Hierarchical Sliding Mode Control for Under-actuated Cranes (eBook)

Preface 6
Acknowledgments 8
Contents 9
1 Introduction 13
Abstract 13
1.1 Crane Types 13
1.1.1 Overhead Cranes 14
1.1.2 Boom Cranes 14
1.1.3 Tower Cranes 15
1.2 Review of Sliding Mode Control 17
1.2.1 Variable Structure Control 17
1.2.2 Sliding Mode Control 20
1.2.3 Equivalent-Control-Based Sliding Mode Control 23
1.2.4 Chattering Reduction 25
1.2.5 Sliding Mode Control Design for State Space Model 27
1.2.6 Robustness Against Uncertainties 29
1.2.7 Sliding Order and Sliding Sets 34
1.3 A Review of Crane Control 35
1.3.1 Open-Loop Control 35
1.3.1.1 Optimal Trajectory Planning 35
1.3.1.2 Input Shaping 36
1.3.2 Closed-Loop Control 37
1.3.2.1 Linear Control 38
1.3.2.2 Partial Feedback Linearization 39
1.3.2.3 Energy-Based Methods 40
1.3.2.4 Robust Control and Adaptive Control 41
1.3.2.5 Predictive Control 42
1.3.2.6 Intelligent Control 43
1.3.2.7 Sliding Mode Control 44
1.4 Challenges of Sliding Mode-Based Crane Control 45
1.4.1 Theoretical Challenges 45
1.4.2 Practical Challenges 46
Appendices 47
A Matlab Codes to Plot Fig. 1.5a 47
B Matlab Codes to Plot Fig. 1.5b 47
C Matlab Codes to Plot Fig. 1.7 47
D Simulink Model to Plot Figs. 1.8 and 1.9 48
E Simulink Model to Plot Figs. 1.10 and 1.11 49
F Matlab Codes to Plot Fig. 1.12 50
G Simulink Model to Plot Figs. 1.13 and 1.14 50
H Simulink Model to Plot Figs. 1.15 and 1.16 51
I Simulink Model to Plot Figs. 1.17, 1.18, 1.19 and 1.20 53
References 54
2 Crane Mathematic Model 63
Abstract 63
2.1 Modeling of Single-Pendulum-Type Cranes 63
2.1.1 Modeling 63
2.1.2 Model with Uncertainties 67
2.1.3 Linearized Model 68
2.1.4 Modeling of Double-Pendulum-Type Cranes 69
2.1.4.1 Modeling 69
2.1.5 Model with Uncertainties 75
2.1.6 Linearized Model 75
Appendices 77
A Matlab Codes to Plot Fig. 2.2 77
B Matlab Codes to Plot Fig. 2.4 78
References 78
3 Overhead Crane Control by Sliding Mode Methods 79
Abstract 79
3.1 Problem Description 79
3.2 First-Order Sliding Mode Control 80
3.2.1 Control Design of Single-Pendulum-Type Overhead Cranes 80
3.2.2 Stability Analysis of the Single-Pendulum-Type Crane Control System 81
3.2.3 Simulations of Nominal Single-Pendulum-Type Overhead Cranes 83
3.2.4 Simulations of Uncertain Single-Pendulum-Type Overhead Cranes 85
3.2.5 Extensions of Double-Pendulum-Type Overhead Cranes 86
3.3 Integral Sliding Mode Control 91
3.3.1 Control Design 91
3.3.2 Stability Analysis 92
3.3.3 Simulations of Single-Pendulum-Type Cranes by ISMC 94
3.3.4 Simulations of Uncertain Single-Pendulum-Type Cranes by ISMC 96
3.4 Terminal Sliding Mode Control 98
3.4.1 Control Design 98
3.4.2 Stability Analysis 100
3.4.3 Simulations of Single-Pendulum-Type Cranes by TSM 102
3.4.4 Simulations of Uncertain Single-Pendulum-Type Cranes by TSM 103
3.5 Second-Order Sliding Mode Control 105
3.5.1 Control Design 105
3.5.2 Stability Analysis 106
3.5.3 Simulations of Single-Pendulum-Type Cranes by Second-Order SMC 108
3.5.4 Simulations of Uncertain Cranes by Second-Order SMC 110
Appendices 112
A Simulink Model to Plot Figs. 3.1 and 3.2 112
B Simulink Model to Plot Figs. 3.5 and 3.6 115
C Simulink Model to Plot Figs. 3.7 and 3.8 119
D Simulink Model to Plot Figs. 3.11 and 3.12 121
E Simulink Model to Plot Figs. 3.15 and 3.16 124
References 127
4 Overhead Crane Control by Hierarchical Sliding Mode 128
Abstract 128
4.1 Problem Description 128
4.2 Aggregated HSMC 129
4.2.1 Control Design 130
4.2.2 Stability Analysis 132
4.2.3 Simulation Results 135
4.3 Incremental HSMC 138
4.3.1 Control Design 139
4.3.2 Stability Analysis 141
4.3.3 Simulation Results 143
4.4 Combining HSMC 146
4.4.1 Control Design 147
4.4.2 Stability Analysis 148
4.4.3 Simulation Results 151
4.5 Adaptive Control Design Based on Hierarchical Sliding Surfaces 155
4.5.1 Control Design 156
4.5.2 Stability Analysis 157
4.5.3 Simulation Results 158
4.6 HSMC Design for Double-Pendulum-Type Overhead Cranes 161
4.6.1 Control Design 161
4.6.2 Stability Analysis 164
4.6.3 Simulation Results 164
Appendices 167
A Simulink Model to Plot Figs. 4.2, 4.3 and 4.4 167
B Simulink Model to Plot Figs. 4.6, 4.7, 4.8 and 4.9 168
C Simulink Model to Plot Figs. 4.11, 4.12, 4.13, 4.14 and 4.15 170
D Simulink Model to Plot Figs. 4.16, 4.17, 4.18 and 4.19 172
E Simulink Model to Plot Figs. 4.21 and 4.22 175
References 176
5 Compensator Design Based on Sliding Mode for Uncertain Overhead Cranes 178
Abstract 178
5.1 Problem Description 178
5.2 Compensator Design Based on HSMC 179
5.2.1 Control Design 179
5.2.2 Stability Analysis 181
5.2.3 Simulation Results 181
5.3 Sliding Mode-Based Fuzzy Compensator Design 183
5.3.1 Control Design 184
5.3.1.1 Design of Fuzzy Compensator 184
5.3.1.2 Design of HSMC-Based Controller 186
5.3.2 Stability Analysis 187
5.3.3 Simulation Results 188
5.4 Sliding Mode-Based Neural Compensator Design 190
5.4.1 Control Design 191
5.4.1.1 Design of Neural Compensator 191
5.4.1.2 Design of SMC-Based Controller 193
5.4.2 Stability Analysis 193
5.4.3 Simulation Results 195
Appendices 198
A Simulink Model to Plot Figs. 5.1 and 5.2 198
B Simulink Model to Plot Figs. 5.4, 5.5 and 5.6 200
C Simulink Model to Plot Figs. 5.8, 5.9 and 5.10 204
References 207
6 Conclusions and Open Problems 208
Abstract 208
6.1 Conclusions 208
6.2 Extensions and Open Problems 209
References 210