APPLIED AND COMPUTATIONAL CONTROL, SIGNALS, AND

CIRCUITS Recent Developments

THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE

APPLIED AND COMPUTATIONAL CONTROL, SIGNALS, AND

CIRCUITS Recent Developments

edited by

Biswa Nath Datta Northern Illinois University, U.S.A.

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging-in-Publication Data

Applied and computational control, signals and circuits : recent developments / edited by Biswa Nath Datta.

p. cm.-- (The Kluwer international series in engineering and computer science; SECS 629) Includes bibliographical references and index. ISBN 978-1-4613-5570-0 ISBN 978-1-4615-1471-8 (eBook) DOI 10.1007/978-1-4615-1471-8 I. Digital control systems. 2. Signal processing—Digital techniques. 3. Electronic

circuit design. I. Datta, Biswa Nath. II. Series.

TJ223.M53 A66 2001 629.8-dc21

Copyright © 2001 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1st edition 2001

A l l rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, L L C

Printed on acid-free paper.

Contents

Preface ix

Editorial Board xiii

Contributors xv

1 Constant disturbance rejection and zero steady state tracking error for nonlinear systems design 1 S. W. Su, B.D.G. Anderson and T.S. Brinsmead 1.1 Introduction.......................... 1 1.2 Problem Description . . . . . . . . . . . . . . . . . . . . . 3 1.3 Sufficient Conditions for Constant Disturbance Rejection. 5 1.4 Guaranteeing Stability with Integrator Augmentation 10 1.5 An Integrator Gain Bound. . . . . . . . . . . . . 13 1.6 Alternative Locations for Including an Integrator . . 15 1.7 MIMO Systems. . . . . . . . . . . . . . . . . . . . . 18 1.8 Controller Design for a Nonlinear Helicopter Model. 22 1.9 Conclusion ...... 25

References . . . . . . . . 26 LA Proof of Theorem 1.10 . 27 I.B Proof of Non-singularity 28 I.C Proof of the Existence of a Stabilising Diagonal Matrix K 29

2 Control Problems in Telecommunications: The Heavy Traffic Approach 31 Harold J. Kushner 2.1 Introduction........................... 31 2.2 The Multiplexer Problem: Formulation. . . . . . . . . . .. 35 2.3 Controlled Admission in a Multiservice System: Formulation 40

2.3.1 Introduction: The Basic System. . . . . . . . . . .. 40 2.3.2 Upper Limit to the Bandwidth for the (BE) Sharing

Customers. . . . . . . . . . . . . . . 45 2.4 A Scheduling and Polling Problem . . . . . 47 2.5 Reflected Stochastic Differential Equations. 50 2.6 Weak Convergence . . . . . . . . . . . . . . 53 2.7 The Multiplexer: Convergence and Optimality. 56

vi Contents

2.8 Data for the Multiplexer Problem ... 2.9 Controlled Admission in ISDN: Proofs 2.10 The Polling Problem: Proofs.

References . . . . . . . . . . . . . . . .

65 70 74 77

3 Multi-Time PDEs for Dynamical System Analysis 85 Jaijeet Roychowdhury 3.1 Introduction.................. . . . . .. 85

3.1.1 Multiple time scales and PDEs . . . . . . . .. 88 3.1.2 Boundary conditions; quasiperiodic and envelope

solutions. . . . . . . . . . . . . . . . . . . 92 3.1.3 Relationship between the DAE and MPDE 95 3.1.4 Numerical methods for the MPDE . 96 3.1.5 Connections with previous methods 99 3.1.6 Examples and applications ..... 100

3.2 Multitime analysis of autonomous systems . 107 3.2.1 The Warped MPDE . . . . . . . . . 112 3.2.2 Voltage-controlled oscillator example 113

3.3 LTV system macromodelling using the linearized MPDE. 118 3.3.1 Obtaining LTV transfer functions from the MPDE 119 3.3.2 Pade approximation of the LTV transfer function. 124 3.3.3 LTV macromodelling examples 128

3.4 Future directions . . . . . . . . . . . . . . . . . . . . 131 References . . . . . . . . . . . . . . . . . . . . . . . . 135

3.A Proof of Theorem 3.2 (MPDE Necessity Condition) . 139 3.B Proof of Theorem 3.3 (Uniqueness of Envelope) 142

3.B.1 Curved boundaries and FM . . . . . . . 142

4 Formal Verification of Circuit Designs 145 R. P. Kurshan 4.1 Introduction........................ 145

4.1.1 Conventional Testing vs. Program Verification 147 4.1.2 Formal Verification. . . . . 149 4.1.3 Verification Methodologies. 151

4.2 Models.......... 152 4.2.1 Program State . 154 4.2.2 Nondeterminism 156 4.2.3 Systems..... 158 4.2.4 Automata.... 162 4.2.5 Program Factorization 4.2.6 Decomposition . 4.2.7 Model Checking .. .

4.3 Algorithms ......... . 4.3.1 Binary Decision Diagrams 4.3.2 Homomorphic Reduction

164 166 167 168 169 172

Contents vii

4.3.3 Localization Reduction 4.4 Conclusion

174 176

References . . . . . . . . . . . . 177

5 Large Scale Power System Computations: Applications of Iterative Techniques 181 D. Chaniotis and M. A. Pai 5.1 Introduction................... 181 5.2 Mathematical Modeling ........... 182 5.3 Basics of GMRES and GMRES(m) Methods 188 5.4 Applications to the Power Flow. . . 196 5.5 Applications to Dynamic Simulation 202 5.6 Conclusions 207

References . . . . . . . . . . . . . . . 208

6 A Direction Set Based Algorithm for Adaptive Least Squares Problems in Signal Processing 213 M.-Q. Chen 6.1 Introduction..... .......... 214 6.2 Structures and Properties of ALS Problems 215

6.2.1 Choices of Aln ) . . . . . . . . . . . . 215 6.2.2 Vector-Matrix Notations. . . . . . 216

6.3 The DS Based Algorithm for ALS Problems 217 6.3.1 Direction Set Methods. . . . . . . . . 217 6.3.2 The Powell and Zangwill DS Algorithm 218 6.3.3 The DS Based Algorithm for ALS Problems. 219 6.3.4 Computational Complexity 221 6.3.5 Convergence Analysis .......... 222

6.4 Choices of Direction Sets. . . . . . . . . . . . . . 223 6.4.1 N Euclidean Coordinate Directions in RN 224 6.4.2 Near Conjugate Direction Sets

6.5 Implementation and Applications 6.5.1 System Identification ..... . 6.5.2 Adaptive Equalizer ...... .

6.6 The DS Based Algorithm for Spectral Estimation . References . . . . .. ............... .

230 231 231 232 233 236

7 Model Reduction Software in the SLICOT Library 239 Andras Varga 7.1 Introduction...................... 239 7.2 Development of model reduction subroutines ... 240

7.2.1 Balancing related model reduction methods 241 7.2.2 Reduction of unstable systems ....... 245 7.2.3 Implementation of software for model reduction. 246

7.3 Integration in user-friendly environments. . . . . . . . . 250

viii Contents

7.3.1 Integration in MATLAB ................ 250 7.3.2 Integration in Scilab . . . . . . . . . . . . . . . . . 251

7.4 Testing and performance comparisons on benchmark problems 251 7.4.1 PS: Power system model - continuous-time. . 252 7.4.2 PSD: Power system model - discrete-time. . . 253 7.4.3 TGEN: Nuclear plant turbo-generator model. 253 7.4.4 PSU: Unstable continuous-time model. . 254 7.4.5 ACT: Badly scaled actuator model 254 7.4.6 Uncertainty models. . . . . . . . . 255 7.4.7 Timing results . . . . . . . . . . . 257

7.5 Testing on industrial benchmark problems 257 7.5.1 ATTAS: Linearized aircraft model 257

7.6

7.7 7.A 7.B 7.C 7.D 7.E

7.5.2 CDP: CD-player finite element model 7.5.3 GAS: Gasifier model ......... . Comparison of available model reduction tools 7.6.1 RASP..... . .. . 7.6.2 Scilab .... . ........ . 7.6.3 MATLAB Control Toolbox .... . 7.6.4 MATLAB Robust Control Toolbox 7.6.5 MATLAB p,-Analysis and Synthesis Toolbox 7.6.6 HTOOLS ... . 7.6.7 MATRIXx ......... . 7.6.8 WOR-Toolbox ....... . Summary of results and perspectives Sample user interface in Fortran .. MATLAB mex-function interface ... Sample MATLAB m-function interface Sample Scilab sci-function interface . State space models for benchmark problems References . . . . . .. .......... .

Index

259 260 262 262 263 263 264 264 264 265 265 265 267 273 274 276 277 281

283

Preface This is an interdisciplinary book blending mathematics, computational mathematics, scientific computing and software engineering with control and systems theory, signal processing and circuit simulations. The book contains six technical chapters: three in control, communication and power systems, one in signal processing and two in circuit design and simulations. Besides these technical chapters, the software section contains a chapter on the description and analysis of a software module for model reduction contained in the newly developed Fortran-based software library, called SLICOT, for control systems design and analysis.

The chapters present the state-of-the-art reviews of some of the recent developments in three inter-related areas of control, signal processing and circuits. They are written by leading experts in these fields on invitation by the editor-in-chief. The invitations were extended to the authors based on recommendations made by our distinguished editorial board.

The chapters should be accessible to a wide interdisciplinary audience: from experts to beginning researchers and graduate students. It is expected that the book will be an important reference for research scientists, prac­ticing engineers, as well as students and teachers in control, power systems, signals, and circuit theory. The book also seems to be suitable for advanced graduate topic-courses.

Overview Of The Chapters

Chapter 1 - Constant disturbance rejection and zero steady state tracking error for nonlinear systems design Steven W. Su, Brian D. o. Anderson, Thomas S. Brinsmead

The problem of disturbance rejection arises in many industrial fields, such as motion-control, active noise control and vibration control. Classi­cally, for linear systems, the problem is solved by including an integrator in the controller. This paper extends this idea to nonlinear systems. Sin­gular perturbation methods are used to guarantee stability. The method is implemented in the control of a simulated helicopter model.

Chapter 2 - Control Problems in Telecommunications: The Heavy Traffic Approach

x Preface

Harold J. Kushner

This chapter demonstrates the usefulness of analytical and numerical methods of stochastic control theory for the design, analysis and control of telecommunication networks. The emphasis is concentrated on a set of potentially powerful methods known as the heavy traffic approach. Three principal problems are considered: the multiplexer system, control admis­sion in multiserver systems such as ISDN, and the polling or scheduling problem.

Chapter 3 - Multi-Time PDEs for Dynamical System Analysis Jaijeet Roychowdhury

Dynamical systems, especially those from electronic communication cir­cuits, often contain signals that have widely separated time scales. Numeri­cal simulation of such systems using standard techniques like time-stepping of differential equations can be very inefficient. This paper reviews recent techniques that reformulate such problems as PDES with artificial time variables, and describes their uses in circuit simulation.

Chapter 4 - Formal Verification of Circuit Designs R. P. K urshan

A very important practical aspect of circuit designs is to check the cor­rectness of the designs. An improper testing and quality control might lead to disastrous situations such as communication network collapses, fatalities from mechanical machinery malfunction, rocket guidance failure, etc., and can result in huge monetary losses.

This chapter describes a method used commercially for verifying the correctness of integrated circuit designs. The method is applicable to the development of "control intensive" software programs as well.

Chapter 5 - Large Scale Power System Computations: Applica­tions of Iterative Techniques Dimitrios Chaniotis and M. A. Pai

The power system computations such as power flow, dynamic simulation, state estimation, etc., give rise to very large and sparse algebraic linear sys­tems. In recent years, iterative Krylov subspace based methods have been proven to be powerful tools in solving such systems. This paper reviews the recent efforts in applying these iterative techniques to the solutions of the above power systems problems. A mathematical analysis is also provided of how the algebraic linear systems arise in solving such problems.

Preface xi

Chapter 6 - A Direction Set Based Algorithm for Adaptive Least Squares Problems in Signal Processing Mei-Qin Chen

A class of adaptive least square problems arise in signal processing appli­cations. This chapter presents a fast direct set based algorithm for solving such least squares problems. The algorithm is structure preserving and the computer simulations show that it is numerically stable. The rate of con­vergence of the algorithm is comparable to that of the conjugate gradient and recursive least squares algorithm. The algorithm has been modified to solve also the constrained adaptive least squares problems arising in spectral estimations.

Chapter 7 - Model Reduction Software in the SLICOT Library Andras Varga

Model reduction is of fundamental importance in many modeling and control applications. Yet, numerically reliable software for this important problem are rare.

This paper gives a close-look to the model reduction routines imple­mented in a recently developed control and systems library, called 8L1-COT. A description of the library itself has previously appeared in the first volume of this series. Testing results and performance comparisons show that 8LICOT model reduction tools are superior to other existing model reduction software.

Acknowledgements

The editors - Biswa Datta, Roland Freund, Floyd Hanson, Robert Plem­mons, and Daniel Pierce - would like to take this opportunity to sincerely thank the other members of the editorial board for their help, suggestions, and guidance with the book.

Thanks are due to Alex Greene of Kluwer Academic Publisher for his enthusiasm and support with the book.

Our special thanks go to Professor M. A. Pai of University of Illinois who initially contacted Alex Greene for publication of this book and without whose continuous help and encouragement this book would probably never have been published.

Finally, the editor Biswa Datta is indebted to the technical editor Eric Behr for his hard work on technical aspects of this book.

Biswa Nath Datta Dekalb, Illinois

Editorial Board Founding Editor and Editor-in-Chief

Biswa N. Datta Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60115, USA E-mail: dattab@math.niu. edu

Associate Editors-in-Chief Roland Freund, Lucent Technologies, Bell Laboratories, USA Floyd B. Hanson, University of Illinois at Chicago, USA Robert J. Plemmons, Wake Forest University, USA

Software Editor Daniel J. Pierce, Boeing Computer Services, USA

Technical Editor Eric Behr, Northern Illinois University, USA

Editors Brian Anderson, A ustralian National University, Australia Radhakisan S. Baheti, National Science Foundation, USA A. Terry Bahill, University of Arizona, USA S.P. Bhattacharyya, Texas A€3M University, USA Daniel Boley, University of Minnesota, USA Stephen Boyd, Stanford University, USA James R. Bunch, University of California at San Diego, USA John Burns, Virginia Polytechnic Institute and State University, USA Christopher 1. Byrnes, Washington University, USA George Cybenko, Dartmouth College, USA Bart De Moor, Katholieke Universiteit Leuven, Belgium Katsuhisa Furuta, Tokyo Denki University, Japan Vicente Hernandez, Universidad Politecnico de Valencia, Spain Daniel Inman, Virginia Polytechnic Institute and State University, USA Thomas Kailath, Stanford University, USA Hidenori Kimura, The University of Tokyo, Japan S.Y. Kung, Princeton University, USA Anders Lindquist, Royal Institute of Technology, Sweden Blaise Morton, Honeywell Research Corporation, USA R.V. Patel, University of Western Ontario, Canada

xiv Editorial Board

Paul Van Dooren, Universite Catholique de Louvain, Belgium M. Vidyasagar, Tata Consulting Services, India N. Viswanadham, Indian Institute of Science, India

Contributors

Brian D. O. Anderson RS1SE, Australian National University Acton ACT, 0200, Australia Brian.Anderson@anu.edu.au

Thomas S. Brinsmead RS1SE, Australian National University Acton ACT, 0200, Australia Thomas.Brinsmead@syseng.anu.edu.au

Dimitrios Chaniotis Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, 1L 61801 chanioti@energy.ece.uiuc.edu

Mei-Qin Chen Department of Mathematics and Computer Science The Citadel Charleston, SC 29409 chenm@citadel.edu

R. P. K urshan Bell Laboratories Murray Hill, NJ 07974 k@research.bell-labs.com

Harold J. Kushner Department of Applied Mathematics Brown University Providence, R1 02912 hjk@dam.brown.edu

xvi Contributors

M. A. Pai Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 pai@ece.uiuc.edu

J aijeet Roychowdhury CeLight, Inc. 485D Route 1 S, Iselin, NJ 08830 jaijeet@yahoo.com

Steven W. Su RSISE, Australian National University Acton ACT, 0200, Australia Steven.Su@anu.edu.au

Andras Varga Institut fUr Robotik und Systemdynamik DLR Forschungszentrum Oberpfaffenhofen Postfach 1116, D-82230 Wessling, Germany Andras.Varga@dlr.de