CONTROL OF COMPLEX SYSTEMS Methods and Technology APPLIED INFORMATION TECHNOLOGY Series Editor: M.G. SINGH UMIST, Manchester, England Editorial Board: K. ASTROM Lund Institute of Technology, Lund, Sweden S. J. GOLDSACK Imperial College of Science and Technology, London, England M.MANSOUR ETH-Zentrum, Zurich, Switzerland G. SCHMIDT Technical University of Munich, Munich, Federal Republic of Germany S. SETHI University of Toronto, Toronto, Canada J.STREETER GEC Research Laboratories, Great Baddow, England A. TITLI LAAS, CNRS, Toulouse, France CONTROL OF COMPLEX SYSTEMS: Methods and Technology M. Drouin, H. Abou-Kandil, and M. Mariton KNOWLEDGE-BASED SYSTEM DIAGNOSIS, SUPERVISION, AND CONTROL Edited by Spyros G. T zafestas PARALLEL PROCESSING TECHNIQUES FOR SIMULATION Edited by M.G. Singh, A. Y. Allidina, and B. K. Daniels ROBUSTNESS IN IDENTIFICATION AND CONTROL Edited by M. Milanese, R. Tempo, and A. Vicino CONTROL OF COMPLEX SYSTEMS Methods and Technology M. Drouin and H. Abou-Kandil University of Paris VI and Laboratory of Signals and Systems Gif-sur-Yvette, France and M. Maritan MAT RA SEP Imagerie et Informatique and Laboratory of Signals and Systems Gif-sur-Yvette, France SPRINGER SC/ENCE+BUSINESS MEDIA, LLC Llb~a~y of Cong~ess Cataloglng-ln-Publlcatlon Data Droutn, M. Cont~ol of complex systems , methods and technology I M. Drou•n and H. Abou-Kandll and M. Marlten. p. CN. -- <Applled Information technologyJ Includes blbl1ograph1cal references. ISBN 978-1-4757-9855-5 ISBN 978-1-4757-9853-1 (eBook) DOI 10.1007/978-1-4757-9853-1 1. Control theory. 2. Computat1onal complex1ty. I. Abou-Kandll, H. !I. Mar1ton, M. III. T1tle. IV. Sentes. CA402.3.076 1990 629.8'312--dc20 89-26612 CIP © 1991 Springer Science+Business Media New York Originally published by Plenum Press, New York in 1991 Softcoverreprint of the hardcover 1st edition 1991 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher PREFACE Since the begining of the sixties, control theorists have developed a large body of knowledge concerning complex or large-scale systems theory. Using the state space approach, their purpose was to extend methods to cope with the increasingly sophisticated automation needs of man-made systems. Despite several remarkable contributions, and some successful applications, it can be stated that this theory has not yet become an engineering tool. On the other hand, the emergence of cheap and reliable microprocessors has profoundly transformed industrial instrumentation and control systems. Process control equipment is organized in multilevel distributed structures, closely related to the concepts introduced by complex systems control theory. This similarity should favor a fruitful intersection for practical applications. However, a gap still exists between the literature on control theory and the world of technological achievements. In the many books on complex systems, few have given attention to the technological aspects of a practical control problem. The present book is an attempt to fill this gap. To do this, it consistently reflects the viewpoints that: -Theory and technology are two indivisible facets of the same problem. -On-line implementation for real time applications is the ultimate goal of a control study. In consequence, the notion of control structure is heavily emphasized. It is shown how the overall control task can be split into several tasks in order fully to exploit the advantages of a distributed computing power. Typical of the philosophy behind the book is the feedback effect of technology on theory, described in chapters VI and VII: through the introduction of Local Area Networks, the information constraints which strongly influenced the early work in large scale systems theory become less significant. No ex-abrupto presentation of control theories is attempted. The general philosophy of the present text is to introduce additional theoretical developments only when they are needed in an application. An exception is chapter II, which was included to make the book more self-sufficient, and also to provide a condensed review of discrete-time optimal control results previously scattered in various papers or more general books. In this sense, the book is addressed to several audiences. First, it can serve as a complement to more classical graduate textbooks on complex systems theory. Chapters I and II could then be overlooked, while the material of chapters IV to VII would provide some ideas on how to implement control solutions. Research workers could find some interest in the original method presented in chapter III and in its refinements given in subsequent chapters. Finally, control engineers should find that the complete book provides a convenient bridge between theory and practice. If the reader is convinced that theory and technology should be combined in a practical control study, and if work on the application of complex systems theory is stimulated, this book will have fulfilled its ambition. v CONTENTS CHAPTER I: COMPLEX CONTROL SYSTEMS .................................................. 1 Introduction ..................................................................................... 1 1.1. Control problem .......................................................................... 2 1.2. Complex technological systems ......................................................... 3 1.3. Control structures ........................................................................ .4 1.4. Decomposition-coordination methods ................................................. 6 1.4.1. Historical background .......................................................... 6 1.4.2. Principle and classification of existing methods ............................. 6 1.4.3. A new method: The "Direct Decomposition" Method ....................... 7 References ....................................................................................... 8 CHAPTER II: BASIC CONCEPTS OF DISCRETE-TIME OPTIMAL CONTROL THEORY ................................................................ 11 Introduction .................................................................................... 11 2.1. Statement of the problem ............................................................... 11 2.2. Derivation of optimality conditions ................................................... I 5 2.2.1. Nonlinear programming ...................................................... 16 2.2.2. The discrete maximum principle ............................................. 1 7 2.2.3. Dynamic programming ........................................................ 19 2.3. Solution of optimality conditions ...................................................... 20 2.3.1. Open-loop and closed-loop control laws .................................... 20 2.3.2. The Two-Point Boundary Value Problem .................................. 23 2.3.3. Hamilton-Jacobi-Bellman Equation ......................................... 24 2.3.4. The Linear Quadratic regulator ............................................... 25 2.3.5. Feedback control for nonlinear systems .................................... 31 2.4. On-line implementation: Suboptimal structures ...................................... 31 2.4.1. Interrni ttent closed-loop structure ............................................ 3 2 2.4.2. Guidance-stabilization structure .............................................. 32 2.4.3. Mixed structure ................................................................ 3 3 Conclusion ..................................................................................... 3 5 References ..................................................................................... 3 6 CHAPTER III: DECOMPOSITION-COORDINATION METHODS: A NEW APPROACH ............................................................... 39 Introduction .................................................................................... 39 3.1. Large-scale systems control ............................................................ 40 3 .1. 1. Problem formulation .......................................................... 4 1 3.1.2. Temporal decomposition ...................................................... 41 3.1.3. The interaction-prediction approach ........................................ .43 vii 3.1.4. Decentralized solution ......................................................... 44 3.1.5. On-line implementation ....................................................... 48 3.1.6. Remarks ........................................................................ 48 3.2. Principle of a direct decomposition method .......................................... 49 3.3. Application to linear systems .......................................................... 51 3.3.1. Temporal decomposition: A centralized solution .......................... 51 3.3.2. Spatio-temporal decomposition: A decentralized solution ................ 56 3.4. Generalization of partial feedback laws for linear systems ......................... 59 Conclusion .................................................................................... 61 References ..................................................................................... 6 2 CHAPTER IV: APPLICATION OF 1HE DIRECT DECOMPOSITION METIIOD .......... 63 Introduction ................................................................................... 63 4.1. The role of criterion decomposition ................................................... 6 3 4.1.1. Where the feedback gain matrix vanishes .................................. 6 3 4.1.2. Where the closed-loop term becomes untractable .......................... 65 4.1.3. Where decentralization affects stabilization ................................. 66 4.1.4. Constrained systems .......................................................... 6 7 4.1.5. Conclusion ..................................................................... 7 2 4.2. Relaxation procedures .................................................................. 7 3 4.2.1. Relaxation matrix tuning ...................................................... 7 4 4.2.2. Mixed relaxations .............................................................. 7 4 4.2.3. Numerical experimentation ................................................... 7 5 4.3. Example .................................................................................. 77 4.4. Extension to linear systems with time-lags ........................................... 7 8 4.5. Extension to nonlinear systems ........................................................ 8 5 Conclusion ..................................................................................... 9 2 References ..................................................................................... 9 2 CHAPTER V: OPTIMIZATION OF 1HE FEEDBACK LOOP .................................. 9 5 Introduction ................................................................................... 9 5 5.1. Problem formulation .................................................................... 9 5 5.2. Optimization of the feedback part in the control law ................................ 96 5.3. Application to power systems ......................................................... 97 5.3.1. Control of a single synchronous machine .................................. 9 8 5.3.2. Control of a turbo-generator unit ........................................... 1 03 5.3.3. Control of a large-scale power network ................................... 108 5.4. ARCODECO: A computer-aided design software ................................. 113 5.5. Application to an industrial problem: Control of a missile ....................... 11 7 5.5.1. Problem description ......................................................... 1 18 5.5.2. Linear design for a simplified model ...................................... 121 5.5.3. Design for several flight conditions ........................................ 122 Conclusion ................................................................................... 127 References ................................................................................... 12 8 CHAPTER VI: PROCESS CONTROL SYSTEMS .............................................. 131 Introduction .................................................................................. 1 3 1 6.1. Evolution of process control systems ............................................... 1 3 1 6.1.1. The transformation of control computers ................................. 13 1 6.1.2. Influence on Man/Machine interaction ..................................... 135 6.1.3. Influence on control concepts .............................................. 13 6 6.2. Local Area Networks ................................................................. 13 7 6.2.1. Basics of Local Area Networks ............................................ 1 3 7 6.2.2. LAN s for industrial process control ....................................... 141 viii 6.2.3. TwoextremeexamplesofLANs ........................................... 142 6.2.4. Conclusion: Towards the MAP standard .................................. 143 6.3. Real time control ....................................................................... 144 6.3.1. Mutitasking ................................................................... 145 6.3.2. Interrupt processing .......................................................... 146 6.3.3. Task management ............................................................ 146 6.3.4. Intertask coordination ....................................................... 14 7 6.3.5. Multiprogramming ........................................................... 149 6.3.6. Dynamic memory allocations ............................................... 14 9 Conclusion ................................................................................... 149 CHAPTER Vll: THE IMPACT OF TECHNOLOOY ON CONTROL METHODS .......... 151 Introduction .................................................................................. 151 7 .1. Multilevel control structures: Real time implementation .......................... 151 7.1.1. A two-level control law design ............................................. 152 7.1.2. Real time implementation of a two-level control for a synchronous machine ....................................................... 155 7.2. The influence of LANs on large-scale systems theory ........................... 157 7 .2.1. Information measure and information selection .......................... 15 8 7 .2.2. An optimal synthesis adapted to LAN s .................................... 161 7.3. Distributed control with a LAN: An experimental application .................... 166 7.3.1. Local and control levels ..................................................... 166 7.3.2. Communication system via Gixinet LAN ................................. 167 7.3.3. Different control structures ................................................. 170 Conclusion ................................................................................... 177 References ................................................................................... 1 7 7 INDEX .................................................................................................. 179 ix CHAPTER I COMPLEX CONTROL SYSTEMS INTRODUCfiON The digital computer made its appearance before the general public in the sixties when it was recognized as one of the enabling technologies of the Apollo program, culminating in the international emotions of man's ftrst steps on the moon. From this glorious start the imprint of computer technology on our day to day life has been steadily increasing, even if sometimes less conspicuously. This is nowhere more obvious than in the technological process industry where the computer and its bedfellow, control, provide many of the tools, the means and the framework without which development would be severely constrained. The phenomenal increase that has taken place in the sophistication of integrated circuit technology and microelectronics now allows us to use desktop machine computers that two decades or so ago were bought by the richest companies to serve a whole plant. This has led to very fast improvements in electronics, software production and communications affecting the role of control technology in at least three key ways: -Automatic regulation of process through digital control - Provision of information regarding any aspect of the plant where and when it is needed through communication engineering - Improved man involvement at operational and management levels through man machine interface technology. Building on the power of these emerging technologies, control researchers have created new methods and fluently discuss process control in terms of decentralized and hierarchical control systems or decomposition-coordination and multilevel algorithms. On the other hand terms like integrated computer control systems, local area networks or real time systems are widely publicized and marketed by equipment manufacturers. Unfortunately the relationship between these methodological and technological vocabularies is often poorly perceived, and this has led to a disappointing situation where the power of modem control systems is not fully utilized to improve plant safety and productivity. The purpose of this book is to introduce a general description of modern control systems stressing the interaction between control concepts and technologies, and to explain how well a new decomposition method is adapted to hierarchical control solutions. In this sense a