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Dissipative Systems Analysis and Control Theory and Applications

:	Bernard Brogliato, Rogelio Lozano, Bernhard Maschke, Olav Egeland
:	Dissipative Systems Analysis and Control Theory and Applications
:	Springer-Verlag
:	9781846285172
:	2
:	CHF 194.40
:

:	Elektronik, Elektrotechnik, Nachrichtentechnik
:	English

:	579
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:	PDF

This second edition of Dissipative Systems Analysis and Control has been substantially reorganized to accommodate new material and enhance its pedagogical features. It examines linear and nonlinear systems with examples of both in each chapter. Also included are some infinite-dimensional and nonsmooth examples. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws.

Rogelio Lozano has worked in a number of institutions with a high reputation for control engineering - the University of Newcastle in Australia, NASA's Langley Research Center and now as CNRS Research Director at the University of Compiègne. He is a very experienced author in the control field having been an associate editor ofAutomatica and now ofInternational Journal of Adaptive Control and Signal Processing. He has published 26 refereed journal articles in the last five years and he is the co-author of 3 previous titles for Springer (not including the first edition of the present title) in theCommunications and Control Engineering andAdvances in Industrial Control series:

Landau, I.D., Lozano, R. and M'Saad, M.Adaptive Control (3-540-76187-X, 1997)

Fantoni, I. and Lozano, R.Non-linear Control for Underactuated Mechanical Systems (1-85233-423-1, 2001)

Castillo, P., Lozano, R. and Dzul, A.,Modelling and Control of Mini-Flying Machines (1-85233-957-8, 2005)

In addition to having served (1991 - 2001) as Chargé de Recherche at CNRS, and as, now, Directeur de Recherche at INRIA, Bernard Brogliato is an Associate Editor forAutomatica (since 2001) a reviewer forMathematical Reviews and writes book reviews forASME Applied Mechanics Reviews. He has served on the organising and other committees of various European and international conferences sponsored by an assortment of organizations, most prominently, the IEEE. He has been responsible for examining the PhD and Habilitation theses of 16 students and takes an active part in lecturing at summer schools in several European countries. Doctor Brogliato is the director of SICONOS (a European project concerned with Modelling, Simulation and Control of Nonsmooth Dynamical Systems) which carries funding of 2 million.

Olav Egeland is Professor at the Norwegian University of Science and Technology (NTNU). He graduated as siv.ing. (1984) and dr.ing. (1987) from the Department of Engineering Cybernetics, NTNU, and has been a professor at the department since 1989. In the academic year 88/89 he was at the German Aerospace Center in Oberpfaffenhofen outside of Munich. In the period 1996-1998 he was Head of Department of Engineering Cybernetics, Vice Dean of Faculty of Electrical Engineering and Telecommunications, and member of the Research Committee for Science and Technology at NTNU. He was Associate Editor of theIEEE Transactions on Automatic Control 1996-1999 and of theEuropean Journal of Control 1998-2000. He received theAutomatica Prize Paper Award in 1996, and the 2000 IEEE Transactions on Control Systems Technology Outstanding Paper Award. He has supervised the graduation of 75 siv.ing. and 19 dr.ing., and was Program Manager of the Strategic University Program in Marine Cybernetics at NTNU. Currently he is coordinator of the control activity of the Centre of Ships and Ocean Structures. He has wide experience as a consultant for industry, and is co-founder of Marine Cybernetics, which is a company at the NTNU incubator. His research interests are within modeling, simulation and control of mechanical systems with applications to robotics and marine systems.

1 Introduction (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.

	Preface	6
	Contents	7
	Notation	13
	1 Introduction	15
	1.1 Example 1: System with Mass Spring and Damper	16
	1.2 Example 2: RLC Circuit	17
	1.3 Example 3: A Mass with a PD Controller	19
	1.4 Example 4: Adaptive Control	20
	2 Positive Real Systems	23
	2.1 Dynamical System State-space Representation	24
	2.2 Definitions	25
	2.3 Interconnections of Passive Systems	28
	2.4 Linear Systems	29
	2.5 Passivity of the PID Controllers	38
	2.6 Stability of a Passive Feedback Interconnection	38
	2.7 Mechanical Analogs for PD Controllers	39
	2.8 Multivariable Linear Systems	41
	2.9 The Scattering Formulation	42
	2.10 Impedance Matching	45
	2.11 Feedback Loop	48
	2.12 Bounded Real and Positive Real Transfer Functions	50
	2.13 Examples	61
	2.14 Strictly Positive Real (SPR) Systems	67
	2.15 Applications	76
	3 Kalman-Yakubovich-Popov Lemma	83
	3.1 The Positive Real Lemma	84
	3.2 Weakly SPR Systems and the KYP Lemma	109
	3.3 KYP Lemma for Non-minimal Systems	114
	3.4 SPR Problem with Observers	127
	3.5 The Feedback KYP Lemma	127
	3.6 Time-varying Systems	129
	3.7 Interconnection of PR Systems	130
	3.8 Positive Realness and Optimal Control	133
	3.9 The Lur