Methods of Developing Sliding Mode Controllers

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.

• About the Authors xiiiAcknowledgments xvIntroduction xvii1 An Introduction to Sliding Mode Controllers 11.1 Introduction 11.2 Advantages and Limitations of Sliding Mode Controllers 21.3 An Overview of Book Contents 3References 42 Classic Sliding-Mode Controller 52.1 Introduction 52.2 Variable-Structure Controllers 52.2.1 Industrial Variable-Structure Controllers 72.2.1.1 Relays 72.2.1.2 Feedback Control with Switching Gains 72.2.1.3 Sliding Mode Controlers 72.3 Classic Sliding Mode Controllers 82.4 Controller Design 92.5 Sliding Mode Controller Design 102.5.1 Reaching Phase 102.5.2 Sliding Phase 112.6 Theoretical Foundations of Sliding Mode Control 112.7 Designing Sliding Mode Controller for Second Order Uncertain Systems 122.7.1 System Dynamical Model 122.7.2 Sliding Surface Determination 132.7.3 Designing Nominal Controller 132.7.4 Designing the Variable Structure 132.8 Classical Sliding Mode Controller Design in MATLAB 15References 243 Terminal Sliding Mode Controller 273.1 Introduction 273.2 Terminal Sliding Mode Controller Design 273.3 Nonsingular Terminal Sliding Mode Controller 303.4 Fast Terminal Sliding-Mode Controller 323.5 Nonsingular Fast Terminal Sliding-Mode Control 343.6 Integral Terminal Sliding-Mode Control 363.7 Extended INTSMC for n-Order Nonlinear Systems 383.8 MATLAB Simulation 393.8.1 Simulation using MATLAB mfiles 403.8.2 Designing Improved Sliding Mode Controllers for Inverted Pendulum in SIMULINK 473.9 Conclusion 55References 574 Dynamic Sliding Mode Control 594.1 Introduction 594.2 Designing the Dynamic Sliding Mode Controller 594.2.1 Statement of the Problem 594.2.2 Controller Design and Stability Analysis 604.3 DSMC MATLAB Programming 614.3.1 Programming in Simulink Environment 65References 685 Fuzzy Sliding Mode Controllers 695.1 Introduction 695.2 Designing Adaptive FSMC 695.2.1 Designing Sliding-Mode Controller Based on Fuzzy Approximator 705.2.2 Fuzzy Approximation 715.3 Designing an Indirect Adaptive Fuzzy Sliding-Mode Controller 725.3.1 Fuzzy Adaptive SMC Simulation Results 735.4 Designing Sliding-Mode Controller Based on Fuzzy Equivalent Control 845.4.1 Fuzzy Equivalent SMC Simulation Results for Inverted Pendulum 845.4.2 Fuzzy Equivalent SMC Simulation Results for Duffing System 95References 1026 Adaptive Sliding-Mode Control 1036.1 Introduction 1036.2 Adaptive Sliding Mode Control Design 1036.3 Designing Adaptive SMC for Inverted Pendulum 104References 1107 Super Twisting SMC 1117.1 Introduction 1117.2 SMC Review 1127.2.1 SMC Design 1127.2.2 Inverted Pendulum Design 1137.3 Super Twisting SMC 1157.4 Super-Twisting SMC Controller Design in MATLAB 1177.4.1 MATLAB Programming 117References 1228 Back-Stepping Sliding-Mode Control 1238.1 Introduction 1238.2 Back-Stepping Controller Design 1248.2.1 Back-Stepping Method 1248.2.2 Chaotic Duffing Oscillator Equations 1268.3 Back-Stepping Control of Chaotic Duffing Oscillator 1288.3.1 Stability Analysis 1298.4 MATLAB Programming of Back-Stepping Controller 1318.4.1 Back-Stepping Controller Design in MATLAB 1328.4.2 Controller Design Based on Back-Stepping Super-Twisting SMC 1328.5 Back-Stepping Super-Twisting Sliding-Mode Controller Design 1408.5.1 Proof of Stability 1418.5.2 MATLAB Programming 1428.5.3 Back-Stepping Super-Twisting SMC Controller Design in MATLAB 143References 1499 Chattering Reduction Methods 1519.1 Introduction 1519.2 Methodology 1529.2.1 Methods to Reduce Chattering Phenomenon 1529.2.2 Sign Function 1539.2.3 Epsilon-Sign Function 1549.2.4 Saturation Function 1559.2.5 Hyperbolic Tangent Function 1569.2.6 Generalized Hyperbolic Tangent Function 1579.2.7 Generalized Hyperbolic Tangent Function 1589.2.8 Super Twisting 159References 16610 Feedback Linearization and Sliding Mode Controllers 16910.1 Introduction 16910.2 Feedback Linearization 17010.2.1 Feedback Linearization of Systems with Canonical Form 17010.2.2 Input-State Linearization 17110.2.3 Input–Output Linearization 17210.3 Inverted Pendulum System Equations 17310.4 Controller Design Based on Feedback Linearization 17310.5 Proof of Stability 17610.5.1 MATLAB Programming 17610.6 Sliding-Mode Control Based on Feedback Linearization Method 18010.6.1 MATLAB Programming 181References 18511 Fixed-Time Terminal Sliding-Mode Controller 18711.1 Introduction 18711.2 Finite-Time Terminal Sliding Mode Controller 18811.2.1 Finite-Time Convergence 18811.2.2 Mathematical Preliminaries 18811.2.3 Finite-Time Terminal Sliding-Mode Controller Design 19011.2.4 MATLAB Programming 19111.3 Fixed-Time Terminal Sliding-Mode Controller 19511.3.1 Fixed-Time Convergence 19511.3.2 Mathematical Preliminaries 19511.3.3 Design and Stability Analysis 19611.3.4 MATLAB Programming 19811.3.5 Nonsingular Fixed-Time Terminal Sliding-Mode Controller 20211.3.5.1 Design of Nonsingular Fixed-Time Terminal Sliding-Mode Controller 20411.3.5.2 MATLAB Programming 209References 21112 Event-Triggering Sliding-Mode Controllers 21312.1 Introduction 21312.2 Designing Event-Triggering Sliding-Mode Controller for Linear Systems 21312.2.1 Definitions and Mathematical Preliminaries 21412.2.2 Controller Design 21512.3 MATLAB Programming and Simulation Results: Event-Triggering Sliding-Mode Controller for Linear Systems 21712.4 Design of Event-Triggering SMC for Nonlinear Systems 21912.5 MATLAB Programming and Simulation Results 224References 229Index 231