系统辨识国外教材.pdf

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System Identification

Series Editors' Foreword

Preface

Acknowledgements

Contents

Notations

Part I: Data-based Identification

Chapter 1: Introduction

1.1 System Theory

1.1.1 Terminology

1.1.2 Basic Problems

1.2 Mathematical Models

1.2.1 Model Properties

1.2.2 Structural Model Representations

1.3 System Identification Procedure

1.4 Historical Notes and References

1.5 Problems

Chapter 2: System Response Methods

2.1 Impulse Response

2.1.1 Impulse Response Model Representation

2.1.2 Transfer Function Model Representation

2.1.3 Direct Impulse Response Identification

2.2 Step Response

2.2.1 Direct Step Response Identification

2.2.2 Impulse Response Identification Using Step Responses

2.3 Sine-wave Response

2.3.1 Frequency Transfer Function

2.3.2 Sine-wave Response Identification

2.4 Historical Notes and References

2.5 Problems

Chapter 3: Frequency Response Methods

3.1 Empirical Transfer-function Identification

3.1.1 Sine Wave Testing

3.1.2 Discrete Fourier Transform of Signals

3.1.3 Empirical Transfer-function Estimate

3.1.4 Critical Point Identification

3.2 Discrete-time Transfer Function

3.2.1 z-Transform

3.2.2 Impulse Response Identification Using Input-output Data

3.2.3 Discrete-time Delta Operator

3.3 Historical Notes and References

3.4 Problems

Chapter 4: Correlation Methods

4.1 Correlation Functions

4.1.1 Autocorrelation Function

4.1.2 White Noise Sequence

4.1.3 Cross-correlation Function

4.2 Wiener-Hopf Relationship

4.2.1 Wiener-Hopf Equation

4.2.2 Impulse Response Identification Using Wiener-Hopf Equation

4.2.3 Random Binary Sequences

4.2.4 Filter Properties of Wiener-Hopf Relationship

4.3 Frequency Analysis Using Correlation Techniques

4.3.1 Cross-correlation Between Input-output Sine Waves

4.3.2 Transfer-function Estimate Using Correlation Techniques

4.4 Spectral Analysis

4.4.1 Power Spectra

4.4.2 Transfer-function Estimate Using Power Spectra

4.4.3 Bias-variance Tradeoff in Transfer-function Estimates

4.5 Historical Notes and References

4.6 Problems

Part II: Time-invariant Systems Identification

Chapter 5: Static Systems Identification

5.1 Linear Static Systems

5.1.1 Linear Regression

5.1.2 Least-squares Estimation

5.1.3 Interpretation of Least-squares Method

5.1.4 Bias

5.1.5 Accuracy

5.1.6 Identifiability

5.1.7 *Errors-in-variables Problem

5.1.8 *Bounded-noise Problem: Linear Case

5.2 Nonlinear Static Systems

5.2.1 Nonlinear Regression

5.2.2 Nonlinear Least-squares Estimation

5.2.3 Iterative Solutions

5.2.4 Accuracy

5.2.5 Model Reparameterization: Static Case

5.2.6 *Maximum Likelihood Estimation

5.2.7 *Bounded-noise Problem: Nonlinear Case

5.3 Historical Notes and References

5.4 Problems

Chapter 6: Dynamic Systems Identification

6.1 Linear Dynamic Systems

6.1.1 Transfer Function Models

6.1.2 Equation Error Identification

6.1.3 Output Error Identification

6.1.4 Prediction Error Identification

6.1.5 Model Structure Identification

6.1.6 *Subspace Identification

6.1.7 *Linear Parameter-varying Model Identification

6.1.8 *Orthogonal Basis Functions

6.1.9 *Closed-loop Identification

6.2 Nonlinear Dynamic Systems

6.2.1 Simulation Models

6.2.2 *Parameter Sensitivity

6.2.3 Nonlinear Regressions

6.2.4 Iterative Solution

6.2.5 Model Reparameterization: Dynamic Case

6.3 Historical Notes and References

6.4 Problems

Part III: Time-varying Systems Identification

Chapter 7: Time-varying Static Systems Identification

7.1 Linear Regression Models

7.1.1 Recursive Estimation

7.1.2 Time-varying Parameters

7.1.3 Multioutput Case

7.1.4 Resemblance with Kalman Filter

7.1.5 *Numerical Issues

7.2 Nonlinear Static Systems

7.2.1 State-space Representation

7.2.2 Extended Kalman Filter

7.3 Historical Notes and References

7.4 Problems

Chapter 8: Time-varying Dynamic Systems Identification

8.1 Linear Dynamic Systems

8.1.1 Recursive Least-squares Estimation

8.1.2 Recursive Prediction Error Estimation

8.1.3 Smoothing

8.2 Nonlinear Dynamic Systems

8.2.1 Extended Kalman Filtering

8.2.2 *Observer-based Methods

8.3 Historical Notes and References

8.4 Problem

Part IV: Model Validation

Chapter 9: Model Validation Techniques

9.1 Prior Knowledge

9.2 Experience with Model

9.2.1 Model Reduction

9.2.2 Simulation

9.2.3 Prediction

9.3 Experimental Data

9.3.1 Graphical Inspection

9.3.2 Correlation Tests

9.4 Historical Notes and References

9.5 Outlook

9.6 Problems

Appendix A Matrix Algebra

A.1 Basic Definitions

A.2 Important Operations

A.3 Quadratic Matrix Forms

A.4 Vector and Matrix Norms

A.5 Differentiation of Vectors and Matrices

A.6 Eigenvalues and Eigenvectors

A.7 Range and Kernel of a Matrix

A.8 Exponential of a Matrix

A.9 Square Root of a Matrix

A.10 Choleski Decomposition

A.11 Modified Choleski (UD) Decomposition

A.12 QR Decomposition

A.13 Singular Value Decomposition

A.14 Projection Matrices

Appendix B Statistics

B.1 Random Entities

B.1.1 Discrete/Continuous Random Variables

B.1.2 Random Vectors

B.1.3 Stochastic Processes

Appendix C Laplace, Fourier, and z-Transforms

C.1 Laplace Transform

C.2 Fourier Transform

C.3 z-Transform

Appendix D Bode Diagrams

D.1 The Bode Plot

D.2 Four Basic Types

D.2.1 Constant or K Factor

D.2.2 (j omega)±n Factor

D.2.3 (1 + j omegaT)±m Factor

D.2.4 e±j omegatau Factor

Appendix E Shift Operator Calculus

E.1 Forward- and Backward-shift Operator

E.2 Pulse Transfer Operator

Appendix F Recursive Least-squares Derivation

F.3 Least-squares Method

F.4 Equivalent Recursive Form

Appendix G Dissolved Oxygen Data

References

Index

Advanced Textbooks in Control and Signal Processing

Series Editors Professor Michael J. Grimble, Professor of Industrial Systems and Director Professor Michael A. Johnson, Professor of Control Systems and Deputy Director Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde, Graham Hills Building, 50 George Street, Glasgow G1 1QE, UK For further volumes: www.springer.com/series/4045

Karel J. Keesman System Identiﬁcation An Introduction

Karel J. Keesman Systems and Control Group Wageningen University Bornse Weilanden 9 6708 WG, Wageningen Netherlands karel.keesman@wur.nl ISSN 1439-2232 ISBN 978-0-85729-521-7 DOI 10.1007/978-0-85729-522-4 Springer London Dordrecht Heidelberg New York e-ISBN 978-0-85729-522-4 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011929048 Mathematics Subject Classiﬁcation: 93E12, 93E24, 93E10, 93E11 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as per- mitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publish- ers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To Wil, Esther, Carlijn, and Rick . . .

Series Editors’ Foreword The topics of control engineering and signal processing continue to ﬂourish and develop. In common with general scientiﬁc investigation, new ideas, concepts and interpretations emerge quite spontaneously, and these are then discussed, used, dis- carded or subsumed into the prevailing subject paradigm. Sometimes these innova- tive concepts coalesce into a new sub-discipline within the broad subject tapestry of control and signal processing. This preliminary battle between old and new usually takes place at conferences, through the Internet and in the journals of the discipline. After a little more maturity has been acquired by the new concepts, then archival publication as a scientiﬁc or engineering monograph may occur. A new concept in control and signal processing is known to have arrived when sufﬁcient material has evolved for the topic to be taught as a specialised tutorial workshop or as a course to undergraduate, graduate or industrial engineers. Ad- vanced Textbooks in Control and Signal Processing are designed as a vehicle for the systematic presentation of course material for both popular and innovative topics in the discipline. It is hoped that prospective authors will welcome the opportunity to publish a structured and systematic presentation of some of the newer emerging control and signal processing technologies in the textbook series. An aim of Advanced Textbooks in Control and Signal Processing is to create a library that covers all the main subjects to be found in the control and signal pro- cessing ﬁelds. It is a growing but select series of high-quality books that now covers some fundamental topics and many more advanced topics in these areas. In trying to achieve a balanced library of course books, the Editors have long wished to have a text on system identiﬁcation in the series. Although we often tend to think of system identiﬁcation as a still-maturing subject, it is quite surprising to realise that the ﬁrst International Federation of Automatic Control symposium on system identiﬁcation was held as long ago as 1967 and that some of the classic textbooks on this topic were published during the 1970s and 1980s. Consequently, the existing literature and diversity of theory and applications areas is now quite extensive and provide a signiﬁcant challenge to any prospective system identiﬁcation course textbook au- thor. The Series Editors were therefore pleased to discover that Associate Professor Karel Keesman of Wageningen University in the Netherlands, was proposing to vii

viii Series Editors’ Foreword take on this task and produce such a course textbook for the series entitled System Identiﬁcation: An Introduction. We are now very pleased to welcome this ﬁnished textbook to the library of Advanced Textbooks in Control and Signal Processing. Although a wide literature exists for systems identiﬁcation, there is a traditional classiﬁcation of techniques into non-parametric and parametric methods, and Pro- fessor Keesman reﬂects this with Part I of his book focussed on the non-parametric methods, and Parts II and III emphasizing the parametric methods. Since every iden- tiﬁcation practitioner wishes to know if the estimated model is a good model for the process, a novel feature of the textbook is Part IV that systematically presents a number of validation techniques for answering that very question. As beﬁts a course textbook, the material develops in increasing technical depth as the reader progresses through the text, but there are starred sections to identify material that is more advanced technically or presents more recent technical devel- opments in the ﬁeld. The presentational style is discursive with the integrated use of examples to illustrate technical and practical issues as they arise along the way. As part of this approach many different system examples have been used ranging from mechanical systems to more complex biological systems. Each chapter has a Problems section, and some solutions are available in the book. To support the math- ematical content (system identiﬁcation involves elements of systems theory, matri- ces, statistics, transform methods (for example, Laplace and Fourier transforms), Bode diagrams, and shift operators), there are ﬁve accessible, short, focussed math- ematical appendices at the end of the book to aid the reader if necessary. This has the advantage of making the textbook fully self-contained for most readers. In terms of processes, Professor Keesman’s approach takes a broad view, and the textbook should be readily appreciated by readers from either the engineering or the scientiﬁc disciplines. Final-year undergraduate and graduate readers will ﬁnd the book provides a stimulating tutorial-style entry to the ﬁeld of system identiﬁcation. For the established engineer or scientist, the mathematical level of the text and the supporting mathematical appendices will allow a speedy and insightful appreciation of the techniques of the ﬁeld. This is an excellent addition to the Advanced Textbooks in Control and Signal Processing series. Industrial Control Centre Glasgow, Scotland, UK M.J. Grimble M.A. Johnson

Preface St. Augustine of Hippo in De Civitate Dei writes ‘Si [···] fallor, sum’ (‘If I am mistaken, I am’) (book XI, 26) ‘I can therefore gladly admit that falsiﬁcationists like myself much prefer an attempt to solve an interesting problem by a bold conjecture, even (and especially) if it soon turns out to be false, to any recital of a sequence of irrelevant truisms. We prefer this because we believe that in this way we learn from our mistakes; and that in ﬁnding that our conjecture was false, we shall have learnt much about the truth, and shall have got nearer to the truth.’ POPPER, K. 1962 Conjectures and Refutations, New York: Basic Books, p. 231 ix

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