solved in polynomial time. Keywords Scheduling · Due-date assignment · Deterioration effect · Learning effect Scheduling problems with learning effect [1–5] or deterioration effect [6–12] have been widely studied in the literature. Recently, Wang [13, 14], Wang and Cheng [15], Wang and Guo [16] and Niu et al. [17] considered scheduling problems with deterioration effect and learning effect simultaneously. The example of deterioration and learning effect can be found in manufacturing environment [18]. Wang [13] considered following model: the actual processing time piA of job Ji is piA = (ai + bt)r α , where ai denotes the normal processing time of job Ji , b ≥ 0 is the common deterioration rate for all the jobs, α ≤ 0 is the common learning rate for all the jobs, and t is the starting time of the job Ji . Using the three-field  α  A notation scheme n [19], Wang [13] proved that the problem 1 pi = (ai + bt)r γ , γ ∈ {Cmax , i=1 Ci } can be solved in polynomial time, where Ci is the completiontime of job Ji , Cmax = max{Ci |i = 1, 2, . . . , n} is the makespan of all n time. Wang jobs, i=1 Ci is the total completion  A  [13] also proved that some p = (ai + bt)r α  γ (γ ∈ {n wi Ci , Lmax }) and special cases of the problems 1 i i=1   A   = (ahi + bt)r α  γ (γ ∈ {Cmax , ni=1 Ci , ni=1 wi Ci , Lmax }) can be solved in Fm phi W. Liu (B) School of Computer Science and Engineering, Northeastern University, Shenyang 110169, China e-mail: [email protected] School of Management and Journalism and Communications, Shenyang Sport University, Shenyang 110102, China C. Jiang Department of Sport and Health Science, Nanjing Sport Institute, Nanjing 210014, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_119

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polynomial time, where wi is the weight of job Ji , Lmax is the maximum lateness, Fm is the m-machine flow shop scheduling. Wang [14] considered the following model: the actual processing time piA of job Ji is piA = ai (β(t) + νr α ), where β(t) is a deterioration function on t, ν > 0. Wang   [14] proved that the problem 1 piA = ai (β(t) + νr α ) γ , γ ∈ {Cmax , ni=1 Ci , ni=1 Ci2 } can be solved in polynomial time. Wang [14] that some special cases of the prob also proved   lems 1 piA = ai (β(t) + νr α ) γ (γ ∈ { ni=1 wi Ci , Lmax }) can be solved in polynomial time. Wang and Cheng [15] considered the following model: the actual proA A α Wang and Cheng [15] proved that the cessing time  Api of job Ji is piα = ai (b + ct)r .   problem 1 pi = ai (b + ct)r γ , γ ∈ {Cmax , ni=1 Ci } can be solved in polynomial time.  Wang and Cheng  [15] also  proved that some special cases of the problems 1 piA = ai (b + ct)r α  γ (γ ∈ { ni=1 wi Ci , Lmax }) can be solved in polynomial time. On the other hand, the study of due date assignment had attracted many researchers’ attention (see [16, 20, 21]). The goal of the due-date assignment is to ensure that jobs are to be completed exactly at their due-dates, in order to minimize both earliness (mainly inventory) and tardiness costs and the cost of assigning due dates [20, 21]. Wang and Guo [16]  considered common due date assignment scheduling problem  1 piA = (ai + bt)r α  ni=1 (δ1 Ei + δ2 Ti + δ3 d ), where Ei = max{d − Ci , 0} (Ti = max{Ci − d , 0}) is the earliness (tardiness) of job Ji , d is the common due date for all jobs, δ1 ≥ 0, δ2 ≥ 0 and δ3 ≥ 0 is the per time unit penalties for earliness, due date respectively. They proved that the problem  tardiness and common  1 piA = (ai + bt)r α  ni=1 (δ1 Ei + δ2 Ti + δ3 d ) can be solved in polynomial time. Brucker [22] considered the single machine common (CON) due-date scheduling  problem 1 |CON | ni=1 i |Cπ − d | + 0 d , where d is the common due date, π denotes ith position, i (i = 0, 1, 2, . . . , n) is a position-dependent weight of the ith position in a sequence, and Lπ = Cπ − dπ is the lateness of the job Jπ . Brucker [22] proved that the problem 1 |CON | ni=1 i |Lπ | + 0 d can be solved in polynomial time. Liu et al. [23]considered the single machine slack (SLK) due-date scheduling problem 1 |SLK| ni=1 i |Cπ − dπ | + 0 q, where dπ = piA + q is the slackdue date, q is a a decision variable. Liu et al. [23] proved that the problem 1 |SLK| ni=1 i |Cπ − dπ | + 0 q can be solved in polynomial time. In this paper, the CON and SLK due-date assignment methods with positionn |CON |  |C dependent weights (i.e., the problems 1 i π − d | + 0 d and i=1  1 |SLK| ni=1 i |Cπ − dπ | + 0 q) are extended to the single machine scheduling problems with learning and deterioration  We  effectA simultaneously. CON , p = (ai + bt)r α  n show that the single machine scheduling problems 1 i i=1   i |Cπ − d | + 0 d and 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q remain can be solved in polynomial time.

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1 Problem Formulation In this study we assume that there are n jobs J = {J1 , J2 , . . . , Jn } to be processed on a single machine, and all the jobs are not interruptible and available at time zero. As in Wang [13], we assume that the actual processing time of job Ji is piA = (ai + bt)r α ,

(1)

where ai denotes the normal processing time of job Ji , b ≥ 0 (α ≤ 0) is the common deterioration rate (learning rate) for all the jobs. Let Ci be the complete time of job Ji , di be the due date of job Ji , and Li = Ci − di be the lateness of job Ji . In this paper, we study the CON model (i.e., di = d , i = 1, 2, . . . , n, where d is a decision variable) and the SLK model (i.e., di = piA + q, i = 1, 2, . . . , n, where q is a decision variable). Our goal is to determine a job sequence π and d (q) such that the following cost is minimized: n 

i |Cπ − dπ | + 0 d /q,

(2)

i=1

where d /q denotes d or q. Adopting the  nthree-field notation, the problems can beA A α p denoted as 1 CON, = (a + bt)r i i i=1 i |Cπ − d | + 0 d and 1|SLK, pi  = (ai + bt)r α | ni=1 i |Cπ − dπ | + 0 q, where 1 denotes a single machine, CON denotes the common due date assignment, and SLK denotes the slack due date assignment.

2 The  n  Problem α 1 CON, pA i=1 i |Cπ − d| + 0 d i = (ai + bt)r   In this section, we consider the problem 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d , and some lemmas are given. Lemma 1 For sequence π = [π, π, . . . , π], the completion time and actual processing time of job Jπ are Cπ =

j  h=1

aπ hα

j  l=h+1

(1 + bl α )

(3)

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and pπ

 j−1 j−1    α  α α α = aπ + bCπ j = aπ j + b aπ h (1 + bl ) j α , h=1

l=h+1

(4) respectively. Proof By the mathematical induction and Wang [13], the results can be easily obtained.     Lemma 2 For the 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d problem, an optimal schedule exists in which the machine is not idle between the processing of jobs and the first job starts at time zero. 

Proof Similar to the proof of Lemma 7.1 in Brucker [22].

For convenience, we introduce a dummy job J0 with the weight 0 and processing time p0 = 0 (the job J0 is always scheduled at time 0, i.e., π = 0), we have n 

i |Cπ − d | + 0 d =

n 

i=1

i |Cπ − d |.

i=0

Then an optimal schedule can be denoted by π = [π, π, . . . , π], where π = 0.   Lemma 3 For the 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d probη A , lem and a given sequence π = [π, π, . . . , π], d = Cπ = i=0 pπ where η is a median for the sequence 0 , 1 , . . . , n , η−1  j=0

j ≤

n  j=η

j and

η 

n 

j ≥

j=0

j .

(5)

j=η+1

Proof From the proof of Lemma 7.2 in Brucker [22], note that the value η is independent of the schedule and times of jobs. Hence, it is also  the actual processing  optimal for the problem 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d .  Lemma π, . . . , π], the objective function of  4 For sequence π = [π,  the 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d can be written as: n  i=1

i |Cπ − d | + 0 d =

n  i=1

Φi aπ ,

(6)

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where Φ1 = θ1 1α + bθ2 1α 2α + bθ3 1α (1 + b2α )3α + · · · + bθn 1α nα

n−1 

(1 + bl α ),

l=2

Φ2 = θ2 2α + bθ3 2α 3α + bθ4 2α (1 + b3α )4α + · · · + bθn 2α nα

n−1 

(1 + bl α ),

l=3

Φ3 = θ3 3α + bθ4 3α 4α + bθ5 3α (1 + b4α )5α + · · · + bθn 3α nα

n−1 

(1 + bl α ),

l=4

... Φn−1 = θn−1 (n − 1)α + bθn (n − 1)α nα , Φn = θn nα , ⎧ 0 , ⎪ ⎪ ⎪ ⎪ 0 + 1 , ⎪ ⎪ ⎪ ⎪... ⎪ ⎪ ⎨ i−1 v , θi = v=0 n v , ⎪ ⎪ v=η+1 ⎪ n ⎪ ⎪ v=η+2 v , ⎪ ⎪ ⎪ ⎪ ... ⎪ ⎩ n ,

and

(7)

for i = 1, for i = 2, for i = 3, . . . , η, for i = η + 1, for i = η + 2,

(8)

for i = n.

Proof Under the condition that a sequence π = [π, π, . . . , π] is given and d = Cπ , from Lemmas 1, 2 and 3, we have n 

i |Cπ − d | + 0 d

i=1

= 0 Cπ +

η  i=1

=

η  i=0

i

η 

=



A pπ

 h−1  i=0

h=1

=

n  i=1

A θi pπ

ωi (Cπ − Cπ )

i=η+1

A pπ +

h=i+1

η

n 

i (Cπ − Cπ ) +



n 

i

i=η+1

i +

n  h=η+1

i  h=k+1

A pπ

A pπ

 n  i=h

i

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= =

n  i=1 n 

 α

θi aπ j + b

 j−1  h=1

α

aπ h

j−1 

α

(1 + bl ) j α

l=h+1

Φi aπ ,

i=1

where Φi (i = 1, 2, . . . , n) are given by equation (7).   Lemma 5 (Hardy et al. [24]) The sum of products nj=1 xj yj is minimized if sequence x1 , x2 , . . . , xn is ordered nondecreasingly and sequence y1 , y2 , . . . , yn is ordered nonincreasingly or vice versa, and it is maximized if the sequences are ordered in the same way.  From Lemma 4, we have that the term ni=1 Φi aπ (see (6)) can be  minimized by Lemma 5 (let xi = Φi , yi = ai ), hence the 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d problem can be solved by the following algorithm: Algorithm 1 Step 1. By Lemma 3, calculate η. Step 2. Calculate xi = Φi and yi = ai by Eqs. (7) and (8). Step 3. From Lemma η 5,Aan optimal job sequence can be determined. . Step 4. Set d = i=0 pπ   Theorem 1 Algorithm 1 solves the 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d problem in O(n log n) time. Proof The correctness of Algorithm 1 follows from the Lemmas 1–5. Steps 1, 2, and 4 require linear time, Step 3 requires O(n log n) time (Lemma 5, Hardy et al. [24]). Thus the overall computational complexity of Algorithm 1 is O(n log n).  The following example is used to illustrate the optimization algorithm (see Algo rithm 1) for the problem 1 CON , piA = (ai + bt)r α  ni=1 i |Cπ − d | + 0 d . Example 1 Consider the CON scheduling model with the position-dependent weights, where n = 7, b = 0.05, α = −0.25. The position-dependent weights are 0 = 3, 1 = 1, 2 = 9, 3 = 10, 4 = 7, 5 = 2, 6 = 4, 7 = 12, and normal processing times are a1 = 13, a2 = 3, a3 = 14, a4 = 17, a5 = 5, a6 = 10, a7 = 2. From Algorithm 1, we have 0 + 1 + 2 + 3 = 23 < 4 + 5 + 6 + 7 = 25, 0 + 1 + 2 + 3 + 4 = 30 > 5 + 6 + 7 = 18, hence η = 4. The values θi and Φi are θ1 = 3, θ2 = 4, θ3 = 13, θ4 = 23, θ5 = 18, θ6 = 16, θ7 = 12, Φ1 = 6.268521, Φ2 = 5.865461, Φ3 = 11.69428, Φ4 = 17.34073, Φ5 = the optimal schedule is π ∗ = 12.63372, Φ6 = 10.45878, Φ7 = 7.377458. Hence  n [J3 , J4 , J5 , J7 , J2 , J6 , J1 ], and the optimal cost i=1 i |Cπ − d | + 0 d = 519.0209.

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3 The  n  Problem α = (a + bt)r 1 SLK, pA i i=1 i |Cπ − dπ | + 0 q i   In this section, we consider the problem 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q. Similar to Sect. 3 and Liu et al. [23], we have the following results:   Lemma 6 For the 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q problem, an optimal schedule exists in which the machine is not idle between the processing of jobs and the first job starts at time zero.   Lemma 7 For the 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q problem and a given sequence π = [π, π, . . . , π], q = Cπ =  ϑ i=0

A pπ , where ϑ is a median for the sequence 0 , 1 , . . . , n , ϑ  j=0

j ≤

n  j=ϑ+1

j and

ϑ+1 

j ≥

j=0

n 

j .

(9)

j=ϑ+2

Lemma [π, π, . . . , π], the objective function of  8 For sequence π =  the 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q can be written as: n 

i |Cπ − dπ | + 0 q =

i=1

n 

Ψi aπ ,

(10)

i=1

where Ψ1 = κ1 1α + bκ2 1α 2α + bκ3 1α (1 + b2α )3α + · · · + bκn 1α nα

n−1 

(1 + bl α ),

l=2

Ψ2 = κ2 2α + bκ3 2α 3α + bκ4 2α (1 + b3α )4α + · · · + bκn 2α nα

n−1 

(1 + bl α ),

l=3

Ψ3 = κ3 3α + bκ4 3α 4α + bκ5 3α (1 + b4α )5α + · · · + bκn 3α nα ... Ψn−1 = κn−1 (n − 1)α + bκn (n − 1)α nα , Ψn = κn nα ,

n−1 

(1 + bl α ),

l=4

(11)

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⎧ 0 + 1 , ⎪ ⎪ ⎪ ⎪ 0 + 1 + 3 , ⎪ ⎪ ⎪ ⎪ ... ⎪ ⎪  ⎪ ⎪ ⎨ iv=0 v , κi = nv=ϑ+2 v , ⎪ n ⎪ ⎪ v=ϑ+3 v , ⎪ ⎪ ⎪ ⎪... ⎪ ⎪ ⎪ ⎪ n , ⎪ ⎩ 0,

for i = 1, for i = 2, for i = 3, . . . , ϑ, for i = ϑ + 1 for i = ϑ + 2

(12)

for i = n − 1 for i = n.

  A α  nSimilar to Sect. 3, from Lemmas 5 to 8, the problem 1 SLK, pi = (ai + bt)r i=1 i |Cπ − dπ | + 0 q can be solved by the following algorithm: Algorithm 2 Step 1. By Lemma 7, calculate ϑ. Step 2. Calculate xi = Ψi and yi = ai by Eqs. (11) and (12). Step 3. From Lemma  5,A an optimal job sequence can be determined. . Step 4. Set q = ϑi=0 pπ   Theorem 2 Algorithm 2 solves the 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q problem in O(n log n) time. The following example is used to illustrate the optimization algorithm (see  Algorithm 2) for the problem 1 SLK, piA = (ai + bt)r α  ni=1 i |Cπ − dπ | + 0 q. Example 2 Consider the SLK model with the position-dependent weights, and the same data in Example 1 is used. From Algorithm 2, we have 0 + 1 + 2 + 3 = 23 < 4 + 5 + 6 + 7 = 25, 0 + 1 + 2 + 3 + 4 = 30 > 5 + 6 + 7 = 18, hence ϑ = 3. The values κi and Ψi are κ1 = 4, κ2 = 13, κ3 = 23, κ4 = 18, κ5 = 16, κ6 = 12, κ7 = 0, Ψ1 = 7.188283, Ψ2 = 13.06342, Ψ3 = 18.69233, Ψ4 = 13.38636, Ψ5 = 10.95622, Ψ6 = 7.667317, Ψ7 = 0.  Hence an optimal sequence is π ∗ = [J3 , J5 , J7 , J2 , J6 , J1 , J4 ], and the optimal cost ni=1 i |Cπ − dπ | + 0 q = 452.7341.

4 Conclusions In this study, we considered the model combining learning effect, deterioration effect, position-dependent weights and due date assignment. The objective function is to minimize a cost function containing the absolute value  in lateness and due date assign ment cost, i.e., ni=1 i |Cπ − d | + 0 d and ni=1 i |Cπ − dπ | + 0 q. For CON and SLK due date assignment, we proved some properties, and solved these two problems with the optimal solution in polynomial time O(n log n) respectively. Funding This research was supported by the Liaoning Province Universities and Colleges Basic Scientific Research Project of Youth Project (Grant No. LQN2017ST04).

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References 1. Biskup, D.: A state-of-the-art review on scheduling with learning effects. Eur. J. Oper. Res. 188, 315–329 (2008) 2. Lu, Y.-Y., Li, G., Wu, Y.-B., Ji, P.: Optimal due-date assignment problem with learning effect and resource-dependent processing times. Optim. Lett. 8, 113–127 (2014) 3. Wang, J.-B., Liu, M., Yin, N., Ji, P.: Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects. J. Ind. Manage. Optim. 13(2), 1025–1039 (2017) 4. Lu, Y.-Y., Wang, J.-B., Ji, P., He, H.: A note on resource allocation scheduling with group technology and learning effects on a single machine. Eng. Optim. 49(9), 1621–1632 (2017) 5. Azzouz, A., Ennigrou, M., Said, L.B.: Scheduling problems under learning effects: classification and cartography. Int. J. Prod. Res. 56(4), 1642–1661 (2018) 6. Gawiejnowicz, S.: Time-Dependent Scheduling. Springer, Berlin (2008) 7. Wang, J.-B., Wang, M.-Z.: Minimizing makespan in three-machine flow shops with deteriorating jobs. Comput. Oper. Res. 40(2), 547–557 (2013) 8. Wang, J.-B., Wang, J.-J.: Single machine group scheduling with time dependent processing times and ready times. Inf. Sci. 275(1), 226–231 (2014) 9. Wang, J.-B., Wang, J.-J.: Single-machine scheduling problems with precedence constraints and simple linear deterioration. Appl. Math. Model. 39(3–4), 1172–1182 (2015) 10. Oron, D.: Scheduling controllable processing time jobs in a deteriorating environment. J. Oper. Res. Soc. 64, 49–56 (2014) 11. Li, L., Wang, J.-J.: Scheduling jobs with deterioration effect and controllable processing time. Neural Comput. Appl. 29(11), 1163–1170 (2018) 12. Wang, J.-B., Li, L.: Machine scheduling with deteriorating jobs and modifying maintenance activities. Comput. J. 61(1), 47–53 (2018) 13. Wang, J.-B.: A note on scheduling problems with learning effect and deteriorating jobs. Int. J. Syst. Sci. 37(12), 827–833 (2006) 14. Wang, J.-B.: Single-machine scheduling problems with the effects of learning and deterioration. Omega Int. J. Manage. Sci. 35(4), 397–402 (2007) 15. Wang, J.-B., Cheng, T.C.E.: Scheduling problems with the effects of deterioration and learning. Asia Pac. J. Oper. Res. 24(2), 245–261 (2007) 16. Wang, J.-B., Guo, Q.: A due-date assignment problem with learning effect and deteriorating jobs. Appl. Math. Model. 34, 309–313 (2010) 17. Niu, Y.-P., Wang, J.-B., Yin, N.: Scheduling problems with effects of deterioration and truncated job-dependent learning. J. Appl. Math. Comput. 47, 315–325 (2015) 18. Nembhard, D.A., Osothsilp, N.: Task complexity effects on between-individual learning/forgetting variability. Int. J. Ind. Ergon. 29, 297–306 (2002) 19. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979) 20. Gordon, V.S., Proth, J.M., Chu, C.B.: A survey of the state of-the-art of common due date assignment and scheduling research. Eur. J. Oper. Res. 139, 1–25 (2002) 21. Gordon, V.S., Proth, J.M., Chu, C.B.: Due date assignment and scheduling: SLK, TWK and other due date assignment models. Prod. Plann. Control 13, 117–132 (2002) 22. Brucker, P.: Scheduling Algorithms, 3rd edn. Springer, Berlin (2001) 23. Liu, W., Hu, X., Wang, X.-Y.: Single machine scheduling with slack due dates assignment. Eng. Optim. 49, 709–717 (2017) 24. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1967)

EM Algorithm-Based Combined Distribution of Mold on the Mold Table Fangjun Luan, Shuai Wang, Zhonghua Han and Hongbin Cui

Abstract In order to solve the problem of combined Distribution of molds on the mold table in the production line of Prefabricated component, this paper proposes a method that combined improved Bottom-Left (BL) Placement Policy with the improved Electromagnetism-like Mechanism (EM) algorithm to solve the problem. Firstly, the mathematical model of the combined distribution of the mold on the mold table is established. The improved EM algorithm is used to optimize the order of the Prefabricated components. Secondly, according to the size of mold and mold table, the molds are distributed to the mold tables. An improved BL Placement Policy is proposed to determine the angle and position of molds on the mold tables. Finally, through the simulation test of the actual production enterprise’s instance data, the effectiveness of the proposed new method is verified to solve the problem of combined distribution problem of mold on the mold table. Keywords Prefabricated component · Mold table · Combined distribution · EM

1 Introduction In the building Prefabricated component [1] production line, the problem of the combined distribution of the mold on the mold table that is called the computational “combined explosion” [2] belongs to the classical nondeterministic polynomial problem [3]. It can be described as a Prefabricated component in the building production line, when the production is on line, it is produced and processed by selecting different mold combinations on mold tables. Each Prefabricated component is produced through the corresponding mold, and the mold is fixed on the mold table, and the mold table is carried as a transport tool. The mold completes the entire process of Prefabricated component production. If the mold cannot be reasonably distributed to the mold table according to the size of the mold, the space utilization of the mold table is low, and the reuse rate of the mold table is high, which seriously restricts the F. Luan · S. Wang (B) · Z. Han · H. Cui Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_120

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production capacity of the enterprise. Therefore, exploring how to solve the problem of the distribution of molds on the mold table in the building Prefabricated component production line has important engineering value for improving the production capacity of enterprises. At present, domestic and foreign scholars have studied various problems in building Prefabricated component enterprises. Wang et al. [4] studied the arrangement of molds in the production process of concrete Prefabricated components, and used genetic algorithm to optimize the arrangement of molds on the mold table in the production of Prefabricated components. Zhang et al. [5] studied the construction process, method and quality assurance measures of small Prefabricated components, and expounded the existing problems and the solutions to be taken. Liu et al. [6] established a production scheduling optimization model for precast concrete members by using mixed integer linear programming algorithm. Through the analysis of related research literatures in recent years, the research on the Prefabricated components has attracted more and more scholars’ attention, but they still focus on the research on the production control and process flow of Prefabricated components. There are still few studies on the distribution problem of mold on the mold table. At present, there are few researches on the application of BL Placement Policy [7] in Prefabricated components. The application of EM algorithm [8] to scheduling optimization is relatively rare. Although EM algorithm calculation has more powerful searching ability to deal with complex problems, the local search of standard EM algorithm random adopts linear search, which is easy to fall into local extremum. This paper uses simulated annealing [9] to modify the electromagnetic algorithm. By combining the improved electromagnetism-like mechanism algorithm based on simulated annealing (SAEM) [10] with the improved BL Placement Policy, the mold is distributed to the mold table, then the superiority of the algorithm is verified.

2 Mathematical Model Description of the Combined Distribution of Mold on the Mold Table [11] 2.1 Problem Description The production workshop of Prefabricated components is a semi-automatic production line. The main types of Prefabricated components are laminated plates. The process includes cleaning operations, fuel injection operations, side mold installation, steel installation, embedded components installation, pouring vibration, and static stop, brushing operation, palletizing operation, steaming operation, demolding, lifting, finished product [12]. The entire process will be carried out on a fixed-space mold table that moves sequentially on the line. Assuming that there are unknown m mold tables that is the same as each other, and the length of the mold table is W and the width is H. The production task requires the production of n different Prefabricated components, each of which corresponds to a separate mold. By adjusting the

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processing sequence of the corresponding components of the mold and the position of the mold on the mold table, the space utilization of the mold table is maximized.

2.2 Model Parameters m W H n Pi wi hi f C ri Si

the number of mold table; length of the mold table; width of the mold table; the number of Prefabricated components to be processed; mold Pi , i ∈ {1, 2, . . . , n}; length of the i mold; width of the i mold; space utilization of the mold table; process spacing between mold and mold; mold placement direction, i ∈ {0, 1}; area of the i mold Pi .

2.3 Basic Assumptions and Constraints Basic Assumptions. The actual mold table plane is simulated as a two-dimensional coordinate image, the x-axis is set to a fixed length W, which represents the length of the mold table, and the y-axis is set to a fixed length H, which represents the width of the mold table, and the two-dimensional coordinate image is set. The lower left corner is the origin (0, 0), the upper left corner of the image is (0, H), the lower right corner is (W,0), and the upper right corner is (W, H). The size of the rectangular mold Pi is known, in order to meet the production process claims, that is, to ensure at least a certain process interval C between the mold and the mold, the upper left corner of the mold Pi is xi1 − C, yi1 + C, if the mold does not rotate, the coordinates of its lower right corner are xi2 , yi2 = (xi1 + wi + C, yi1 − h i + C), and if the mold is rotated by 90°, the width and height are exchanged, and the coordinates of the lower right corner are xi2 , yi2 = (xi1 + h i + C, yi1 − wi + C), Use the variable ri to indicate whether the mold Pi is rotated by 90°, ri = 0 means no rotation, and ri = 1 means rotation, then the following equation [12–14]: 

xi2 = xi1 + (1 − ri )wi + ri h i + C yi2 = yi1 − (1 − ri )h i − ri wi + C

(1)

The position and direction of the mold Pi can be determined by upper left corner coordinate, length and width wi, h i and whether the variable ri is rotated.

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Constraints. For the combination assignment of the mold to the mold table, the following four constraints [13] are: (1) Meet the process requirements in the production process of Prefabricated components, and there is a certain process interval between each mold; (2) The distribution between any two molds on the mold table does not overlap each other; (3) The molds of the components are all located inside the mold base; (4) The molds need to be placed orthogonally and cannot be placed at an angle. The mathematical constraints on the combination of the molds on the mold tables are combined, and the mathematical model of the combined distribution: ⎧ x j1 ≥ xi1 + (1 ⎪ ⎪  i + ri h i + 3C  − ri )w ⎪ ⎪ ⎪ ≥ x + 1 − r x i1 j1 j w j + r j h j + C ⎪  ⎪ ⎪ ⎪ ≤ y − 1 − r y i1 j1 j h j − rjwj + C ⎪ ⎪ ⎨ y j1 ≤ yi1 − (1 − ri )h i − ri wi + C ⎪ x i1 ≥ C ⎪ ⎪ ⎪ ⎪ x ⎪ i1 + (1 − ri )wi + ri h i + 2C ≤ W ⎪ ⎪ ⎪ yi1 ≤ H − C ⎪ ⎪ ⎩ yi1 − (1 − ri )h i − ri wi + 2C ≥ 0

(2)

2.4 Optimization Target In the process of the mold assembly being distributed on the mold table, the optimization target is the space utilization of the mold table, that is, the ratio of the sum of the mold table areas of all the arrays and the area of the mold table used: n

f =

N Si I =1 wi · h i = W × H ×m W × H ×m i=1

(3)

3 Positioning Algorithm of Mold on Mold Table 3.1 BL Placement Policy The BL Placement Policy was first applied to Nesting Problems. The goal is to find a higher material utilization rate in the material cutting process. The basic principle

EM Algorithm-Based Combined Distribution of Mold …

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is to move the component down to the left as much as possible without interference between other components of the plate until it is blocked by other components or plate boundaries.

3.2 Positioning Algorithm Based on Improved BL Placement Policy Mold on Mold Table [14] Algorithm Description. The mold is placed on the mold table, and there are two ways of horizontal and vertical placement. Based on the BL Placement Policy, a new positioning algorithm of the mold on the mold table is proposed: the actual mold table plane is simulated as a two-dimensional coordinate image. In the process of placing the mold on the mold table, firstly, the first placement angle of the mold placed on the unit mold table is judged, and the judgment result determines the order and position of the next mold, If the first mold is placed horizontally: (1) The position where the second mold is selected is first placed on the right side of the first mold. If the right area does not satisfy the placement condition, the upper side of the first mold is selected for placement. If the upper area does not satisfy the placement condition, then select the next mold table to place. (2) If the second mold satisfies the right side of the first mold, the third mold is placed at the upper side of the first mold. If the upper area does not meet the placement conditions, select the next mold table; If the first mold is placed vertically: (1) The position where the second mold is selected is first placed on the right side of the first mold. If the right area does not meet the placement conditions, the next mold table is selected for placement. (2) If the second mold satisfies the condition placed in the right area of the first mold, the third mold is placed at the upper side of the second mold. If the upper area does not satisfy the placement condition, then select the next mold table to place. Algorithm Step. Step 1: Judging the placement angle of the mold Pi (i = 1, 2, 3, . . . , n) on the mold table m j ( j = 1, 2, 3, . . . , m) (a = 1, indicating that the mold is placed laterally; a = 0, indicating that the mold is placed vertically. a = 1, calculate x0 = wi + C, y0 = h i + C, i = i + 1, go to Step 2; a = 0, exchange wi and h i values, calculate x0 = wi + C, y0 = h i + C, i = i + 1, go to Step 4. Step 2: Place the mold Pi (i = 2, 3, . . . , n) on the right side of the mold on the mold table (y-axis alignment). If the conditions wi ≤ W − x0 and h i ≤ H meet, update x0 , y0 , i = i + 1, go to Step 6. If the conditions wi ≤ W − x0 and h i ≤ H don’t meet, go to Step 3. Step 3: Place Pi (i = 2, 3, . . . , n) on the upper side of the mold on the mold table (xaxis alignment), if the conditions wi ≤ W and h i ≤ H −y0 meet, i = i +1, j = j +1, go to Step 1. If the conditions wi ≤ W and h i ≤ H − y0 don’t meet, j = j + 1, then go to Step 1. Step 4: Place the mold Pi (i = 2, 3, . . . , n) on the right side of the mold on the mold table (y-axis alignment). If the conditions wi ≤ W − x0 and h i ≤ H meet, update

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x0 , y0 , i = i + 1, go to Step 5. If the conditions wi ≤ W − x0 and h i ≤ H don’t meet, j = j + 1, then go to Step 1. Step 5: Place the mold Pi (i = 2, 3, . . . , n) on the upper right side of the mold on the mold table (x0 alignment), if conditions h i ≤ H − y0 , i = i + 1, j = j + 1 meet, then go to Step 1, if the condition wi ≤ W − x0 and h i ≤ H − y0 don’t meet, j = j + 1, then go to Step 1. Step 6: Place the mold Pi (i = 2, 3, . . . , n) on the upper left side of the mold on the mold table (x, y0 axis alignment), if conditions wi ≤ W and h i ≤ H − y0 meet, i = i + 1, j = j + 1, then go to Step 1, if conditions wi ≤ W and h i ≤ H − y0 don’t meet, j = j + 1, then go to Step 1.

4 Research on Global Optimization Algorithm 4.1 Electromagnetism-Like Mechanism Algorithm The EM algorithm is a random population-based heuristic global optimization algorithm. The optimization idea of EM algorithm is to treat each solution in the feasible domain as a charged particle. The amount of charge of each charged particle is determined by its corresponding objective function value, the degree of attraction or repulsion of the charged particles to other charged particles in the population is determined by the amount of charge. The better the objective function value, the larger the charge amount, and the greater the attraction or repulsive force. Then the next moving direction of each charged particle is determined by the attraction or repulsive force, so that each particle in the population moves toward the region of the optimal solution particle, and finally the global optimal solution is obtained. EM algorithm consists of four steps: initialization, local search, calculation of resultant force, and particle movement.

4.2 Improved EM Algorithm EM algorithm improvement. In the local search process, the standard EM algorithm adopts a random linear search method, which makes the search direction of the algorithm fixed, which makes the search range of the standard EM algorithm small and it’s easy to fall into local extremum and not to jump out, and finally the algorithm cannot find the global optimal solution. This paper introduces the idea of simulated annealing to solve the problem that the standard EM algorithm has a small search range and is easy to fall into local extremes and cannot jump out. In the local search process of the standard EM algorithm, combined with the annealing operation of the simulated annealing algorithm, the solution with poor target fitness is accepted with a certain probability, thereby

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expanding the local search range of the standard EM algorithm, increasing the diversity of the particles, and improving the algorithm flexibility ratio, which makes the search direction of the algorithm change in the random search process, which can make the standard EM algorithm jump out of the local extremum in the local iterative search process, and finally achieve the purpose of increasing the accuracy of the algorithm and searching for the global optimal solution. SAEM algorithm steps. Step 1: Initializing algorithm parameter γ and initial annealing temperature T0 . Step 2: Calculate the maximum step size for each particle to move in each dimension based on the parameter γ . Step 3: Local search for each particle based on the calculated maximum moving step size. Step 4: If the fitness value of the obtained new particle is smaller than the fitness value of the original particle, go to Step 7, otherwise go to Step 5. Step 5: Calculate the difference between the fitness of the new feasible solution and the fitness of the previously   feasible solution. According to the probability  value  P = exp − f (X  ) − f (X ) /T0 > random[0, 1] judge whether to accept the new feasible solution, and random[0, 1] is the random number between [0, 1]. Step 6: If the equilibrium state of temperature T0 is reached, the function Tk+1 = C Tk is updated according to the temperature, and annealing is started to lower the temperature, and C ∈ [0, 1]. Step 7: Stop the local search process until the number of times is equal to Lsiter or new particle can be searched. Recalculate the fitness values of all particles in the new population and find the optimal particle as xbest . Step 8: Determine whether the algorithm meets the end criterion, if it meets, terminate the algorithm process, otherwise go to Step 3.

5 Simulation 5.1 Constructing Simulation Data To take a certain enterprise as an example: a batch of laminated plates is produced, and a total of 4 projects are produced at the same time, a total of 39 pieces, as shown in Table 1. The size of the mold table is 400 (cm) * 600 (cm). The unit length of the Prefabricated component is cm. The initial population size using the optimization algorithm is NP = 30, and M is the maximum number of iterations for the global search, M = 300. L is the maximum number of iterations for local search, L = 5, δ is the local search parameter, δ[0, 1].

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Table 1 Production list of Prefabricated components Number

Length

Width

Quantity

Number

Length

Width

Quantity

1

325

182

2

12

285

207

2

2

275

182

2

13

304

164

2

3

302

188

2

14

286

184

2

4

295

186

2

15

291

216

2

5

330

180

4

16

296

177

1

6

282

172

2

17

274

215

3

7

290

156

2

18

294

166

1

8

293

163

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5.2 Optimize Simulation Results and Analysis The data in Table 2 is the optimization results of the above 39 processing components, no optimization algorithm, using the EM algorithm and using the SAEM algorithm, and m and f respectively represent the number of used mold tables and the space utilization of the mold table. It can be analyzed from Table 2 that the optimization goal of SAEM algorithm is better than EM algorithm, and EM algorithm is better than non-optimization algorithm. The SAEM algorithm can receive solutions with poor fitness of the objective function with a certain probability in the updating process of feasible solution. This expands the search scope of the SAEM algorithm, increases the diversity of individuals, improves the ability and accuracy of the algorithm to search for optimal solutions, and thus obtains better target values. As shown in Fig. 1, it can be seen from the simulation curves of 39 Prefabricated components by EM algorithm and SAEM algorithm that the EM algorithm stops evolution around the 40th generation, and the objective function f stops at 64.62%. The SAEM algorithm immersed in local extremum in the 120th generation, and the fitness was 69.23%. Until the 260th generation, the SAEM algorithm re-evolved and jumped out of the local extremum, and finally got a better objective function of 74.56%. As shown in Fig. 2, the mold table is distributed in the no-optimization algorithm and the SAEM algorithm. The number of mold tables used in the no-optimization Table 2 Comparison results before and after using the optimization algorithm

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Fig. 2 No optimization algorithm (a) and using the SAEM algorithm (b) mold table diagram

algorithm is 18, and the number of mold tables used after optimization using the SAEM algorithm is 13, greatly reducing the number of the mold table.

6 Conclusion In this paper, the problem of the combined distribution of molds on the mold tables in the prefabricated building production line is taken as the research object, combined with the characteristics of the Prefabricated components, a new way that combines

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improved BL positioning algorithm with an improved electromagnetic algorithm is proposed to optimize the positioning and sorting. The experiment shows that the optimized method significantly reduces the number of mold tables and improves the space utilization of mold table, the research results of this problem can provide practical guidance and help for the production process of Prefabricated components enterprises, and improve the utilization of existing resources and the production capacity of enterprises. Acknowledgements Shenyang Science and Technology Bureau Double Hundred Project “Transformation of Digital Factory Technology in Lean Production Mode in Prefabricated Building Prefabricated component Manufacturing Enterprises” (Z18-5-015) January 2018–December 2019.

References 1. Chen, F., Ren, C., Lu, Z., Guo, S., Wang, Z.: Application of ERP and MES system in intelligent manufacturing of prefabricated building components. J. Concrete World, 103, 39–41 (2018) 2. Wu, T., Yang, J., Liu, Z., Jiang, X.: Optimization of two-dimensional layout problem based on improved discrete firefly algorithm. J. Chin. Sci. Pap. 13(2), 153–156 (2018) 3. Song, P., Cui, Y., Chen, X., Yang, Y.: Discrete particle swarm optimization algorithm for solving rectangular components layout problem. J. Mech. Eng. 1, 86–87 (2007) 4. Wang, Z., Chen, X.: Optimization of die arrangement in the production of preformed panels based on genetic algorithm. J. Eng. Manage. 33(1), 45–49 (2019) 5. Zhang, L., Wang, Y.: Construction and quality control of small concrete precast members of high speed railway. J. Sichuan Hydropower 37(1), 99–101 (2018) 6. Liu, M., et al.: Research on production scheduling optimization model of precast concrete members based on MILP algorithm. J. Eng. Manage. 32(6), 121–126 (2018) 7. Healy, P., Creavin, M., Kuusik, A.: An optimal algorithm for rectangle placement. Oper. Res. 24, 73–80 (1999) 8. Jiang, Y., Pan, F.: Improved heuristic algorithm for modern industrial production scheduling. J. IJMIC 30(4), 284–292 (2018) 9. Han, Z., Sun, Y., Lin, S.: Research on electromagnetic algorithms for solving LBFFSP. J. Control Eng. 24(8), 1–8 (2015) 10. Liu, A., Yang, Y., Li, F., Xing, Q., Lu, H., Zhang, Y.: Chaotic simulated annealing particle swarm optimization research and its application. J. Zhejiang Univ. (Eng. Sci.) 47(10), 1722– 1730 (2013) 11. Zhang, J., Chen, J., Zhang, H.: Job-shop schedule modelling and parents-crossover evolutionary optimization for integrated production schedules. J. IJCAT 58(4), 288–295 (2018) 12. Li, Y.: Discussion on the production process of fabricated building components. J. Concr. Cem. Prod. 12, 65–68 (2017) 13. Liu, H., He, Y.: Two-dimensional irregular shape layout algorithm based on center NFP. J. China Mech. Eng. 18(6), 723–731 (2007) 14. Bilel, N., Mohamed, N.: A novel multi-criteria self-organising migrating algorithm for engineering problems. IJCAT 57(3), 219–227 (2018)

Multi-rotor UAV Track Planning Based on Improved Artificial Potential Field Liying Yang, Kaiyuan Bi, Yuqing He and Zhonghua Han

Abstract An improved artificial potential field (APF) method is proposed to solve the multi-rotor UAV flight path planning problem in this paper. Firstly, the grid method is adopted to build the environment model. After that, the A* algorithm is for generating the global path, and performs optimization for the node on the global path. Finally, the potential function of the traditional APF method is improved that an attraction force made by the global path to the multi-rotor drone is introduced, so the UAV can move guided by both obstacle and target together. Simulation results show that the proposed method can effectively correct the defects and deficiencies of the traditional APF method. The trajectory planning quality of multi-rotor UAVs in static and dynamic environments can be improved with the combination of the global advantages of A* algorithm and the APF method based real-time obstacle avoidance capability. Keywords Track planning · Grid model · A* algorithm · Artificial potential field

L. Yang · K. Bi (B) · Y. He State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China e-mail: [email protected] L. Yang e-mail: [email protected] Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, China K. Bi · Z. Han Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, China Z. Han Department of Digital Factory, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_121

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1 Introduction As a typical autonomous capability of mobile robots, track planning has always been the focus of research in the field of multi-rotor drones. Effective track planning is the premise of ensuring the precise operation of multi-rotor UAVs. It has important theoretical significance and practical application value in the research field of multirotor UAVs [1, 2]. Comprehensively analyze the research results in the field of robot path planning at home and abroad. The methods commonly used in track planning include A* algorithm, artificial potential field method, ant colony algorithm, genetic algorithm, particle swarm algorithm [3–5] etc. Among them, A* algorithm, as the most widely used heuristic search algorithm, has better planning ability in static global planning, but it has weak planning ability in high complexity space or dynamic space. The artificial potential field method is fast and easy to implement, and has good real-time planning and obstacle avoidance capabilities. However, due to the lack of global information, there are defects that are likely to cause local minimum points and unreachable target points. Biointelligence optimization algorithms such as ant colony algorithm (ACA), genetic algorithm (GA) and particle swarm optimization (PSO) algorithm can balance the solution time and solution quality, but it is easy to fall into local optimum in the planning process, and the real-time performance is relatively low. Based on the comprehensive consideration of the accuracy, real-time and effectiveness of multi-rotor UAV flight path planning, this paper proposes an improved APF method. The method first considers the multi-rotor UAV high-definition flight environment as a two-dimensional environment and models it using the grid method. Then use the A* algorithm to generate an accurate global path. Node optimization is performed on the global path to prepare for the improved artificial potential field method. Under the premise that the global path is known, the potential function of the traditional APF method is improved, and the global path information is introduced, which can make up for the deficiency of the traditional APF method [6–8]. Simulation give the results that the improved APF method can handle the multi-rotor UAV online track planning problem, and solves the local minimum point defect in the traditional APF method. The algorithm has high accuracy and real-time performance, and is effective in both static and external dynamic interference environments.

2 Global Path Generation 2.1 Grid Method Modeling The grid method can divide the finite environment space into equal-sized twodimensional or three-dimensional grids, and uses the grid center as a unit of calculation and assigns coordinates [9]. The grid with obstacle is represented by a dark

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Fig. 1 Grid method modeling effect

color and assigned a value of 1. The grid without obstacle is represented by a light color and assigned a value of 0. The more the number of divided grids, the more accurate the description of the obstacles, and the higher the environmental resolution and model accuracy. For the multi-rotor UAV in a state of constant altitude flight, the three-dimensional environment model can be simplified into a two-dimensional environment, and the modeling effect is shown in Fig. 1.

2.2 A* Algorithm Global Path Planning The characteristics of A* algorithm are the same as the greedy and the heuristic search algorithm. On the path planning problem, the A* algorithm is a heuristic algorithm with high search efficiency, and it can meet the real-time nature of UAV path planning in static environment. At the same time, the A* algorithm, as a greedy algorithm, can make up for the shortcomings of the heuristic search algorithm and search for the optimal path. The A* algorithm cost function formula is as follows. f (n) = g(n) + h(n)

(1)

where f (n) is the cost function of node, g(n) represents the cost from starting point to node n, and h(n) represents the heuristic function from each node to the target. The distance calculation of the cost function in the algorithm uses the Euclidean distance. Suppose the UAV is currently in the m-node, there are any candidate nodes j on the neighborhood around the node m, j = 1, 2, 3, . . . , n, the node j is ( jx , j y , jz ), the target is e(ex , e y , ez ), and g(m) is the value of the starting point to the node m, using the A* algorithm. The cost function is shown in Eqs. 2–4. f ( j) = g( j) + h( j)

(2)

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Fig. 2 Global planning effect

 g( j) = g(m) +  h( j) =

2  ( jx − m x )2 + j y − m y + ( jz − m z )2

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(3) (4)

The environment model is built by the grid method. The A* algorithm calculates the cost value of the nodes to be selected and stores them in the open set by the cost function in the grid model. Then, in the open set, the least cost node is filtered out and placed in the close set, and the node placed in the closed set is used as the current node to continue the extended search. The value update is performed during each extended search to ensure that the parent node pointer of each node is the optimal path from the starting point to this node. When the A* algorithm searches for the end point and stores it in the closed set, it uses the parent node pointer of each node to backtrack and complete the path search. Considering the actual flight capability of multi-rotor UAVs, this paper uses an 8-direction search strategy in the grid model. To ensure the flight safety of multirotor drones, the grid below the obstacles is defined as not traversing diagonally. The global path generated by the A* algorithm is shown in Fig. 2.

2.3 Global Path Node Optimization The use of the grid model for track planning will inevitably lead to redundant nodes and redundant turning points, resulting in a planned path that is not smooth enough, which is not conducive to the flight of multi-rotor drones. Therefore, it is necessary to optimize the path nodes by removing redundant nodes and redundant turning points. A redundant node refers to an intermediate node on a straight line segment. Such a node is redundant and is more convenient for analysis and calculation after removal. The way to remove redundant nodes is to extract the sequence of path nodes, and take three consecutive path nodes as a set of points to determine whether they are

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Fig. 3 Global optimization effect after node optimization

on a straight line. If so, remove the intermediate nodes and add the next node in the sequence to the set of points. Continue to judge, if not, retain the last two points of the group and add the next node in the sequence to continue to judge, and so on until all redundant nodes are removed. The turning point that occurs between two nodes that can arrive straight without obstacles is a redundant turning point. Such a point causes the planned path to be not the shortest path nor smooth enough. The method of removing the excess turning point is to start with the first node in the sequence and connect to the third node. If there is no obstacle grid intersecting, connect the fourth node. If there is an obstacle grid intersecting at this time, connect the first node and the third node, delete the intermediate node and update the path. Next, start from the third node and connect with the nodes that follow, and so on until all the excess turning points are removed, so that only the starting point, the target, and the key turning point are included in the path. The global planning effect after node optimization processing is shown in Fig. 3.

3 Improved APF Method 3.1 Traditional APF Method The APF method was proposed by Khatib in 1986. The principle is to construct a virtual gravitational field and a repulsive field in space to find a collision-free path. The target generates a gravitational field, the surrounding obstacles make a repulsion field, and the superimposed virtual potential field acts on the motion agent, and the gravitation and repulsion force generated to guide the agent to move in the environment. If the position of the multi-rotor drone in the environment is X = (x, y)T , then the gravitational potential function (GPF) at this point is:

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Uatt =

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(5)

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where Uatt is the gravitational field of the target point, ka is the gravitational gain coefficient, X is multi-rotor UAV’s arbitrary position vector, X G is the vector of target position, X 0 is the obstacle position vector, Ur ep is the repulsive field of the obstacle, kr is the repulsive gain coefficient, ρ(X, X G ) and ρ(X, X 0 ) represent the distance from the drone to the target point and the minimum distance from the drone to the obstacle, ρ0 is the maximum range of influence of a single obstacle, only when the drone is less than ρ0 from the obstacle, it will be affected. The expressions of gravitation and repulsion can be obtained by solving the negative gradients of the gravitational potential function and the repulsion potential function, respectively. Fatt = ka ρ(X, X G ) Fr ep =

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(8)

The combined force of gravity and repulsion guides the movement of the drone, F = Fatt + Fr ep , and the force analysis of the drone is as follows (Fig. 4). Fig. 4 UAV force analysis chart

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Fig. 5 Local minimum points

3.2 Analysis of Defects in Traditional APF Method The APF method has the advantages of fast calculation speed, high real-time performance, smooth generation path, etc., but there are still some defects, the most important of which is the problem of local minimum points. When the gravity and the repulsive force of the drone are equal in the opposite direction, the drone mistakenly thinks that the target point has been reached and stops flying, resulting in the failure of the track planning, as shown in Fig. 5a. When there is an obstacle near the target point, and the target point is within the influence range of the obstacle, the target point is no longer the lowest point of the potential energy. At this time, the drone can never reach the target point, resulting in the failure of the track planning, as shown in Fig. 5b.

3.3 Improved APF Method For the problem shown in Fig. 5b, the nth power of the distance between the drone and the target point is introduced in the repulsion potential function, and the improved repulsion potential function ensures that the target point is the minimum point of the potential field in the whole environment. The improved repulsion potential function is as follows.   2 1 1 1 k − ρ n (X, X G ), ρ(X, X 0 ) ≤ ρ0 r ρ(X,X 0 ) ρ0 Ur ep = 2 (9) 0, ρ(X, X 0 ) > ρ0 where n is an arbitrary number greater than zero. Solving the repulsion potential function negative gradient to get the repulsion expression is as follows.

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 Fr ep =

Fr ep1 +Fr ep2 , ρ(X, X 0 ) ≤ ρ0 0, ρ(X, X 0 ) > ρ0

(10)

where Fr ep1 and Fr ep2 are the two components of Fr ep , the direction of Fr ep1 points from the obstacle to the drone, and the direction of Fr ep2 points from the drone to the target point. The expression is as follows.   ⎧ 1 1 ρ n (X,X G ) ∂ρ(X,X 0 ) ⎨ Fr ep1 = kr − ρ(X,X ) ρ0 ρ 2 (X,X 0 ) ∂X  0 2 1 1 n−1 ⎩ Fr ep2 = n kr G) − ρ0 ρ (X, X G ) ∂ρ(X,X 2 ρ(X,X 0 ) ∂X

(11)

After adding the distance term to the repulsion potential function, since the magnitude of the repulsion is positively correlated with the distance from the drone to the target, the target is guaranteed to be the minimum force point, so the defect shown in Fig. 5b can be effectively compensated to some extent. However, in some other situations, such as the situation shown in Fig. 5a, local minimal defects are not effectively resolved. Therefore, this paper proposes an improved APF method guided by the global path to figure out this problem. The idea of improving APF method is to introduce the planned global path after node processing into the environment model. In the planning process, the APF method of introducing the distance term is first used for the track planning. When the drone stops flying, it needs to make a judgment. If the drone has reached the target point, the planning is over. When the drone motion stops but does not reach the target point, it is judged that the drone has fallen into a local minimum point during the planning process. At this time, a judgment is made to determine whether the drone is on the global path. If it is on the global path, the drone will fly directly to the next track point of the global path, causing it to jump out of the local minimum point. If it is not on the global path, the gravitational force of the global path to the drone will be introduced at this moment. Make the drone jump out of the local minimum. After the drone jumps out of the local minimum point, the APF method of introducing the distance term is used to perform the track planning until the target point is found. The planning process of the improved APF method is shown in Fig. 6. When the drone is trapped in a local minimum during the track planning process and the drone is not in the global path. The global path will create a gravitational field and create an attraction for the drone to help the drone escape from the local minima. The gravitational potential function and the gravitational formula added at this time are as follows. Uatt_ p =

1 2 λρ (X, X P ) 2

Fatt_ p = λρ(X, X P )

∂ρ(X, X P ) ∂X

(12) (13)

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Calculate the magnitude and direction of the resultant force Calculate the gravitational pull of the global path to the drone

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Y End

where Uatt_ p is the global path gravitational field, λ represents the gravitational gain coefficient of the global path, X represents the position vector of the multi-rotor UAV into the local minimum point (not on the global path), X P is the drone to the global path Foot, ρ(X, X P ) is the shortest distance from the drone to the global path. When the global path is processed through node optimization, it is more convenient to calculate the distance from the UAV to the global path. The solution method is shown in Fig. 7. The drone first finds the two track points closest to the drone on the global path, which is point A and point B in Fig. 7. Then get the current position of the drone, the distance from the current position to the line AB is the shortest distance from the drone to the global path. The direction of Fatt_ p is the vertical direction from the drone to the global path. In this case, the final force of the drone is as follows. F = Fatt + Fatt_ p + Fr ep

(14)

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Fig. 7 The distance from the drone to the global path

4 Simulation and Result The effectiveness of the proposed path planning method is verified on the Matlab simulation platform. The size of the environment area is set to 12 × 12, the starting point of the multi-rotor UAV is (0, 0), and the target point is (10, 10). Multiple obstacles with an impact radius of 1 are set in different locations in the environment. In the parameter setting, the gravitational gain coefficient ka is 15, the repulsive gain coefficient kr is 5, the real number n is 0.5, the global path gravitational gain coefficient λ is 10, and the drone moving step is 0.2. When the difference between the absolute value of the horizontal and vertical coordinates of the drone and the target point is less than 0.1, it is considered that the drone has reached the target point. Figure 8 shows the simulation results of the traditional APF method. The red point is the trajectory of the drone, the triangle is the obstacle, and the circle represents the obstacle range. In Fig. 8a, when there is an obstacle around the target point and the

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target point is within the influence range of the obstacle, the drone oscillates back and forth in the minimum potential energy region, and cannot reach the target point. In Fig. 8b, the local minimum value during the planning process appears. At this time, the drone oscillates back and forth in the local minimum area and cannot reach the target point either. The improved APF method was used to simulate the above two cases, and the results are shown in Fig. 9. The simulation results show that the improved APF method can effectively make up for the shortcomings of the traditional APF method, and finally the drones have reached the target point. Figure 9c shows the introduction of dynamic obstacles. The planning results show that this method is also applicable to the local dynamic environment.

5 Conclusion In this paper, the multi-rotor UAV track planning is taken as the research background, and the track planning method is researched around the A* algorithm and the APF method. Firstly, use the grid method and the A* algorithm to generate a global path, and then perform node optimization on the global path. Then, the traditional APF method is improved by the introduced global information, which reduces the blindness of the traditional APF algorithm. It effectively solves the defects that the traditional APF method easier to get to the local minimum, and cannot reach the target. Finally, in order to verify the effectiveness of the improved algorithm, a comparative analysis was carried out on the Matlab platform, and the validity was verified in both static and dynamic environments. The experimental results show that the improved APF method proposed in this paper improves the original defects, retains the high real-time and dynamic obstacle avoidance of the original algorithm, and can meet the requirements of multi-rotor UAV track planning. Acknowledgements This work was supported by National Key Research and Development Program of China (No. 2017YFD0701002), National Natural Foundation of China (No. 61503369).

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References 1. Jasim, W.: Robust path tracking control for quadrotors with experimental validation. J. Int. J. Model. Ident. Control 29(1), 1–13 (2018) 2. Boujelben, M., Rekik, C., Derbel, N.: A reactive approach for mobile robot navigation in static and dynamic environment using fuzzy logic control. J. Int. J. Model. Ident. Control 27(4), 293–302 (2017) 3. Goerzen, C., Kong, Z., Mettler, B.: A survey of motion planning algorithms from the perspective of autonomous UAV guidance. J. Intell. Rob. Syst. 57, 65–100 (2010) 4. Kitamura, Y., Tanaka, T., Kishino, F.: 3-D path planning in a dynamic environment using an octree and an artificial potential field. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Piscataway, NJ, USA, pp. 474–481. IEEE (1995) 5. Saini, V., Dewan, L.: Sparse parameter estimation of LTI models with lp sparsity using genetic algorithm. J. Int. J. Model. Ident. Control 29(1), 14–21 (2018) 6. Cheng, X.H., Qi, Y.: Indoor indicator path planning algorithm based on grid method. J. Chin. Inertial Technol. 26(2), 236–240+267 (2018) 7. Yao, Y., Zhou, X.S., Zhang, K.L., Dong, D.: Dynamic trajectory planning for unmanned aerial vehicle based on sparse A* search and improved artificial potential field. J. Control Theory Appl. 27(7), 953–959 (2010) 8. Liang, X.X., Liu, C.Y., Song, X.L., Zhang, Y.K.: Research on improved artificial potential field approach in local path planning for mobile robot. J. Comput. Simul. 35(4), 291–294+361 (2018) 9. Liu, X.L., Jiang, L., Jin, Z.F.: Mobile robot path planning based on environment modeling of grid method in unstructured environment. J. Mach. Tool Hydraulics 1–7 (2016)

Tracking Control Design for a Class of Mobile Robot with a Single Trailer via Differential Flatness Approach Chunxiao Wang, Huajun Fu and Zhongcai Zhang

Abstract In this paper, a nonlinear disturbance observer (NDO) is designed for mobile robot with a single trailer. To realize the tracking control objective, the considered mobile robot is transformed into chained-form system by differential flatness approach. The global asymptotic stability of the presented disturbance observer is guaranteed by appropriately choosing design function. Under this NDO, a tracking controller is proposed to force the system trajectory track the desired trajectory. Keywords Tractor-Trailers · Tracking · Nonlinear disturbance observer · Disturbances · Integral sliding-model control

1 Introduction For the past few years, the modeling and control of mobile robots with trailers have attracted wide attention. The single trailer mobile robot system is a special type of mobile robot system, which is composed of the tractor and the trailer through mutual hinges [1]. Such robots are often used in automated factories, airports, stations, nuclear environments and other occasions to perform tasks such as material transfer, baggage handling, cargo transportation, etc. Due to the limitation of natural environment conditions, many environments are not suitable or convenient for human exploration activities, thus a series of robots with different functions are derived. Among them, the use of mobile robots to replace human beings in extreme weather, terrain, environment to complete scientific research tasks and produce life tasks is an important means [2]. The trailer mobile robot consists of a tractor and one or more trailers, and runs in the same plane. The basic design of tractor consists of driving wheels and steering wheels. In this design, the rear two wheels of tractor are driving wheels and the front two wheels are steering wheels. The driving wheels can move forward and backward, C. Wang · H. Fu · Z. Zhang (B) School of Engineering, Qufu Normal University, Rizhao 276826, People’s Republic of China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_122

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and the steering wheels can move left and right. The Trailer in the system is in passive following state, and no driving device is designed. It can be seen from the above that whether the structure design of the tractor is reasonable or not directly affects the rational operation of the whole mobile robot system. Because of the complex nonholonomic constraints in the system, the motion control of the tractor-trailers mobile robot has become a hot topic of robotics in this field. At present, there are many researches on the motion planning and path tracking of tractor-trailers mobile robots [3–6]. To achieve good control performance, the external disturbances caused by dissipative force and friction force can not be ignored in both modeling and control design. In this paper, a new type of nonlinear disturbance observer (NDO) for traction trailer mobile robot with external disturbance is studied. Two methods are used to analyze the stability of traction trailer. In the process of research, it is generally assumed that the wheels are pure rolling and no sliding. The trailer system can be regarded as a two-link manipulator system. In [7], a nonlinear disturbance observer (DO) is proposed for two-link robots with different torques or force vectors. Many methods, such as sliding mode method [8] and neural network method [9, 10], have been put forward in the literature. In this paper, we first transform the considered mobile robot is transformed into chained-form system by differential flatness approach. Then a nonlinear disturbance observer (NDO) is designed and its global asymptotic stability is also discussed in detail. Under this NDO, a tracking controller is proposed to force the system trajectory track the desired trajectory. Finally, we validate the effectiveness of the above control algorithm through simulation. For the new type of traction trailer mobile robot with external disturbance, the main methods are the following attractions. (i) The change rate of total interference can be non-zero. (ii) The observer gain function does not depend on the maximum speed and physical parameters of the trailer.

2 Problem Formulation and a Basic Observer Towed mobile robot system can be classified into two types according to the linkage mechanism: one is standard link, the other is non-standard link. For the sake of simplicity, the model of the trailer system studied in this section is in standard form, as shown in the Fig. 1. As can be seen from the figure above, the kinematic equations of motion for the towed mobile robot can be described by [11] x˙c = v cos θ0 y˙c = v sin θ0 φ˙ = τ v θ˙0 = tan φ l v θ˙1 = sin(θ0 − θ1 ) d1

(1)

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Fig. 1 Mobile robot with a single trailer

where θ0 respectively θ1 are the orientations of the car and the trailer relative to the x-axis, v(t) represents the speed of the car, l represents the length between the front and rear wheels of the car, and φ represents the angle of the steering wheel relative to the cross axle of the towed mobile robot. The location of the towed mobile robot in question is expressed in the coordinates (xc , yc ), d1 represents the length from the wheels of trailer to the rear wheels of the towed mobile robot. The two input signals are the driving velocity v and the steering velocity τ of the towed mobile robot. From the fifth equation in (1), we have v sin(θ0 − θ1 ) d1 v v sin θ0 cos θ1 − sin θ1 cos θ0 = d1 d1

θ˙1 =

(2)

The first, second and fourth expressions in (1) are expressed as x˙c = v cos θ0 y˙c = v sin θ0 v θ˙0 = tan φ l

(3)

Furthermore, the dynamic model of the car can be described from [12] ⎡

⎤ ⎡ ⎤ x˙c cos θ0 0   ⎣ y˙c ⎦ = ⎣ cos θ0 0 ⎦ v τ 0 0 θ˙0

(4)

The autonomous vehicle is a nonholonomic system. Driving wheel pure rolling without skidding is an incomplete constraint:

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y˙c cos θ0 − x˙c sin θ0 = 0

(5)

and the radius of curvature of any trajectory can be expressed as R(t) =

L tan φ

(6)

Rmin is usually the bound of the value of R(t). For general non-linear systems without drift q, ˙ q ∈ Rn , τ ∈ Rm , dynamic feedback linearization includes finding a form of feedback compensator ζ˙ = a(q, ζ ) + b(q, ζ )u τ˙ = c(q, ζ ) + d(q, ζ )u

(7)

with input u ∈ Rm and state ζ ∈ Rv , as a result, the closed-loop system of (3) and (7) will be equivalent to a linear system after the state transformation δ = S(q, ζ ) to a linear system. Then, the closed-loop system can be regarded as a series of decoupled integrator input-output chains from u i to ρi . The precise linearization process of vehicle model (4) is explained. Considering coordinates of axle center as plane output ρ = (xc , yc ). Differentiation with respect of time, then generated [13, 14]  ρ˙ =

x˙c y˙c



 =

cos θ0 0 sin θ0 0

  v τ

(8)

thus we can see that η˙ is only affected by v. Next, we need to add an integrator (whose state is represented by ζ ) to the linear speed input   cos θ0 v = ζ, ζ˙ = α ⇒ ρ˙ = ζ sin θ0

(9)

where the linear acceleration of the car is expressed by α. Differentiating further one obtains     − sin θ0 cos θ0 + ζ θ˙0 ρ¨ = ζ˙ sin θ0 cos θ0    α cos θ0 −ζ sin θ0 = (10) sin θ0 ζ cos θ0 τ and if ζ = 0, then the matrix multiplied by the modified input (α, τ ) is nonsingular. We get the following equation under this assumption −1      u1 α cos θ0 −ζ sin θ0 = sin θ0 ζ cos θ0 u2 τ

(11)

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and ρ¨ is denoted as 

ρ¨1 ρ¨ = ρ¨2





u1 = u2

 =u

(12)

which means the required linear acceleration and the required angular velocity can be expressed in terms of the converted control inputs u 1 and u 2 . Then return to the initial control inputs v and τ , and the dynamic compensation generated is ζ˙ = u 1 cos θ0 + u 2 sin θ0 v=ζ u 2 cos θ0 − u 1 sin θ0 τ = ζ

(13)

Being ζ ∈ R, it is n + v = 3 + 1 = 4, equal to the output differentiation order in (12). Then, in the new coordinate representation we can obtain z 1 = xc z 2 = yc z 3 = x˙c = v cos θ0

(14)

z 4 = y˙c = v sin θ0 Therefore, the extended system is completely linearized and described by the integrator chain in (12), and can be rewritten as z¨ 1 = u 1 , z¨ 2 = u 2 ,

(15)

Assuming that the trailer is affected by uncertainties, the following second-order systems with disturbances are considered 

 z˙ 11 = z 12 z˙ = z 22 , 21 z˙ 12 = u 1 + d1 z˙ 22 = u 2 + d2

(16)

where z 11 , z 12 , z 21 and z 22 are states, u 1 and u 2 are the control inputs, d1 (t) and d2 (t) are the disturbances. Combining the above equations with (16) gives 

z¨ 11 = u 1 + d1 z¨ 21 = u 2 + d2

(17)

where θ0 = z 11 , θ1 = z 21 , T = [u 1 , u 2 ]T , d = [d1 , d2 ]T , and the dynamic equations of motion for the towed mobile robot can be described by θ¨ = T + d(t)

(18)

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where θ = [θ0 , θ1 ]T ∈ R2 and T (t) ∈ R2 are displacement, and control vectors, respectively. d(t) ∈ R2 represents a disturbance torque or force vector. The purˆ generated by pose of this term is to design an observer so that the estimator d(t) the observer approximates the disturbance d(t) exponentially at any θ (t), θ˙ (t), and t ∈ [t0 , ∞).

2.1 Initial Observer One of the main ideas of observer/estimator design is to time the actual output by estimating the difference between the output and the modification. Therefore, (18) can be written as d = θ¨ − T,

(19)

d˙ˆ = −cdˆ + c(θ¨ − T ).

(20)

a DO is proposed as

In this article, we assume that the derivative of the total disturbance d satisfies d˙ = h(t)

(21)

ˆ e(t) = d − d.

(22)

where d(t) ∈ L ∞ and h(t) ∈ L 2 . Observer error can be defined as

Combining (21) with the observer (20) yields e˙ = d˙ − d˙ˆ = h(t) + cdˆ − cd = h(t) − ce(t).

(23)

Further, we can obtain e˙ = −ce + h(t).

(24)

It can be shown that the observer error vector e(t) globally and asymptotically converges to zero since h(t) ∈ L 2 . In addition, in the observer equation (20), there is an acceleration signal θ¨ which is not available in many robotic manipulators. By choosing a special constant c, the acceleration term can be eliminated.

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2.2 Modified Observer Motivated by [7], let us define an auxiliary variable vector z = dˆ − p(θ, θ˙ )

(25)

where z ∈ R2 . The design function vector p(θ, θ˙ ) is a deterministic sequel. The constant c in (20) can be obtained by solving subsequent nonlinear equations: cθ¨ =



∂ p(θ,θ˙ ) ∂ p(θ,θ˙ ) ∂θ ∂ θ˙

 θ˙  θ¨

(26)

Invoking (25) and (26) with (20) yields dp(θ, θ˙ ) z˙ = d˙ˆ − dt

 θ˙  θ˙ ) ∂ p(θ,θ˙ ) = d˙ˆ − ∂ p(θ, ∂θ ∂ θ˙ θ¨ = −c(z + p(θ, θ˙ ) + T ). Now, the augment variable z is given by z˙ = −c(z + p(θ, θ˙ ) + T ).

(27)

It is noting that z is measurable. We now define the estimation of the disturbance d(t) as dˆ = z + p(θ, θ˙ )

(28)

It can be seen easily that only the angular θ and angular velocity θ˙ are used without the acceleration signal θ¨ .

2.3 Stability of the NDO We could obtain the observer error equation from (22), (27), and (28) dp(θ, θ˙ ) e˙ = d˙ − d˙ˆ = h(t) − z˙ − dt = h(t) + cz − c(−T − p(θ, θ˙ ) +

dp(θ, θ˙ ) dt

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= h(t) + c(dˆ − p(θ, θ˙ )) + c(θ¨ − d + p(θ, θ˙ )) −cθ¨0 = −ce + h(t) Now, e˙ is given by e˙ = −ce + h(t)

(29)

where h(t) ∈ L 2 . The estimation dˆ approaches the disturbance d is asymptotically stable. Theorem 1 For the mobile robot with a single trailer (18), when we chose the function in the observer (27) and (28) as p(θ, θ˙ ) = cθ˙ ,

(30)

and the controller is specified by the coming expression (34), then the disturbance ˆ can track the actual disturbance d(t), and meanwhile the system estimation d(t) states θ and θ˙ can track their desired trajectories θd and θ˙d respectively. Proof We could obtain p(θ, θ˙ ) by (30), it yields dp(θ, θ˙ ) ∂ p(θ,θ˙ ) = ∂θ dt

∂ p(θ,θ˙ ) ∂ θ˙

 θ˙  = cθ¨ . θ¨

(31)

By the observer error dynamics (29), we can obtain that e(t) converges to zero exponentially. Now let us consider the system (18). In order to realize the tracking control objective, we assume that the ideal values of θ , θ˙ , θ¨ are θd , θ˙d , θ¨d . Define the tracking error as (t) = θ (t) − θd (t).

(32)

Then system (18) can be expressed as (θ¨ − θ¨d ) + 2(θ˙ − θ˙d ) + 3(θ − θd ) + θ¨d + 2θ˙d + 3θd = T + dˆ + e(t) + 2θ˙ + 3θ.

(33)

Based on (33), we select the control torque T as following ˆ − 2θ˙ − 3θ. T (t) = θ¨d + 2θ˙d + 3θd − d(t)

(34)

Then the error dynamics becomes ¨ (t) + 2˙ (t) + 3(t) = e(t)

(35)

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Equation (35) guarantees that (t) and ˙ (t) tend to zero. ˆ is bounded According to the definition on z(t) and the convergence of e(t), d(t) ˆ guarantees and thus z(t) is bounded. The boundedness of all signals θ , θ˙ , z(t), and d(t) that the control signal T (t) is bounded. This ends the proof of Theorem 1.

3 Conclusions In this work, a trajectory tracking controller has been designed for a mobile robot with a single trailer via differential flatness approach. A nonlinear disturbance observer is proposed such that the disturbance estimation can track the actual disturbance. Then, based on the disturbance observer, a trajectory tracking controller is designed to guarantee that the system states can track the desired trajectory. Next, we will mainly study the control problem of underactuated crane system [15, 16]. Acknowledgements This work was supported by the National Natural Science Foundation of China (61673243 and 61703232), the China Postdoctoral Science Foundation (2018M632645), the Natural Science Foundation of Shandong Province (ZR2017QF013, ZR2017MF068), the Major Research Project of Shandong Province (2017GSF18116), and the Experimental Technical Research Project of Qufu Normal University (SJ201706).

References 1. Koller, D., Luong, Q.T., Weber, J., et al.: Vision-based autonomous road vehicle guidance. In: Handbook of Pattern Recognition and Computer Vision, 2nd edn, pp. 817–854. World Scientific Publishing Co, Singapore (1999) 2. Colle, E., Galerne, S.: A robust set approach for mobile robot localization in ambient environment. Auton. Rob. 3, 1–17 (2018) 3. Astolfi, A., Bolzern, P., Locatelli, A.: Path-tracking of a tractor-trailer vehicle along rectilinear and circular paths: a Lyapunov-based approach. IEEE Trans. Rob. Autom. 20(1), 154–160 (2004) 4. Altafini, C., Speranzon, A., Wahlberg, B.: A feedback control scheme for reversing a truck and trailer vehicle. IEEE Trans. Rob. Autom. 17(6), 915–922 (2001) 5. Liu, Z.J., Lu, Q., Yang, P., Chen, L.L.: Path planning for tractor-trailer mobile robot system based on equivalent size. In: Proceedings of the 7th World Congress on Intelligent Control and Automation, Chongqing, pp. 5744–5749 (2008) 6. Gonzlez-Cantos, A.: Backing-up maneuvers of autonomous tractor-trailer vehicles using the qualitative theory of nonlinear dynamical systems. Int. J. Rob. Res. 28(1), 49–65 (2009) 7. Chen, W.-H., Ballance, D.J., Gawthrop, P.J., O’Reilly, J.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47(4), 932–938 (2000) 8. Huang, A.C., Chen, Y.C.: Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties. IEEE Trans. Control Syst. Technol. 12(5), 770–775 (2004) 9. Abdollahi, F., Talebi, H., Patel, R.: A stable neural network based observer with application to flexible-joint manipulators. IEEE Trans. Neural Netw. 17(1), 118–129 (2006) 10. Chaoui, H., Sicard, P., Gueaieb, W.: ANN-based adaptivecontrol of robotic manipulators with friction and joint elasticity. IEEE Trans. Ind. Electron. 56(8), 3174–3187 (2009)

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11. Rigatos, G.: Nonlinear Control and Filtering using Differential Flatness Approaches: Applications to Electromechanical Systems. Springer International Publishing AG, Switzerland (2015) 12. Rgatos, G.G.: Flatness-based adaptive fuzzy control for nonlinear dynamical systems. In: IEEE/ASME, International Conference on Advanced Intelligent Mechatronics, Budapest, Hungary (2011) 13. Oriolo, G., De Luca, A., Vendittlli, M.: WMR control via dynamic feedback linearization: design, implementation and experimental validation. IEEE Trans. Control Syst. Technol. 10(6), 835–852 (2002) 14. Rgatos, G.G.: Extended Kalman and particle Filtering for sensor fusion in motion control of mobile robots. Math. Comput. Simul. 81(3), 590–607 (2010) 15. Zhang, Z., Wu, Y., Huang, J.: Differential-flatness-based finite-time antiswing control of underactuated crane systems. Nonlinear Dyn. 87(3), 1749–1761 (2017) 16. Zhang, Z., Li, L., Wu, Y.: Disturbance-observer-based antiswing control of underactuated crane systems via terminal sliding mode. IET Control Theory Appl. 12(18), 2588–2594 (2018)

On Interconnected Observer Design for Nonlinear System Mei Zhang, Ze-tao Li, Michel Cabassud and Boutaïeb Dahhou

Abstract This paper investigates the possibility of decomposing a control system into an interconnection of actuator and process subsystems; this allows monitoring the properties of the interconnected system globally and locally. For that, observer for the nonlinear interconnected system is studied. Specially, the interconnection between the two subsystems is assumed to be inaccessible to measurement. The aim is then to accurately estimate online the states vector of each subsystem, as well as the unknown interconnection. Numerical simulations confirm the effectiveness of the designed observer. Keywords Interconnected system · Unknown interconnection · States estimation · Left invertibility · Actuator subsystem · Process subsystem

1 Introduction In practice, interconnected dynamical systems appear in many control applications whether naturally or intentionally due to control design purpose. An interconnected system consists of a series of interconnected dynamical units, and therefore exhibits very complicate dynamics [1]. M. Zhang · Z. Li (B) Electrical Engineering School, Guizhou University, Guiyang 550025, China e-mail: [email protected] M. Zhang e-mail: [email protected] M. Cabassud CNRS, LGC, 31030 Toulouse, France e-mail: [email protected] Université de Toulouse, UPS, LGC, 31030 Toulouse, France B. Dahhou CNRS, LAAS, 31400 Toulouse, France e-mail: [email protected] Université de Toulouse, UPS, LAAS, 31400 Toulouse, France © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_123

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Over the past years, the topic of states estimation for interconnected system has received extensively attention in the literature, see e.g. in [1–3]. A large number of publications focused on this problem with satisfactory results are in a centralized manner, resulting in various types of observers like high gain observer [3], sliding mode observer [4], adaptive observer [5] etc. However, note that a centralized observer may not be practical for the interconnected systems due to the complexity of implementation, and the state or parts of the state cannot be measured due to uneconomic measurement costs or physical circumstances like high temperatures, where no measurement equipment is available, for example. A solution to overcome this difficulty is to decompose the systems into an interconnection of several subsystems so that the observers can be designed in a decentralized manner. A typical approach of state estimation is to design observers for each subsystem individually and the overall estimator is formed by gathering of all the observers, different kinds of methodologies are developed, like in [6–9]. With respect to the above mentioned methods, one major challenge is the availability of the measurement of the interconnections between subsystems. For example, the output of the actuator can be either uneconomic or unrealistic to measure its output. A promising approach was reported in [10] where the problem of state-observation is addressed for nonlinear systems that modeled by an ODE–PDE series association. This problem has also been studied for interconnected system formed by a nonlinear system followed by a linear system, like in [8]. This paper considers the issues of both state and unknown interconnection estimation for the interconnected system represented by two nonlinear associations connected in series. Two underlying issues are worth to be highlighted to better understand the nature of the considered estimation problem. Firstly, the measurement output used in the observer of former subsystem is assumed not accessible; the solution is to replace it by an estimate via observer of latter subsystem. Secondly, in the latter subsystem, the estimated interconnection that provided for the previous subsystem is treated as an additional state, forming a new extended subsystem; and expression for the new state is obtained by computing derivatives of output equation of the previous subsystem.

2 Motivations and Problem Formulations The problem of states observation is addressed for nonlinear systems that can be modeled by two interconnected nonlinear dynamical units, the actuator and the process subsystems, as shown in Fig. 1. The aim is to accurately estimate the states Fig. 1 Interconnected system structure

On Interconnected Observer Design for Nonlinear System

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vector of both subsystems, as well as the interconnection. We consider a dynamical process subsystem as an input affine form:   x˙ = f (x) + g(x)ua , x(t0 ) = x0 : y = h(x) p

(1)

where x ∈ n is the state of the process subsystem, y ∈ p is the output of the global system, which is also the output of the process subsystem.ua ∈ m is the input of process subsystem, which is also the output of the actuator subsystem. ua is assumed to be inaccessible. f and g are smooth vector field on n and h is smooth vector field on p . An input affine structure is also assumed for the actuator subsystem:   x˙ a = fa (xa ) + g (xa )u, xa (t0 ) = xa0 a : u = h (x ) a a a a

(2)

where xa ∈ n is the state, u ∈ l is the input, ua ∈ Rm is the output of the actuator subsystem, which is also the input of the process subsystem. fa and ga are smooth vector field on n and h is smooth vector field on m . Considering interconnected system depicted by (1) and (2), it is desirable to monitor the performance of the interconnected system with aspect to individual subsystems and the overall system. However, the major difficulty for employing the existing methods is to satisfy the assumption that inputs and outputs of each subsystem are available, since the connection point between the two blocks is not accessible to measurement. This is because the connection is the output of the actuator subsystem where online measurement is either difficult to obtain due to physical reasons or the measurement is uneconomical since actuators are often far from the controller. As shown in Fig. 1, the particular aim in our design is to accurately estimate online the state vector x and xa of each subsystem, as well as the unmeasured interconnection vector ua .

3 Interconnected Observer Design The structure of the proposed observer is depicted as a two level interconnected observer system which consists of two state estimators, the actuator and the process state estimators. The specific idea of the proposed interconnected observer is as follows. First, an existing observer is supposed to be already available for the nonlinear subsystem a with measured output ua , then we implement that observer using an to produce such an estimate, we extend the estimate of ua , denoted by u˜ a . In order state space of the process subsystem p to include ua as an additional state. By computing derivatives of ua in actuator subsystem, we can obtain an expression corresponding to times derivatives of the output ua which is a function of u, derivatives

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of u and xa . Then an observer is constructed for this extended process subsystem. State estimator of actuator subsystem, together with state estimator of process subsystem, a kind of interconnected observer designed method is then proposed for the studied interconnected nonlinear system.

3.1 Observer Design for the Interconnected System First, consider a converging observer for actuator subsystem is: (3) where ka , Ga are smooth gain functions with respect to their arguments. Ga is a subset of n . To this end, introduce the state estimation error as: ea := xa − xˆ a Then subtracting corresponding equation of (2) and (3), we get the following error dynamics as:       e˙ a (t, ea ) = fa (xa ) + ga (xa )u − fa xˆ a − ga xˆ a u − K u, xˆ a , ua

(4)

. where The observer defined by (3) could be implemented on condition that ua is accessible, but it is not the fact in the case. Since ua in our design represents the output of the actuator subsystem which is assumed unmeasured, therefore we have to replace ua with an estimated u˜ a by the available measurements. (5) denote We seek again estimation error by subtracting corresponding equation in (2) and (5), thus yielding the new error dynamics as follows: .     e˜ a (t, e˜a ) = e˙ a (t, ea ) + K u, xˆ a , ua − K u, xˆ a , u˜ a

(6)

In order to ensure exponential stability of the error dynamics (6), we need an  assumption regarding the sensitivity of K u, xˆ a , ua with respect to changes in ua . The following Assumption provides a sufficient condition for achieving this purpose. This subject of following statement is inspired by [8].

On Interconnected Observer Design for Nonlinear System

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    Assumption 1 for any u ∈ U, t, xˆ a , uˆ a ∈ A.C R+ , R , there exists a real constant γ3 satisfies:      K u, xˆ a , ua − K u, xˆ a , u˜ a  ≤ γ3 ua − u˜ a 

(7)

.

Assumption 2 implies that the definition of e˜ a (t, e˜ a ) in (6) is not affected. Theorem 1 if Assumption 1 is satisfied, then the observer described in (5) is an exponential observer for the actuator subsystem described in (2).

3.2 State Estimator Design for Process Subsystem In order to produce an observer for the process subsystem (1) subject to unknown inputs, we solve this problem by extending this unknown input as an additional state, and propose an observer for the extended system. Let: xu  ua x˙ u = u˙ a According to [8], we define a function ε(u, u˙ , xa ) with respect to the time derivative of the output ua in (2). ∂ha ∂ha (8) (u, xa )fa (u, xa ) (u, xa )˙u + ∂u ∂xa     Assumption 2 For any u ∈ U, t, xˆ a ∈ A.C R+ , R , there exists a real constant γ4 satisfies: x˙ u = ε(u, u˙ , xa ) =

     ε u, u˙ , xˆ a − ε(u, u˙ , xa ) ≤ γ4 xa − xˆ a  Similar to Assumptions 1 and 2 implies global Lipchitz-type condition on function ε, and it can also be replaced by local smoothness condition since u, u˙ , xa are bounded in physical problem. Then new actuator and new process subsystem can be expressed as:   x˙ = f (x) + g(x)xu : x˙ u = ε(u, u˙ , xa ) p

(9)

  Define z = z1 z2 = x xu , then system (9) can be extended as: 

z˙ = l(z1 )G(z1 )z + F(z1 ) + ε¯ (u, u˙ , xa ) y = Cx

(10)

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  0 g1 (z1 ) f1 (z1 ) , F(x1 ) = , C = In 0 , ε¯ (u, u˙ , xa ) = 0 0 0

where: G(z1 ) = T  0 ε(u, u˙ , xa ) ,In is n × n identity matrix, l(z1 ) is a scalar real function with respect to their arguments and αl ≤ |l(z1 )| ≤ βl . An extended high gain observer for (10) can be given in the following way: .            zˆ = l zˆ 1 G zˆ 1 zˆ + F zˆ 1 + ε¯ u, u˙ , xˆ a + H zˆ 1 yˆ − y yˆ = C zˆ T      T ˆ1 = where: H = Hz1 Hz2 = −1 zˆ 1 S−1 θ C ,  z

I 0  0 G1 zˆ 1

(11)



3.3 Interconnected Observer System (5), together with (11), constitutes the interconnected observer for the studied interconnected system, as follows:

.        xˆ a = fa xˆ a , u + ka ga , xˆ a ha xˆ a − zˆ 2 .            zˆ = l zˆ 1 G zˆ 1 zˆ + F zˆ 1 + ε¯ u, u˙ , xˆ a + H zˆ 1 yˆ − y

(12)

where virtual measurement u˜ a in (6) is replaced by its estimation zˆ 2 .

4 Numerical Simulations Result In order to test the performance of the proposed observers, A case study is developed on an intensified HEX reactor. More relative information could be found in [11].

4.1 System Modelling  The actuator subsystem model is described as: xTa = xa1 xa2 xa3 xa4 =     = = X dX1 X dX2 , uT = u1 u2 F1 F2 pc1 pc2 , uTa =   1 dt 2 dt       P1 P2 P1 P2 Cv sg X1 Cv sg X2 , C = c1 c2 c3 c4 = Cv sg 0 Cv sg 0 where F is flow rate (m3 s−1 ), P is the fluid pressure drop across the valve (Pa), sg is specific gravity of fluid, X is the valve opening, Cv is valve coefficient Aa is the diaphragm area, pc is the pneumatic pressure, m is the mass of the control valve stem, μ is the friction of the valve stem, k is the spring compliance, the actuator

On Interconnected Observer Design for Nonlinear System

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subsystem is then described as: ⎧ ⎤ ⎤ ⎡ ⎡ Aa 0 1 0 0 0 ⎪ m ⎪ ⎪ μ k 1 ⎥ ⎢ 1 ⎢ ⎪ 0 ⎥ ⎪ ⎥xa + ⎢ 0 0 ⎥u ⎨ x˙ a = ⎢ − m − m 0 Aa ⎦ ⎦ ⎣ 0 ⎣ 0 0 1 0 m μ2 k2 ⎪ ⎪ − 0 0 0 0 − ⎪   m m  ⎪ ⎪ ⎩u P1 P2 0C 0 x C a=

v

v

sg

(13)

a

sg

T  For the process subsystem, define the state vector as xT = [x1 , x2 ]T = Tp , Tu , T  the control input uTa = [ua1 , ua2 ]T = Fp , Fu , the output vector of measurable  T  T variables yT = y1 , y2 = Tp , Tu , where ρp , ρu are density of the process fluid and utility fluid (in kg m−3 ), Vp , Vu are volume of the process fluid and utility fluid (in m3 ), cpp , cpu are specific heat of the process fluid and utility fluid (in J kg−1 K−1 ), U is the overall heat transfer coefficient (in J m−2 K−1 s−1 ). A is the reaction area (in m2 ). Fp , Fu are mass flowrate of process fluid and utility fluid (in kg s−1 ). Tp is the process fluid temperature. Tu is the utility fluid temperature of previous cell. Tpi , Tui are the inlet temperature of process fluid and utility fluid. Then the process subsystem can be described in the following state-space form: ⎧ ⎨ ⎩

where f(x) = 

(Tpi −Tp )

f1 (x) f2 (x) 

x˙ = f(x) +

i=1

=

gi (x)ua

(14)

y = h(x, ua ) 



2 

hp A  T ρp Cp p V p  p hu A Tu ρu Cp u V u

− Tu − Tp

  , and g(x) =

  g1 , g2 =

0

, y1 = x1 , y2 = x2 . 0 By using (8), we can obtain a function for the derivatives for ua : Vp

(Tui −Tu ) Vu

∂ha ∂ha (u, xa )fa (u, xa ) (u, xa )˙u + ∂u ∂xa 

  Aa  P1 Aa  P2 P2 0 Cv sg 0 xa + Cv sg m Cv sg u m

u˙ a = ε(u, u˙ , xa ) =   1 = Cv P sg

(15)

T  Define the state vector as xT1 = [x11 , x12 ]T = Tp , Tu , unmeasured state xT2 = T  [x21 , x22 ]T = [ua1 , ua2 ]T = Fp , Fu , the output vector of measurable variables   T T yT = y1 , y2 = Tp , Tu , then the Eqs. (14) and (15) can be rewritten in the following state-space form:

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⎧ ⎨ x˙ 1 = G1 (x1 )x2 + g1 (x1 , u) x˙ = ε(u, u˙ , xa ) ⎩ 2 y = x1  where, G1 (x1 ) =



(Tpi −x11 ) Vp

0

0 (Tui −x12 ) Vu

, and f1 (x) =



hp A ρp Cp p Vp (x11 hu A ρu Cp u Vu (x12

(16)

− x12 ) − x11 )

 .

4.2 Simulation Results Numerical simulations were carried out. Considering the actuator and process model given by (13) and (16), observers (12) were designed for estimating unmeasured inlet flows Fp , Fu , and monitoring performance final product Tp , Tu . An initial value Fu = 4.22e−5 m3 s−1 , and Fp = 4.17e−6 m3 s−1 were considered, then followed by an abrupt change of Fu t = 60 s. After that, at t = 100 s, Fp begins to deteriorate. Simulation Results are illustrated in Figs. 2, 3, 4 and 5. From Figs. 2 and 3, after a short transient time, the estimated outlet fluid temperature Tˆ p and Tˆ u in dash line give an accurate estimation value to the measurement Tp and Tu in solid line. At 60 s, the estimated Tˆ p unexpectedly decrease, and finally it stabilizes at a new level, a drop of 0.2 °C is occurred, then another drops happens at t = 100 s before it reaches the new stable level with another 0.9 °C reduction. The

Fig. 2 Outlet temperature of process fluid, solid line denotes measured value Tp while dash line is the estimated one Tˆ p

Fig. 3 Outlet temperature of utility fluid, solid line denotes measured value Tu while dash line is the estimated one Tˆ u

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Fig. 4 The computation and estimation of process fluid flow rate; solid line is the computed value Fp , dash line is the estimated one Fˆ p

Fig. 5 The computation and estimation of utility fluid flow rate; solid line is the computed value Fu , dash line is the estimated one Fˆ u

similar result is obtained in the estimated Tˆ u of utility fluid in Fig. 3. It is shown that the measured Tu drops 0.2 and 0.5 °C at 60 s, 100 s respectively. The estimated Tˆ u in dash line tracks Tu after observer converges. The simulation curve indicates that the observer proposed is proper for tracking system performances. As shown in Fig. 4, in the first place, the estimated process fluid flow rate Fˆ p in dash line converges to the simulated value Fp in solid line after transient response. After that, at 100 s, the simulated Fp in solid line decrease unexpectedly, fortunately, the estimated value in dash curve gives a quick response to the variation, and it takes 1.5 s to track Fp again. The decrease implies parameter changes in process fluid actuator which satisfied the assumption. Figure 5 demonstrates the results for utility fluid flow rate. At time 60 s, as expected, the simulated utility fluid flow rate in solid line jumps. It also proves in Fig. 5 that the estimated utility fluid flow rate Fˆ p in dash line tracks well Fp in solid line. Now, it is clear that the proposed interconnected observer is effective even the unknown connection is time-varying either individually or simultaneously. Therefore the proposed observer proves the capacity of performance monitoring, as well as estimation of unknown connection of an interconnected system.

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5 Conclusion The paper considers the issues of both state and unmeasured interconnection estimation for a class of interconnected dynamic system. To achieve this purpose, the unknown outputs information of the latter subsystem are replaced by their estimation through the observer proposed in the former subsystem. Moreover, an extended high gain observer is considered to exactly estimate the states of the former subsystem subject to unknown inputs. While through computing the derivatives of the output vectors in the latter subsystem, the unknown input can be expressed as a function of the inputs, derivatives of the inputs and the states of the actuator subsystem. Numerical simulation examples are given to illustrate the effectiveness of the proposed methods. Acknowledgements This work was supported by Science and Technology Foundation of Guizhou Province, China ([2016]1053), and Key Project of Science and Technology Foundation of Guizhou Province, China ([2016]2302). And [2017]5788.

References 1. Yang, J., Zhu, F., Yu, K., Bu, X.: Observer-based state estimation and unknown input reconstruction for nonlinear complex dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 20(3), 927–939 (2015) 2. Besançon, G., Hammouri, H.: On observer design for interconnected systems. J. Math. Syst. Estimation Control 8(3), 1–26 (1998) 3. Vijay, P., Tade, M.O., Ahmed, K., Utikar, R., Pareek, V.: Simultaneous estimation of states and inputs in a planar solid oxide fuel cell using nonlinear adaptive observer design. J. Power Sources 248, 1218–1233 (2014) 4. Djeghali, N., Djennoune, S., Bettayeb, M., Ghanes, M., Barbot, J.P.: Observation and sliding mode observer for nonlinear fractional-order system with unknown input. ISA Trans. 63, 1–10 (2015) 5. Farza, M., M’Saad, M., Menard, T., Fall, M.L., Gehan, O., Pigeon, E.: Simple cascade observer for a class of nonlinear systems with long output delays. IEEE Trans. Automat. Control 60, 3338–3343 (2015) 6. Keliris, C., Polycarpou, M.M., Parisini, T.: A robust nonlinear observer-based approach for distributed fault detection of input-output interconnected systems. Automatica 53, 408–415 (2015) 7. Sandberg, H., André, H., Johansson, K.H.: Distributed fault detection for interconnected second-order systems with applications to power networks consensus protocols in practice. In: First Workshop on Secure Control Systems (SCS), Stockholm (2010) 8. Grip, H.F., Saberi, A., Johansen, T.A.: Observers for interconnected nonlinear and linear systems. Automatica 48(7), 1339–1346 (2012)

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9. Dashkovskiy, S., Naujok, L.: Quasi-ISS/ISDS observers for interconnected systems and applications. Syst. Control Lett. 77, 11–21 (2015) 10. Antonio Susto, G., Krstic, M.: Control of PDE-ODE cascades with Neumann interconnections. J. Franklin Inst. 347(1), 284–314 (2010) 11. Théron, F., Anxionnaz-Minvielle, Z., Cabassud, M., Gourdon, C., Tochon, P.: Characterization of the performances of an innovative heat-exchanger/reactor. Chem. Eng. Process. Process Intensification 82, 30–41 (2014)

Development and Research of Grid Short-Circuit Capacity Tester Wei Chen, Pu Deng, Zhenghang Hao, Zhuo Chen and Aiping Pang

Abstract The short-circuit capacity is a key parameter required for power system operation and control. This paper proposes a method for measuring the short-circuit capacity of bus in power grid by the non-fault disturbance caused by switching shunt capacitors. The short-circuit capacity can be calculated accurately by the proposed measuring principle. Based on this, a prototype is developed for field testing and research. In this paper, it establishes models for substation bus measurements based on MATLAB/Simulink and RTDS. The simulation analysis of various situations shows that the measurement error of the results of this developed short-circuit capacity tester is less than 5%, which is easy to use technically. Keywords Power systems · Short-circuit capacity · Real-time simulation

1 Introduction For a long time, the calculation of short-circuit capacity in power systems has been faced with the problems of complexity, timeliness and accuracy. The continuous expansion of power grid makes the data scale of short-circuit capacity calculation very large and difficult to manage and maintain. The mode of power grid changes W. Chen (B) · P. Deng · Z. Hao Power Grid Planning and Research Center, Guizhou Power Grid Corporation, Guiyang 550002, Guizhou, China e-mail: [email protected] P. Deng e-mail: [email protected] Z. Hao e-mail: [email protected] W. Chen · Z. Hao · Z. Chen · A. Pang College of Electrical Engineering, Guizhou University, Guiyang 550025, Guizhou, China e-mail: [email protected] A. Pang e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_124

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significantly due to unplanned factors. It causes the calculation of short circuit capacity can’t keep up with the change of power grid, which brings many issues to the grid operation. Due to the complexity and timeliness of short-circuit capacity calculation, the actual grid topology and component parameter library required for short-circuit capacity calculation are often out of practice, resulting in a low correct operation rate of distribution network protection. As one of the most important technical factors in power system, its data requirements cover all stages of power grid planning, design, construction, operation and maintenance [1, 2]. Various methods for obtaining the short-circuit capacity in power grid have been developed to varying degrees over the decades [3, 4]. How to measure the short-circuit capacity of a busbar is an urgent problem in current grid measurement technology. And this method has no need to manually set up faults or stop any load lines, and does not have a security impact on the system. Therefore, the power system needs a method which can measure short-circuit capacity without fault disturbance to make up for the limitations of the calculations. This paper presents a principle and technology of the measurement of short-circuit capacity in power grid. In order to solve the practical problems of timeliness, accuracy, reliability and convenience in obtaining short-circuit capacity. Based on this, a prototype is developed for field testing and research.

2 Basic Principle of Measurement The short-circuit capacity described in this paper is the three-phase short-circuit capacity of the bus, which is determined by the thevenin equivalent reactance (also known as system short-circuit reactance) of the positive sequence impedance at the node of the bus in the grid. The bus of substations at all levels can be shown in Fig. 1. The basic principle of this measurement is as follows. (1) For the general power system and its substation, the circuit model is built as shown in Fig. 2a. Fig. 1 Substation bus to be tested in power grid

Power grid Power plant 1

Power plant 2

The main transformer Measure PL,QL Point of Common Coupling, PCC(Bus) Switching disturbance Shunt capacitor

Measure the voltage before and after the disturbance, V1,V2, Measure the vector Angle before and after the disturbance, Short-circuit capacity, S

Load 1 Load 2 Load 3

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V1 PCC

Zs

Zs C

IC

Zld

Zld Es

Es

(a) The circuit model of substation bus

(b) The circuit model based on substitution

short-circuit capacity calculation

theorem

Fig. 2 The circuit model of short-circuit capacity calculation

Zs

Zs

Zld

Ic

Zld

Es

(a) The circuit model after switching capacitor

(b) The circuit model under the excitation of capacitor current alone

Fig. 3 The circuit model of short-circuit capacity calculation

Es is the intra-system potential, and Zld is the impedance calculated according to all the loads on the bus. The calculation formula is as follows: Z ld =

V12 V2 +j 1 PL QL

(1)

In Formula (1), PL and QL represent the total load of active and reactive power carried by the bus. V 1 represents the voltage before the capacitor is cutting. (2) The capacitor can be represented as a current source worked in steady, and its current is equal to the current of the capacitor, as shown in Fig. 2b. I C can be obtained from Formula (2).

IC =

V1 QC

(2)

In Formula (2) QC is the compensation capacity of the capacitor. (3) After switching the capacitor, the circuit model is shown in Fig. 3a. At this time, only E s is used as the excitation source in the circuit. When the current source work in the circuit alone, its model is shown in Fig. 3b. After measurement, the amplitude of the voltage before and after switching capacitor, and the voltage phase difference before and after switching capacitor can be measured. A phasor diagram shown in Fig. 5. This vector triangle reflects the vector relationship of circuit before and after switching capacitor.

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Fig. 4 Vector relationship before and after cutting capacitor

V2

ΔV V1

In Fig. 4, V 1 is the bus voltage before cutting capacitor, V 2 is the bus voltage after cutting capacitor, V is the voltage drop caused by the excitation of equivalent current source alone. The following formula can be obtained according to Fig. 4. The Formula (4) can be obtained according to Fig. 3b. It can be deduced the short-circuit capacity of the bus from Formulas (1) to (4). |V | =

 S=



V12 + V22 − 2V1 V2 cos θ

V V + = IC Z ld ZS V1 V

(3) (4)

2 Q C2 − PL2 − Q L + Q C

(5)

3 Field Test 3.1 Introduction of Experiment Platform The real-time simulator RTDS is a device developed by the Manitoba D.C Research Center in Canada and manufactured by RTDS for real-time simulation of electromagnetic transients in power system. RTDS is divided into a software platform and a hardware board. RSCAD (Real Time Simulator CAD) software platform serves as a graphical user interface for interpersonal interaction, including power system and control component model library and compiler. Users can build models and their monitoring interfaces on the DRAFT and RUNTIME panels respectively. The hardware boards installed in the RTDS cabinet mainly include GTWIF, GPC/PB5, GTAO/AI, GTDO/DI, etc.

3.2 Experiment Scheme In the real-time simulation and prototype test, we use a PRC standard recommended example: . The topology of the example is shown in Fig. 5. It is a 50 Hz three-phase A.C system with

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LV Q1

HV

L1=20km

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L2=10km

MV L4=10km L3(a)=5km

L5=15km

L3(b)=5km

Q2 L6=1km

M3 M2

Fig. 5 The topology of the standard example

8 bus (No. 1–8) and other electrical equipment. When a three-phase short circuit occurs, the bus 1–8 are short-circuit points. This example model was established based on the platform of MATLAB/Simulink offline simulation and RTDS real-time simulation. The measured quantity and interaction quantity are got the output and imported the input through the GTAO board and GTAI board of RTDS during the RTDS experiment. The wiring between the prototype and RTDS is shown in Fig. 6. The experimental steps are as follows. (1) Firstly, build the above example model on the MATLAB/Simulink offline simulation platform. Set up five kinds of conditions to simulate the short-circuit capacity tester, and record the values. (2) Next, build a same model on the RTDS real-time simulation platform, then complete the experimental wiring shown in Fig. 6 and insure that it is absolutely correct. Run the RTDS model and verify the correctness of the model through the RTDS monitoring platform. (3) Run the power amplifier, check that the output voltage and current of the power amplifier are consistent with RTDS. (4) The steady data of three-phase voltage of 10 kV bus and transient data of capacitor disturbance are transmitted to the prototype through Ethernet. Start the prototype, switch the capacitor by setting RTDS, the short-circuit capacity can be calculated after starting the measurement program.

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Fig. 6 The wiring diagram of the experiment on RTDS

(5) The short-circuit capacity tester was used on the RTDS real-time simulation platform to measure the 10 kV bus under the same five conditions as in Sp.1, record the values. Compared and analyzed it with theoretical value and the results of MATLAB/Simulink.

4 Comparative Analysis of Experimental Results 4.1 Cross-Validation Simulation Under Typical Conditions In order to ensure the reliability of simulation, this experiment used two completely different simulators for cross-validation simulation. That is, both RTDS and MATLAB/Simulink simulators are used for simulation. When the two simulators get the same results under various simulation scenarios, the simulation is considered effective. Five typical conditions are set in the experiment, and the following is illustrated by taking condition 1 as an example. Condition 1 means that the synchronous generators G1 and G2 are connected to the grid, and 10 kV bus is running without any load. At this time, the short-circuit capacity of each node of the grid should have the maximum value. Test 1 in condition 1

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Fig. 7 The waveform of the voltage difference on RTDS and MATLAB/Simulink

Fig. 8 The waveform of the short-circuit current on RTDS and MATLAB/Simulink

means that a group of 50Mvar shunt capacitors are put into the 10 kV no-load bus in the RTDS model, observe the voltage waveform before and after putting the shunt capacitor, as shown in Fig. 7a. The voltage difference V before and after putting is 0.792 kV. Putting into a group of 50 Mvar shunt capacitors on the 10 kV no-load bus in the MATLAB/Simulink model, observe the voltage waveform before and after putting the shunt capacitor, as shown in Fig. 7b. The voltage difference V before and after putting is 0.797 kV. It can be seen from Fig. 7 that the two simulation waveforms have the same change rule under the same disturbance of the capacitor. Observe the voltage steadystate value difference before and after putting the capacitor: 0.792 kV in RTDS, 0.797 kV in MATLAB/Simulink. It means that cross-validation is consistent under this condition. Test 2 in condition 1 means that a three-phase short-circuit fault are put into the 10 kV no-load bus in the RTDS model, observe the current waveform, as shown in the Fig. 8a. The RMS of the short-circuit current I k is 25.48 kA. Putting a threephase short-circuit fault on the 10 kV no-load bus in the MATLAB/Simulink model, observe the current waveform, as shown in the Fig. 8b. The RMS of the short-circuit current I k is 25.51 kA.

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Table 1 Results of the prototype on MATLAB/Simulink under different conditions Working conditions

Description

Theoretical value

Result of MATLAB/Simulink

Error of MATLAB/Simulink (%)

1

Complete topology, T5 and T6 parallel running

464

472

1.72

2

Complete topology, T5 and T6 split running

241

244

1.24

3

Q1 and Q2 split, T5 and T6 parallel running

407

413

1.5

4

Q1 and Q2 split, T5 and T6 split running

220

225

2.27

5

Complete topology, G1 and G2 exit

451

459

1.78

4.2 Simulation Experiment Result Analysis After the cross-validation of five typical working conditions is consistent, the shortcircuit capacity tester can be tested in RTDS, and the results will be compared and analyzed with the results of MATLAB/Simulink offline simulation. Simulation results are shown in the following Tables 1 and 2. It can be seen from above tables that the test results of MATLAB/Simulink and RTDS are almost identical under these five conditions, and the maximum error of the obtained measurement results of the two platforms is 2.27 and 1.81%. It is the simulation error in the extreme case where the short-circuit capacity is close to the value of the load. This value fully demonstrates the measurement principle proposed in this paper and the accuracy of the prototype. Therefore, this method solves the accuracy problem of the previous measurement, thus has practical value.

5 Conclusion The measurement principle of the non-fault measurement method of grid bus shortcircuit capacity proposed in this paper is rigorously theoretically deduced, and the measurement method has high accuracy. At the same time, it will not affect the grid safety. The method does not limit the specific operation mode of the grid, does not affect the normal operation of the grid transmission and distribution, does not require

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Table 2 Results of the prototype on RTDS under different conditions Working conditions

Description

Theoretical value

Result of RTDS

Error of RTDS (%)

1

Complete topology, T5 and T6 parallel running

464

470

1.29

2

Complete topology, T5 and T6 split running

241

245

1.66

3

Q1 and Q2 split, T5 and T6 parallel running

407

411

0.98

4

Q1 and Q2 split, T5 and T6 split running

220

224

1.81

5

Complete topology, G1 and G2 exit

451

457

1.33

complete grid parameters, and has safety, convenience and timeliness, effectively making up for the limitations of short-circuit capacity calculation. Based on this method, the short-circuit capacity extension solution of the adjacent substations can be calculated by the fixed short-circuit capacity test terminal, thereby forming a regional short-circuit capacity monitoring system. Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Fund of China (51567005) and Guizhou Province Joint Fund Project (LH[2017]7230, [2017]5788). Guizhou Science and Technology Innovation Talents Team Project [2018]5615.

References 1. Xu, J., Wang, T.: Research on short circuit capacity and voltage stability monitoring method of AC/DC hybrid system. Eng. J. Wuhan Univ. 50(1), 64–68, 96 (2017) 2. Tan, Z., Chen, Z., et al.: Architecture analysis and simulation research of distributed generation for flexible distribution network. In: ICMIC 2018, Article number: 8529981 3. Wu, Y., Hu, B., Zhu, M.: Experimental study on calculation of short-circuit capacity of Busbars in Tongchuan and Yaoxian substation using load interference. Northwest China Electric Power 2, 1–10 (1996) 4. Pan, H.: Measurement of short-circuit capacity of connection point of intermediate frequency furnace. Appl. Electr. Eng. 2, 24–26 (2013)

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Wei Chen is a postgraduate student. Her research direction is power system analysis and control. Zhenghang Hao is received Ph.D. degree in electrical engineering from Tianjing University, Tianjing, China. At present he is an Professor with the Electrical Engineering Department at Guizhou University.

A 3-D Deployment and Coverage Algorithm for Aircraft Cargo Rui Wang, Chengrui Bai, Lei Gao and Hui Sun

Abstract Cargo environment safety plays an important role in civil aviation. It is a huge threat if an emergency event happens, for example, a fire breaks out on a plane. An accurate alarm of fires can help the crew tackle with it in time and avoid larger property loss. However, there exists false fire alarms during a flight which usually leads to unexpected landing. Using Wireless Sensor Network (WSN) for fire monitoring can remarkably decrease false alarms. This paper proposes a WSN deployment and coverage strategy in aircraft cargo so that every place is under at least one sensor’s monitor to avoid ignoring any possible fire source in order to help improve the accuracy of fire alarm. The simulation results demonstrate that our algorithm can successfully deploy a WSN with 100% coverage rate, which is usually called k-coverage when k = 1. Keywords Artificial Bee Colony algorithm · 3-D coordinates · Cargo

1 Introduction Civil aviation has become one of the most important industries in China. Statistical Bulletin of Civil Aviation Industry Deployment in 2018 points out that passenger traffic reached 611.73 million in 2018 [1]. As a sunrise industry, civil aviation is growing rapidly and steadily. For civil aviation, safety is of vital importance including cabin environment. An accurate fire alarm could help the aircrew cope with it timely, thus saving passengers’ lives and avoiding larger property loss. However, false alarm usually happens and causes extra huge property loss. For example, at 21:35 on Nov. 13th, 2017, when a Boeing 737 aircraft of China Southern Airlines CZ6404 was in the cruise phase, a fire alarm happened in the cargo. The crew immediately decided R. Wang · C. Bai · L. Gao · H. Sun (B) Department of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] H. Sun Department of Engineering Design and Mathematics, University of the West of England, Frenchy Campus, Coldharbour Lane, Bristol BS16 1QY, UK © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_125

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the alternative landing spot and made a safe landing. Eventually, the cargo fire alarm proved to be false due to sensor fault [2]. Multiple similar events indeed cause huge property damage and waste a lot of time. Therefore, improving alarm accuracy has great significance. Nowadays, a single fire detector is deployed in the aircraft cargo. Once there is sensor fault or measurement bias, false alarm cannot be effectively avoided. Wang et al. studied the issue of contaminant concentration estimation by using consensus Kalman filter under Wireless Sensor Network (WSN), eventually, the concentration estimations converge accurately and quickly [3]. Furthermore, the accuracy of estimation was improved. This algorithm effectively avoids sensor fault and measurement bias so that the judgement of fire can be more accurate. Compared to Wired Sensor Network, using Wireless Sensor Network could not only prevent us from wiring troublesome, but also avoid the potential risks caused by cable aging. Additionally, the weight of an airplane can be decreased. Considering the advantages above, a WSN based monitoring system of contaminant or fire has great superiority. Notay et al. deployed WSN on airplane for Structural Health Monitoring, as shown in Fig. 1. This network was simulated on OPENT modeler. The result validated this algorithm [4]. Therefore, WSN deployment on aircraft is promising and has practical significance. Fig. 1 WSN based structural health monitoring for an airplane [4]

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Many approaches have been proposed on WSN deployment and coverage. Among Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Artificial Immune System(AIS), ABC is less complex with almost equal performance and has good scalability [5]. On a 2-D plane, Udgata et al. applied Artificial Bee Colony (ABC) algorithm to irregular terrain WSN deployment [6]. Yuan proposed a layered method in WSN deployment, which decreases the complexity of algorithm [7]. With the development of studies on WSN, the 2-D plate sensing model is unable to adapt to practical application scenarios. So 3-D WSN deployment issue is proposed, which is far more complex [8]. In 3-D space, Sun et al. proposed a grid base dimension reduction process. Then genetic algorithm was used to deploy WSN on hill terrain [9]. Yu mapped the 3-D hill terrain to 2-D plane, and the grid division was implemented. Through the usage of ABC algorithm, WSN is deployed on the unique terrain [10]. In this paper, we study the issue of WSN deployment in aircraft cargo. The main contribution of this paper is that a metaheuristic method, Artificial Bee Colony, is applied to the 3-D WSN deployment algorithm. A sphere sensing model is applied to all sensor nodes, and the positions are calculated directly in 3-D coordinate system. Eventually, the whole monitored region is under 100% coverage rate. The simulations prove that this algorithm is suitable for WSN deployment in enclosure space, such as aircraft cargo.

2 Related Concepts Concept 1 K-coverage. It is required that each location of the target region is covered by at least k sensors, where k is a positive integer whose value is usually no less than 1. In this paper, we just consider accomplishing 100% coverage rate, so k = 1. Concept 2 Sensing Neighbor Node Set, N s . For any sensor node i, its sensing neighbor nodes are those located within sensing radius R S . It is defined as follows. N S (i) = { j ∈ |d(i, j) ≤ R S , i ∈ , j = i}

(1)

Concept 3 Network Coverage Rate, η. The denominator is the area of monitored region M. The numerator is the sensing region made of all the sensors nodes’ sensing region within monitored region M. It is expressed as follows. ar ea η=

 

 Si



 M

i∈ϕ

ar ea(M)

where ϕ represents the set of all sensor nodes on work in monitored region M. Si is the area of sensing region of node i.

(2)

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Network coverage rate is an important target when assessing network coverage quality. It represents the ability of WSN to collect information. Concept 4 0–1 Sensing Model. It is also called plate sensing model. We assume that the sensing region of a sensor node is the circle plate whose center is the location of node i. Points within the sensing radius can be sensed by the sensor, and on the contrary, those out of the sensing radius cannot be sensed. As formula (3) shows.  Csi (P) =

1 , d(si , P) ≤ R 0 , d(si , P) > R

(3)

3 ABC Based 3-D WSN Deployment Strategy Artificial Bee Colony Algorithm was first proposed by Dervis Karaboga which is used to solve optimization problem of multi-variables [11]. It is divided into four stages, they are initialization stage, employed bee stage, onlooker bee stage and scout bee stage.

3.1 Initialization Stage In terms of original ABC algorithm, NP food sources are generated by random search during initialization stage, and then each food source is allocated to an employed bee. The number of employed bees is NP, too. The producing formula is as follow. + ri j × (vmax − vmin ) vij = vmin j j j

(4)

When it comes to WSN deployment and coverage in 3-D regular space, every potential solution’s dimension is N. It means that there are N sensor nodes to be deployed. We should consider three directions x, y, z of the coordinate of each sensor node. Thus, three generating formulas produce NP potential solutions in each direction. We modify the generating formulas as follows.   xij = x min + rij × x max − x min   yij = y min + rij × y max − y min   z ij = z min + rij × z max − z min

(5)

where i represents the randomly searched potential solutions, i = 1, 2, …, NP. j represents the sensor nodes, j = 1, 2, …, N, ri j ∈ [0, 1].

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3.2 Employed Bee Stage Employed bee i randomly selects a food source k. k is randomly selected from NP potential solutions, i = k. Then the ith employed bee searches a new food source, called the candidate food source between i and k. The search formula is as follow.

vi j (k + 1) = vi j (k) + ϕi j × vi j (t) − vk j (t)

(6)

Therefore, in the scenario proposed in this paper, the paper generates candidate solutions in three directions x, y, z, where ϕ ∈ [−1, 1].

xi j = xi j + ϕi j × xi j − xk j

yi j = yi j + ϕi j × yi j − yk j

zij = z i j + ϕi j × z i j − z k j

(7)

Then calculate the fitness value of each candidate solution. The original formula is shown as follows, where k represents the current number of cycles.  f iti (k) =

1 , 1+ f i (k)

f i (k) ≥ 0 1 + | f i (k)|, f i (k) < 0

(8)

The formula above is usually used to search the minimum value of an optimization function. The value of function may be positive or negative. In terms of WSN deployment issue, the actual problem is to search one solution that makes the coverage rate maximum. The coverage rate is always between 0 and 1. For ABC algorithm, the larger the fitness value is, the better the quality of food source is, then the better the quality of solution is. Then the bigger fitness value will replace the smaller one. All NP candidate solutions should be processed in this way, so that NP new potential solutions are generated.

3.3 Onlooker Bee Stage NP onlooker bees come out. Each of them selects a food source according to probability p. pi (k) =

0.9 × Fiti (k) +0.1 Fitmax (k)

(9)

where Fitmax (k) is the maximum potential solution in the kth cycle. The modified formula (9) guarantees that the potential solution with the max fitness value can always be selected by at least one onlooker bee. For other potential

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solutions, the probability to be selected is larger if its fitness value is larger. The employed bee searches a new candidate solution near the selected solution. If a better solution is found, the old solution is alternated by the new one. If the new one is worse, this situation is recorded by the system. The effect of the onlooker bee stage is to try to find new candidate solutions with better quality near the existing solutions. Inferior solutions may be abandoned.

3.4 Scout Bee Stage The variable mentioned above is used to calculate how many times a potential solution hasn’t been updated by a new candidate solution during onlooker bee stage. If this variable exceeds a predefined threshold value, this solution is then abandoned. A new potential solution is searched globally with formula (9) above.

4 Simulation As shown in Table 1, the protection radius of fire detector is given by National Standard GB 50116-2013 in Code for design of automatic fire alarm system [12]. Fire smoke can be detected within protection radius. For fire monitoring, the smoke is detected by the sensor when it flows with air into the fire detector. The cargo is an enclosed space, so air flowing is slow, and smoke flows slowly, too. It is not helpful for finding fire if the fire detector is located so far away. Obviously, several detectors should be deployed to cover the whole space. The alarm would be delayed if sensing radius Rs is set too large. Considering the GB standard and sensing redundancy, sensing radius Rs is set as 2 m. The simulations in this paper are based on MATLAB 2017a and use Boeing 737200 cargo as an example. The length of the cargo is about 6 meters, width is about 3.5 m and height is about 1.6 m. 0–1 sensing model is considered for this case. NP is set 10. Max cycle number is set 1000. 100% coverage rate is accomplished using the algorithm mentioned in Sect. 3. Table 1 Protection area and radius of smoke fir detector and heat fire detector Types of fire detectors

Ground area S/m2

Room height h/m

Protection area A/m2

Protection radius R/m

Smoke fire detector

S ≤ 80

h ≤ 12

80

6.7

S > 80

6 < h ≤ 12

80

6.7

h≤6

60

5.8

S ≤ 30

h≤6

30

4.4

S > 30

h≤8

20

3.6

Heat fire detector

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The coordinates generated by ABC is usually randomly, which means that a sensor node may be deployed at any location. In fact, however, sensors can only be deployed at places such as the wall and proof. They can’t be hung in the air. So the proposed algorithm should be modified at this step. All the generated deployment locations that can’t be reached are moved to the nearest locations which can be reached. Then candidate solutions are generated based on the new points. The simulation results are shown as Figs. 2 and 3. Figure 2 shows that 100% coverage rate is fulfilled by 6 sensor nodes, and it is also called k-coverage when k = 1. The red points are the centers of sensor nodes. Their coordinates are (22, 18, 16), (34, 0, 4), (0, 10, 7), (44, 35, 7), (12, 35,

Fig. 2 A sketch map of the deployment of sensor nodes in cargo

1 0.995 0.99 0.985 0.98 0.975 0.97 0.965 0.96 0

100

200

300

400

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Fig. 3 Coverage rate that varied with the number of cycles

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12), (60, 15, 11). All these locations are on the wall or proof of the cargo. It’s easy to deploy sensor nodes at these locations. So it proves to be feasible. Figure 3 shows the optimal solution is found in 100 cycles, which means this algorithm is fit to this kind of scenario.

5 Conclusions A ABC based 3-D deployment and coverage algorithm is proposed in this paper. All the sensors use a sphere sensing model. It is directly calculated in a 3-D coordinate system. The simulation results prove that this algorithm is fit to enclosed space scenarios like aircraft cargo. In the future, we consider to study k-coverage when k > 1 with this algorithm. Besides, the deployment algorithm for dynamic networking will be considered when sensor faults occur. Acknowledgements This work was supported by the Civil Aviation Science and Technology Project (MHRD20150220), the Fundamental Research Funds for the Central Universities-Civil Aviation University of China (3122017003) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

References 1. CAAC Issues Statistical Bulletin of Civil Aviation Industry Development in 2018. http://www. caac.gov.cn/en/XWZX/201905/t20190524_196356.html 2. Fire Alarm Incident on a China Southern Airlines Flight Successfully Handled. http://www. caac.gov.cn/en/XWZX/201712/t20171208_47933.html 3. Wang, R., Wang, X.Y., Sun, H., Huang, Y.T., Chen, Z.Q.: Analysis of estimator and energy consumption with multiple faults over the distributed integrated WSN. Int. J. Model. Ident. Control (2019) 4. Notay, J.K., Safdar, G.A.: A wireless sensor network based structural health monitoring system for an airplane. In: 17th International Conference on Automation and Computing, pp. 240–245. IEEE Press, Huddersfield (2011) 5. Kumar, M., Gupta, V.: A review paper on sensor deployment techniques for target coverage in wireless sensor networks. In: 2016 International Conference on Control, Instrumentation, Communication and Computational Technologies, pp. 452–456. IEEE Press, Kumaracoil (2016) 6. Udgata, S.K., Sabat, S.L., Mini, S.: Sensor deployment in irregular terrain using Artificial Bee Colony algorithm. In: 2009 World Congress on Nature & Biologically Inspired Computing, pp. 1309–1314. IEEE Press, Coimbatore (2009) 7. Yuan, H.: Wireless sensor nodes deployment based on improved swarm optimization algorithm. Appl. Res. Comput. 27, 2704–2705+2708 (2010) 8. Wang, D.D., Xu, T.R.: K-coverage and multi connectivity method for 3D surface wireless sensor network. Appl. Res. Comput. 35, 2110–2113 (2018) 9. Sun, Z.L.: Research of coverage strategy in three-dimensional environment for wireless sensor networks. Master, Dalian University of Technology, (2013) 10. Yu, W.J.: Research on Artificial Bee Colony based Deployment Problem in Wireless Sensor Network. University of Electronic Science and Technology of China, Doctor (2018)

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11. Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algorithm. J. Global Optim. 39, 459–471 (2007) 12. Code for design of automatic fire alarm system. http://www.mohurd.gov.cn/wjfb/201509/ t20150911_224820.html

Optimal Tilt Integral Derivative Controller with Filter Design for Quadrotor Based on Adaptive Particle Swarm Optimization Yimin Zhou, Bo Han, Kranthi Kumar Deveerasetty and Junhai Cao

Abstract In this paper, a Tilt Integral Derivative controller with Filter (TIDF) is proposed for attitude control of an unmanned aerial vehicle (UAV). The parameters of the proposed controller are optimized using Adaptive Particle Swarm Optimization (APSO) employing an Integral Square Error (ISE). Further, the fitness function in the APSO is modified and the inertia weight of the current velocity is updated based on the fitness value of each individual at the previous moment. Experiments are performed to examine the performance of the developed controller. Compared with the traditional controllers, the proposed controller has higher performance on the robustness and stability. Keywords Tilt Integral Derivative controller with Filter (TIDF) · Adaptive Particle swarm optimization (APSO) · Parameter optimization · Unmanned aerial vehicle (UAV)

1 Introduction Unmanned Aerial Vehicle (UAV) has gained a lot of attention in the early 2000s in the field of robotics. The primary focus is the attitude control of the quadrotor and many papers have been written concerning their flight dynamics. Various control methods have been proposed for the quadrotor trajectory tracking. The goal is to develop a control strategy that allows the states of the quadrotor to converge to the set of time-varying reference states of an arbitrary set. The performance of the quadrotor can be achieved by using nonlinear control techniques, however, many researchers have also developed linear control techniques Y. Zhou (B) · B. Han · K. K. Deveerasetty · J. Cao Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China e-mail: [email protected] B. Han School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_126

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[1–4] by linearizing the dynamics around an operating point, usually to be the hover. The most popular nonlinear controller techniques for the quadrotor controller are sliding mode control [5–7], backstepping [8] and feedback linearization [9]. The quadrotor dynamics is separated as an inner loop containing the attitude and the position is separated as an outer loop of the quadrotor. The outer loop is added to control the inner loop. Feedback linearization control is transformed from the nonlinear system into an equivalent linear system through a suitable control input and variation. The above all nonlinear control techniques require an accurate nonlinear quadrotor dynamics model otherwise it could cause significant stabilization errors. To correct the errors in the model parameters estimation, linear adaptive methods are useful to be applied, such as Model Reference Adaptive Control (MRAC) [10]. The mass uncertainty of the UAV can be compensated by using nonlinear adaptive controller based on backstepping technique [11]. A three-layer control architecture is developed, where the controller is designed to stabilize the UAV helicopter by considering external disturbances. The second part is designed to use a nonlinear outer-loop controller to efficiently control the UAV position and yaw angles and the third part is a flight-scheduling layer for coordinating flight missions [12]. A nonlinear Model Predictive Control (MPC) is designed in the distributed UAV formation flight control law to overcome the obstacle avoidance [13]. The PI controller is implemented in the height control system using velocity stabilizing in the inner loop. Roll, pitch and yaw attitude are controlled with the aid of angular rate to stabilize the inner loops [14, 15]. A fuzzy logic controller is employed to render a satisfactory trajectory tracking for the quadrotor in the presence of disturbance and model uncertainties [16]. Furthermore, a Proportional Integral Derivative controller with Filter (PIDF) is proposed for the position and attitude control of the quadrotor [17, 18]. In this paper, a tilted integral derivative controller is proposed to deal with the disturbances and uncertainties. The remainder of the paper is organized as follows. Section 2 explains the dynamic model of the quadrotor. The proposed TIDF is introduced in Sect. 3 and the involved parameters are optimized by Adaptive Particle Swarm Optimization algorithm in the same Section. Experiments are performed to testify the effectiveness of the proposed optimization algorithm in Sect. 4. Conclusion is given in Sect. 5.

2 Quadrotor Modeling and Control Architecture The main mathematical equation and control architecture for the quadrotor is explained in this section.

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2.1 Dynamical Model of the Quadrotor In order to obtain the mathematical model of the quadrotor, two basic coordinate systems are firstly established: inertial coordinate system E(O X Y Z ) and aircraft coordinate system B(O X Y Z ). In Fig. 1, Euler angles are respectively defined as follows: • Roll φ: the angle between the projection of O y onto the OY Z plane and the Y axis; • Pitch θ : the angle between the projection of Oz onto the O X Z plane and the Z axis; • Yaw ψ: the angle between the projection of Ox onto the O X Y plane and the X axis. For simplicity, several assumptions are made to develop the quadrotor model [1]: • The quadrotor construction is rigid and symmetric; • The propellers are rigid; • Thrust and drag are proportional to the square of the propellers speed. According to these assumptions, it is feasible to describe the dynamics of the rigid body and aerodynamic forces caused via rotor rotation. The involved system parameters are listed in Table 1.

Fig. 1 The illustration of the structure analysis of the quadrotor

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Table 1 The parameters of the quadrotor Symbol Physical meaning m l

b d Ix Iy Iz g Jr

Quadrotor quality Length of the rotor arm from the origin of the coordinate system Thrust coefficients Drag coefficients X-axis moment of inertia Y-axis moment of inertia Z-axis moment of inertia Gravity acceleration Rotor inertia

Value 1.5 0.25

3.179 × 10−5 7.932 × 10−7 1.96 × 10−2 1.96 × 10−2 3.93 × 10−2 9.8 0.044

By using the Newton-Euler formula [2], the equations of the motion are given as, ⎧   ⎪ ¨ = θ˙ ψ˙ I y −Iz − Jr θ˙  + l U2 φ ⎪ ⎪ Ix ⎪  Ix  Ix ⎪ ⎪ Iz −I x Jr ˙ ⎪ ¨ ˙ ˙ θ = φψ − φ + Ily U3 ⎪ ⎪ ⎨  Iy  Iy I −I ψ¨ = φ˙ θ˙ x Iz y + Ilz U4 ⎪ ⎪ ⎪ x¨ = (cos φ sin θ cos ψ + sin φ sin ψ)U1 /m ⎪ ⎪ ⎪ ⎪ y¨ = (cos φ sin θ sin ψ − sin φ cos ψ)U1 /m ⎪ ⎪ ⎩ z¨ = −g + (cos φ cos θ )U1 /m

(1)

While the inputs to the four rotors are expressed as, ⎧ U1 ⎪ ⎪ ⎨ U2 ⎪ U3 ⎪ ⎩ U4

= b(21 + 22 + 23 + 24 ) = b(−22 + 24 ) = b(21 − 23 ) = d(−21 + 22 − 23 + 24 )

(2)

The simplified mathematical model is transformed into a state space equation by using modern control theory. Then, according to the parameters of the quadrotor in Table 1 and the transfer function: G(s) = (s I − A)−1 B, the transfer function of each control channel can be obtained as: ⎧ ¨ ⎪ G 1 = uφ2 = s 3 +109s65s+4560 2 +1023 s+2935 ⎪ ⎪ ⎪ θ¨ 56.95s+4391 ⎪ ⎪ G = = 2 3 ⎪ u3 s +105s 2 +870s+4430 ⎪ ⎨ ψ¨ G 3 = u 4 = s 2105 +413 (3) 1.63 ⎪ G 4 = uz¨4 = s(s+5) ⎪ ⎪ ⎪ −190s+567 ⎪ ⎪ G 5 = θx¨ = s(57.95s+4400) ⎪ ⎪ ⎩ G 6 = φy¨ = −276.4s+743.5 s(61s+4463)

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Because of the delayed response of GPS sensors, a non-linear time-delay should be added to the position control loop: G = e−T s

(4)

where T = 0.1s is the delay time.

2.2 Control Architecture Based on the model of the quadrotor, the Active Disturbance Rejection Controller (ADRC) is used to develop the basic control frame, seen in Fig. 2. This control structure has two loops, the outer loop and the inner loop, which can be considered as a cascade or hierarchical control structure. The outer loop is used to provide the desired attitude angle, and the inner loop is used to track these angles to obtain the desired space Descartes position. The altitude is controlled via U1 , while U4 controls the yaw motion. The desired roll and pitch angles are generated to the attitude controller from the position subsystem, which are controlled by U2 and U3 , respectively. Once the desired (xb , yb , z b , ψb ) are set, the position controller can generate the required (θb , φb ) to the attitude controller. The measured quantities are provided as a feedback signal to both the control loops. The proposed controller design is explained in the next Section.

Fig. 2 The structure of the ADRC

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3 Tilt Integral Derivative Controller with Filter 3.1 The TIDF Design In the proposed controller for position control, the proportional mode of the typical PID controller is substituted with a tilted mode, consisting of a transfer function of 1 1 . The TID controller can ensure an optimal transfer function. In the TID controller, ss the derivative component is useful to amend the stability of the system and increase the controller response speed as well. However, if any noise exists in the control input, it could lead to large bias on the input signals which would complicate in real-time applications. To overcome this problem, a first-order filter is introduced in the derivative component and the involved parameter is adjusted to reduce the chattering due to high-frequency noise suppression. The structure of the designed TIDF is demonstrated in Fig. 3. To the best knowledge of the authors, no investigation has been done on the TIDF controller structures for the UAV. In this paper, an optimal design of TIDF controller based on PSO for the attitude control of a UAV is proposed. The main objectives of this paper are: • To design and implement a new TIDF controller for attitude controller of a UAV. • To exhibit the benefits of the proposed TIDF controller over a PID controller. • To design TIDF in Simulink environment for UAV studies and evaluate the dynamic system response.

Fig. 3 The structure of the TIDF controller

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3.2 Adaptive Particle Swarm Optimization (APSO) 3.2.1

APSO Design

APSO is applied to tune the parameters in the TIDF controller. PSO is a heuristic algorithm which is inspired by the social behaviour of bird foraging. Each particle has its own position X and velocity V in the searching space. During the optimization process, the positions and velocities of each particle are modified based on the current velocity, current position, the best individual position obtained by the particle itself and the best global position obtained by the whole particle swarm. Therefore, each particle has a tendency towards the best position. The modified process of each particle is shown in Fig. 4. The velocity and the position of the ith particle are updated as follows, Vi iter +1 = ωVi iter + c1r1 (Pbest − X i iter ) + c2 r2 (G best − X i iter ),

(5)

X i iter +1 = X i iter + Vi iter +1

(6)

where Vi and X i are the velocity and position of the ith particle; the upper label iter denotes the current iteration; Pbest represents the individual best position obtained by the ith particle; G best represents the global best position among the swarm. c1 and c2 are called cognitive factor and social factor, respectively, which can influence the Pbest and G best of the updated position; r1 and r2 are the random numbers among (0, 1); ω is the inertia weight. The PSO algorithm has the advantages of simple operation and fast convergence. However, as the number of iterations increases, the particles could be trapped into local minimums. In order to solve the local optimal problem in the optimization calculation process, the adaptive mechanism of the inertia weight is introduced into

Fig. 4 The optimization movement of particles in the search space

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the update process. The inertia weights can be dynamically modified to maintain a balance between global search capabilities and local search capabilities. The swarm is divided into different groups based on the individual fitness, and different adaptive operations are used to maintain the diversity of the inertia weights. The inertia weight of the particle with larger fitness value is smaller, which is used for local optimization to accelerate the convergence of the algorithm. The inertia weight of the particle with smaller fitness value is larger, which is used to jump out of the local minimum to achieve global optimization. In this particular method, the particles Pi with the fitness value f i and the inertia weight ω are adjusted as follows, (1) ⎧  ⎪ ⎨ f i > f avg , ⎪ ⎩ ω = ω − (ω − ωmin )|

 f i − f avg

fm −

 f avg

|,

(7)

where f i is the fitness value of the particle Pi , f avg denotes the average fitness value,  is obtained by averaging the fitness value, which is better than favg ; f m represents f avg the fitness value of the optimal particle, ωmin is the minimum value of ω. Here, ωmin = 0.5. These particles are the best particles in the swarm, and they are relatively close to the global optimal position and should correspond to a small inertial weight. The inertia weight of the particle Pi is adjusted according to the particle fitness value. The better the particles, the smaller the inertial weight and the stronger the local optimization. (2) 

 f avg < f i < f avg ,

ω = ω.

(8)

These particles are the general particles in the group with good global optimization and local optimization capabilities, so their inertia weight would be kept as the same values. (3) ⎧ ⎪ ⎨ f i < f avg , 1 (9) ⎪ ⎩ ω = 1.5 − (ω − 1 + a exp(−a | f − f  |) , 1 2 m avg where a1 is the upper bound of ω and a2 is used to control the adjustment ability of ω. These particles are the poor particles in the group and their inertia weights are adjusted based on the adaptive algorithm.

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APSO Corresponding to TIDF

There are 5 adjustable parameters required in the TIDF controller for the attitude control system: n, K P , K I , K D and NC . n is set as 3, and the rest four parameters are used as the particles in the PSO. Choosing the appropriate fitness function is the basis for updating velocity and position of the particles. Based on the integrated time absolute error (ITAE) criterion, the system error, control quantity and overshoot are comprehensively considered under the stability, dynamic performance and steadystate performance requirements of the system. The fitness function expression are as follows, ⎧ e = ϕd − ϕ, ⎪ ⎪ ⎪ ⎪ ⎨ J = (ω1 ∗ |e| ∗ t + ω2 ∗ u 2 + ω3 ∗ |e|)dt, (e > 0), ⎪ ⎪ ⎪ ⎪ ⎩ J = (ω1 ∗ |e| ∗ t + ω2 ∗ u 2 )dt, (e < 0),

(10)

where J is the fitness value of the particles, ω1 = 1, ω2 = 0.01, ω3 = 0.99. The pseudocode of the optimization procedure is shown in Algorithm 1. Algorithm 1 APSO optimization procedure 1: Initial the particle swarm 2: for i = 1 to 50 do 3: calculate the fitness value of each particle X i 4: if Fitness value X i > history best value Pbest then 5: Pbest = X i 6: end if 7: if X best > G best then 8: G best = X best 9: end if 10: for each particle do 11: Update inertia weight by Eq. (7), (8), (9) 12: Update velocity by Eq. 5 13: Update position by Eq. 6 14: end for 15: end for

4 Experimental Analysis The parameter settings of the APSO are shown in Table 2. Assuming the roll, angle pitch angle and yaw angle as 60◦ , the performance comparison before and after optimization is shown in Table 3.

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Table 2 The parameters of the APSO Parameter c1 c2 itermax Dimension Size Vmax Vmin Ub Lb

Value [ωc , ωo , b0 ] 2 2 50 4 50 [1, 1, 1] [−1, −1, −1] [100, 100, 100, 100] [0.001, 0.001, 0.001, 60]

Table 3 Performance comparison with and without optimization Angle Performance Before optimization Pitch Yaw Roll

Overshoot/% Adjustment time/s Overshoot/% Adjustment time/s Overshoot/% Adjustment time/s

13 0.52 18 0.48 23 0.42

After optimization 7 0.38 10 0.27 6 0.26

The variation curve of each parameter and the simulation result after optimization are shown in Figs. 5, 6, 7, 8 and 9. The simulation results demonstrate that the TIDF controller optimized by APSO has smaller overshoot and adjustment time, and it has higher control performance for the attitude control of the quadrotor.

Fig. 5 The optimal individual fitness value

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Fig. 6 The parameters of the optimized curve

Fig. 7 Pitch angle control curve with and without optimization

5 Conclusion In this paper, an attitude controller of quadrotor based on TIDF id designed. Noted that manually tuning the parameters of the TIDF is time-consuming and difficult to achieve the optimal solution. In order to overcome this problem, the parameter optimization method of the attitude control system based on APSO is proposed. The results demonstrate that the APSO can effectively solve the problem of the parameters adjustment of the TIDF controller. The optimized attitude TIDF controller has better

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Fig. 8 Yaw angle control curve with and without optimization

Fig. 9 Roll angle control curve with and without optimization

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dynamic and steady-state characteristics, and the adjustment time is short and easy to be implemented. Acknowledgements This work is supported under the Shenzhen Science and Technology Innovation Commission Project Grant Ref. JCYJ20160510154736343 and Ref. JCYJ20170818153635759, and Science and Technology Planning Project of Guangdong Province Ref. 2017B010117009, and Guangdong Provincial Engineering Technology Research Center of Intelligent Unmanned System and Autonomous Environmental Perception.

References 1. Jategaonkar, R.V.: Flight Vehicle System Identification: A Time Domain Methodology. American Institute of Aeronautics and Astronautics (2015) 2. Cowling, I.D., Yakimenko, O.A., Whidborne, J.F., Cooke, A.K.: A proto type of an autonomous controller for a quadrotor UAV. In: European Control Conference (ECC), pp. 1–8 (2007) 3. Bouabdallah, S., Noth, A., Siegwart, R.: PID vs LQ control techniques applied to an indoor micro quadrotor. In: Intelligent Robots and Systems (IROS), vol. 3, pp. 2451–2456 (2004) 4. Pounds, P., Mahony, R., Corke, P.: Modelling and control of a quadrotor robot. In: Australian Conference on Robotics and Automation (2006) 5. Bouabdallah, S., Siegwar, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: International Conference on Robotics and Automation, pp. 2247–2252 (2005) 6. Xu, R., Ozguner, U.: Sliding mode control of a quadrotor helicopter. In: Conference on Decision and Control (CDC), pp. 4957–4962 (2006) 7. Lee, D., Kim, H.J., Sastry, S.: Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. Int. J. Control Autom. Syst. 7(3), 419–428 (2009) 8. Madani, T., Benallegue, A.: Backstepping control for a quadrotor helicopter. In: International Conference on Intelligent Robots and Systems, pp. 3255–3260 (2006) 9. Das, A., Subbarao, K., Lewis, F.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Appl. 3(3), 303–314 (2009) 10. Whitehead, B., Bieniawski, S.: Model reference adaptive control of a quadrotor UAV. In: AIAA Guidance Navigation and Control Conference, p. 8148 (2010) 11. Huang, M., Xian, B., Diao, C., Yang, K., Feng, Y.: Adaptive tracking control of under actuated quadrotor unmanned aerial vehicles via back stepping. In: American Control Conference (ACC), pp. 2076–2081 (2010) 12. Cai, G., Chen, B.M., Dong, X., et al.: Design and implementation of a robust and nonlinear flight control system for an unmanned helicopter. Mechatronics 21, 803–820 (2011) 13. Chao, Z., Zhou, S.L., Ming, L., Zhang, W.G.: UAV formation flight based on nonlinear model predictive control. Math. Prob. Eng. 1–15 (2012) 14. Alexis, K., Nikolakopoulos, G., Tzes, A.: Model predictive quadrotor control: attitude, altitude and position experimental studies. IET Control Theory Appl. 6(12), 1812–1827 (2012) 15. Tsay, T.S.: Guidance and control laws for quadrotor UAV. WSEAS Trans. Syst. Control 9, 606–613 (2014) 16. Mardan, M., Esfandiari, M., Sepehri, N.: Attitude and position controller design and implementation for a quadrotor. Int. J. Adv. Rob. Syst. 14(3) (2017) 17. Deveerasetty, K.K., Zhou, Y.: PID with derivative filter and integral sliding mode controller techniques applied to an indoor micro quadrotor. In: International Conference on Control, Automation and Systems, pp. 439–444 (2018) 18. Deveerasetty, K.K., Zhou, Y., Yang, Z., Wu, Q.: Robust control design for the trajectory tracking of a quadrotor. In: International Conference on Cyborg and Bionic Systems, pp. 351–356 (2018)

Apron-Aware Network Congestion Control Strategy Based on Opportunistic Transmission Weixing Chen, Meihan Meng and Jingfang Su

Abstract To improve data transmission efficiency of the apron network, multiple copies of packets are injected into the network. However, this method will result in more redundant data in the network, which further leads to network congestion. To solve the congestion, a Congestion Control Strategy based on Irregular Cellular Automaton (CCSICA) is introduced in this paper. In the apron environment, according to the interaction characteristics of the cellular automaton and surrounding neighbors, the existence of the replica of the neighboring node is fully considered. Then design the corresponding state transfer rules to achieve the purpose of more rational use of limited network resources. The simulation results show that the network overhead ratio and message delivery ratio can be improved dramatically by our proposed strategy. Keywords Apron sensing · Opportunistic network · Cellular automaton · Load balancing

1 Introduction In recent years, with the rapid development of China’s civil aviation industry, airport apron network monitoring has also gradually increased. Due to the extensive apron area, sparse nodes, ineffective node, limited communication distance of mobile nodes, and electromagnetic interference, the network is divided into several sub-areas that are not connected to each other, so that information transmission between nonconnected areas is blocked. The opportunity network [1] combines the characteristics of the intermittent connected network [2] and the delay tolerant network [3] mainly W. Chen · M. Meng (B) · J. Su Department of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] W. Chen e-mail: [email protected] J. Su e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_127

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relying on the opportunity of mobile node encounters for data multi-hop forwarding transmission to connecting the non-connected sub-domains. However, in order to improve the data transmission success rate, the multi-copy forwarding routing method is adopted. However, the continuous spread of message copies in the network can cause the relay node’s cache to be congested, causing the node to no longer accept new copies. For the above problems, researchers at home and abroad have conducted research on congestion control and load balancing of opportunistic networks. Wu et al. [4] proposed an adaptive cache management strategy for message delivery probability estimation. The probability of message delivery is estimated by constructing the node connection state and analyzing the service capabilities of the sensing node. Reference [5] defined utility function using the number of encounters and TTL. Document [6] used the remaining cache of neighbor nodes to transfer part of the information in the local node cache to achieve effective congestion control, but did not consider the discarded problem with the same replica node. Wang et al. [7] proposed a cache management algorithm based on message survival attributes, which mainly analyzes the impact of message forwarding times and time-to-live on message delivery. The cache replacement process is limited to retain newly generated messages and discard messages that are about to expire. Reference [8] designed a multi-path parallel data forwarding method to reduce the link load and stimulate the self-private node data forwarding. However, it ignores the congestion status of each node in the area where the node is located. Reference [9] proposed a congestion control strategy with node state awareness. The data forwarding process is dynamically adjusted by predicting the network state at the next moment. Reference [10] proposed a congestion control strategy based on early unloading, which uses other available paths to unload the node cache in advance to reduce the possibility of congestion, but does not classify the cache type. In summary, to solve the network congestion problem caused by insufficient cache in the data transmission process in the apron. A well-designed cache discarding strategy is a key issue in improving the success rate of the opportunity network transmission on the apron. This paper fully considers the inherent regularity of the apron network and the dynamics of the network. In the process of moving data transmission on the apron Agent node, the idea of irregular cellular automata is combined. Full consideration is given to the existence of replicas of neighboring nodes, and corresponding copy discarding rules are formulated, thereby effectively avoiding the impact of congestion on message transmission.

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2 Apron Monitoring System and Model Based on Opportunistic Network 2.1 Analysis of Apron-Aware Network Problems A detailed analysis of the data communication process of the apron has the following two aspects. (1) The area of the apron is broad. The sensor nodes carried by the apron ground service vehicles move frequently, which causes the network topology to change continuously with time, and is often divided into several non-connected subareas. At the same time, the lower wireless channel capacity makes the data end-to-end delay longer and data congestion larger. (2) Due to the heterogeneity of the apron monitoring network, the apron ground service vehicles such as fuel trucks, cleaning vehicles, and ferry vehicles, as well as passenger flow factors, make the end-to-end delay longer. The relay node carries a large data copy and a long moving time, which results in faster storage space consumption. Compared with the traditional MANET, the apron network transmission based on the opportunistic network has higher requirements on the cache capacity of the node. Therefore, through a detailed analysis of the apron-aware network. To solve the problem of buffer over-saturation and data congestion during apron data transmission is a key issue to improve the transmission efficiency of the apron network.

2.2 Cellular Automaton Model The cellular automata (CA) model is a self-organizing dynamic system with microscopic individual interactions, time and space and state discretization. It is mainly a system defined by 4-tuples (L, S, N, F), which means that L is a rule-divided network; S is a state set with limitedcells;  N is a set of cell neighborhoods; f is an function of (t+1) (t) evolution rule, Si, j = f n i, j , the node state of the moment of t + 1 is determined by the state of the set of neighbors of the node according to a certain evolution rule f at the moment of t. Take Conway’s life game [11] as an example, which describes the survival and reproduction rules of biological groups, and calculates the living conditions of each creature in the next generation through the living rules of the organism (some rules). The evolution rules of cell survival and death are mathematically expressed as:  Survival rule: i f

Si,(t)j

= 1, then

Si,(t+1) j

=

1 n i,(t)j = 2, 3 0 n i,(t)j = 2, 3

(1)

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 Death rule: i f

Si,(t)j

= 0, then

Si,(t+1) j

=

1 n i,(t)j = 3 0 n i,(t)j = 3

(2)

where, the cells are distributed on a regular two-dimensional grid; The cell defines two states: death 0, survival 1; The state of the cell is determined by the state of the previous time and the state of the last eight cells around it;

3 Congestion Control Strategy Algorithm Based on Cellular Automata The network operating state in the apron environment is similar to a life game, mapping a node to a cell, and the node can form a cell space with surrounding neighbor nodes that communicate. However, since the apron nodes are not distributed in the regular grid, this paper adopts the irregular cellular automaton model (irregular CA, ICA) model. The establishment and disconnection of the wireless connection between the mobile node and the nodes in each sub-domain on the apron can be regarded as the dynamic change of the cell neighbor. The ICA structure framework is shown in Fig. 1. The reservation or the discarding of each replica cache by the current node is determined by the node’s own cache and the replica transmission of the neighboring node. In order for ICA to automatically perform cache discarding and retention, each cell is equipped with a learning automaton (Learning Automatic, LA). Based on ICA, establish an airport network transmission model simulation. First of all, map a single node in the apron to a cell, and the neighbor nodes in the communication state form a cell space. The movement of nodes in the network and the establishment and disconnection of wireless connections between nodes can be seen as Dynamic changes in cell neighbors.

C1 Ci C2 C ...

Cn

Ci

Fig. 1 ICA structure diagram

Cell neighborhood node Cell node Cell space

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For each node in the apron, node i interacts with all neighboring nodes around it to know the holding status of each copy of node i on the neighboring nodes. The status update of the node is performed by the value of the congestion degree Con(i). The definition of congestion is as shown in Eq. (3).  Con(i) =

ni Mi

Con(i) ≤ 1

(3)



n i : The number of copies currently available to the node, Mi : Node cache capacity. The node congestion degree Con(i) definition reflects the node’s cache occupancy ratio. If the node with high congestion continues to maintain the current receiving rate, the probability of node congestion is greater. For the LA allocated in each copy in the node cache, the executable actions e1 and e2 respectively represent the reservation or discarding of each cached copy in the node, and the probability of the corresponding action is represented by Pr eceive and Pdiscar d . (1) Give the LA command signal τi (n) of the Ci ; (2) Generate a corresponding command signal for the action of each copy. As shown below: ⎧ sum (r ) sum i (r −1) ⎪ ⎨ 1, i e (r ) −  e j (r − 1) > 0; j τi (r ) = j=1 j=1 ⎪ ⎩ 0, other s;

(4)

where, τi (r ) is the value of the command signal of the same copy for the node at the r round; sum i (r ) is the number of neighbors of node i of the rth; e j (r ) is the action of node j retaining the copy in the rth round. According to the value of τi (r ), the copy probability Pdiscar d is updated according to the following formula: Pdiscar d (r + 1) = Pdiscar de (r ) + θ (r ) · (1 − Pdiscar d (r ))

(5)

Pdiscar d (r + 1) = Pdiscar d (r ) · (1 − ϕ(r ))

(6)

The probability of retention on a copy of the corresponding node is as follows: Pr eceive (r + 1) = 1 − Pdiscar d r + 1

(7)

Among them:

L A parameter =

excitation parameter = θ (r ), 0 < θ (r ) < 1 penalt y parameter = ϕ(r ), 0 < θ (r ) < 1

(8)

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Second, the penalty and incentive for LA can be the ratio of the number of neighbor nodes holding the copy m to the number of neighbors in the r round node i, as shown in the equation: θ (r ) = μ ·

Rim ,0 < μ < 1 sum i (r )

(9)

ϕ(r ) = σ ·

Rim ,0 < σ < 1 sum i (r )

(10)

where μ and σ is a coefficient. At the beginning of each round r, the discard probability of each copy on the node is updated according to the above procedure. Due to the movement of the apron node, the previous round of congestion detection and node cache processing, the neighbor nodes holding the same copy will also change. If the number of neighbor nodes currently holding the same copy is less than that detected in the previous round, then the copy is considered to have less congestion on the network in the current partial network environment. Since more identical copies in the partial area are discarded, the chances of receiving other important copies are increased, thereby increasing the success rate of delivery.  Finally, each node first detects n i and selects the discarded packet, and secondly the node selects which the copy should be accepted at the next moment in the neighboring node. Thirdly, choose to accept or reject. After each round of discarding and receiving, update Con(i) to perform a new round of testing. The algorithm flow chart is shown Fig. 2.

4 Simulation Environment and Analysis 4.1 Simulation Environment This paper is simulated and verified under the ONE (opportunistic network environment) simulation platform [11, 12]. A ClusterMovement mobile model conforming to the apron dynamics mobility characteristics is adopted for nodes in the nonconnected sub-domain. The nodes are divided into three groups. The MapRouteMovement mobile module is used for the mobile node. That is, the node moves on a predefined map path. This paper adopts the flooding routing algorithm (Epidemic routing). The specific scene parameter settings are shown in Table 1.

4.2 Performance Analysis of Different Node Numbers The message delivery ratio, network overhead ratio, and message communication delay for different number nodes are shown in Figs. 3, 4, and 5, respectively.

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Fig. 2 Flow chart of proposed CCSICA algorithm

Here, the message delivery ratio refers to the ratio of the number of copies successfully delivered to the target node in the simulation time to the total number of copies created by the simulation, expressed as shown in Eq. (11): deliver y_ratio =

deliver ed cr eated

(11)

The network overhead ratio is determined by both the total number of copies forwarding’s and the number of successfully arrived copies, as expressed by Eq. (12):

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Table 1 Simulation environment parameter settings Parameter

Numerical value

Simulation time/h

24 h

Simulation range/(m × m)

4500 × 3400

Number of each grouping node/(pcs)

5, 10, 15, 20, 25, 30, 35, 40

Number of mobile nodes/(pcs)

3, 6, 9, 12, 15, 18, 21, 24

Total number of nodes/(pcs)

18, 36, 54, 72, 90, 108, 126, 144

Size of the cache space/(M)

5, 10, 15, 20, 25, 30, 35

Packet node speed/(m s−1 )

0.5–1.5

Mobile node speed/(m

s−1 )

Message size/KB Data collection interval/s transfer speed/(KB

3–5 50–150

s−1 )

0.1 250

Data packet life cycle/h

5

Node communication range/m

30

Fig. 3 Delivery ratio for different number of nodes

Fig. 4 Network overhead ratio for the number of different nodes

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Fig. 5 Communication delay for different number of nodes

Oer dhead_ratio =

r elayed − deliver ed deliver ed

(12)

where, relayed: the total number of forwards that the node actually completed; Delivered: the number of copies that successfully reached the destination. From Fig. 3, the message delivery ratio of the three congestion control strategies increases with the increase of nodes different node numbers. The delivery ratio of CCSICA is the highest, because the algorithm saves energy consumption and increases the life cycle of nodes by designing the discarding rules of replicas. It is about 16% and 20% higher than DL and DY, respectively. As can be seen from Fig. 4, the network overhead is constantly increasing. This is because as the number of nodes increases, the contact between nodes is more frequent. During the delivery process, the number of copies forwarded is increased, so network overhead increases. However, CCSICA mitigates network overhead by discarding the same copy in a local scope. As can be seen from Fig. 5, the communication delay of the node is the trend of first falling and then rising. When the number of nodes is 90, the communication delay of the CCSICA policy, the DL policy, and the DY policy is minimized. However, the communication delay of the CCSIA policy remains basically unchanged when the number of nodes is 90–144. It is about 2700 s, which is better than the classic algorithm DL and DY strategy.

4.3 Performance Analysis Under Different Cache Spaces It can be seen from Fig. 6 that the message delivery rate increases with the increase of the cache in different cache spaces. This is because the increase of the buffer space will increase the number of copies carried by the node, and the chance that the message copy will be delivered to the destination node will become larger. So the delivery rate has increased. The delivery rate of CCSICA is about 5% higher than DL, and about 10% higher than DY, which indicates that the algorithm can effectively improve the delivery rate. From Fig. 7, as the cache space increases, the network overhead of CCSICA is

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Fig. 6 Delivery ratio for different cache spaces

Fig. 7 Network overhead ratio for different cache spaces

smaller and more stable than the other two strategies. Overall, the network overhead is reduced by about 20%. The communication delay from Fig. 8 is increased. This is because as the cache space increases, the number of copies received by the node increases. Therefore, the chances of encountering nodes increase, and the communication time to reach the destination node becomes longer. However, CCSICA reduces communication latency by approximately 20 and 10% compared to DL and DY. From the above simulation experiments, CCSICA under different node numbers and different cache spaces, whether in the delivery ratio, network overhead ratio or communication delay, has been improved. This is because when the algorithm implements congestion control, it considers the holding of the replica of the surrounding nodes in addition to considering the cache copy of the node itself. Fig. 8 Communication delay for different cache spaces

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5 Conclusion In the opportunistic network that uses the storage-porting-forwarding method for data transmission, in order to solve the network congestion caused by multiple copies in the network, and avoid the one-sidedness and limitation of the existing congestion control. A congestion control strategy based on irregular cellular automata is proposed. The strategy is centered on each node and forms a local network environment with all neighboring nodes. Detect the copy and formulate a corresponding discarding policy to avoid network congestion caused by too many identical copies. Through simulation verification, the mechanism can improve the delivery ratio of messages and reduce the network overhead ratio and communication delay without predicting network parameters in advance. Fund Project (1) Tianjin Municipal Education Commission Natural Science Research Fund Project (2018KJ237); (2) National Natural Science Foundation Civil Aviation Joint Research Fund Project (U1433107); (3) Central University Basic Research Business China Civil Aviation University Special Project (3122017002).

References 1. Bambang, S., Michael, P.H.: Transfer reliability and congestion control strategies in opportunistic networks: a survey. IEEE Commun. Surv. Tutorials 16, 538–555 (2014) 2. Wu, D.P., Zhang, H.P., Wang, H.G., et al.: Quality-of-protection-driven data forwarding for intermittently connected wireless networks. Wirel. Commun. 22, 66–73 (2015) 3. Navaz, A.S.S.: An efficient intrusion detection scheme for mitigating nodes using data aggregation in delay tolerant network. Int. J. Sci. Eng. Res. 6, 421–428 (2015) 4. Wu, D.P., Zhang, P.N., Wang, R.Y.: Adaptive buffer management strategy with message delivery probability estimating method in opportunistic networks. J. Electron. Inf. Technol. 36(2), 390– 395 (2014) 5. Keykhaie, S., Rostaei, M.: Congestion- and selfishness-aware social routing in delay tolerant networks. In: Proceedings of the 7th International Conference on Computer and Knowledge Engineering, Mashhad, pp. 439–444 (2017) 6. Davis, F.A., Marquart, J.K., Menke, G.: Benefits of delay tolerant networking for earth science missions. In: 2012 IEEE Aerospace Conference. Big Sky, USA, pp. 1–11 (2012) 7. Wang, H.Q., Hu, H.Z., Zhu, J.M., et al.: Cache management algorithm for DTN infection routing protocol. J. Univ. Electron. Sci. Technol. China 44(3), 403–409 (2015) 8. Lu, H., Yin, L., Li, C., et al.: Congestion control in delay tolerant networks with selfish nodes. J. Sens. Lett. 10(8), 1621–1631 (2012) 9. Wu, D.P., Fu, X.W., Zhang, H.P., et al.: A delay-tolerant network congestion control strategy for node state perception. J. Acta Electron. Sin. 44(01), 186–192 (2016) 10. Yan, H.C., Zhang, Q.J., Sun, Y.: Study on congestion control strategy of space delay/interruption tolerance network. J. Commun. 37(01), 142–150 (2016) 11. Keranen, A., Ott, J., Karkkainen, T.: The ONE simulator for DTN protocol evaluation. In: Proceedings of the 2nd International Conference on Simulation Tools and Techniques, pp. 1– 10. ICST, Brussels (2009) 12. Wang, Z., Wang, X.H., Sui, J.Q.: Research on opportunity network simulator ONE and its extension. J. Appl. Res. Comput. 29(01), 272–277 (2012)

Bearing Fault Diagnosis Based on Improved Denoising Auto-encoders Weixing Chen, Chaochen Cui and Xiaojing Li

Abstract Most of the fault characteristics of the wind power were manually marked, and the characteristics of manual labeling were based on expert experience, and in some cases, the operation law of the equipment cannot be objectively reflected. Therefore, an improved Denoising Auto-Encoders for multi-sensor data fusion diagnosis (IDAE) method was proposed. A multi-sensors data was constructed by onedimensional layer-by-layer stacking to construct a two-dimensional matrix to realize data fusion and ensure the robustness of fault diagnosis. Then using the unsupervised learning ability of the convolutional Auto-Encoding neural network enables the network to automatically extract fault features from the unlabeled data, ensuring the comprehensiveness, objectivity and adaptability of the fault features. Experiments on the actual historical data of Huarui FL1500 wind turbine in a wind farm in Shandong show that the proposed method has better robustness and automation in fault diagnosis of bearing fault diagnosis. Keywords Wind turbine · Bearing fault diagnosis · The improved Denoising Auto-encoders · Data fusion · Unsupervised learning

1 Introduction With the rapid development of wind energy field, the reliability of wind turbine operation has gradually become a key to the utilization of image wind energy. As an important part of the transmission chain, generator bearing directly affects the operation of the unit [1]. At present, there are two ways to deal with the situation W. Chen · C. Cui (B) · X. Li Department of Aviation Automation, Civil Aviation University of China, Tianjin 300300, China e-mail: [email protected] W. Chen e-mail: [email protected]

© Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7_128

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in the field of equipment operation and maintenance: (1) Adopting regular maintenance, this method has certain blindness and consumes manpower and material resources; (2) Repair after the fault occurs, which will affect the normal operation of the equipment [2–4]. Previous researchers have used data mining methods in equipment fault diagnosis [1–5]. This method has drawbacks that cannot be ignored. The feature extraction algorithm relies on manual extraction and expert knowledge in the field [6]. For different devices, the fault state has different characteristics, and it is necessary to constantly search for fault features, which increases the difficulty and workload of manual operations, and affects the generalization ability of the model [6]. Deep learning has become a research hotspot in the field of machine learning in recent years, and has achieved good results in the field of fault diagnosis. Literature [7] proposed a three-layer convolutional neural network model to detect bearing faults using vibration signals, but the disadvantage is that raw data cannot be processed; Literature [8] proposed a hierarchical adaptive deep convolutional neural network for bearing fault diagnosis from raw vibration data; However, its input is a onedimensional signal, and studies have shown that the input of more sensor signals can make the model more robust [9, 10]. Although the literature [11] can handle multisensor signal input, it cannot extract unlabeled data. Due to the incompleteness of industrial field data, label-free learning of input data is required. Literature [12] proposed a convolutional auto-encoder, which is an unsupervised learning method based on feature learning of convolutional neural networks. Reference [6] refers to the diagnosis of bearing faults. Although the training data can be unlabeled and automatically classified, the self-encoder has poor anti-noise ability. The core of the unsupervised network is the need for a more robust hidden layer expression. Based on this Vincent [13] proposed a noise reduction self-encoder. Due to the high computational cost of the noise reduction self-encoder, the scalability of highdimensional features is lacking [14]. Based on this, this paper attempts to fuse an improved noise reduction autoencoder and convolutional neural network, construct a multi-signal input noise reduction convolution self-encoder, and reference it to the fault diagnosis of the bearing. By using a convolutional neural network model, sensor fusion can be implemented at the data level, which can enhance the accuracy and stability of fault diagnosis. In addition, a deep network based on an improved noise reduction automatic coding framework is combined with convolution and deconvolution to perform unsupervised feature learning from the bridged device data. The model can effectively learn features from high-dimensional data to help the classifier achieve higher detection accuracy and faster speed.

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2 Introduction to Theoretical Methods 2.1 Classical Convolutional Neural Network Convolutional neural networks are an important part of deep learning, and their powerful feature extraction capabilities are widely used in classification problems [15]. Convolutional neural networks consist of multiple levels of trainable linear and nonlinear architectures involving linear and nonlinear operations. The input and output of each part is an array called a feature map. Typically, each section consists of two layers: a convolutional layer and a feature pool layer. A typical CNN is constructed by stacking one or more such two-layer structures with hierarchical layers. The forward propagation process is as follows:       f (X) = f k . . . f 2 f 1 X, δ (1) , δ (2) . . . , δ k

(1)

where X is the original input data, such as image, matrix, etc. In this paper, input a multi-dimensional matrix composed of multiple one-dimensional signals. δ (1) , δ (2) , . . . , δ k are learnable parameters such as weight, offset, etc. f 1 , f 2 , . . . , f k are the operations of each stage. The output of these functions is an intermediate feature map.

2.1.1

Convolutional Layer

In the convolutional layer, in the convolutional layer, the input is convolved with a set of learnable convolution kernels to generate a new feature map as an input to the next layer. The following operation: X k(l)

= f

 K 

 (l) Wkk 

∗

X k(l−1)

+

B(l) k

(2)

k=1

where l is the number of layers of the network, k  = 1, 2, . . . , K  is the sequence (l) (l−1) K Wkk is a convolution operation of number of the feature output map, k=1  ∗ Xk (l) the kth feature map of the lth layer, Wkk  is the convolution kernel of the lth layer, Bk(l) is the offset matrix, f is a nonlinear activation function, Given the superior performance of the rectified linear unit (ReLU) activation function in recent research work [16]. Therefore, the rectified linear unit (ReLU) is used as the activation function in this paper.

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Pooling Layer

The pooling layer achieves spatial invariance by reducing the dimensions of feature mapping. Combine nearby feature values into a single value with appropriate operators such as max-pooling (using the max operator) or average-pooling (using the average operator). The neighborhood can be stepped in steps greater than one. Pooled windows can have different sizes. This article uses the maximum value as follows:   yi jk = max yi  j  k  : i ≤ i < i + p, j ≤ j < j + q

(3)

where p and q are the length and width of the pooled window, respectively.

2.2 Improved Noise Reduction Automatic Encoder Frame The improved noise reduction automatic encoder is a special neural network structure, which is improved by the noise reduction self-encoder and has the robustness of the noise reduction self-encoder and can greatly improve the calculation speed of the network. The main feature of the network structure is to use the weak large number theorem to convert the optimization problem of infinitely many corrupted data into the expected problem. At the same time, the objective function of the noise reduction self-encoder is expanded by the Taylor formula to approximate the expected loss function. The network structure is shown in Fig. 1, with a clean input layer, a damaged version of the input layer, an output layer and a hidden layer. It artificially adds noise to the input layer, destroys the original pure input, and then connects the damaged version of the input layer with the traditional stacked self-encoder, training to adjust Fig. 1 Principle of an automatic encoder

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the weight of the hidden layer, so that the output value is as close as possible to the clean input. Layer data. Its hidden layer has important features of the original signal to achieve unsupervised feature extraction. The training process is as follows: X X ) through a By transforming the clean input into a corrupted input  X ∼ qD (  random mapping, the encoding function from the corrupted input layer to the hidden layer is as follows: H = f (W ·  X + B)

(4)

where, W is the connection right from the input layer to the hidden layer, B is the offset, and f is the activation function. The decoding function of the hidden layer to the output layer is as follows:   Y = f  W  · H + B

(5)

where, W  is the connection right of the hidden layer to the output layer, and B  is the offset vector. In the training of the model, let each output signal reproduce the input signal as much as possible. The nonlinear representation of the objective function of the noise reduction self-encoder is as follows: n ∂2 L 1 2  J (W ) = L + σxd 2 d=1 ∂ H 2h h=1

D

2 where, L = E p(  X | X ) X − Y  ,

 T diagonal. x = E ( x˜ − μx )( x˜ − μx )

D

2 σxd



are

∂ Hh ∂ X the

2 (6)

dth

term

of

the

3 Convolution Auto-encoder Network Diagnostic Model The unsupervised feature learning based on the self-encoder framework proposed in this paper is described below. First, the data collected from multiple sensors is stacked into a two-dimensional input matrix row by row according to time series. The time and state information from the sensor can be constructed by this, and datalevel multi-sensor fusion is realized as the input of the network. In the encoder part, the signal input, through the convolution layer, the pooling layer, the reconstruction operation, the full connection layer and the feature coding to extract the features; In the decoder part, through the fully connected layer, the reconstruction operation, the deconvolution layer, the upsampling layer and the sample reconstruction layer reconstruct the signal.2 is a flow chart of the proposed fault diagnosis method (Fig. 2). The following is a detailed description of each layer of the model. In the convolutional layer of the encoder section, the input signal maps the new feature to the next layer [14] through the convolution kernel, as shown in the following equation:

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Fig. 2 Diagnostic flow chart

C k = f (W k ∗ X + B k )

(7)

where W k is the kth convolution kernel; C k is the convolutional layer output; B k is the output offset; Another operation in the convolutional neural network is pooling, which can achieve spatial invariance by reducing the dimensions of feature mapping [17]. This article uses the maximum pooling, as shown below: Pk = max pooling(Ck , l)

(8)

Among them, according to the iterative convolution and pooling process, the dimensions of the pooled feature map can be reduced, thereby obtaining m pooling and feature mapping. Signal reconstruction is then performed to map the features into a one-dimensional vector, and then feature encoding is performed by a full join operation, which completes the information of all merged feature maps. The calculation method of its fully connected layer is as follows:   F = f Wv · v + B f

(9)

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where a and b are the weights and offsets of the full connection, respectively. Decoding begins after encoding, and signal reconstruction, as shown in the following equation:   v = f W v · F

(10)

where a is the weight of the fully connected layer. There is no offset at this layer due to the need to ensure that the information needed for the decoding process comes from the feature encoding [8]. The second reconstruction operation cuts the one-dimensional vector into m pooled feature maps, which corresponds to the first reconstruction operation. The kth feature map is a P k . In the upsampling layer, use the original sampling window to insert the same value as the previous sample to get C k , as shown in the following equation:   C k = upsampling P k + B k

(11)

The deconvolution is: Y=

   f W k ◦ F k + B k

(12)

The objective function uses the method defined in [8]: Loss =

N   (i)     X − Y (i) avg x(i) N

(13)

i=1

  where avg x(i) is the average value of the sample x(i) .

4 Experimental Evaluation 4.1 Data Preprocessing To assess the effectiveness of the method. This paper conducts experiments based on the actual historical data of a Huarui FL1500 wind turbine in a wind farm in Shandong; the safety monitoring data is shown in Table 1. The data set includes a total of 3000 sets of test record data of the model as a sample, of which 2000 groups are used as training data and 1000 groups are used as test data. Since the amplitude of each channel is different, the data is first normalized so that the sample data is mapped to the range [0, 1] as follows:     L ds = max x (k) − min x (k) , k ∈ {1, . . . , N }

(14)

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W. Chen et al. Security data type

Data item

Working condition of data

Bearing temperature Output power Environment temperature Cabin temperature Bearing vibration

Fault type

Outer Ring (OR) Inner Ring (IR) Retainer (R) Rolling Element (RE) The composite fault

L mor m = (d − min(x (k) ))/L ds

(15)

4.2 Experiment and Analysis In order to analyze the robustness of multi-sensor data fusion for fault diagnosis, the method of this paper and the single sensor model using vibration data are respectively used to diagnose the generator bearing fault. Both methods use the same data set and the same network parameters. Figure 3 is a comparison of the results of two methods for fault diagnosis of generator bearings. As can be seen from Fig. 3, multi-sensor fusion has a better accuracy for bearing fault diagnosis than a single sensor. 100 95 90

accuracy rate/100%

Fig. 3 Diagnostic accuracy rate

85 80 75 70 65 60

Single sensor Multiple sensors

55 50

0

1

2

3

4

5

6

Experiment No

7

8

9

10

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0.3

Loss

0.25 0.2 0.15 0.1 0.05 0 0

100 200

300 400

500 600 700

800 900 1000

epoch

Because this method does not need to use any optimization algorithm to learn the parameters in the model, it greatly improves the calculation speed of the network. Figure 4 compares the convergence speed of the proposed method with the general noise reduction auto-encoder. It can be seen from Fig. 4 that the proposed method is superior to the conventional noise reduction self-encoder in convergence speed. In order to better observe the learning ability of the network for features, the t-SNE dimensionality reduction algorithm is introduced, and the input layer, the first hidden layer, the second hidden layer and the output layer of the encoder are visualized. The visualization effect is shown in Fig. 5. The same color represents the same category. It can be seen that as the number of layers increases, the characteristics of different types of faults are gradually separated. The raw data of the five faults are mixed together, as shown in Fig. 5a. After passing through the first layer, the features begin to have a tendency to separate, but there is no obvious separation, as shown in Fig. 5b. In Fig. 5c, it is found that one type is separated and the two types of data start to cluster, but there are still two kinds of data mixed together. The two types of data are inner ring faults and mixed faults as shown in Fig. 5d. Finally, after the last layer of the encoder the five types have all been clustered. In order to compare the performance of the proposed method, the method is compared with the SVM and K-means methods respectively. The correct rate of various fault diagnosis is shown in Table 2. As can be seen from Table 2, the diagnostic accuracy of SVM is 89.5%, the diagnostic accuracy of K-means is 80.5%, and the diagnostic accuracy of this method is 97.2%.

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Fig. 5 Visualization of different layers

Table 2 Ratio of diagnostic results of different methods Fault type

Sample size

Accuracy rate/% SVM

K-means

IDAE

OR

269

87.6

80.3

96.3

IR

246

90.2

80.8

97.5

R

270

89.6

81.6

96.5

RE

215

91.3

79.3

98.6

1000

89.5

80.5

97.2

Total

5 Conclusion In the fault diagnosis of the wind power, this paper attempts a convolutional automatic encoder network based on multi-sensors input. The following conclusions can be drawn: (1) The network can realize multi-sensor data fusion and improve the accuracy of diagnosis; (2) The improved noise reduction self-encoder has faster first speed than the ordinary noise reduction self-encoder; (3) For the incompleteness of the label,

Bearing Fault Diagnosis Based on Improved Denoising …

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the unsupervised learning method is adopted, which has strong adaptive ability and can be used for fault diagnosis of different devices. Fund Project Central University’s basic research business Civil Aviation University of China special fund project, Project No. 3122017041; National Natural Science Foundation Civil Aviation Joint Research Fund Project, Project No. U1433107.

References 1. Hongshan, Z., Huihai, L.: Fault detection of wind turbine main bear based on deep learning network. Acta Energiae Solaris Sin. 39(3), 88–595 (2018) 2. Zhang, J., Wang, H., Chen, W.: Study on error prediction in air conditioner set based on data mining. Measur. Control Technol. 34(8), 37–40+44 (2015) 3. Fu, T.C.: A review on time series data mining. Eng. Appl. Artif. Intell. 24(1), 164–181 (2011) 4. A readme giving the name and email address of the corresponding author 5. Sun, Y., Qu, R., Chen, W.: Research of data mining oriented integrated error diagnosis of solid state power. Comput. Measur. Control 23(10), 3274–3276+3280 (2015) 6. Qu, J., Yu, L., Yuan, T., et al.: Adaptive fault diagnosis algorithm for rolling bearings based on one-dim. Chin. J. Sci. Instrum. 39(07), 134–143 (2018) 7. Janssens, O., et al.: Convolutional neural network based fault detection for rotating machinery. Sound Vib. 377, 331–345 (2016) 8. Guo, X., Chen, L., Shen, C.: Hierarchical adaptive deep convolution neural network and its application to bearing fault diagnosis. Measurement 93, 490–502 (2016) 9. Park, J.W., Sim, S.H., Jung, H.J.: Displacement estimation using multimetric data fusion. IEEE/ASME Trans. Mechatron. 18(6), 1675–1682 (2013) 10. Olofsson, B., Antonsson, J., Kortier, H.G., Bernhardsson, B., Robertsson, A., Johansson, R.: Sensor fusion for robotic workspace state estimation. IEEE/ASME Trans. Mechatron. 21(5), 2236–2248 (2016) 11. Xia, M., Li, T., Xu, L., Liu, L., de Silva, C.W., et al.: Fault diagnosis for rotating machinery using multiple sensors and convolutional neural networks. IEEE/ASME Trans. Mechatron. 23(1), 101–110 (2018) 12. Wang, L., Ouyang, W., Wang, X., Lu, H.: Visual tracking with fully convolutional networks. In: Proceedings of 2015 IEEE International Conference on Computer Vision, pp. 3119–3127, Dec 2015 13. Viccent, P., Larovhelle, H., Bengio, Y., et al.: Extracting and composing robust feature with denoising autoencoders. In: Proceeding of the 25th International Conference on Machine learning. Helsinki, Finland, pp. 1096–1103 (2008) 14. Yuan, F., Zhang, L., Shi, J., et al.: Theories and of auto-encoder neural networks: a literature survey. Chin. J. Comput. 1–28 (2018) (18 Oct 2018) 15. Xing, C., Ma, L., Yang, X.: Stacked denoise autoencoder based feature extraction and classification for hyperspectral images. Sensors 2016, Art. no. 3632943 (2016) 16. Chen, M., Xu, Z., Weinberger, K., et al.: Marginalized denoising autoencoders for domain adaptation. In: Proceedings of the International Conference on Machine Learning, Edinburgh, Scotland, pp. 1627–1634 (2012) 17. Ahmad, T., Fairuz, R.A., Zakaria, F., Lsa, H.: Selection of a subset of EEG channels of epileptic patient during seizure using PCA. In: Proceedings of World Scientific and Engineering Academy and Society (WSEAS), pp. 270–273 (2008)

Author Index

B Bai, Chengrui, 1335 Bai, Yuting, 631 Bi, Kaiyuan, 1291

C Cabassud, Michel, 423, 1313 Cai, Baigen, 653 Cai, Jin, 165 Cai, Man-jun, 373 Cai, Mingjie, 1055 Cao, Han, 1107 Cao, Junhai, 1345 Chang, Jincai, 443 Chao, Di, 123 Chao, Fan, 937, 959, 969 Cheng, Lei, 1011, 1107 Cheng, Lianglun, 727 Cheng, Xingong, 215 Cheng, Zhongtao, 1025 Chen, Hao, 141 Chen, Jiajie, 609 Chen, Jinbao, 1069 Chen, Jing, 521 Chen, Jinxiang, 575 Chen, Qiang, 239 Chen, Qingwei, 851 Chen, Sizhong, 947 Chen, Wei, 23, 1325 Chen, Weixing, 1359, 1371 Chen, Xinrui, 565 Chen, Yan, 263 Chen, Yang, 1011 Chen, Yiwen, 675 Chen, Yong, 947 Chen, Yuanfang, 1249

Chen, Zhuo, 63, 907, 917, 1325 Chin, C. S., 99 Chou, Yongxin, 1163 Cui, Chaochen, 1371 Cui, Dong, 503 Cui, Hongbin, 1281

D Dahhou, Boutaib, 423, 1313 Deng, Pu, 907, 917, 1325 Deng, Wencong, 597 Deng, Xin, 249 Deveerasetty, Kranthi Kumar, 1345 Ding, Feng, 979 Ding, Hai-gang, 531 Ding, Ningning, 1 Ding, Yichun, 707 Ding, Youchuang, 555 Dou, Xinling, 1047 Du, Yanli, 619 Du, Yaoyao, 347

F Fan, Zhiyong, 811 Fei, Qiuling, 521 Feng, Ying, 675 Feng, Yunduo, 755 Fu, Dongmei, 325, 497, 719 Fu, Huajun, 1303

G Gao, Bing, 1083 Gao, Guanbin, 239 Gao, GuoQiang, 1107

© Springer Nature Singapore Pte Ltd. 2020 R. Wang et al. (eds.), Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019), Lecture Notes in Electrical Engineering 582, https://doi.org/10.1007/978-981-15-0474-7

1383

1384 Gao, Jie, 1083 Gao, Lei, 1335 Gao, Yanming, 1261 Gao, Zepeng, 947 Gao, Zhijun, 195 Ge, Chunxiao, 1001 Ge, Junjie, 969 Gong, Jin, 1069 Guihang, Liu, 897 Guo, Feng, 503 Guo, Shiguang, 1193 Gu, Ya, 1163

H Han, Bo, 1345 Han, Lu, 575 Han, Xue, 423 Han, Zhonghua, 195, 205, 1205, 1281, 1291 Hao, Zhenghang, 1325 Hassan, Asif, 831 He, Linxi, 455 He, Menglin, 423 He, Qianwei, 1139 He, Shuibing, 1249 He, Yuqing, 1291 He, Zhiqin, 937, 959, 969 Huang, Jian, 697, 777 Huang, Jiawang, 165 Huang, Yongtao, 33 Huang, Zihao, 1139 Hu, Chaofang, 1171 Hu, Jiang, 947 Huo, Xin, 875 Hu, Xingliu, 485 Hu, Xiumin, 937, 959 Hu, Zhijie, 141 Hu, Zhongzhi, 609, 1035

J Jian, Dan, 443 Jiang, Bowen, 737 Jiang, Chong, 1271 Jiang, Tongwei, 185 Jiang, Wei, 653 Jiaping, Zhang, 1151 Jing, Shaoxue, 133 Jing, Tao, 41 Jin, Xuebo, 631, 927

K Kong, Jianlei, 631, 927

Author Index L Lan, Xuejing, 1181 Lei, Tinghao, 917 Li, Aijun, 305, 315 Liang, Binxiu, 455 Liang, Zhaowei, 1025 Liao, Shun, 23 Liao, Weiqiang, 11 Li, Chan, 1011 Li, Chen, 141 Li, Chunyan, 401, 585 Li, Guihai, 821, 1239 Li, Hengyu, 843 Li, Huai, 1229 Li, Jiahao, 497 Li, Jian, 63 Li, Jiangyun, 455, 465 Li, Jiawei, 315 Li, Junchen, 393 Li, Meiling, 383 Li, Mengxin, 185, 383 Lin, Baifeng, 185 LingHu, Jinhua, 347 Lin, Lu, 359 Lin, Shuo, 205 Lio, C. S., 99 Li, Pucheng, 393 Li, Shurong, 801, 1215 Liu, Baoku, 947 Liu, Bojian, 315 Liu, Chunguang, 205 Liu, Dan, 653 Liu, Fei, 63 Liu, Feng, 767 Liu, Gang, 821, 1239 Liu, Guihang, 863 Liu, Jiantong, 747 Liu, Jianying, 165 Liu, Jicheng, 1163 Liu, Jinkun, 597 Liu, Jun, 843 Liu, Le, 373 Liu, Lei, 989, 1025, 1139, 1151 Liu, Leiming, 497 Liu, Li, 1261 Liu, Minglei, 53 Liu, Qingquan, 875 Liu, S., 153 Liu, Weiwei, 1271 Liu, Xianyue, 11 Liu, Xiaopeng, 465 Liu, Xinshi, 325, 719 Liu, Yafei, 239

Author Index Liu, Yan, 455, 465, 475 Liu, Yang, 41, 325 Liu, Yanwen, 433 Liu, Yinlin, 433 Liu, Yiwen, 1181 Liu, Yongqiang, 653 Liu, Yuchao, 75, 1119 Liu, Yuehan, 1205 Liu, Zhe, 801, 1215 Liu, Zhexu, 811 Liu, Z. Y., 153 Li, Xia, 335 Li, Xiaojing, 1371 Li, Xiaoyan, 141 Li, Xu, 1139 Li, Yang, 789, 1047 Li, Yiping, 541, 685 Li, Yongzhong, 907 Li, Zetao, 423, 1313 Li, Zhonghua, 263 Li, Zhu, 1025 Li, Ziyue, 75, 1119 Luan, Fangjun, 1281 Lü, Jiangbo, 11 Luo, Jun, 843 Luo, Yu, 831 Lu, Xutan, 755 Lv, Hengxing, 227 Lv, Yongfeng, 227

M Ma, Changhui, 215 Ma, He, 141 Ma, Jiawei, 63 Ma, Jie, 33 Ma, Junxia, 521 Man, Jia-xiang, 531 Ma, Xiao, 413 Ma, Yue, 359 Mei, Lei, 249 Mei, Rong, 597 Meng, Fanwei, 153, 281, 297 Meng, Meihan, 1359 Miao, Qing, 413 Mu, Lingxia, 1131

N Na, Jing, 239 Niu, Yanjie, 281, 297 Nong, Jing, 907 Nong, Xiaoqi, 1011

1385 O Osman, Tokhi M., 87 Ouyang, Huimin, 215, 249

P Pang, Aiping, 53, 63, 907, 917, 937, 959, 1325 Pan, Huihui, 821 Pan, Ping, 347 Pan, Tianhong, 133 Pei, Wenlong, 383 Peng, Jiayu, 195 Peng, Rui, 1011 Peng, Tongrui, 87 Peng, Xiaojun, 907 Peng, Zhengyang, 821, 1239 Pu, Lina, 831

Q Qi, Fei, 359 Qu, Xiangyu, 541, 685

R Ren, Jiabo, 1055 Ren, Wenfeng, 619 Ren, Xuemei, 227 Rong, Panxiang, 1095

S Shao, Nuan, 373 Shao, Shuyi, 1001 Shen, Jie, 1035 Shen, Tong, 777 Shi, Haibo, 1205 Shi, Kan, 643 Shi, Weijia, 875 Shiwei, Zhao, 897 Shi, Wenye, 969 Shi, Xudong, 41, 123, 173 Si, Haifei, 485 Si, Wen, 195 Si, Ze, 325, 719 Song, Haoyue, 1239 Song, Hong-jiao, 373 Song, Houbing, 1249 Su, Dan, 697 Su, Jingfang, 1359 Sun, Aiqin, 643 Sun, Chunxiao, 401, 585 Sun, Guobing, 1095

1386 Sun, Hui, 1335 Sun, Jiankun, 755 Sun, Zhenghao, 767 Sun, Zhengyang, 1119 Sun, Zichao, 475 Su, Tingli, 631, 927

T Tang, Xinliang, 789 Teng, Da, 811 Tian, Qunhong, 643 Tian, Xutian, 1205 Tu, Siqi, 801

W Wang, Baigeng, 1215 Wang, Baofang, 1055 Wang, Bingyuan, 335 Wang, Chunxiao, 1303 Wang, Fengde, 643 Wang, Fengyuan, 917 Wang, Gang, 767 Wang, Guanqun, 685 Wang, Guodong, 707, 831 Wang, Haihong, 1261 Wang, Hong, 465 Wang, Jian, 653 Wang, Jie, 413 Wang, Jiecheng, 443 Wang, Jingjing, 1261 Wang, Jiqiang, 609 Wang, Kun, 23 Wang, Lijun, 597 Wang, Na, 1171 Wang, Qian, 141 Wang, Rui, 33, 1335 Wang, Shuai, 1281 Wang, Shubo, 239 Wang, Tao, 727 Wang, Wei, 315, 663 Wang, Xiaohui, 685 Wang, Xiaolan, 23 Wang, Xiaoyi, 631 Wang, Xiuqi, 1035 Wang, Xu, 173 Wang, Yakun, 173 Wang, Yang, 1 Wang, Yingmin, 503 Wang, Yizhi, 485 Wang, Yongji, 989 Wang, Yu, 305

Author Index Wang, Yue, 1193 Wang, Yun-fei, 531 Wang, Zhanbao, 63 Wang, Zhengjie, 747 Wang, Zhuo, 443 Wu, Bei, 1107 Wu, Chunhong, 719 Wu, Huaiyu, 1011 Wu, Xueli, 1047 Wu, Yanxuan, 755 Wu, Zhicheng, 947

X Xiao, Li, 1069 Xiao, Qing, 113 Xing, Shujian, 1 Xiong, Ling, 1011 Xiong, Weili, 521 Xu, Danyang, 887 Xue, Dan, 141 Xu, Gaofei, 541, 685 Xu, Huigang, 1163 Xu, Ling, 979 Xu, Mingchu, 851 Xu, Ning, 141 Xu, Rui, 185, 383 Xu, Wenbiao, 1181 Xu, Xiangyang, 41 Xu, Xiaohua, 1249 Xu, Xiaoyun, 1047 Xu, Zhen, 851

Y Yang, Aiqiang, 927 Yang, Chenguang, 675 Yang, Daqian, 697 Yang, Jack, 707 Yang, Jun, 239 Yang, Junfeng, 281, 297 Yang, Lei, 393 Yang, Lin, 947 Yang, Liying, 1291 Yang, Xiaofei, 1001 Yang, Ye, 989, 1025, 1139 Yang, Yonggang, 555 Yang, Zhangang, 165 Yang, Zhong, 485 Yan, Hao, 737 Yan, X. R., 153 Yao, Yufeng, 87 Ye, Hui, 1001

Author Index Yin, Pengqi, 33, 1193 Yin, Wen, 393 Yin, Yilan, 575 Yuan, Chi, 887 Yuan, Shaoshuai, 173 Yue, Zhuangzhuang, 249 Yu, Muzhou, 281, 297 Yu, Xiang, 1131 Yu, Xinghong, 631 Yu, Zhen, 1229

Z Zeng, Derui, 801 Zeng, Peipei, 263 Zeng, Shi, 907 Zeng, Yuhang, 989 Zhai, G. Q., 153 Zhai, Guangqing, 433 Zhang, Bin, 1095 Zhang, Gaowei, 413 Zhang, Guangming, 249 Zhang, Haojia, 305 Zhang, Jianhua, 401, 443, 585, 789, 1047 Zhang, Jiaping, 1139 Zhang, Jingyuan, 205 Zhang, Mei, 1313 Zhang, Menghua, 215 Zhang, Peng, 863 Zhang, Qingfang, 63 Zhang, Rencheng, 11 Zhang, R. Y. K., 153 Zhang, Shu, 75 Zhang, Shuaihua, 335 Zhang, Shuguang, 1193 Zhang, Weicun, 475, 497, 609 Zhang, Wenjie, 281 Zhang, Xiao, 979 Zhang, Xiaoying, 23

1387 Zhang, Yan, 413 Zhang, Yaokun, 1025 Zhang, Yong, 141 Zhang, Yongfeng, 215 Zhang, Youmin, 887, 1131 Zhang, Yu, 123 Zhang, Zhide, 747 Zhang, Zhongcai, 1303 Zhao, Feng, 575 Zhao, Hongxu, 123 Zhao, Hui, 875 Zhao, Jinfang, 273 Zhao, Ji-yun, 531 Zhao, Lingxue, 1171 Zhao, Shiwei, 863 Zhaowei, Liang, 1151 Zhao, Xiangfa, 1095 Zhao, Xitong, 1011 Zhao, Yanxiao, 707, 831, 1249 Zhao, Yuan, 273 Zhao, Yuzhuang, 947 Zheng, Fang, 335 Zheng, Hongzhi, 195 Zhong, Jie, 727 Zhou, Changsheng, 433 Zhou, Hongbo, 53, 937 Zhou, Shao-Wu, 113 Zhou, Yimin, 1345 Zhou, Yugang, 565 Zhu, Feng, 1047 Zhuge, Jingchang, 1 Zhu, Li, 1151 Zhu, Liangkuan, 565 Zhu, Peiyi, 1163 Zhu, Quanmin, 87 Zhu, Shixing, 555 Zhu, Zhengtao, 707 Zihao, Huang, 1151 Zuo, Zheqing, 737