Methods of Developing Sliding Mode Controllers delivers a practical review of sliding mode controllers (SMCs) and their challenges with coverage of related theorems, stability analysis, and how to program and simulate SMCs in MATLAB and Simulink. The book details the latest methods of their development and their applications in the automotive, aerospace, and robotics industries.
Initial chapters detail a range of different types of controllers. A combination of sliding and backstepping control is introduced and simulated and the phenomenon of chattering and effective solutions to reduce it are provided, along with suitable examples and analytical tables of the results. The final two chapters are related to fixed-time and event-triggered SMCs. Extensive Matlab/Simulink supported examples and simulation program code/block diagrams are included throughout.
Methods of Developing Sliding Mode Controllers: Design and Matlab Simulation explores sample topics including: - Classic SMCs, covering variable structures, including relays and feedback control with switching gains, as well as controller design and theoretical foundations - Terminal SMCs, covering nonsingular and fast variations, dynamic SMCs, and fuzzy SMCs, covering fuzzy approximation and equivalent control as well as indirect design - Super twisting SMCs, adaptive SMCs, and backstepping SMCs, covering the backstepping method and chaotic duffing oscillator equations - Sign, Epsilon-sign, saturation, hyperbolic tangent, and generalized hyperbolic tangent functions for chatter reduction
Methods of Developing Sliding Mode Controllers: Design and Matlab Simulation is a concise yet comprehensive and highly practical reference on the subject for graduate/postgraduate students in electrical engineering, mechanical engineering, and biomedical engineering along with academics and professionals in fields related to SMCs.
Table of Contents
About the Authors xiii
Acknowledgments xv
Introduction xvii
1 An Introduction to Sliding Mode Controllers 1
1.1 Introduction 1
1.2 Advantages and Limitations of Sliding Mode Controllers 2
1.3 An Overview of Book Contents 3
References 4
2 Classic Sliding-Mode Controller 5
2.1 Introduction 5
2.2 Variable-Structure Controllers 5
2.2.1 Industrial Variable-Structure Controllers 7
2.2.1.1 Relays 7
2.2.1.2 Feedback Control with Switching Gains 7
2.2.1.3 Sliding Mode Controlers 7
2.3 Classic Sliding Mode Controllers 8
2.4 Controller Design 9
2.5 Sliding Mode Controller Design 10
2.5.1 Reaching Phase 10
2.5.2 Sliding Phase 11
2.6 Theoretical Foundations of Sliding Mode Control 11
2.7 Designing Sliding Mode Controller for Second Order Uncertain Systems 12
2.7.1 System Dynamical Model 12
2.7.2 Sliding Surface Determination 13
2.7.3 Designing Nominal Controller 13
2.7.4 Designing the Variable Structure 13
2.8 Classical Sliding Mode Controller Design in MATLAB 15
References 24
3 Terminal Sliding Mode Controller 27
3.1 Introduction 27
3.2 Terminal Sliding Mode Controller Design 27
3.3 Nonsingular Terminal Sliding Mode Controller 30
3.4 Fast Terminal Sliding-Mode Controller 32
3.5 Nonsingular Fast Terminal Sliding-Mode Control 34
3.6 Integral Terminal Sliding-Mode Control 36
3.7 Extended INTSMC for n-Order Nonlinear Systems 38
3.8 MATLAB Simulation 39
3.8.1 Simulation using MATLAB mfiles 40
3.8.2 Designing Improved Sliding Mode Controllers for Inverted Pendulum in SIMULINK 47
3.9 Conclusion 55
References 57
4 Dynamic Sliding Mode Control 59
4.1 Introduction 59
4.2 Designing the Dynamic Sliding Mode Controller 59
4.2.1 Statement of the Problem 59
4.2.2 Controller Design and Stability Analysis 60
4.3 DSMC MATLAB Programming 61
4.3.1 Programming in Simulink Environment 65
References 68
5 Fuzzy Sliding Mode Controllers 69
5.1 Introduction 69
5.2 Designing Adaptive FSMC 69
5.2.1 Designing Sliding-Mode Controller Based on Fuzzy Approximator 70
5.2.2 Fuzzy Approximation 71
5.3 Designing an Indirect Adaptive Fuzzy Sliding-Mode Controller 72
5.3.1 Fuzzy Adaptive SMC Simulation Results 73
5.4 Designing Sliding-Mode Controller Based on Fuzzy Equivalent Control 84
5.4.1 Fuzzy Equivalent SMC Simulation Results for Inverted Pendulum 84
5.4.2 Fuzzy Equivalent SMC Simulation Results for Duffing System 95
References 102
6 Adaptive Sliding-Mode Control 103
6.1 Introduction 103
6.2 Adaptive Sliding Mode Control Design 103
6.3 Designing Adaptive SMC for Inverted Pendulum 104
References 110
7 Super Twisting SMC 111
7.1 Introduction 111
7.2 SMC Review 112
7.2.1 SMC Design 112
7.2.2 Inverted Pendulum Design 113
7.3 Super Twisting SMC 115
7.4 Super-Twisting SMC Controller Design in MATLAB 117
7.4.1 MATLAB Programming 117
References 122
8 Back-Stepping Sliding-Mode Control 123
8.1 Introduction 123
8.2 Back-Stepping Controller Design 124
8.2.1 Back-Stepping Method 124
8.2.2 Chaotic Duffing Oscillator Equations 126
8.3 Back-Stepping Control of Chaotic Duffing Oscillator 128
8.3.1 Stability Analysis 129
8.4 MATLAB Programming of Back-Stepping Controller 131
8.4.1 Back-Stepping Controller Design in MATLAB 132
8.4.2 Controller Design Based on Back-Stepping Super-Twisting SMC 132
8.5 Back-Stepping Super-Twisting Sliding-Mode Controller Design 140
8.5.1 Proof of Stability 141
8.5.2 MATLAB Programming 142
8.5.3 Back-Stepping Super-Twisting SMC Controller Design in MATLAB 143
References 149
9 Chattering Reduction Methods 151
9.1 Introduction 151
9.2 Methodology 152
9.2.1 Methods to Reduce Chattering Phenomenon 152
9.2.2 Sign Function 153
9.2.3 Epsilon-Sign Function 154
9.2.4 Saturation Function 155
9.2.5 Hyperbolic Tangent Function 156
9.2.6 Generalized Hyperbolic Tangent Function 157
9.2.7 Generalized Hyperbolic Tangent Function 158
9.2.8 Super Twisting 159
References 166
10 Feedback Linearization and Sliding Mode Controllers 169
10.1 Introduction 169
10.2 Feedback Linearization 170
10.2.1 Feedback Linearization of Systems with Canonical Form 170
10.2.2 Input-State Linearization 171
10.2.3 Input-Output Linearization 172
10.3 Inverted Pendulum System Equations 173
10.4 Controller Design Based on Feedback Linearization 173
10.5 Proof of Stability 176
10.5.1 MATLAB Programming 176
10.6 Sliding-Mode Control Based on Feedback Linearization Method 180
10.6.1 MATLAB Programming 181
References 185
11 Fixed-Time Terminal Sliding-Mode Controller 187
11.1 Introduction 187
11.2 Finite-Time Terminal Sliding Mode Controller 188
11.2.1 Finite-Time Convergence 188
11.2.2 Mathematical Preliminaries 188
11.2.3 Finite-Time Terminal Sliding-Mode Controller Design 190
11.2.4 MATLAB Programming 191
11.3 Fixed-Time Terminal Sliding-Mode Controller 195
11.3.1 Fixed-Time Convergence 195
11.3.2 Mathematical Preliminaries 195
11.3.3 Design and Stability Analysis 196
11.3.4 MATLAB Programming 198
11.3.5 Nonsingular Fixed-Time Terminal Sliding-Mode Controller 202
11.3.5.1 Design of Nonsingular Fixed-Time Terminal Sliding-Mode Controller 204
11.3.5.2 MATLAB Programming 209
References 211
12 Event-Triggering Sliding-Mode Controllers 213
12.1 Introduction 213
12.2 Designing Event-Triggering Sliding-Mode Controller for Linear Systems 213
12.2.1 Definitions and Mathematical Preliminaries 214
12.2.2 Controller Design 215
12.3 MATLAB Programming and Simulation Results: Event-Triggering Sliding-Mode Controller for Linear Systems 217
12.4 Design of Event-Triggering SMC for Nonlinear Systems 219
12.5 MATLAB Programming and Simulation Results 224
References 229
Index 231
