Brogliato / Lozano / Maschke Dissipative Systems Analysis and Control

Theory and Applications
2. Auflage 2006
ISBN: 978-1-84628-517-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 579 Seiten

Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional and nonsmooth examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is consistently substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and adaptive controllers are covered thoroughly).

The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties.

Autoren/Hrsg.

Brogliato, Bernard

Lozano, Rogelio

Maschke, Bernhard

Egeland, Olav

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Notation;13
4;1 Introduction;15
4.1;1.1 Example 1: System with Mass Spring and Damper;16
4.2;1.2 Example 2: RLC Circuit;17
4.3;1.3 Example 3: A Mass with a PD Controller;19
4.4;1.4 Example 4: Adaptive Control;20
5;2 Positive Real Systems;23
5.1;2.1 Dynamical System State-space Representation;24
5.2;2.2 Definitions;25
5.3;2.3 Interconnections of Passive Systems;28
5.4;2.4 Linear Systems;29
5.5;2.5 Passivity of the PID Controllers;38
5.6;2.6 Stability of a Passive Feedback Interconnection;38
5.7;2.7 Mechanical Analogs for PD Controllers;39
5.8;2.8 Multivariable Linear Systems;41
5.9;2.9 The Scattering Formulation;42
5.10;2.10 Impedance Matching;45
5.11;2.11 Feedback Loop;48
5.12;2.12 Bounded Real and Positive Real Transfer Functions;50
5.13;2.13 Examples;61
5.14;2.14 Strictly Positive Real (SPR) Systems;67
5.15;2.15 Applications;76
6;3 Kalman-Yakubovich-Popov Lemma;83
6.1;3.1 The Positive Real Lemma;84
6.2;3.2 Weakly SPR Systems and the KYP Lemma;109
6.3;3.3 KYP Lemma for Non-minimal Systems;114
6.4;3.4 SPR Problem with Observers;127
6.5;3.5 The Feedback KYP Lemma;127
6.6;3.6 Time-varying Systems;129
6.7;3.7 Interconnection of PR Systems;130
6.8;3.8 Positive Realness and Optimal Control;133
6.9;3.9 The Lur’e Problem (Absolute Stability);149
6.10;3.10 The Circle Criterion;174
6.11;3.11 The Popov Criterion;180
6.12;3.12 Discrete-time Systems;184
7;4 Dissipative Systems;191
7.1;4.1 Normed Spaces;192
7.2;4.2 Lp Norms;192
7.3;4.3 Review of Some Properties of Lp Signals;194
7.4;4.4 Dissipative Systems;207
7.5;4.5 Nonlinear KYP Lemma;236
7.6;4.6 Dissipative Systems and Partial Differential Inequalities;245
7.7;4.7 Nonlinear Discrete-time Systems;261
7.8;4.8 PR tangent system and dissipativity;263
7.9;4.9 Infinite-dimensional Systems;266
7.10;4.10 Further Results;269
8;5 Stability of Dissipative Systems;271
8.1;5.1 Passivity Theorems;271
8.2;5.2 Positive Deffniteness of Storage Functions;280
8.3;5.3 WSPR Does not Imply OSP;284
8.4;5.4 Stabilization by Output Feedback;286
8.5;5.5 Equivalence to a Passive System;290
8.6;5.6 Cascaded Systems;295
8.7;5.7 Input-to-State Stability (ISS) and Dissipativity;296
8.8;5.8 Passivity of Linear Delay Systems;302
8.9;5.9 Nonlinear H Control;309
8.10;5.10 Popov’s Hyperstability;324
9;6 Dissipative Physical Systems;329
9.1;6.1 Lagrangian Control Systems;329
9.2;6.2 Hamiltonian Control Systems;340
9.3;6.3 Rigid Joint–Rigid Link Manipulators;354
9.4;6.4 Flexible Joint–Rigid Link Manipulators;357
9.5;6.5 A Bouncing System;361
9.6;6.6 Including Actuator Dynamics;363
9.7;6.7 Passive Environment;372
9.8;6.8 Nonsmooth Lagrangian Systems;377
10;7 Passivity-based Control;387
10.1;7.1 Brief Historical Survey;387
10.2;7.2 The Lagrange-Dirichlet Theorem;389
10.3;7.3 Rigid Joint–Rigid Link Systems: State Feedback;400
10.4;7.4 Rigid Joint–Rigid Link: Position Feedback;422
10.5;7.5 Flexible Joint–Rigid Link: State Feedback;428
10.6;7.6 Flexible Joint–Rigid Link: Output Feedback;436
10.7;7.7 Including Actuator Dynamics;440
10.8;7.8 Constrained Mechanical Systems;442
10.9;7.9 Controlled Lagrangians;446
11;8 Adaptive Control;449
11.1;8.1 Lagrangian Systems;450
11.2;8.2 Linear Invariant Systems;470
12;9 Experimental Results;481
12.1;9.1 Flexible Joint Manipulators;481
12.2;9.2 Stabilization of the Inverted Pendulum;510
12.3;9.3 Conclusions;518
13;A Background Material;521
13.1;A.1 Lyapunov Stability;521
13.2;A.2 Differential Geometry Theory;529
13.3;A.3 Viscosity Solutions;534
13.4;A.4 Algebraic Riccati Equations;537
13.5;A.5 Some Useful Matrix Algebra;545
13.6;A.6 Well-posedness Results for State Delay Systems;551
14;References;553
15;Index;583

Leseproben

(P. 1)

Dissipativity theory gives a framework for the design and analysis of control systems using an input-output description based on energy-related considerations. Dissipativity is a notion which can be used in many areas of science, and it allows the control engineer to relate a set of efficient mathematical tools to well known physical phenomena. The insight gained in this way is very useful for a wide range of control problems.

In particular the input-output description allows for a modular approach to control systems design and analysis. The main idea behind this is that many important physical systems have certain input-output properties related to the conservation, dissipation and transport of energy.

Before introducing precise mathematical de.nitions we will somewhat loosely refer to such input-output properties as dissipative properties, and systems with dissipative properties will be termed dissipative systems.

When modeling dissipative systems it may be useful to develop the state-space or input-output models so that they reffect the dissipativity of the system, and thereby ensure that the dissipativity of the model is invariant with respect to model parameters, and to the mathematical representation used in the model. The aim of this book is to give a comprehensive presentation of how the energy-based notion of dissipativity can be used to establish the input-output properties of models for dissipative systems.

Also it will be shown how these results can be used in controller design. Moreover, it will appear clearly how these results can be generalized to a dissipativity theory where conservation of other physical properties, and even abstract quantities, can be handled. Models for use in controller design and analysis are usually derived from the basic laws of physics (electrical systems, dynamics, thermodynamics).

Then a controller can be designed based on this model. An important problem in controller design is the issue of robustness which relates to how the closed loop system will perform when the physical system di.ers either in structure or in parameters from the design model. For a system where the basic laws of physics imply dissipative properties, it may make sense to define the model so that it possesses the same dissipative properties regardless of the numerical values of the physical parameters.

Then if a controller is designed so that stability relies on the dissipative properties only, the closed-loop system will be stable whatever the values of the physical parameters. Even a change of the system order will be tolerated provided it does not destroy the dissipativity. Parallel interconnections and feedback interconnections of dissipative systems inherit the dissipative properties of the connected subsystems, and this simplifies analysis by allowing for manipulation of block diagrams, and provides guidelines on how to design control systems.

A further indication of the usefulness of dissipativity theory is the fact that the PID controller is a dissipative system, and a fundamental result that will be presented is the fact that the stability of a dissipative system with a PID controller can be established using dissipativity arguments. Note that such arguments rely on the structural properties of the physical system, and are not sensitive to the numerical values used in the design model.