1 Literature survey and background 1
1.1 Introduction 1
1.2 Variable structure systems 2
1.3 Discrete time variable structure control systems 3
1.4 Fusion of artificial intelligence algorithms with SMC 5
1.4.1 Artificial intelligence 6
1.4.2 Fuzzy sliding mode control 8
1.4.3 Adaptive fuzzy sliding mode control 9
1.4.4 Neural network based sliding mode control 12
1.4.5 Neural fuzzy based sliding mode control 13
1.5 Sliding mode observation 14
1.6 Applications and practice of sliding mode control 14
1.7 Summary 15
2 Preliminary methodologies 17
2.1 Introduction 17
2.2 Nonlinear systems and their control 17
2.2.1 Nonlinear systems 17
2.2.2 Control of nonlinear systems 18
2.3 Variable structure control 19
2.3.1 Variable structure systems 20
2.3.2 Sliding mode in variable structure systems 21
2.3.3 Sliding mode control design by the reaching law approach 23
2.4 Discrete time sliding mode control 28
2.4.1 Discrete time sliding mode control 28
2.4.2 DSMC control design by the reaching law approach 30
2.5 Fuzzy logic control 35
2.5.1 Mamdani fuzzy logic systems 37
2.5.2 Takagi-sugeno fuzzy logic systems 40
2.6 Fuzzy adaptive control 43
2.7 Summary 44
3 Adaptive fuzzy sliding mode control 46
3.1 Introduction 46
3.2 Fuzzy universal approximation 46
3.2.1 Fuzzy basis functions 46
3.2.2 Fuzzy universal approximation 47
3.3 AFSMC for SISO nonlinear systems 48
3.3.1 Problem statement 48
3.3.2 Conventional sliding mode control 49
3.3.3 Indirect adaptive control law based on fuzzy logic schemes 50
3.3.4 Lyapunov stability analysis 51
3.3.5 Simulation studies 54
3.4 AFSMC for MIMO nonlinear systems 62
3.4.1 Problem statement 62
3.4.2 Conventional sliding mode control 63
3.4.3 Adaptive fuzzy control law design 65
3.4.4 Simulation studies 73
3.5 Summary 79
4 Sliding mode observation 81
4.1 Introduction 81
4.2 State observation 83
4.3 Sliding mode observation 84
4.4 Nonlinear sliding mode observers for stochastic systems 85
4.4.1 Preliminaries and problem formulation 86
4.4.2 Adaptive sliding mode observer design 87
4.4.3 Convergence analysis of the observer 88
4.4.4 Simulation studies 91
4.5 Summary 94
5 Adaptive observer based nonlinear stochastic system control with sliding mode schemes 95
5.1 Introduction 95
5.2 Problem statement and preliminaries 97
5.3 Adaptive observer design based on sliding mode schemes 99
5.3.1 Design of the observer 99
5.3.2 Convergence of the observer 100
5.4 Adaptive observer based nonlinear stochastic system control 103
5.4.1 Sliding mode controller based on sliding mode observer 103
5.4.2 Stability analysis of overall closed-loop systems 105
5.5 Simulation studies 106
5.6 Summary 109
6 Hovering control of a helicopter simulator 110
6.1 Overview of hovering control 110
6.2 Dynamic models of helicopter simulator 112
6.2.1 Aerodynamic analysis of rotor thrust 113
6.2.2 Mathematical models of helicopter simulator 115
6.2.3 Time discretization of nonlinear systems 117
6.3 Fuzzy sliding mode controller design 120
6.3.1 Perfect control law 120
6.3.2 Design of controller 121
6.3.3 Design procedures for controller 123
6.4 Simulation studies 123
6.4.1 Parameters and initial conditions 123
6.4.2 Design of conventional fuzzy logic control 124
6.4.3 Simulation results 126
6.5 Summary 127
7 Adaptive control for robotic manipulators 129
7.1 Overview of the control of robotic manipulators 129
7.2 Dynamic models of robot manipulators 133
7.3 Rigid and flexible joint robotic manipulators 136
7.4 Dynamics of a two-link rigid robot manipulator 137
7.5 Controller design for an SCARA robot 139
7.6 Simulation studies 148
7.7 Summary 154
8 Controller design for vehicle suspension systems 156
8.1 Overview of vehicle suspension systems 156
8.1.1 Vehicle suspension systems 156
8.1.2 Literature review 159
8.2 Mathematical models and control problem 161
8.2.1 System dynamic model 163
8.2.2 Objective of control 164
8.3 Proportional integral sliding mode control 165
8.3.1 Introduction 165
8.3.2 Linear quadratic regulators 166
8.3.3 PI sliding mode control 167
8.3.4 Simulation studies 168
8.4 Singular perturbation based sliding mode control 170
8.4.1 Introduction 170
8.4.2 Linear dynamic models for suspension systems 171
8.4.3 Control law design based on the sliding mode scheme 173
8.4.4 Nonlinear suspension systems 174
8.4.5 Control law design based on the fuzzy sliding mode scheme 177
8.5 Summary 182
9 Fuzzy PID and sliding made control 184
9.1 Introduction of fuzzy PID control 184
9.1.1 Structure of a fuzzy PID control system 184
9.1.2 Design of a fuzzy PID controller 185
9.2 Problem statement and configuration of control systems 188
9.2.1 Mathematical model of a servo motor 188
9.2.2 Mathematical model of a two-container water tank system 189
9.2.3 Mathematical model of a hydraulic cylinder 192
9.3 Applications of fuzzy PID control and sliding mode control 195
9.3.1 Control ofa servo motor 195
9.3.2 Control of a two-container water tank system 198
9.3.3 Control of a hydraulic cylinder 202
9.4 Summary 207
References 208