Modelling, Robustness and Sensitivity Reduction in Control Systems

Transcription

1 Modelling, Robustness and Sensitivity Reduction in Control Systems

2 NATD ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board 01 publishers in conjunction with the NATO Scientilic Allairs Division A Life Sciences B Physics C Mathematical and Physical Sciences D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences G Ecological Sciences H Cell Biology Plenum Publishing Corporation London and New York D. Reidel Publishing Company Dordrecht, Boston, Lancaster and Tokyo Martinus Nijhoff Publishers Boston, The Hague, Dordrecht and Lancasler Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Series F: Computer and Systems Sciences VoI. 34

3 Modelling, Robustness and Sensitivity Reduction in Control Systems Edited by Ruth F Curtain Mathematics Institute, University 01 Groningen 9700 AV Groningen, The Netherlands Springer-Verlag Berlin Heidelberg GmbH Published in cooperation with NATO Scientilic Alfairs Divison

4 Proceedings of the NATO Advanced Research Workshop on Modelling, Robustness and Sensitivity Reduction in Control Systems he!d in Groningen, The Netherlands, December 1-5, 1986 ISBN ISBN (ebook) DOI / Library of Congress Cataloging in Publication Data. NATO Advanced Research Workshop on Mocelling, Robustness, and Sensitivity Reduction in Control Systems (1986' Groningen, Netherlands) Modelling, robustness, and sensitivity reduction in control systems. (NATO ASI series. Series F, Computer and systems sciences ; val. 34) "Published in cooperation with NATD Scientilic Alfairs Divizion." "Proceedings of the NATD Advanced Research Workshop on Modelling, Robustness and Sensitivity Reduction in Control Systems held in Groningen, The Netherlands, December 1-5, 1986."-T.p. versa. 1. Automatic control-congresses. 2. Control theory-congresses. 1. Curtain, Ruth F. II. North Atlantic Traaty Organization. Scientific Aflairs Division. III. Title. IV. Series: NATD ASI series. Series F, Computer and systems sciences, voi. 34. TJ2122.N ISBN (U.S.) This work is subject to copyright. AII rights are reserved, whether the whole or part 01 the material is concerned, specilically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms ar in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its vers ion of June 24, 1985, and a copyright fee must always be paid. Violations fali under the prosecution act of tha German Copyright Law. Springer-Verlag Berlin Heidelberg 1987 Originally published by Springer-Verlag Berlin Heidelberg in /

5 PREFACE This volume contains the proceedings of the NATO Advanced Research Workshop on "Modelling, Robustness and Sensi ti vity Reduction in Control Sytems" which was held at the University of Groningen, the Netherlands, during the first week of December, Modelling is a fundamental and difficult problem in ali the sciences; to design a controller one needs a model. While for some applications one has a good physical model, of ten one only has measurements of the inputs and outputs of the system available. Hodelling from measurement data was one important theme of the workshop. To control theorists, this has traditionally meant the stochastic approach of "System Identification" but here the newer deterministic approaches shared the spotlight. Of course ali models are approximate, but o~e sometimes requires a lower order, simpler model which still retains the main features of the original model with respect to the problem of control design. Approximation in this sense is of ten cal led model reduction and this theme was discussed during the workshop. Given that we only ha ve approximate models available, the concept of robustness has always played an important role in controller design. Robust controllers are those which can control not only the given nominal model, but also neighbouring perturbations while at the same time guaranteeing an acceptable performance; they are robust with respect to model uncertainties. Typical performance requirements are tracking ability, stability and the suppression of disturbances, usually with respect to certain frequency bands, and so another very desirable property of a controller is that its performance has a low sensitivity to external disturbances. Robustness and sensitivity reduction of controllers were two related themes of the workshop. During the last decade major advances have been made in the theory of approximation (model reduction) and robustness and sensitivity reduction of controllers by exploiting known results in two areas of mathematics: in classical mathematical analysis suph as the work in interpolation theory by Nevanlinna, Pick, Fejer and Caratheodory, and in more recent developments in Operator Theory, such as the work of Adamjan, Arov and Krein in the seventies. This synthesis has resulted in a new research area CD in Systems and Control Theory known as H - Control which was the main theme of this workshop and is closely related to the other themes of

6 VI approximation, robustness and sensitivlty reduction. These proceedings contain new contributions in these areas which range from abstract mathematical papers to some very concrete and challenging applications; an interesting interplay between mathematics and engineering. As is well known, NATO workshops are primarily supported by the NATO Scientific Affairs Division and we are grateful to them for their sponsorship and generous financial support. This workshop was designated as belonging to the "Double Jump" programme, which means that the sectors: university, indu3try and government research institutions should ali be involved in the workshop. A glance at the list of participants will verify that this was the case as far as participation in the 3cientific part of the workshop i3 concerned. With respect to the financial support, we have the pleasure of thanking the following long list of government agencies and companies: the Dutch Academy of Sciences, the Dutch Organization for the Advancement of Pure Scientific Research, the British Science and Engineering Research Council, the University and the Province of Groningen, de Nederlandse Aardolie Maatschappij (the Dutch OiI Company), de N. V. Nederlandse Gasunie (the Dutch Gas Company), Hollandse Signaalappa~aten B.V. and Hoogovens Groep B.V. Finally we would like to thank the Mathematics Institute of the University of Groningen for the support in organizing the workshop in particular the assistance of the workshop secretary, Janieta Schlukebir. Ruth F. C urtain for the International Committee: Prof. R.F. Curtain, Mathematics Institute, University of Groningen Dr. K. Glover, Dept. Engineering, University of Cambridge, U.K. Prof. B. Francis, Dept. Engineering, University of Toronto, Canada Prof. J.C. Doyle, Honeywell SRC, MN , 2600 Ridgeway Parkway, Minneapolis, U.S.A./ Dept. Electrical Engineering, California Institute of Tecnnology, Pasadena, CA 91125, USA.

7 TABLE OF CONTENTS 1. H~-Hathematical Foundations B.A. FRANCIS m A guide to H -control theory J.A. BALL, C. FOIAS, J.W. HELTON and A. TANNENBAUM Nonlinear interpolation theory in H m N.J. YOUNG Super-optimal Hankel norm approximations A.C.M. RAN Hankel norm approximation for infinite dimensional systems and Wiener-Hopf factorization M.G. SAFONOV lmaginary-axis zeros in multivariable Hm-optimal control H. KWAKERNAAK A polynomial approach to Hm-optimization of control systems Hodel Approximation and Robustness in Control Design K. GLOVER and J.R. PARTlNGTON Bounds on the achievable accuracy in model reduction L. BARATCHART Recent and new results in rational L 2 -approximation J.C. DOYLE, K. LENZ and A. PACKARD Design examples using ~-synthesis: FCS during reentry Space shuttle lateral axis 127 A.l.G. VARDULAKIS A necessary and sufficient condition for robustness of stability under known additive perturbation 155

8 VIII D.H. OWENS Recursive methods for control design based on approximate models G. GROBEL and D. JOOS Performance-robust design via a multi-criteria/multi-model approach- a flight control case study Hodelling and Signal Processing J.C. WILLEMS Unfalsified modelling in dynamical systems P. DEWILDE and Ed. F. DEPRETTERE Approximative invers ion of positive matrices wi th applications to modelling S. BITTANTI The periodic prediction problem for cyclostationary processes - an introduction Hodelling and System Identification L. LJUNG 251 System identification: design variables and the design objective C. HEIJ Approximate modelling of deterministic systems B. HANZON Some new results on and applications of an algorithm of Agashe CD 5. H -techniques 1. POSTLETHWAITE, D.W. GU, S.D.O'YOUNG and M.S. TOMBS An application of HOO-design and some computational improvements 305

9 IX E.A. JONCKHEERE and J.C. JUANG Hankel and Toeplitz operators in linear quadratic and HOO-designs 323 M. SAEK1, M.J. GR1MBLE, E. KORNEGOOR and M.A. JOHNSON HOO-optimal control, LQG polynomial systems techniques and numerical solution procedures Optimal Sensitivity Reduction G. ZAMES, A. TANNENBAUM and C. F01AS Optimal HOO-interpolation: a new approach F. Ff(;NAN1, D. FLAMM and S.K. M1TTER Some Min-Max optimization problems in infinite-dimensional control systems J.B. PEARSON and M.A. DAHLEH Control system design to minimize maximum errors A.B. (Jzr; OLER and M. H1RA(X} LU 1mplications of a characterization result on strong and reliable decentralized control J.A. BALL and D.W. LUSE Sensitivity minimization as a Nevanlinna-Pick interpolation problem F.M. CALL1ER and J. W1NK1N The spectral factorization problem for S1SO distributed systems List of Participants 491