Advances in Variable Structure and Sliding Mode Control

✍ Scribed by Christopher Edwards, Enric Fossas Colet, Leonid Fridman

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 477
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1
• Category: Library

✦ Synopsis

Sliding Mode Control is recognized as an efficient tool to design controllers which are robust with respect to uncertainty. The resulting controllers have low sensitivity to plant parameters and perturbations and allow the possibility of decoupling the original plant system into two components of lower dimension. In addition many controllers ensure finite time convergence to the switching surface and can be straightforwardly implemented. However, in addition to this traditional area of exploitation, sliding mode concepts are being increasingly deployed for the design of observers for estimation and identification.

Many of the chapters in this book are based on expansions of selected presentations from the 8th IEEE International Workshop on Variable Structure Systems VSS'04, which was held in Barcelona, Spain in September 2004. The editors have tried to identify the key contributions from this workshop, which define the state-of-the-art, represent new directions building on existing work, and highlight new emerging application areas.

✦ Table of Contents

front-matter.pdf......Page 1
1 Introduction......Page 18
2 Basic Definitions......Page 19
3 Stability analysis of uncertain second order systems......Page 22
3.1 Proof of Theorem 2......Page 24
4 Extended Invariance Principle......Page 28
5 Global Position Regulation of Manipulators......Page 31
6 Conclusions......Page 34
References......Page 35
1 Introduction......Page 37
2 Definitions and Notations......Page 38
3 Finite-time stability of continuous system......Page 40
4 Finite-time stability of discontinuous systems......Page 44
5 Finite-time stabilization of a chain of integrators......Page 49
References......Page 54
1 Introduction......Page 56
2 The Simplex Method......Page 58
4 Moving simplex method......Page 62
5 Nominal system affine in the control law......Page 68
6 Fixed simplex method for affine systems......Page 71
A Geometry of a simplex......Page 77
References......Page 78
1 Introduction......Page 79
2 Controlling limit cycles......Page 80
3 Method I......Page 84
4 Method II......Page 87
5 Method III......Page 89
6 A 2-D representative example......Page 90
7 Conclusions......Page 96
References......Page 98
1 Introduction......Page 100
2 Problem Description......Page 103
3 Lyapunow Function......Page 104
4 Sliding Sector......Page 109
5 VS Controller......Page 110
6 Simulations......Page 112
7 Conclusion......Page 116
References......Page 117
1 Introduction......Page 118
2 Observer Based Chattering Suppression......Page 121
3 Describing Function Method......Page 122
4 State-dependent Gate Method......Page 127
References......Page 132
1 Introduction......Page 133
2 Twisting algorithm and its DF analysis......Page 135
3 Super-twisting algorithm and its DF analysis......Page 138
4 Prescribed control law and its DF analysis......Page 142
5 Sub-optimal algorithm and its DF analysis......Page 144
6 Analysis of SOSM in the frequency domain......Page 146
References......Page 149
1 Introduction......Page 151
2 A "Black-box" control problem......Page 153
3 Homogenuous sliding modes......Page 156
4 Quasi-continuous homogenuous sliding-mode control......Page 158
5 Output-feedbach sliding-mode control......Page 162
6 Proof of Theorem 3......Page 165
7 Simulation example......Page 169
8 Conclusions......Page 171
References......Page 174
1 Introduction......Page 177
2 Slinding mode controller......Page 179
3 Control of a synchronous motor......Page 186
4 Control of a walking biped robot......Page 193
References......Page 197
1 Introduction......Page 200
2 Preliminaries......Page 201
3 Problem Statement......Page 204
4 Unit Vector Control......Page 205
5 Model Matching Output Feedback Control......Page 206
6 UV-MRAC Design and Analysis......Page 212
7 Modulation Functions......Page 217
8 Simulation Results......Page 221
9 Conclusion......Page 223
A Proof Theorem 3......Page 226
References......Page 228
1 Introduction......Page 231
2 Analysis of integral sliding mode controllers......Page 232
3 Design of integral sliding mode controllers......Page 236
4 Generalization of the nonlineae case......Page 245
References......Page 249
1 Introdution......Page 251
2 Decompositioin of the min-max problem......Page 253
3 Min-Max Sliding Mode Control......Page 261
4 Example......Page 267
References......Page 270
1 Introduction......Page 272
2 Motivation and problem statement......Page 273
3 Output Information Algorithm......Page 275
4 Observer Design......Page 281
5 Example......Page 288
6 Concluding Remarks......Page 291
References......Page 292
1 Introduction......Page 294
2 A sliding mode observer based scheme......Page 295
3 A laboratory scale crane setup......Page 301
4 Application to a dc-motor......Page 307
5 Conclusion......Page 311
References......Page 312
1 Introduction......Page 314
2 Identification of Time Invariant Parameters......Page 316
3 Identification of Time Varying Parameters......Page 325
4 Examples......Page 332
5 Conclusion......Page 339
References......Page 341
Appendix: Proofs......Page 343
1 Introduction......Page 349
2 Multirate Output Feedback......Page 350
3 Quasi-sliding Mode Control......Page 352
4 M;ultirate Output Feedback Based Quasi-sliding Mode Control......Page 354
5 Chattering free Discrete-time Slinding Mode Controller......Page 360
References......Page 368
1 Introduction......Page 370
2 Tyre/Road Friction......Page 372
3 Controller Design......Page 376
4 Overserver Design......Page 378
5 Conclusions......Page 383
References......Page 385
Appendix A......Page 386
1 Introduction......Page 390
2 Modelling of a Piezoelectric Actuator......Page 391
3 Problem Statement and Sliding Mode Control......Page 396
4 Implementation of MSC......Page 400
5 Closed-Loop Control Experiments......Page 403
6 A Dual-Stage Servo System......Page 409
7 Conclusion......Page 413
References......Page 415
1 Introduction......Page 417
2 IM drives......Page 418
3 DC Motor Control......Page 430
References......Page 436
1 Introduction......Page 440
2 Tracking problem......Page 441
3 Indirect Control......Page 461
4 Conclusions......Page 468
References......Page 473
A Proof of Proposition 3.4......Page 474
back-matter.pdf......Page 476