Filtered repetitive control with nonlinear systems

Foreword......Page 5
Preface......Page 6
Contents......Page 8
Symbols......Page 13
1 Introduction......Page 16
  1.1.1 Basic Concept......Page 17
  1.1.2 Internal Model Principle......Page 18
 1.2 Brief Overview of Repetitive Control for Linear System......Page 22
  1.3.1 Major Repetitive Controller Design Method......Page 23
 1.4 Objective and Structure of This Book......Page 28
 References......Page 30
  2.1.1 Noncausal Zero-Phase Filter......Page 33
  2.1.2 Sensitivity and Complementary Sensitivity Function......Page 35
  2.1.3 Small Gain Theorem......Page 37
  2.1.4 Positive Real System......Page 39
  2.2.1 Schur Complement......Page 40
  2.2.2 Feedback Linearization......Page 41
  2.2.3 Additive State Decomposition......Page 46
  2.3.1 Barbalat's Lemma......Page 50
  2.3.2 Ordinary Differential Equation......Page 51
  2.3.3 Functional Differential Equation......Page 53
 2.4 Rejection Problem and Tracking Problem......Page 57
 References......Page 59
3 Repetitive Control for Linear System......Page 61
  3.1.1 Continuous-Time Transfer Function......Page 62
  3.1.2 Discrete-Time Transfer Function......Page 65
 3.2 Repetitive Control Based on State-Space Model......Page 67
  3.2.2 Repetitive Controller Design......Page 68
  3.2.3 Numerical Simulation......Page 79
 References......Page 82
4 Robustness Analysis of Repetitive Control Systems......Page 84
 4.1 Measurement of Stability Margin......Page 85
 4.2 Robustness Analysis of Internal Model System......Page 88
  4.3.1 Stability Margin of Repetitive Control System......Page 91
  4.3.2 Limitation of Repetitive Control System......Page 92
  4.3.3 Filtered Repetitive Control......Page 95
 References......Page 97
 5.1 Repetitive Control for System with State-Related Nonlinearity......Page 98
  5.1.1 Problem Formulation......Page 99
  5.1.2 Repetitive Controller Design Under Assumption 5.1......Page 101
  5.1.3 Repetitive Controller Design Under Assumption 5.2......Page 103
  5.2.1 Problem Formulation......Page 109
  5.2.2 Repetitive Controller Design......Page 110
 References......Page 112
6 Filtered Repetitive Control with Nonlinear Systems: An Adaptive-Control-Like Method......Page 114
 6.1 Problem Formulation......Page 115
 6.2 Simple Example......Page 116
 6.3 New Model of Periodic Signal......Page 117
  6.4.1 Controller Design......Page 118
  6.4.2 Stability Analysis......Page 120
 6.5 Filtered Repetitive Controller Design with Saturation......Page 121
  6.6.1 Problem Formulation......Page 123
  6.6.2 Controller Design......Page 124
  6.6.4 Numerical Simulation......Page 125
  6.7.1 Problem Formulation......Page 128
  6.7.2 Assumption Verification......Page 130
 6.8 Summary......Page 131
  6.9.1 Proof of Lemma 6.1......Page 132
  6.9.2 Detailed Proof of Theorem 6.1......Page 133
  6.9.3 Proof of Lemma 6.2......Page 135
 References......Page 136
 7.1 Problem Formulation......Page 138
 7.2 Additive-State-Decomposition-Based Repetitive Control Framework......Page 141
  7.2.1 Decomposition......Page 142
  7.2.2 Controller Design......Page 144
 7.3 Application to TORA Benchmark Problem......Page 148
  7.3.1 Additive State Decomposition of TORA Benchmark......Page 149
  7.3.2 Filtered Repetitive Controller Design for Primary System......Page 150
  7.3.3 Stabilizing Controller Design for Secondary System......Page 151
  7.3.4 Controller Synthesis for Original System......Page 153
  7.3.5 Numerical Simulation......Page 155
 7.4 Summary......Page 156
  7.5.1 Proof of Theorem 7.2......Page 157
  7.5.2 Proof of Proposition 7.1......Page 158
 References......Page 159
8 Sampled-Data Filtered Repetitive Control With Nonlinear Systems: An Additive-State-Decomposition Method......Page 161
  8.1.1 System Description......Page 162
  8.1.2 Objective......Page 163
 8.2 Sampled-Data Output-Feedback Robust Repetitive …......Page 164
  8.2.1 Additive State Decomposition......Page 165
  8.2.2 Controller Design for Primary System and Secondary System......Page 167
  8.2.3 Controller Synthesis for Original System......Page 172
  8.3.1 Problem Formulation......Page 173
  8.3.2 Controller Design......Page 174
  8.3.3 Controller Synthesis and Simulation......Page 176
  8.3.4 Comparison......Page 178
 References......Page 180
9 Filtered Repetitive Control with Nonlinear Systems: An Actuator-Focused Design Method......Page 182
 9.1 Motivation and Objective......Page 183
  9.2.1 General Idea......Page 185
  9.2.2 Three Examples......Page 187
  9.2.3 Filtered Repetitive Control System Subject to T-Periodic Signal......Page 191
 9.3 Actuator-Focused Repetitive Controller Design Method......Page 192
  9.3.1 Linear Periodic System......Page 193
  9.3.2 General Nonlinear System......Page 197
  9.4.1 Linear Periodic System......Page 199
  9.4.2 Minimum-Phase Nonlinear System......Page 201
  9.4.3 Nonminimum-Phase Nonlinear System......Page 203
  9.6.1 Proof of Theorem 9.3......Page 206
  9.6.2 Uniformly Ultimate Boundedness Proof for Minimum-Phase Nonlinear System......Page 207
  9.6.3 Uniformly Ultimate Boundedness Proof for Nonminimum-Phase Nonlinear System......Page 208
 References......Page 209
 10.1 Preliminary Lemma for Contraction Mapping......Page 211
 10.2 Problem Formulation......Page 213
  10.3.1 Saturated D-Type Repetitive Controller Design......Page 215
  10.3.2 Convergence Analysis......Page 216
  10.4.1 Problem Formulation......Page 219
  10.4.3 Assumption Verification......Page 220
  10.4.5 Numerical Simulation......Page 221
 10.5 Summary......Page 223
 10.6 Appendix......Page 224
 References......Page 227