Applications of Sliding Mode Control (eBook)

Preface 6
Contents 8
1 On the Sliding Control 10
1.1 Introduction 10
1.2 Classical Sliding Mode 11
1.2.1 Notion of Sliding Mode 12
1.2.2 Invariance Terms of the Sliding Mode 14
1.2.3 Reaching Phase and Sliding Phase 18
1.2.4 Synthesis of the Sliding Mode Control 20
1.3 Generalized Sliding Mode 22
1.3.1 Feedback Linearization 22
1.3.2 Observable Single Input--Single Output Systems Case with Zero Dynamics 23
1.4 Higher Order Sliding Mode 27
1.4.1 Position of the Problem 27
1.4.2 Principle 28
1.4.3 The ``Twisting'' Algorithm 28
1.4.4 Second Order Sliding Mode Control 30
1.4.5 Example 32
1.5 Conclusion 35
References 35
2 Conditions of Disturbances Rejection for Discrete First, Second Order and Repetitive Sliding Mode Controllers 37
2.1 Introduction 37
2.2 Conditions of Disturbances Rejection in Discrete Multivariable Sliding Mode Control 39
2.3 Conditions of Disturbances Rejection in Discrete Multivariable Second Order Sliding Mode Control 43
2.4 Conditions of Disturbances Rejection in Discrete Multivariable Repetitive Sliding Mode Control 46
2.5 Simulation Results 48
2.6 Conclusion 58
References 59
3 Output Feedback Robust Exponential Higher Order Sliding Mode Control 61
3.1 Introduction 61
3.2 Higher Order Sliding Mode Control 63
3.2.1 Problem Formulation 63
3.2.2 Control Design 64
3.3 Output Feedback Control 67
3.4 Application to Induction Machine 70
3.4.1 Mathematical Model of the Induction Motor 70
3.4.2 Controllers Synthesis 72
3.5 Conclusion 78
References 79
4 Synthesis of an Optimal Sliding Function Using LMIs Approach for Time Delay Systems 81
4.1 Introduction 81
4.2 Discrete Second Order Sliding Mode Control 83
4.3 Discrete Second Order Sliding Mode Control Using LMIs Approach 85
4.4 Simulation Example 88
4.4.1 Synthesis of Sliding Function's Coefficients Using Pole Placement Method 89
4.4.2 Synthesis of Sliding Function's Coefficients Using LMIs Approach 90
4.5 Conclusion 92
References 92
5 Robust Flight Control of an Underactuated Quadrotor via Sliding Modes 95
5.1 Introduction 96
5.2 Dynamic Model 98
5.2.1 Dynamics 98
5.2.2 Properties 101
5.3 Sliding Mode Flight Control 101
5.3.1 Sliding Mode Attitude Control 102
5.3.2 Sliding Mode Position Control 103
5.4 Numerical Simulation 106
5.4.1 Simulation Parameters 106
5.4.2 Simulation Results 107
5.5 Conclusions 110
References 111
6 Sliding Mode Control of an Inverted Pendulum 113
6.1 Introduction 113
6.2 First Order Sliding Mode Control 114
6.3 Second Order Sliding Mode Control 117
6.3.1 Twisting Algorithm 117
6.3.2 Super-Twisting Algorithm 118
6.4 Application to an Inverted Pendulum 119
6.4.1 Application of First Order Sliding Mode Control 119
6.4.2 Application of Second Order Sliding Mode Control 120
6.5 Conclusion 124
References 126
7 Robust Adaptive Manoeuvering Control of an Autonomous Surface Vessel in the Presence of Ocean Currents and Parametric Model Uncertainty 127
7.1 Introduction 127
7.2 Preliminaries 129
7.2.1 Notations 129
7.2.2 RBFNN Approximation 129
7.3 Vehicle Model 130
7.4 Problem Statement 132
7.5 Control Design 133
7.5.1 Path Following Control Design 133
7.6 Numerical Simulations 139
7.7 Conclusion 141
References 142
8 Sliding Mode with Time Delay Control for Robot Manipulators 143
8.1 Introduction 144
8.2 System Description 145
8.3 First Order Sliding Mode with Time Delay 146
8.3.1 Design of Controller 146
8.3.2 Stability Analysis 147
8.3.3 Effect of Switching Action 149
8.4 Second Order Sliding Mode with Time Delay 149
8.4.1 Design of Controller 149
8.4.2 Stability Analysis 151
8.5 Simulation Examples 152
8.5.1 Conventional SMC Simulated on Robotic Arm 154
8.5.2 FOSMTDC Simulated on Robotic Arm 154
8.5.3 SOSMTDC Simulated on Robotic Arm 154
8.5.4 Simulation Results and Discussion 163
8.6 Conclusion 163
References 164
9 Kinematics and a Comparison Between Two SM Control Strategies for a 5DOF Serial Robot for Tele-Echography 165
9.1 Introduction 166
9.2 Preliminaries 167
9.2.1 Mechanical Structure of the Robot 167
9.2.2 Kinematics of the Protech Robot 168
9.2.3 Dynamic of the Protech Robot 170
9.3 Control Design 172
9.3.1 Classical Sliding Mode Control 172
9.3.2 Second Order Sliding Mode Control 173
9.4 Simulation Results 175
9.5 Conclusion 181
References 181
10 Estimated Model-Based Sliding Mode Controller for an Active Exoskeleton Robot 183
10.1 Introduction 184
10.1.1 General Introduction 184
10.1.2 Motivation 184
10.1.3 Previous Works 185
10.1.4 Comparison and Contribution 186
10.2 Mechatronic Design 186
10.3 Kinematic Measurement 189
10.4 Control Design 191
10.5 Experimental Results 193
10.6 Conclusion 195
References 195
11 An Adaptive Finite-Time Consensus Control for Higher-Order Nonlinear Multi-agent Systems 198
11.1 Introduction 198
11.2 Mathematical Preliminaries 200
11.3 Problem Formulation 202
11.4 Homogeneous Finite-Time Consensus Control with Integral Sliding Mode Control 205
11.5 Results 212
11.6 Conclusion 218
References 218
12 MPPT Controllers Based on Sliding-Mode Control Theory and Fuzzy Logic in Photovoltaic Power Systems: A Comparative Study 221
12.1 Introduction 222
12.2 Description of the PV System 223
12.2.1 The Photovoltaic Effect 223
12.2.2 The Effect of Climatic Conditions on the PV Panel 225
12.3 Modeling the Boost Converter 225
12.4 MPPT Controller 228
12.4.1 Fuzzy Logic MPPT Controller 228
12.4.2 MPPT Based on Sliding Mode Control Theory 230
12.4.3 Stability Analysis 232
12.5 Simulation of the Fuzzy Logic and the Sliding MPPT Controllers and Results 233
12.6 Conclusion 237
References 237
13 Sliding Bifurcations and Sliding Mode Controller for a Two-Cell DC/DC Buck Converter 238
13.1 Introduction 238
13.2 Discrete Model of the Two-Cell DC/DC Buck Converter 240
13.3 Sliding Bifurcations in the Two-Cell DC/DC Buck Converter Controlled Using a Dynamic Feedback Controller 243
13.3.1 Dynamic Feedback Controller 243
13.3.2 Sliding Bifurcations 250
13.4 Sliding Mode Controller 261
13.4.1 Previous Work 262
13.4.2 Application of the Sliding Mode Controller to the Two-Cell DC/DC Buck Converter 264
13.5 Conclusion 268
References 269
14 DTC-SVM-Based Sliding Mode Controllers with Load Torque Estimators for Induction Motor Drives 274
14.1 Introduction 274
14.2 Mathematical Model of Induction Machines 275
14.2.1 Voltage Source Inverter 276
14.2.2 Basic Principle of the Conventional DTC 277
14.2.3 DTC-SVM Principle 277
14.3 DTC-SVM-Based PI Controllers 278
14.3.1 Torque Controller 278
14.3.2 Flux Reference Coordinates Computing 278
14.3.3 Voltage Reference Coordinates Computing 279
14.3.4 PI-DTC-SVM Scheme 279
14.4 DTC-SVM-Based SM Controllers 279
14.4.1 SM Control Principle 280
14.4.2 Speed SM Controller 281
14.4.3 Flux SM Controller 282
14.4.4 SM-DTC-SVM Scheme 283
14.4.5 Adaptive Load Torque Estimator 283
14.5 Simulation Results and Discussions 286
14.5.1 Case of Known Loads 286
14.5.2 Performance Criteria 291
14.5.3 Case of Ill-Known Loads Without Load Gain Estimators 294
14.5.4 Case of Ill-Known Loads with Load Gain Estimators 296
14.6 Conclusion 298
References 300
15 An Enhanced High Order Sliding Mode based Method for Detecting Inter-Turn Short-Circuit Fault in Induction Machine with Decoupled Current Control 303
15.1 Introduction 303
15.2 Modeling of Induction Machine 306
15.2.1 Healthy IM Model 306
15.2.2 Faulty IM Model 307
15.2.3 Impact of ITSC Fault 309
15.3 HOSM Observer 312
15.3.1 HOSM Observer Design 313
15.3.2 HOSM Observer Simulation 315
15.4 Control Scheme and Decoupling 316
15.4.1 Classical Decoupled Current Control for IM 317
15.4.2 HOSM Decoupled Current Control Design 319
15.5 Fault Detection and Residual Generation 328
15.6 Conclusion 330
References 331
16 Sliding Mode Control Applied to Electrohydraulic System 334
16.1 Introduction 334
16.2 Model of the Electrohydraulic System 336
16.3 Position Control of a Symmetric System 337
16.3.1 Proportional Control 338
16.3.2 Proportional Integral Control 339
16.3.3 Anti Wind-Up Approach 340
16.3.4 Sliding Mode Control 341
16.3.5 Sliding Mode Control with ``Realizable Reference'' 344
16.4 Position Control of a Non-symmetric System 347
16.4.1 Proportional Control 347
16.4.2 Proportional Integral Control 347
16.4.3 Anti Wind-Up Approach 348
16.4.4 Sliding Mode Control 349
16.4.5 Sliding Mode Control with Realizable Reference 356
16.4.6 Sliding Mode Observer Design 358
16.5 Conclusion 363
References 365