| Titre : | Uncertainty and feedback : h loop-shaping and the v-gap metric | | Type de document : | texte imprimé | | Auteurs : | Glenn Vinnicombe, Auteur | | Editeur : | London : Imperial College Press | | Année de publication : | 2001 | | Importance : | 316 p. | | Présentation : | couv. ill. en coul., ill. | | Format : | 21,8 cm. | | ISBN/ISSN/EAN : | 978-1-86094-163-4 | | Langues : | Anglais (eng) | | Catégories : | AUTOMATISME
| | Index. décimale : | 25-04 Théorie des systèmes:systèmes asservis | | Résumé : | The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H∞ loop-shaping is emerging as a powerful but straightforward method of designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The ν-gap metric is an attempt to resolve this paradox -- by indicating in what sense a model should be accurate if it is to be useful for feedback design.This book develops in detail the H∞ loop-shaping design method, the ν-gap metric and the relationship between the two, showing how they can be used together for successful feedback design. | | Note de contenu : | 1 An introduction to H∞, control
1.1 Norms on signals and systems
1.2 The stability of feedback systems
1.3 Robust stability
1.4 Solution to the H∞ control problem
1.5 Graphs of linear systems*
2 H∞ Loop-shaping
2.1 Introduction
2.2 The loop shaping design procedure of McFarlane and Glover
2.3 Inner functions, and properties of bp,c
2.4 bp,c and the Riemann sphere
2.5 Direct bounds on the closed-loop transfer functions
2.6 Choosing the weights, Part 1: For performance
3 The v-gap metric
3.1 Introduction
3.2 The v-gap metric
3.3 Robust stability and performance theorems
3.4 Parametric uncertainty and the v-gap metric
3.5 Choosing the weights , Part 2: Forrobustness
3.6 Closed-loop errors and the v-gap
3.7 Extending the metric
3.8 The L2-gap and the graph topology
CHAPTER 4 More H∞ loop-shaping
4.1 The optimal controller, and the optimal stability margin
4.2 A frequency response interpretation of bopt(P)
4.3 Choosing the weights , Part 3: For feasibility
4.4 An extended loop shaping design procedure
4.5 Robust tracking
CHAPTER 5 Complexity and robustness
5.1 Introduction
5.2 Less conservative robustness results
5.3 Examples
5.4 The discrete time case
5.5 Complexity definitions
CHAPTER 6 Design examples
6.1 A benchmark design example
6.2 Complexity based design example
CHAPTER 7 Topologies, metrics and operator theory
7.1 Topologies and metrics
7.2 Operator theory, and the non-rational case
7.3 Comparison with the gap metric
7.4 Examples
CHAPTER 8 Approximation in the graph topology
8.1 The nearest non-stabilizable plant
8.2 Upper and lower bounds for approximation
CHAPTER 9 The best possible H∞ robustness results
9.1 Introduction
9.2 Results based on homotopy arguments
9.3 Additive and normalized coprime factoruncertainty
9.4 Alternative characterizations of the set P ( H , β)
9.5 Applications and examples
APPENDIX A State-space formulae and proofs
A.1 Existence of coprime factors
A.2 Calculation of δv
A.3 Observer based two degree of freedom compensators
Index
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Uncertainty and feedback : h loop-shaping and the v-gap metric [texte imprimé] / Glenn Vinnicombe, Auteur . - London : Imperial College Press, 2001 . - 316 p. : couv. ill. en coul., ill. ; 21,8 cm. ISBN : 978-1-86094-163-4 Langues : Anglais ( eng) | Catégories : | AUTOMATISME
| | Index. décimale : | 25-04 Théorie des systèmes:systèmes asservis | | Résumé : | The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H∞ loop-shaping is emerging as a powerful but straightforward method of designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The ν-gap metric is an attempt to resolve this paradox -- by indicating in what sense a model should be accurate if it is to be useful for feedback design.This book develops in detail the H∞ loop-shaping design method, the ν-gap metric and the relationship between the two, showing how they can be used together for successful feedback design. | | Note de contenu : | 1 An introduction to H∞, control
1.1 Norms on signals and systems
1.2 The stability of feedback systems
1.3 Robust stability
1.4 Solution to the H∞ control problem
1.5 Graphs of linear systems*
2 H∞ Loop-shaping
2.1 Introduction
2.2 The loop shaping design procedure of McFarlane and Glover
2.3 Inner functions, and properties of bp,c
2.4 bp,c and the Riemann sphere
2.5 Direct bounds on the closed-loop transfer functions
2.6 Choosing the weights, Part 1: For performance
3 The v-gap metric
3.1 Introduction
3.2 The v-gap metric
3.3 Robust stability and performance theorems
3.4 Parametric uncertainty and the v-gap metric
3.5 Choosing the weights , Part 2: Forrobustness
3.6 Closed-loop errors and the v-gap
3.7 Extending the metric
3.8 The L2-gap and the graph topology
CHAPTER 4 More H∞ loop-shaping
4.1 The optimal controller, and the optimal stability margin
4.2 A frequency response interpretation of bopt(P)
4.3 Choosing the weights , Part 3: For feasibility
4.4 An extended loop shaping design procedure
4.5 Robust tracking
CHAPTER 5 Complexity and robustness
5.1 Introduction
5.2 Less conservative robustness results
5.3 Examples
5.4 The discrete time case
5.5 Complexity definitions
CHAPTER 6 Design examples
6.1 A benchmark design example
6.2 Complexity based design example
CHAPTER 7 Topologies, metrics and operator theory
7.1 Topologies and metrics
7.2 Operator theory, and the non-rational case
7.3 Comparison with the gap metric
7.4 Examples
CHAPTER 8 Approximation in the graph topology
8.1 The nearest non-stabilizable plant
8.2 Upper and lower bounds for approximation
CHAPTER 9 The best possible H∞ robustness results
9.1 Introduction
9.2 Results based on homotopy arguments
9.3 Additive and normalized coprime factoruncertainty
9.4 Alternative characterizations of the set P ( H , β)
9.5 Applications and examples
APPENDIX A State-space formulae and proofs
A.1 Existence of coprime factors
A.2 Calculation of δv
A.3 Observer based two degree of freedom compensators
Index
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