滑模控制系统的分析与设计

This book mainly introduces some new design methods and ideas about sliding mode control, which are applied to the differential inclusion systems, nonlinear systems, discrete systems, chaotic systems and the delta operator sys-tems, etc. In particular, the effect of input nonlinearity is fully considered in analyzing and implementing a sliding mode control scheme. Incorporating some control algorithms, such as H∞ control, passive control, adaptive control and ge-neralized H2 control, etc, into sliding mode control extends the application range.

CONTENTS
Preface
1 Introduction: An overview of sliding mode control 1
1.1 Introduction 1
1.2 The basic concepts of sliding mode control 2
1.3 Sliding mode control design 5
1.3.1 Reaching condition 6
1.3.2 The invariance of sliding mode control 11
1.4 The chattering phenomenon 12
1.5 The content of this book 13
References 14
2 New sliding surface design 18
2.1 Generalized H2 sliding mode control of uncertain chaotic systems 18
2.1.1 Problem formulation 19
2.1.2 Sliding surface design and stability analysis 20
2.1.3 Sliding mode controller design 25
2.1.4 Numerical example 26
2.2 H∞ sliding mode control of discrete singular systems 28
2.2.1 Problem formulation 29
2.2.2 Sliding surface design and stability analysis 30
2.2.3 Sliding mode controller design 35
2.2.4 Numerical example 36
2.3 Conclusion 39
References 40
3 New reaching law design 43
3.1 The reaching law with an exponential decay term 43
3.2 Global sliding mode control of continuous systems 47
3.2.1 Problem formulation 48
3.2.2 Sliding surface design 49
3.2.3 The sliding mode controller design 50
3.2.4 Numerical example 51
3.3 The reaching law with a boundary layer 54
3.4 Sliding mode control of discrete systems 55
3.4.1 Problem formulation 55
3.4.2 Sliding surface design 56
3.4.3 Sliding mode controller design 60
3.4.4 Numerical example 61
3.5 Conclusion 64
References 64
4 Sliding mode control of differential inclusion systems 67
4.1 Sliding mode control of polytopic differential inclusion systems 67
4.1.1 Problem formulation 68
4.1.2 Main results 69
4.1.3 Numerical example 71
4.2 Sliding mode tracking control of polytopic differential inclusion systems 75
4.2.1 Problem formulation 76
4.2.2 Sliding surface design 78
4.2.3 The sliding mode controller design 79
4.2.4 Numerical example 81
4.3 Passivity-based sliding mode control of polytopic stochastic differential inclusion systems 84
4.3.1 Problem formulation 85
4.3.2 Sliding surface design and stability analysis 87
4.3.3 The sliding mode controller design 90
4.3.4 Numerical examples 91
4.4 Conclusion 95
References 95
5 Sliding mode control for robust output tracking of nonlinear systems 99
5.1 Problem Formulation 99
5.2 Sliding surface design and stability analysis 100
5.3 Sliding mode controller design 103
5.4 Numerical example 104
5.5 Conclusion 107
References 107
6 H∞ sliding mode control of uncertain time delay systems with input nonlinearity 109
6.1 H∞ sliding mode control 109
6.1.1 Problem formulation 110
6.1.2 Sliding surface design and the stability analysis 111
6.1.3 The sliding mode controller design 113
6.2 Ｈ∞ non-fragile observer-based sliding mode control 115
6.2.1 Problem formulation 115
6.2.2 Non-fragile observer design 116
6.2.3 Sliding mode controller design 117
6.2.4 Stability analysis 118
6.2.5 Numerical example 121
6.3 Conclusion 124
References 124
7 Non-fragile observer-based sliding mode passive control of uncertain time delay systems 126
7.1 Problem formulation 126
7.2 Non-fragile observer-based passive control 127
7.2.1 The non-fragile observer design 128
7.2.2 The passivity and asymptotic stability 129
7.2.3 The sliding mode controller design 131
7.3 Numerical example 133
7.4 Conclusion 136
References 137
8 Adaptive sliding mode control of uncertain chaotic systems 139
8.1 Problem formulation 139
8.2 Main results 140
8.2.1 Adaptive sliding mode controller design 140
8.2.2 Stability analysis of the sliding mode dynamics 144
8.3 Extending to sliding mode H∞ control 145
8.4 Numerical example 148
8.5 Conclusion and discussion 152
References 152
9 Observer-based adaptive sliding mode control of delta operator systems 154
9.1 Problem formulation 155
9.2 Observer-based adaptive sliding mode control 156
9.2.1 The observer design 157
9.2.2 The analysis of asymptotic stability 157
9.2.3 Adaptive sliding mode controller design 162
9.3 Numerical example 164
9.4 Conclusion 168
References 168
10 Sliding mode control with disturbance observer for a class of nonlinear systems 170
10.1 Problem formulation 171
10.2 Main results 171
10.2.1 Disturbance observer design 171
10.2.2 Sliding mode controller design 175
10.3 Numerical example 176
10.4 Conclusions 180
References 180

　　Sliding mode control is an effective robust control strategy， which has many attractive features such as robustness to parameter variations and insensitivity to matched disturbances. It is successfully applied to a wide variety of practical engineering systems such as robot manipulators， electrical motors， power systems， aircrafts， underwater vehicles， spacecrafts， flexible space structures， and automotive engines， and so on.
　　The sliding mode control design generally consists of two stages. Firstly， it is to choose an appropriate sliding surface on which the system has desired properties such as stability， disturbance rejection capability， and tracking ability. That is， the sliding mode dynamics has desired performances. Secondly， a discontinuous control law is designed to force the system state trajectories to the sliding surface in a finite time and remains in it thereafter. Because of the discontinuity of sliding mode controller， high frequency oscillations of the state trajectory known as chattering phenomenon are the major disadvantages to the widespread use of sliding mode control in many practical control systems.
　　How to reduce chattering is an important and challenging problem. Many meaningful results have been presented to overcome this drawback， such as， boundary layer and reaching law approach. In recent years， I have been working on the research in this field and wanting to write an academic monograph about the current new progress of sliding mode control.
　　The content of this book mainly originates from my latest research results. Some new sliding surface designs and reaching law approaches are proposed to reduce the chattering. The objective models include differential inclusion systems， nonlinear systems， discrete systems， chaotic systems， delta operator systems and so on. In practice， due to physical limitation， there do exist nonlinearities in the control input， input nonlinearities， such as saturation， quantization， backlash， dead-zones， and so on， naturally originate from actuators in system realization and might cause a serious degradation of the system performance. Thus the effect of input nonlinearity is also taken into account.