Motion Control of Underactuated Mechanical Systems (eBook)

Preface 6
Contents 8
Acronyms 12
1 Introduction 13
1.1 Background 13
1.1.1 Underactuated Systems 13
1.1.2 Nonlinear Dynamics and Control 15
1.1.3 Parameter Identification 18
1.1.4 Motion Control of Underactuated Systems 19
1.2 Motivations and Objectives 21
1.3 Outline 21
2 Preliminaries 25
2.1 Fundamentals of Nonlinear Systems 25
2.2 Fundamental Properties 27
2.3 Concepts of Stability 27
2.4 Barbalat's Lemma 30
2.5 Boundedness and Ultimate Boundedness 30
2.6 Feedback Linearization 31
2.7 Artificial Neural Networks 34
2.7.1 Universal Function Approximation Property 36
3 Identification of Underactuated Mechanical Systems 1
3.1 Introduction 38
3.2 Identification of the Furuta Pendulum 39
3.2.1 Dynamic Model 39
3.2.2 Filtered Regression Model 41
3.2.3 Discretization of the Filtered Regression Model 43
3.2.4 Experimental Platform 44
3.2.5 Motion Control Experiment 45
3.2.6 Joint Velocity Calculation 46
3.2.7 Least Squares Algorithm 47
3.2.8 Results of the Identification Procedure 48
3.3 Identification of the Inertia Wheel Pendulum 51
3.3.1 Dynamic Model 51
3.3.2 Filtered Regression Model 53
3.3.3 Discretization of the Filtered Regression Model 54
3.3.4 Experimental Platform 55
3.3.5 Motion Control Experiment 56
3.3.6 Joint Velocity Calculation 56
3.3.7 Least Squares Algorithm 57
3.3.8 Results of the Identification Procedure 58
3.4 Concluding Remarks 60
4 Composite Control of the Furuta Pendulum 61
4.1 Introduction 61
4.2 Dynamic Model 62
4.3 Control Problem Formulation 63
4.4 Design of the Proposed Scheme 64
4.4.1 Feedback Linearization Part 64
4.4.2 Energy-Based Compensation 65
4.4.3 Summary of the Composite Controller 69
4.5 Analysis of the Closed-Loop Trajectories 70
4.6 Controller for the Performance Comparison 71
4.6.1 Output Tracking Controller 71
4.7 Experimental Evaluation 72
4.7.1 Experimental Results 72
4.7.2 Performance Comparison 75
4.8 Concluding Remarks 78
5 Feedback Linearization Control of the Furuta Pendulum 79
5.1 Introduction 79
5.2 Dynamic Model and Error Dynamics 80
5.3 Control Problem Formulation 82
5.4 Design of the Proposed Scheme 82
5.5 Analysis of the Closed-Loop Trajectories 83
5.5.1 Ultimate Bound 88
5.5.2 Boundedness of the Error Trajectories 89
5.6 Controllers for the Performance Comparison 90
5.6.1 PID Controller 90
5.6.2 Output Tracking Controller 91
5.7 Experimental Evaluation 92
5.7.1 Experimental Results 92
5.7.2 Performance Comparison 95
5.8 Concluding Remarks 101
6 Adaptive Neural Network Control of the Furuta Pendulum 103
6.1 Dynamic Model and Error Dynamics 104
6.2 Control Problem Formulation 106
6.3 Design of the Proposed Scheme 106
6.4 Analysis of the Closed-Loop Trajectories 109
6.5 Controllers for the Performance Comparison 118
6.5.1 PID Controller 118
6.5.2 Jung and Kim Controller 119
6.5.3 Chaoui and Sicard Controller 119
6.6 Experimental Evaluation 120
6.6.1 Experimental Results and Performance Comparison 120
6.7 Concluding Remarks 128
7 Composite Control of the IWP 1
7.1 Introduction 129
7.2 Dynamic Model 131
7.3 Control Problem Formulation 132
7.4 Design of the Proposed Scheme 132
7.4.1 Feedback Linearization Controller 132
7.4.2 Energy-Based Compensation 134
7.4.3 Summary of the Composite Controller 138
7.5 Analysis of the Closed-Loop Trajectories 138
7.6 Integral Extension 140
7.7 Controller for the Performance Comparison 141
7.7.1 LQR Motion Controller 141
7.8 Experimental Evaluation 141
7.8.1 Swing-up Control + Motion Control 142
7.8.2 Experimental Results 143
7.8.3 Performance Comparison 145
7.9 Concluding Remarks 150
8 Feedback Linearization Control of the IWP 151
8.1 Dynamic Model and Error Dynamics 153
8.2 Control Problem Formulation 155
8.3 Design of the Proposed Scheme 155
8.4 Analysis of the Closed-Loop Trajectories 156
8.5 Controllers for the Performance Comparison 160
8.5.1 State Feedback Controller 160
8.5.2 Particular Feedback Linearization Controller 161
8.6 Experimental Evaluation 164
8.6.1 Experimental Results 165
8.6.2 Performance Comparison 167
8.7 Concluding Remarks 168
9 Adaptive Control of the IWP 169
9.1 Introduction 169
9.2 Dynamic Model and Error Dynamics 170
9.3 Control Problem Formulation 173
9.4 Design of the Proposed Schemes 173
9.4.1 Model-Based Controller 173
9.4.2 Neural Network-Based Controller 175
9.4.3 Regressor-Based Adaptive Controller 177
9.5 Analysis of the Closed-Loop Trajectories 178
9.5.1 Analysis for the Neural Network-Based Adaptive Controller 178
9.5.2 Analysis for the Regressor-Based Adaptive Controller 180
9.6 Controller for the Performance Comparison 181
9.7 Experimental Evaluation 181
9.7.1 Experimental Results 181
9.7.2 Performance Comparison 183
9.8 Concluding Remarks 185
10 Discussion on Generalizations and Further Research 187
10.1 Introduction 187
10.2 Generalization for Linear Systems 188
10.3 Motion Control for 2-DOF Underactuated Mechanical Systems 191
10.4 Motion Control of Higher DOF Underactuated Mechanical System: FJR as Case Study 192
10.4.1 Model 192
10.4.2 Control Problem 193
10.4.3 Open-Loop System 193
10.4.4 Output Design and Feedback Linearization Control 194
10.5 Concluding Remarks 197
Appendix A MATLAB Codes for Parameter Identification of the Underactuated Mechanical Systems in Chap. 33 198
A.1 Identification of the Furuta Pendulum 198
A.2 Identification of the Inertia Wheel Pendulum 204
Appendix B Conditions to Ensure that Matrix A in Chaps.5 and 6 is Hurwitz 210
Appendix C Convergence Proof of the Swing-up Controller for the IWP in Chaps.7 and 8 213
Bibliography 217
Index 228