Methods of Developing Sliding Mode Controllers: Design and Matlab Simulation

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Reihaneh Kardehi Moghaddam (Azad University of Mashhad, Iran) Mostafa Rabbani (Iran University of Science and Technology)

Methods of Developing Sliding Mode Controllers

Design and Matlab Simulation

Reihaneh Kardehi Moghaddam (Azad University of Mashhad, Iran), Mostafa Rabbani (Iran University of Science and Technology)

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English

Wiley-IEEE Press
03 January 2025

Cybernetics & systems theory; Engineering: general; Electronics & communications engineering

Series: IEEE Press Series on Control Systems Theory and Applications

Comprehensive, fast-access guide to different types of sliding mode controllers and their programming and simulation in MATLAB and Simulink

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.

By: Reihaneh Kardehi Moghaddam (Azad University of Mashhad Iran), Mostafa Rabbani (Iran University of Science and Technology)
Imprint: Wiley-IEEE Press
Country of Publication: United States
ISBN: 9781394314485
ISBN 10: 1394314485
Series: IEEE Press Series on Control Systems Theory and Applications
Pages: 256
Publication Date: 03 January 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reihaneh Kardehi Moghaddam, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran, and School of Computing, Macquarie University, Sydney, Australia. Dr. Kardehi Moghaddam’s main fields of research are optimization of extracted power from renewable energy sources, nonlinear fractional order sliding mode controllers, intelligent optimization methods and deep neural networks. She has supervised four doctoral dissertations and 45+ Master’s dissertations. Mostafa Rabbani, PhD researcher, Department of Electrical Engineering, Azad University of Mashhad, Mashhad, Iran. His main field of research is nonlinear control of uncertain nonlinear systems.