Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach

✍ Scribed by B. Bandyopadhyay, S. Janardhanan

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 160
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1
• Category: Library

✦ Synopsis

Sliding mode control is a simple and yet robust control technique, where the system states are made to confine to a selected subset. With the increasing use of computers and discrete-time samplers in controller implementation in the recent past, discrete-time systems and computer based control have become important topics. This monograph presents an output feedback sliding mode control philosophy which can be applied to almost all controllable and observable systems, while at the same time being simple enough as not to tax the computer too much. It is shown that the solution can be found in the synergy of the multirate output sampling concept and the concept of discrete-time sliding mode control.

✦ Table of Contents

Contents......Page 8
1.1.1 Variable Structure Systems......Page 17
1.1.2 Continuous-time Sliding Mode......Page 18
1.1.3 Continuous-time Sliding Mode Control......Page 21
1.1.4 Equivalent Control and the Reaching Law Approach......Page 25
1.1.5 Discrete-time Sliding Mode Control......Page 26
1.2 Multirate Output Feedback......Page 27
1.2.1 Multirate Output to State Relationship......Page 29
1.2.2 Advantage of Multirate Output Sampling over Discrete-time Observer......Page 30
1.3 Motivation for Multiratio Output Feedback......Page 31
2.1 Quasi-Sliding Mode Control in Deterministic Systems......Page 33
2.1.1 Illustrative Example......Page 34
2.2 Multirate Output Feedback based Quasi-Sliding Mode Control for Uncertain Systems......Page 35
2.2.2 Review of State Feedback based QSM control of Uncertain Systems......Page 36
2.2.3 Output Feedback Sliding Mode Control Algorithm based on New Reaching Law......Page 38
2.2.4 Illustrative Example......Page 40
3.1.1 Relaxation of Quasi-sliding mode criterion......Page 42
3.2.1 A Brief Review on State Feedback based DSMC Control Strategy for Matched Uncertain Systems......Page 43
3.2.2 Multirate Output Feedback Control Algorithm......Page 44
3.2.3 Numerical Example......Page 46
3.2.4 Comparison with State Feedback based Control......Page 49
3.3.1 Problem Statement......Page 50
3.3.2 Multirate Output Feedback based Control Law......Page 51
3.3.3 Illustrative Example......Page 53
3.3.4 Comparative Study......Page 54
3.4.1 Problem Statement......Page 59
3.4.2 State Based Discrete-Integral Sliding Mode......Page 60
3.4.3 Multirate Output Feedback based DISMC......Page 61
3.4.4 Illustrative Example......Page 63
4.2 The Probnlem Statement......Page 65
4.3 Design of the Sliding Surface......Page 67
4.4.1 Contribution of the Disturbance Term during Multirate Sampling......Page 69
4.4.2 Relationship between State and Multirate Output in Time-Delay Systems......Page 70
4.5.1 Multirate Output to State Relationship in Time-Delay Systems......Page 71
4.5.2 Multirate Output Feedback based Sliding Mode Control Algorithm for Form 1 Systems......Page 72
4.5.3 Simulation Results......Page 73
4.6.1 State based Control Algorithm......Page 74
4.6.2 Multirate Output Feedback Discrete-time Sliding Mode Control Algorithm for Form 2 Systems......Page 75
4.6.3 Simulation Results......Page 76
4.7.1 Multirate Output Feedback based Control Algorithm......Page 77
4.7.2 Simulation Results......Page 79
4.8.1 Reaching Law......Page 80
4.8.2 Multirate Output Feedback based Discrete time Sliding Mode Control Law for Time-Delay Systems with Uncertainty......Page 81
4.8.3 Simulation Results......Page 82
4.8.4 Performance in System without Disturbance......Page 84
5.1.1 Introduction......Page 85
5.1.3 Two-part Control......Page 86
5.1.4 Determination of the Nominal Zero Dynamics Trajectory......Page 88
5.1.5 Multirate Output Feedback Based Tracking Control......Page 90
5.1.6 Numerical Example......Page 91
5.2.2 Background: Finitely Discretizable Systems......Page 95
5.2.3 Multirate Output Sampling in Nonlinear Systems......Page 97
5.2.5 Illustrative Example......Page 99
5.3.2 Discrete-time VSC with P d R d Sliding Sector......Page 107
5.3.3 Multirate Output Feedback DSMC Controller for P d R d Sliding Sector......Page 113
6.2 Continuous-time Terminal Sliding Mode Control......Page 118
6.3 Discretization of TSM......Page 119
6.4 Discrete-time Terminal Sliding Mode Control......Page 121
6.4.1 DTSM Algorithm......Page 122
6.4.2 Illustrative Example......Page 123
6.5.1 Multirate Output Feedback based DTSM Algorithms for LTI Systems......Page 125
6.5.2 Multirate Output Feedback based Discrete-time Terminal Sliding Mode in Output Feedback Linearizable Nonlinear Systems......Page 130
7.1.1 Stepper Motor Model......Page 134
7.1.2 Discrete Time Sliding Mode Control Using Multirate Output Feedback: Regulator Case......Page 137
7.1.3 Simulation Results......Page 138
7.2.1 Power System Modeling......Page 141
7.2.2 Controller Implementation......Page 143
7.3 VBibration Control of Smart Structure using Multirate Output Feedback based Sliding Mode Control......Page 145
7.3.1 Modeling of a Smart Cantilever beam......Page 146
7.3.2 Multirate Output Feedback based Sliding Mode Controller design for Vibration Control......Page 147
References......Page 151