Advanced Discrete-Time Control (eBook)

Professor Jian-Xin Xu received the Bachelor degree from Zhejiang University, China in 1982. He attended the University of Tokyo, Japan, where he received Master's and PhD degrees in 1986 and 1989 respectively. All degrees are in Electrical Engineering. He worked for one year in the Hitachi research Laboratory, Japan; for more than one year in Ohio State University, U.S.A. as a Visiting Scholar; and for 6 months in Yale University as a Visiting Research Fellow. In 1991 Professor Xu joined the National University of Singapore and is currently a professor at Department of Electrical and Computer Engineering. His research interests lie in the fields of intelligent and robust control and applications to motion control, mechatronics, and robotics. He is a Fellow of IEEE.Up to now he produced more than 500 peer-reviewed journal and conference papers, 2 monographs and 3 edited books. He has been supervising/co-supervising 29 PhD, 20 Master students, and 15 research staff including postdoctoral fellows and research fellows. He has completed 20 funded research projects and currently he work on AUV biomimetic locomotion and control.Dr Khalid Abidi received his BSc. degree in Mechanical Engineering from the Middle East Technical University, Ankara, Turkey in 2002 and the MSc. degree in Electrical Engineering and Computer Science from Sabanci University, Istanbul, Turkey in 2004. He obtained his PhD degree in Electrical and Computer Engineering, specializing in the area of Control Engineering, from the National University of Singapore in 2009. Dr Abidi is currently a lecturer of Electrical Power Engineering at Newcastle University based in Singapore. Prior to joining Newcastle University Dr Abidi worked as an Assistant Professor of Mechatronics Engineering at Bahcesehir University, Istanbul, Turkey from September 2009 until June 2014. His research interests include: Theory and modelling of dynamical systems, Discrete-Time systems, Time-delay systems, Learning Control, Robust Control, Applied Nonlinear Control, Robotics and Mechatronic Systems.

Preface 7
Contents 9
1 Introduction 13
1.1 Background 13
1.2 Contributions 17
1.3 Organization 19
2 Discrete-Time Sliding Mode Control 21
2.1 Introduction 21
2.2 Problem Formulation 23
2.3 Classical Discrete-Time Sliding Mode Control Revisited 27
2.3.1 State Regulation 27
2.3.2 Output Tracking 30
2.4 Discrete-Time Integral Sliding Mode Control 33
2.4.1 State Regulation with ISM 33
2.4.2 Output-Tracking ISM Control: State Feedback Approach 36
2.4.3 Output Tracking ISM: Output Feedback Approach 42
2.4.4 Output Tracking ISM: State Observer Approach 50
2.4.5 Systems with a Piece-Wise Smooth Disturbance 54
2.4.6 Illustrative Example 55
2.5 Discrete-Time Terminal Sliding Mode Control 63
2.5.1 Controller Design and Stability Analysis 63
2.5.2 TSM Control Tracking Properties 67
2.5.3 Determination of Controller Parameters 68
2.6 Conclusion 73
3 Discrete-Time Periodic Adaptive Control 74
3.1 Introduction 74
3.2 Discrete-Time Periodic Adaptive Control 75
3.2.1 Discrete-Time Adaptive Control Revisited 75
3.2.2 Periodic Adaptation 77
3.2.3 Convergence Analysis 77
3.3 Extension to More General Cases 79
3.3.1 Extension to Multiple Parameters 79
3.3.2 Extension to Mixed Parameters 82
3.3.3 Extension to Tracking Tasks 84
3.3.4 Extension to Higher Order Systems 85
3.4 Illustrative Example 87
3.5 Conclusion 89
4 Discrete-Time Adaptive Posicast Control 90
4.1 Introduction 90
4.2 Problem Formulation 92
4.2.1 Continuous-Time Adaptive Posicast Controller (APC) 93
4.3 Discrete-Time Adaptive Posicast Controller Design 93
4.3.1 Control of a 1st Order Input Time-Delay System in Discrete-Time 94
4.3.2 Adaptive Control of an Input Time-Delay System 95
4.3.3 Extension to Higher Order Systems 99
4.3.4 Stability Analysis 102
4.4 Extension to More General Cases 104
4.4.1 Uncertain Upper-Bounded Time-Delay 104
4.4.2 Extension to Nonlinear Systems 108
4.5 Illustrative Examples 113
4.5.1 Linear Systems 113
4.5.2 Nonlinear Systems 116
4.6 Conclusion 117
5 Discrete-Time Iterative Learning Control 119
5.1 Introduction 119
5.2 Preliminaries 120
5.2.1 Problem Formulation 121
5.2.2 Difference with Continuous-Time Iterative Learning Control 122
5.3 General Iterative Learning Control: Time Domain 123
5.3.1 Convergence Properties 124
5.3.2 D-Type and D2-Type ILC 126
5.3.3 Effect of Time-Delay 129
5.4 General Iterative Learning Control: Frequency Domain 131
5.4.1 Current-Cycle Iterative Learning 132
5.4.2 Considerations for L(q) and Q(q) Selection 134
5.4.3 D-Type and D2-Type ILC 135
5.5 Special Case: Combining ILC with Multirate Technique 137
5.5.1 Controller Design 137
5.5.2 Multirate Structure 137
5.5.3 Iterative Learning Scheme 138
5.5.4 Convergence Condition 139
5.6 Illustrative Example: Time Domain 143
5.6.1 P-Type ILC 143
5.6.2 D-Type and D2-Type ILC 144
5.7 Illustrative Example: Frequency Domain 146
5.7.1 P-Type ILC 146
5.7.2 D-Type and D2-Type ILC 147
5.7.3 Current-Cycle Iterative Learning Control 148
5.7.4 L(q) Selection 150
5.7.5 Sampling Period Selection 152
5.8 Conclusion 154
6 Discrete-Time Fuzzy PID Control 155
6.1 Introduction 155
6.2 Design of Fuzzy PID Control System 157
6.2.1 Fuzzy PID Controller with Parallel Structure 157
6.2.2 Tuning of the Fuzzy PID Controller 162
6.3 Stability and Performance Analysis 165
6.3.1 BIBO Stability Condition of the Fuzzy PID Control System 165
6.3.2 Control Efforts Between Fuzzy and Conventional PID Controllers 169
6.4 Illustrative Example 171
6.5 Conclusion 173
7 Benchmark Precision Control of a Piezo-Motor Driven Linear Stage 174
7.1 Introduction 174
7.2 Model of the Piezo-Motor Driven Linear Motion Stage 175
7.2.1 Overall Model in Continuous-Time 176
7.2.2 Friction Models 176
7.2.3 Overall Model in Discrete-Time 178
7.3 Discrete-Time Output ISM Control 179
7.3.1 Controller Design and Stability Analysis 180
7.3.2 Disturbance Observer Design 182
7.3.3 State Observer Design 184
7.3.4 Ultimate Tracking Error Bound 185
7.3.5 Experimental Investigation 187
7.4 Discrete-Time Terminal Sliding Mode Control 192
7.5 Sampled-Data ILC Design 193
7.5.1 Controller Parameter Design and Experimental Results 193
7.6 Conclusion 196
8 Advanced Control for Practical Engineering Applications 198
8.1 Introduction 198
8.2 Periodic Adaptive Control of a PM Synchronous Motor 199
8.2.1 Problem Definition 199
8.2.2 Control Strategy and Results 200
8.3 Multirate ILC of a Ball and Beam System 204
8.3.1 System Model 204
8.3.2 Target Trajectory 205
8.3.3 Controller Configurations 206
8.3.4 System Verifications 206
8.4 Discrete-Time Fuzzy PID of a Coupled Tank System 209
8.4.1 System Description 210
8.4.2 Experiment 210
8.5 Iterative Learning Control for Freeway Traffic Control 211
8.5.1 Traffic Model and Analysis 212
8.5.2 Density Control 216
8.5.3 Flow Control 219
8.6 Conclusion 222
Appendix Derivation of BIBO Stability Condition of Linear PID Control System 224
References 225