Identification of Continuous-Time Systems-Linear and Robust Parameter Estimation

143 Pages·2019·7.518 MB·\143

by  Allamaraju Subrahmanyam (Author), Ganti Prasada Rao (Author)

Identification
of Continuous-Time
Systems
ENGINEERING SYSTEMS AND SUSTAINABILITY SERIES
Series Editor: Ganti Prasada Rao
Co-Editors: D. Subbaram Naidu, Hugues Garnier, and Zidong Wang
Published Titles
Identification of Continuous-Time Systems: Linear and Robust
Parameter Estimation
Allamaraju Subrahmanyam and Ganti Prasada Rao
Nonlinear Stochastic Control and Filtering with
Engineering-Oriented Complexities
Guoliang Wei, Zidong Wang, and Wei Qian
Multi-Stage Flash Desalination: Modeling, Simulation, and
Adaptive Control
Abraha Woldai
ENGINEERING SYSTEMS AND SUSTAINABILITY SERIES Identification
Series Editor: Ganti Prasada Rao
Co-Editors: D. Subbaram Naidu, Hugues Garnier, and Zidong Wang
of Continuous-Time
Systems
Published Titles
Linear and Robust
Identification of Continuous-Time Systems: Linear and Robust
Parameter Estimation
Parameter Estimation
Allamaraju Subrahmanyam and Ganti Prasada Rao
Nonlinear Stochastic Control and Filtering with
Engineering-Oriented Complexities
Guoliang Wei, Zidong Wang, and Wei Qian
Multi-Stage Flash Desalination: Modeling, Simulation, and
Adaptive Control
Abraha Woldai
Allamaraju Subrahmanyam
Ganti Prasada Rao
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2020 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-0-367-37143-2 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize
to copyright holders if permission to publish in this form has not been obtained. If any copyright material
has not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the
CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Allamaraju, Subrahmanyam, author. | Prasada Rao, Ganti, 1942-
author.
Title: Identification of continuous-time systems : linear and robust
parameter estimation / Allamaraju Subrahmanyam and Ganti Prasada Rao.
Description: First edition. | New York, N.Y. : CRC Press/Taylor & Francis
Group, 2020. | Series: Engineering systems and sustainability | Includes
bibliographical references and index.
Identifiers: LCCN 2019032828 (print) | LCCN 2019032829 (ebook) | ISBN
9780367371432 (hardback) | ISBN 9780429352850 (ebook)
Subjects: LCSH: Automatic control--Mathematical models. | Linear time
invariant systems. | System identification. | Parameter estimation.
Classification: LCC TJ212.2 .A44 2020 (print) | LCC TJ212.2 (ebook) | DDC
629.8/95--dc23
LC record available at https://lccn.loc.gov/2019032828
LC ebook record available at https://lccn.loc.gov/2019032829
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2020 by Taylor & Francis Group, LLC
List of Figures .......................................................................................................vii
CRC Press is an imprint of Taylor & Francis Group, an Informa business
List of Tables ...........................................................................................................ix
No claim to original U.S. Government works
Preface ......................................................................................................................xi
Printed on acid-free paper Acknowledgments ................................................................................................xv
Authors ................................................................................................................xvii
International Standard Book Number-13: 978-0-367-37143-2 (Hardback)
List of Abbreviations ..........................................................................................xxi
978-0-367-37145-6 (Paperback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
1. Introduction and Overview ..........................................................................1
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers 1.1 Background .............................................................................................1
have attempted to trace the copyright holders of all material reproduced in this publication and apologize 1.2 Introduction .............................................................................................3
to copyright holders if permission to publish in this form has not been obtained. If any copyright material
1.3 Role of Model Parameterizations in System Identification...............4
has not been acknowledged please write and let us know so we may rectify in any future reprint.
1.3.1 Poisson Moment Functional Approach ...................................6
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- 1.3.2 Integral Equation Approach......................................................6
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
1.3.3 Biased Estimation .......................................................................8
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers. 1.3.4 Reducible Models (for Multivariable Systems) .......................8
1.3.5 Distribution of Estimation Errors .............................................9
For permission to photocopy or use material electronically from this work, please access www.copyright.
1.4 Error Quantification: An Engineering Necessity .............................13
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the 2. Markov Parameter Models .........................................................................17
CCC, a separate system of payment has been arranged.
2.1 Introduction ...........................................................................................17
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are 2.2 Markov Parameter Models ..................................................................18
used only for identification and explanation without intent to infringe.
2.2.1 Generalizations .........................................................................19
2.2.2 Choice of λ .................................................................................20
Library of Congress Cataloging‑in‑Publication Data
2.2.3 Markov Parameter Estimation ................................................23
Names: Allamaraju, Subrahmanyam, author. | Prasada Rao, Ganti, 1942- 2.2.4 Identification of Structure .......................................................24
author.
2.3 Finitization of the Markov Parameter Sequence ..............................25
Title: Identification of continuous-time systems : linear and robust
parameter estimation / Allamaraju Subrahmanyam and Ganti Prasada Rao. 2.3.1 Controller Form Realization ...................................................25
Description: First edition. | New York, N.Y. : CRC Press/Taylor & Francis 2.4 Identifiability Conditions ....................................................................28
Group, 2020. | Series: Engineering systems and sustainability | Includes
2.5 Convergence Analysis of the Algorithm ...........................................32
bibliographical references and index.
Identifiers: LCCN 2019032828 (print) | LCCN 2019032829 (ebook) | ISBN 2.6 Illustrative Examples ............................................................................36
9780367371432 (hardback) | ISBN 9780429352850 (ebook) 2.7 Summary and Conclusions .................................................................41
Subjects: LCSH: Automatic control--Mathematical models. | Linear time
invariant systems. | System identification. | Parameter estimation.
Classification: LCC TJ212.2 .A44 2020 (print) | LCC TJ212.2 (ebook) | DDC 3. Time Moment Models ..................................................................................43
629.8/95--dc23 3.1 Introduction ...........................................................................................43
LC record available at https://lccn.loc.gov/2019032828
3.2 Time Moment Models ..........................................................................44
LC ebook record available at https://lccn.loc.gov/2019032829
3.3 Finitization of Time-Moment Sequence ............................................47
3.3.1 Implementation Issues .............................................................48
Visit the Taylor & Francis Web site at
3.4 Illustrative Examples ............................................................................51
http://www.taylorandfrancis.com
3.5 Choice of Basis of Parameterization ...................................................54
and the CRC Press Web site at
3.6 Summary and Conclusions .................................................................61
http://www.crcpress.com
v
vi Contents
4. Robust Parameter Estimation .....................................................................63
4.1 Introduction ...........................................................................................63
4.2 Problem Description ............................................................................64
4.3 Solution to the Suboptimal Problem ..................................................67
4.4 Bounds on Parameter Errors ...............................................................76
4.5 Summary and Conclusions .................................................................78
5. Error Quantification .....................................................................................81
5.1 Introduction ..........................................................................................81
5.1.1 Role of Priors .............................................................................83
5.1.2 A Plausible Philosophy ............................................................85
5.1.3 Chapter Layout ..........................................................................86
5.2 Robust Parameter Estimation .............................................................86
5.3 Quantification of Parameter Errors ....................................................87
5.4 Illustrative Examples ............................................................................90
5.5 Conclusions ...........................................................................................92
6. Conclusions ....................................................................................................95
6.1 Linear Model Parameterizations for System Identification ............95
6.2 Robust Estimation ................................................................................96
6.3 Error Quantification .............................................................................97
Bibliography ..........................................................................................................99
Subject Index ......................................................................................................113
Author Index .......................................................................................................117
List of Figures
Figure 1.1 Indirect identification of CT parameters via DT parameters .....7
Figure 1.2 Direct identification of CT parameters via DT parameters ........8
Figure 1.3 Poisson filter chain ............................................................................8
Figure 2.1 Expansion of the complex plane: (I) Actual ZOC,
(II) Expanded ZOC. (a) λ<0 for real and heavily
damped poles; and (b) λ>0 for lightly damped
and imaginary pole .........................................................................21
Figure 2.2 Pattern of MP convergence (Example 2.1) ....................................37
Figure 2.3 Pattern of MP convergence—Subsystem 1 (Example 2.2) .........38
Figure 2.4 Pattern of MP convergence—Subsystem 2 (Example 2.2) .........38
Figure 3.1 Pattern of parameter convergence—Noise: 10% white
(Example 3.1) ....................................................................................52
Figure 3.2 Pattern of parameter convergence—Noise: 10% colored
(Example 3.1) ....................................................................................52
Figure 3.3 Results of restricted complexity model estimation using
basis  (Example 3.3) ...................................................................57
PF
Figure 3.4 Results of restricted complexity model estimation using
basis  (Example 3.3) .................................................................58
SVF
Figure 3.5 Results of restricted complexity model estimation using
basis  (Example 3.3).................................................................59
LAG
Figure 3.6 Comparison of approximations (Example 3.3). Basis-1:
 , Basis-2:  , Basis-3:  .....................................................60
MP SVF LAG
Figure 3.7 Results of restricted complexity model estimation using
basis  (Example 3.4) .................................................................61
SVF
Figure 4.1 Patterns of parameter convergence ..............................................73
Figure 4.2 Decay of determinants ...................................................................74
Figure 4.3 Response to a sudden change in steady-state gain of the
system ...............................................................................................74
Figure 5.1 Frequency domain error bounds (Example 5.1) ..........................91
Figure 5.2 Frequency domain error bounds (Example 2.2) .........................92
vii

List of Tables
Table 2.1 Parameter estimates (Example 2.1) .................................................37
Table 2.2 Parameter estimates—Subsystem 1 (Example 2.2) .......................39
Table 2.3 Parameter estimates—Subsystem 2 (Example 2.2) .......................39
Table 2.4 Results of Monte Carlo experiments with MP approach
(Example 2.3) ......................................................................................39
Table 2.5 Comparison of percentage REN (Example 2.3) ............................40
Table 3.1 Parameter estimates—Noise: 10% white (Example 3.1) ...............51
Table 3.2 Parameter estimates—Noise: 10% colored (Example 3.1) ............51
Table 3.3 Parameter estimates—Noise: 10% white (Example 3.2) ...............53
Table 3.4 Parameter estimates—Noise: 10% colored (Example 3.2) ............53
Table 3.5 Results of Monte Carlo simulation experiments—Noise:
white (Example 3.2) ...........................................................................53
Table 3.6 Results of Monte Carlo simulation experiments—Noise:
colored (Example 3.2) ........................................................................54
Table 3.7 Parameter estimates (Example 3.3) .................................................56
Table 3.8 Comparison of condition numbers (Example 3.3) ........................60
Table 3.9 Parameter estimates (Example 3.4) .................................................60
ix