Variable structure and Lyapunov control
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| Format: | Buch |
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| Sprache: | English |
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London u.a.
Springer
1994
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| Schriftenreihe: | Lecture notes in control and information sciences
193 |
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| 245 | 1 | 0 | |a Variable structure and Lyapunov control |c Alan S. I. Zinober (ed.) |
| 264 | 1 | |a London u.a. |b Springer |c 1994 | |
| 300 | |a XXII, 401 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 193 | |
| 650 | 7 | |a Controleleer |2 gtt | |
| 650 | 7 | |a Liapounov, fonctions de |2 ram | |
| 650 | 7 | |a Réaction, systèmes à |2 ram | |
| 650 | 4 | |a Feedback control systems | |
| 650 | 4 | |a Lyapunov functions | |
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| 650 | 0 | 7 | |a Rückkopplung |0 (DE-588)4050851-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Unsicherheit |0 (DE-588)4186957-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sliding-Mode |0 (DE-588)4320090-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Methode |0 (DE-588)4167990-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Zinober, Alan S. I. |e Sonstige |4 oth | |
| 830 | 0 | |a Lecture notes in control and information sciences |v 193 |w (DE-604)BV005848579 |9 193 | |
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Datensatz im Suchindex
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| DE-BY-TUM_location | Mag |
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| adam_text | Table of Contents
List of Contributors xix
1 An Introduction to Sliding Mode Variable Structure Control .... 1
Alan S.I. Zinober
1.1 Introduction 1
1.2 Regulator System 2
1.3 Model Following Control System 3
1.4 The Sliding Mode 3
1.5 Nonlinear Feedback Control 5
1.6 Second Order Example 7
1.7 Quadratic Performance 10
1.8 Eigenstructure Assignment 11
1.9 Sensitivity Reduction 13
1.10 Eigenvalue Assignment in a Region 14
1.10.1 Eigenvalue Assignment in a Sector 14
1.10.2 Eigenvalue Assignment in a Disc 15
1.10.3 Eigenvalue Assignment in a Vertical Strip 16
1.11 Example: Remotely Piloted Vehicle 17
1.12 Conclusions 20
1.13 Acknowledgement 20
xii
2 An Algebraic Approach to Sliding Mode Control 23
Heberti Sira Ramirez
2.1 Introduction 23
2.2 Basic Background to Differential Algebra 24
2.2.1 Basic Definitions 24
2.2.2 Fliess s Generalized Controller Canonical Forms .... 27
2.2.3 Input Output Systems 28
2.3 A Differential Algebraic Approach to Sliding Mode Control of
Nonlinear Systems 30
2.3.1 Differential Algebra and Sliding Mode Control of
Nonlinear Dynamical Systems 30
2.3.2 Dynamical Sliding Regimes Based on Fliess s GCCF . . 32
2.3.3 Some Formalizations of Sliding Mode Control for
Input Output Nonlinear Systems 34
2.3.4 An Alternative Definition of the Equivalent Control
Dynamics 35
2.3.5 Higher Order Sliding Regimes 36
2.3.6 Sliding Regimes in Controllable Nonlinear Systems ... 37
2.4 A Module Theoretic Approach to Sliding Modes in Linear
Systems 38
2.4.1 Quotient Modules 40
2.4.2 Linear Systems and Modules 41
2.4.3 Unperturbed Linear Dynamics 41
2.4.4 Controllability 42
2.4.5 Observability 42
2.4.6 Linear Perturbed Dynamics 43
2.4.7 A Module Theoretic Characterization of Sliding Regimes 43
2.4.8 The Switching Strategy 44
2.4.9 Relations with Minimum Phase Systems and Dynamical
Feedback 45
2.4.10 Non Minimum Phase Case 45
2.4.11 Some Illustrations 45
2.5 Conclusions 46
3 Robust Tracking with a Sliding Mode 51
Raymond Davits, Christopher Edwards and Sarah K. Spurgeon
3.1 Introduction 51
3.2 Problem Formulation 52
3.3 Design of the Sliding Manifold 55
3.4 Nonlinear Controller Development and Associated Tracking
Properties 61
3.5 Design Example: Temperature Control of an Industrial Furnace 68
3.6 Conclusions 71
3.7 Acknowledgements 71
xiii
4 Sliding Surface Design in the Frequency Domain 75
Hideki Hashimoto and Yusuke Konno
4.1 Introduction 75
4.2 Sliding Mode using the LQ Approach 76
4.2.1 Linear Quadratic Optimal Sliding Mode 76
4.2.2 Frequency Shaped LQ Approach 77
4.3 /f2/#°° approach 78
4.3.1 H2/H°° Optimal Control 78
4.3.2 Generalized Plant Structure 79
4.3.3 Controller Solution 80
4.4 Simulation 82
4.4.1 Plant Model 82
4.4.2 Controller Design 83
4.4.3 Simulation Results 84
4.5 Conclusions 84
5 Sliding Mode Control in Discrete Time and Difference Systems ... 87
Vadim I. Utkin
5.1 Introduction 87
5.2 Semi Group Systems and Sliding Mode Definition 88
5.3 Discrete time Sliding Mode Control in Linear Systems 93
5.4 Discrete Time Sliding Modes in Infinite Dimensional Systems . 96
5.5 Sliding Modes in Systems with Delays 99
5.6 Finite Observers with Sliding Modes 101
5.7 Control of Longitudinal Oscillations of a Flexible Bar 103
5.8 Conclusions 106
6 Generalized Sliding Modes for Manifold Control of Distributed
Parameter Systems 109
Sergey Drakunov and limit Ozguner
6.1 Introduction 109
6.2 Manifold Control: Generalization of the Sliding Mode Control
Concept 110
6.3 Canonical Form of the Distributed Parameter System 112
6.3.1 Problem Statement 113
6.3.2 Linear Transformation 114
6.3.3 Nonsingularity of the Integral Transform 115
6.4 Manifold Control of Differential Difference Systems 117
6.5 Wave Equation 119
6.5.1 Supressing Vibrations of a Flexible Rod 119
6.5.2 Rod with Additional Mass 121
6.5.3 Semi Infinite Rod with Distributed Control 123
6.5.4 Dispersive Wave Equation 124
6.6 Diffusion Equation 125
6.7 Fourth Order Equation 127
6.7.1 The Euler Bernoulli Beam 127
xiv
6.7.2 General Fourth Order Equation 128
6.8 Conclusions 129
7 Digital Variable Structure Control with Pseudo Sliding Modes . . . 133
Xinghuo Yu
7.1 Introduction 133
7.2 Sampling Effect on a VSC System 133
7.3 Conditions for Existence of Discrete Time Sliding Mode .... 136
7.4 Digital VSC Systems 138
7.4.1 Control Strategy 139
7.4.2 Partitions in the State Space 140
7.4.3 Design of SDVSC; Acquisition of Lower Bounds .... 141
7.4.4 Design of SDVSC; Acquisition of Upper Bounds .... 142
7.4.5 Modification of SDVSC — Elimination of Zigzagging . 144
7.5 Simulation Results 146
7.5.1 Two Dimensional System 146
7.5.2 Example 1 148
7.5.3 Example 2 150
7.6 Conclusions 151
8 Robust Observer Controller Design for Linear Systems 161
Hebertt Sira Ramtrez, Sarah K. Spurgeon and Alan S.I. Zinober
8.1 Introduction 161
8.2 Matching Conditions in Sliding Mode State Reconstruction and
Control of Linear Systems 163
8.2.1 Matching Conditions in Sliding Mode Controller Design 163
8.2.2 Matching Conditions in Sliding Mode Observer Design . 165
8.2.3 The Matching Conditions for Robust Output Regulation 167
8.3 A Generalized Matched Observer Canonical Form for State
Estimation in Perturbed Linear Systems 168
8.4 A Matched Canonical Realization for Sliding Mode Output
Feedback Regulation of Perturbed Linear Systems 172
8.4.1 Observer Design 173
8.4.2 Sliding Mode Controller Design 174
8.5 Design Example: The Boost Converter 176
8.6 Conclusions 179
8.7 Acknowledgments 179
9 Robust Stability Analysis and Controller Design with Quadratic
Lyapunov Functions 181
Martin Corless
9.1 Introduction 181
9.2 Quadratic Stability 183
9.2.1 Systems Containing Uncertain Scalar Parameters .... 183
9.2.2 Systems Containing a Single Uncertain Matrix 185
9.2.3 Quadratic Stability and #TO 186
XV
9.2.4 Systems Containing Several Uncertain Matrices 187
9.3 Quadratic Stabilizability 189
9.3.1 Linear vs. Nonlinear Control 189
9.3.2 Matching, Generalized Matching and Other Structural
Conditions 190
9.3.3 A Convex Parameterization of Linear Quadratically
Stabilizing Controllers 191
9.3.4 Systems Containing Uncertain Matrices 192
9.4 Controllers Yielding Robustness in the Presence of Persistently
Acting Disturbances 194
9.4.1 Discontinuous Controllers 194
9.4.2 Continuous Controllers 195
9.5 Miscellaneous 196
9.6 Acknowledgements 196
10 Universal Controllers: Nonlinear Feedback and Adaptation 205
Eugene P. Ryan
10.1 Introduction 205
10.2 Class I: Universal Adaptive Stabilizer 207
10.2.1 Coordinate transformation 208
10.2.2 Adaptive Feedback Strategy 209
10.2.3 Stability Analysis 211
10.3 Class II: Nonlinearly Perturbed Linear Systems and Tracking by
Output Feedback 214
10.3.1 Class of Reference Signals 215
10.3.2 Coordinate Transformation 216
10.3.3 Adaptive Output Feedback Strategy 216
10.3.4 Stability Analysis 217
10.4 Class III: Two Input Systems 218
10.4.1 Example 221
11 Lyapunov Stabilization of a Class of Uncertain Affine Control Systems 227
David P. Goodall
11.1 Introduction 227
11.2 Decomposition into Controlled and Uncontrolled Subsystems . 228
11.3 The Class of Uncertain Systems 230
11.4 Subsystem Stabilization 231
11.5 Proposed Class of Generalized Feedback Controls 235
11.6 Global Attractive Manifold M 237
11.7 Lyapunov Stabilization 241
11.8 Example of Uncertain System Stabilization via Discontinuous
Feedback 243
xvi
12 The Role of Morse Lyapunov Functions in the Design of Nonlinear
Global Feedback Dynamics 249
Efthimios Kappos
12.1 Introduction 249
12.2 Nonlinear Systems and Control Dynamics 252
12.3 Morse Specifications 255
12.4 Obstructions to Smooth Controllability 258
12.4.1 Local Smooth Controllability 259
12.4.2 Global Obstructions 260
12.5 Some Special Cases 263
12.5.1 Constant Control Distribution 263
12.5.2 Constant Rank Control Distribution of Dimension n 1 . 265
12.6 Conclusions 266
13 Polytopic Coverings and Robust Stability Analysis via Lyapunov
Quadratic Forms 269
Francesco Amato, Franco Garofalo and Luigi Glielmo
13.1 Introduction 269
13.2 Some Applications of Polytopic Coverings to the Robust
Stability Problem 271
13.2.1 Systems Subject to Time Varying Parameters 271
13.2.2 Systems Subject to Slowly Varying Parameters 272
13.3 Polytopic Coverings: A Survey of the Existing Literature .... 274
13.4 A More General Algorithm 279
13.5 Examples 283
13.5.1 Example 1 283
13.5.2 Example 2 284
13.6 Conclusions 286
14 Model Following VSC Using an Input Output Approach 289
Giorgio Bariolini and Antonella Ferrara
14.1 Introduction 289
14.2 Some Preliminary Issues 291
14.3 The Underlying Linear Structure of the Controller 294
14.4 Discontinuous Parameter Adjustment Mechanisms 299
14.5 Pole Assignment via Discontinuous Identification of the
Parameters of the Feedforward Filter 302
14.6 Illustrative Examples 305
14.7 Conclusions 306
15 Combined Adaptive and Variable Structure Control 313
Alexander A. Stotsky
15.1 Introduction 313
15.2 Problem Statement 315
15.3 Direct Integral Adjustment Law 317
15.4 Direct Integral and Pseudo Gradient Adjustment Law 319
xvii
15.5 Prediction Error Estimation and Indirect Algorithms 323
15.5.1 Lyapunov Design 323
15.5.2 Additional Relay Term 324
15.5.3 Sliding Mode Approach 325
15.5.4 Comparative Analysis of the Two Proposed Indirect
Algorithms with Bounded Disturbances 326
15.5.5 Convergence of the Parameters 327
15.6 Combined Algorithms 328
15.7 Combined Algorithms for SISO Plants 329
15.8 Conclusions 331
16 Variable Structure Control of Nonlinear Systems: Experimental
Case Studies 335
D. Dan Cho
16.1 Introduction 335
16.2 Fuel Injection Control 336
16.2.1 Importance of Analytic Control Methodology for Fuel
Injection 336
16.2.2 VSC Approach to the Synthesis of Fuel Injection Control 340
16.2.3 Implementation and Test Track Results 344
16.2.4 Discussions 350
16.3 Magnetic Levitation Control 350
16.3.1 Dynamics of Open Loop Unstable Magnetic Levitation . 350
16.3.2 VSC Approach to Levitation Control: Robust and
Chatter Free Tracking 353
16.3.3 Comparison with Classical Control 357
16.3.4 Discussion 361
16.4 Conclusions 361
16.5 Acknowledgments 362
17 Applications of VSC in Motion Control Systems 365
Ahmet Denker and Okyay Kaynak
17.1 Introduction 365
17.2 Design of VSC Controllers 366
17.3 Application to a Motion Control System 367
17.4 Robustness at a Price: Chattering 373
17.5 VSC Design for Robotic Manipulators 375
17.5.1 Merging Sliding Mode and Self Organizing Controllers . 377
17.5.2 SLIMSOC 378
17.5.3 Simulation Results 380
17.6 Conclusions 382
18 VSC Synthesis of Industrial Robots 389
Karel Jezernik, Boris Curk and Joze Harnik
18.1 Introduction 389
18.2 Variable Structure Control Synthesis 391
xviii
18.3 Estimation of the Disturbance 393
18.4 Simulation Results 396
18.5 Conclusions 400
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| id | DE-604.BV008878622 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T12:53:20Z |
| institution | BVB |
| isbn | 3540198695 0387198695 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005872772 |
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| physical | XXII, 401 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spellingShingle | Variable structure and Lyapunov control Lecture notes in control and information sciences Controleleer gtt Liapounov, fonctions de ram Réaction, systèmes à ram Feedback control systems Lyapunov functions Regelungssystem (DE-588)4134712-2 gnd Rückkopplung (DE-588)4050851-1 gnd Unsicherheit (DE-588)4186957-6 gnd Sliding-Mode (DE-588)4320090-4 gnd Ljapunov-Methode (DE-588)4167990-8 gnd |
| subject_GND | (DE-588)4134712-2 (DE-588)4050851-1 (DE-588)4186957-6 (DE-588)4320090-4 (DE-588)4167990-8 |
| title | Variable structure and Lyapunov control |
| title_auth | Variable structure and Lyapunov control |
| title_exact_search | Variable structure and Lyapunov control |
| title_full | Variable structure and Lyapunov control Alan S. I. Zinober (ed.) |
| title_fullStr | Variable structure and Lyapunov control Alan S. I. Zinober (ed.) |
| title_full_unstemmed | Variable structure and Lyapunov control Alan S. I. Zinober (ed.) |
| title_short | Variable structure and Lyapunov control |
| title_sort | variable structure and lyapunov control |
| topic | Controleleer gtt Liapounov, fonctions de ram Réaction, systèmes à ram Feedback control systems Lyapunov functions Regelungssystem (DE-588)4134712-2 gnd Rückkopplung (DE-588)4050851-1 gnd Unsicherheit (DE-588)4186957-6 gnd Sliding-Mode (DE-588)4320090-4 gnd Ljapunov-Methode (DE-588)4167990-8 gnd |
| topic_facet | Controleleer Liapounov, fonctions de Réaction, systèmes à Feedback control systems Lyapunov functions Regelungssystem Rückkopplung Unsicherheit Sliding-Mode Ljapunov-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005872772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
| work_keys_str_mv | AT zinoberalansi variablestructureandlyapunovcontrol |