Uncertainty and feedback : H [infinity] loop-shaping and the [nu]-gap metric / Glenn Vinnicombe

Author: Vinnicombe, Glenn
Published: London : Imperial College Press, [2001]
Copyright Date: ©2001
Physical Description: 1 online resource (xxi, 316 pages) : illustrations

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Contents

""Contents""; ""List of Figures""; ""List of Symbols""; ""Introduction""; ""CHAPTER 1 An introduction to Hâ?ž, control""; ""1.1 Norms on signals and systems""; ""1.1.1 The signal spaces L2 and H2""; ""1.1.2 The function spaces Lâ?ž and Hâ?ž""; ""1.2 The stability of feedback systems""; ""1.2.1 Coprime factor representations""; ""1.2.2 Winding numbers and the principle of the argument""; ""1.2.3 The Nyquist stability criterion""; ""1.3 Robust stability""; ""1.3.1 Tools for robust stability analysis""; ""1.3.2 Additive uncertainty"", ""1.3.3 Multiplicative and inverse multiplicative uncertainty""""1.3.4 The role of alternate uncertainty representations""; ""1.3.5 Coprime factor uncertainty""; ""1.3.6 A general framework""; ""1.4 Solution to the Hâ?ž control problem""; ""1.5 Graphs of linear systems*""; ""1.5.1 Graph representations""; ""Notes and References""; ""CHAPTER 2 Hâ?ž Loop-shaping""; ""2.1 Introduction""; ""2.2 The loop shaping design procedure of McFarlane and Glover""; ""2.2.1 Bounds on the loop shape""; ""2.2.2 Bounds on the closed-loop transfer functions""; ""2.3 Inner functions, and properties of bp, c"", 2.4 bp, c and the Riemann sphere2.5 Direct bounds on the closed-loop transfer functions -- 2.5.1 Characterization of the closed-loop transfer functions -- 2.5.2 Bounds for single-input, single-output systems -- 2.5.3 Gain and phase margins -- 2.5.4 Bounds for multivarlable systems -- 2.6 Choosing the weights, Part 1: For performance -- Summary -- Notes and references -- CHAPTER 3 The v-gap metric -- 3.1 Introduction -- 3.1.1 Properties of the v-gap metric -- 3.1.2 An alternative definition of the v -gap metric, ""3.1.3 Comparison with the gap metric -- the importance of the duality property, and its use in design""""3.1.4 Examples""; ""3.2 The v-gap metric""; ""3.2.1 Definition of the metric""; ""3.2.2 A frequency response formula for the metric""; ""3.2.3 Î?v is a metric""; ""3.3 Robust stability and performance theorems""; ""3.3.1 Basic results""; ""3.3.2 Sufficient conditions""; ""3.3.3 Necessary conditions""; ""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"", and ""3.8 The L2-gap and the graph topology""""Summary""; ""Notes and References""; ""CHAPTER 4 More Hâ?ž 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""; ""4.5.1 Command decoupling""; ""Notes and References""; ""CHAPTER 5 Complexity and robustness""; ""5.1 Introduction""; ""5.2 Less conservative robustness results""; ""5.3 Examples""; ""5.4 The discrete time case""

Subject(s)

ISBN

9781848160453 (electronic bk.)
1848160453 (electronic bk.)
186094163X
9781860941634

Bibliography Note

Includes bibliographical references and index.

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