95,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
True Digital Control: Statistical Modelling and Non–Minimal State Space Designdevelops a true digital control design philosophy that encompasses data–based model identification, through to control algorithm design, robustness evaluation and implementation. With a heritage from both classical and modern control system synthesis, this book is supported by detailed practical examples based on the authors’ research into environmental, mechatronic and robotic systems. Treatment of both statistical modelling and control design under one cover is unusual and highlights the important connections between these disciplines.
Starting from the ubiquitous proportional–integral controller, and with essential concepts such as pole assignment introduced using straightforward algebra and block diagrams, this book addresses the needs of those students, researchers and engineers, who would like to advance their knowledge of control theory and practice into the state space domain; and academics who are interested to learn more about non–minimal state variable feedback control systems. Such non–minimal state feedback is utilised as a unifying framework for generalised digital control system design. This approach provides a gentle learning curve, from which potentially difficult topics, such as optimal, stochastic and multivariable control, can be introduced and assimilated in an interesting and straightforward manner.
Key features:
- Covers both system identification and control system design in a unified manner
- Includes practical design case studies and simulation examples
- Considers recent research into time–variable and state–dependent parameter modelling and control, essential elements of adaptive and nonlinear control system design, and the delta–operator (the discrete–time equivalent of the differential operator) systems
- Accompanied by a website hosting MATLAB examples
True Digital Control: Statistical Modelling and Non–Minimal State Space Design is a comprehensive and practical guide for students and professionals who wish to further their knowledge in the areas of modern control and system identification.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 554
Veröffentlichungsjahr: 2013
Ähnliche
Contents
Cover
Title Page
Copyright
Dedication
Preface
List of Acronyms
List of Examples, Theorems and Estimation Algorithms
Chapter 1: Introduction
1.1 Control Engineering and Control Theory
1.2 Classical and Modern Control
1.3 The Evolution of the NMSS Model Form
1.4 True Digital Control
1.5 Book Outline
1.6 Concluding Remarks
References
Chapter 2: Discrete-Time Transfer Functions
2.1 Discrete-Time TF Models
2.2 Stability and the Unit Circle
2.3 Block Diagram Analysis
2.4 Discrete-Time Control
2.5 Continuous to Discrete-Time TF Model Conversion
2.6 Concluding Remarks
References
Chapter 3: Minimal State Variable Feedback
3.1 Controllable Canonical Form
3.2 Observable Canonical Form
3.3 General State Space Form
3.4 Controllability and Observability
3.5 Concluding Remarks
References
Chapter 4: Non-Minimal State Variable Feedback
4.1 The NMSS Form
4.2 Controllability of the NMSS Model
4.3 The Unity Gain NMSS Regulator
4.4 Constrained NMSS Control and Transformations
4.5 Worked Example with Model Mismatch
4.6 Concluding Remarks
References
Chapter 5: True Digital Control for Univariate Systems
5.1 The NMSS Servomechanism Representation
5.2 Proportional-Integral-Plus Control
5.3 Pole Assignment for PIP Control
5.4 Optimal Design for PIP Control
5.5 Case Studies
5.6 Concluding Remarks
References
Chapter 6: Control Structures and Interpretations
6.1 Feedback and Forward Path PIP Control Structures
6.2 Incremental Forms for Practical Implementation
6.3 The Smith Predictor and its Relationship with PIP Design
6.4 Stochastic Optimal PIP Design
6.5 Generalised NMSS Design
6.6 Model Predictive Control
6.7 Concluding Remarks
References
Chapter 7: True Digital Control for Multivariable Systems
7.1 The Multivariable NMSS (Servomechanism) Representation
7.2 Multivariable PIP Control
7.3 Optimal Design for Multivariable PIP Control
7.4 Multi-Objective Optimisation for PIP Control
7.5 Proportional-Integral-Plus Decoupling Control by Algebraic Pole Assignment
7.6 Concluding Remarks
References
Chapter 8: Data-Based Identification and Estimation of Transfer Function Models
8.1 Linear Least Squares, ARX and Finite Impulse Response Models
8.2 General TF Models
8.3 Optimal RIV Estimation
8.4 Model Structure Identification and Statistical Diagnosis
8.5 Multivariable Models
8.6 Continuous-Time Models
8.7 Identification and Estimation in the Closed-Loop
8.8 Concluding Remarks
References
Chapter 9: Additional Topics
9.1 The δ-Operator Model and PIP Control
9.2 Time Variable Parameter Estimation
9.3 State-Dependent Parameter Modelling and PIP Control
9.4 Concluding Remarks
References
Appendix A: Matrices and Matrix Algebra
A.1 Matrices
A.2 Vectors
A.3 Matrix Addition (or Subtraction)
A.4 Matrix or Vector Transpose
A.5 Matrix Multiplication
A.6 Determinant of a Matrix
A.7 Partitioned Matrices
A.8 Inverse of a Matrix
A.9 Quadratic Forms
A.10 Positive Definite or Semi-Definite Matrices
A.11 The Rank of a Matrix
A.12 Differentiation of Vectors and Matrices
References
Appendix B: The Time Constant
Reference
Appendix C: Proof of Theorem 4.1
References
Appendix D: Derivative Action Form of the Controller
Appendix E: Block Diagram Derivation of PIP Pole Placement Algorithm
Appendix F: Proof of Theorem 6.1
Reference
Appendix G: The CAPTAIN Toolbox
G.1 Transfer Functions and Control System Design
G.2 Other Routines
G.3 Download
References
Appendix H: The Theorem of D.A. Pierce (1972)
References
Index
This edition first published 2013 © 2013 John Wiley & Sons, Ltd
Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This books use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
Library of Congress Cataloging-in-Publication Data
Taylor, C. James. True digital control : statistical modelling and non-minimal state space design / C. James Taylor, Peter C. Young, Arun Chotai. pages cm Includes bibliographical references and index. ISBN 978-1-118-52121-2 (cloth) 1. Digital control systems–Design. I. Young, Peter C., 1939- II. Chotai, Arun. III. Title. TJ223.M53T38 2013 629.8'95–dc23
2013004574
A catalogue record for this book is available from the British Library
ISBN: 978-1-118-52121-2
To Ting-Li
To Wendy
In memory of Varsha
Preface
This book develops a True Digital Control (TDC) design philosophy that encompasses data-based (statistical) model identification, through to control algorithm design, robustness evaluation and implementation. Treatment of both stochastic system identification and control design under one cover highlights the important connections between these disciplines: for example, in quantifying the model uncertainty for use in closed-loop stochastic sensitivity analysis. More generally, the foundations of linear state space control theory that are laid down in early chapters, with Non-Minimal State Space (NMSS) design as the central worked example, are utilised subsequently to provide an introduction to other selected topics in modern control theory. MATLAB®1 functions for TDC design and MATLAB® scripts for selected examples are being made available online, which is important in making the book accessible to readers from a range of academic backgrounds. Also, the CAPTAIN Toolbox for MATLAB®, which is used for the analysis of all the modelling examples in this book, is available for free download. Together, these contain computational routines for many aspects of model identification and estimation; for NMSS design based on these estimated models; and for offline signal processing. For more information visit: http://www.wiley.com/go/taylor.
The book and associated software are intended for students, researchers and engineers who would like to advance their knowledge of control theory and practice into the state space domain; and control experts who are interested to learn more about the NMSS approach promoted by the authors. Indeed, such non-minimal state feedback is utilised throughout this book as a unifying framework for generalised digital control system design. This includes the Proportional-Integral-Plus (PIP) control systems that are the most natural outcome of the NMSS design strategy. As such, the book can also be considered as a primer for potentially difficult topics in control, such as optimal, stochastic and multivariable control.
As indicated by the many articles on TDC that are cited in this book, numerous colleagues and collaborators have contributed to the development of the methods outlined. We would like to pay particular thanks to our good friend Dr Wlodek Tych of the Lancaster Environment Centre, Lancaster University, UK, who has contributed to much of the underlying research and in the development of the associated computer algorithms. The first author would also like to thank Philip Leigh, Matthew Stables, Essam Shaban, Vasileios Exadaktylos, Eleni Sidiropoulou, Kester Gunn, Philip Cross and David Robertson for their work on some of the practical examples highlighted in this book, among other contributions and useful discussions while they studied at Lancaster. Philip Leigh designed and constructed the Lancaster forced ventilation test chamber alluded to in the text. Vasileios Exadaktylos made insightful suggestions and corrections in relation to early draft chapters of the book. The second author is grateful to a number of colleagues over many years including: Charles Yancey and Larry Levsen, who worked with him on early research into NMSS control between 1968 and 1970; Jan Willems who helped with initial theoretical studies on NMSS control in the early 1970s; and Tony Jakeman who helped to develop the Refined Instrumental Variable (RIV) methods of model identification and estimation in the late 1970s. We are also grateful to the various research students at Lancaster who worked on PIP methods during the 1980s and 1990s, including M.A. Behzadi, Changli Wang, Matthew Lees, Laura Price, Roger Dixon, Paul McKenna and Andrew McCabe; to Zaid Chalabi, Bernard Bailey and Bill Day, who helped to investigate the initial PIP controllers for the control of climate in agricultural glasshouses at the Silsoe Research Institute; and to Daniel Berckmans and his colleagues at the University of Leuven, who collaborated so much in later research on the PIP regulation of fans for the control of temperature and humidity in their large experimental chambers at Leuven.
Finally, we would like to express our sincere gratitude to the UK Engineering and Physical Sciences, Biotechnology and Biological Sciences, and Natural Environmental Research Councils for their considerable financial support for our research and development studies at Lancaster University.
C. James Taylor, Peter C. Young and Arun Chotai Lancaster, UK
1. MATLAB®, The MathWorks Inc., Natick, MA, USA.
List of Acronyms
ACFAutoCorrelation FunctionAICAkaike Information CriterionAMLApproximate Maximum LikelihoodARAuto-RegressiveARIMAXAuto-Regressive Integrated Moving-Average eXogenous variablesARMAAuto-Regressive Moving-AverageARMAXAuto-Regressive Moving-Average eXogenous variablesARXAuto-Regressive eXogenous variablesBICBayesian Information CriterionBJBox–JenkinsCAPTAINComputer-Aided Program for Time series Analysis and Identification of Noisy systemsCLTFClosed-Loop Transfer FunctionCTContinuous-TimeDARXDynamic Auto-Regressive eXogenous variablesDBMData-Based MechanisticDCDirect CurrentDDCDirect Digital ControlDFDirectional ForgettingDTDiscrete-TimeDTFDynamic Transfer FunctionEKFExtended or generalised Kalman FilterEWPExponential-Weighting-into-the-PastFACEFree-Air Carbon dioxide EnrichmentFIRFinite Impulse ResponseFISFixed Interval SmoothingFPEFinal Prediction ErrorGBJGeneralised Box–JenkinsGPCGeneralised Predictive ControlGRIVBJGeneralised RIVBJ or RIVCBJGRWGeneralised Random WalkGSRIVGeneralised SRIV or SRIVCIPMInstrumental Product MatrixIRWIntegrated Random WalkIVInstrumental VariableIVARMAInstrumental Variable Auto-Regressive Moving-AverageKFKalman FilterLEQGLinear Exponential-of-Quadratic GaussianLLSLinear Least SquaresLLTLocal Linear TrendLPVLinear Parameter VaryingLQLinear QuadraticLQGLinear Quadratic GaussianLTRLoop Transfer RecoveryMCSMonte Carlo SimulationMFDMatrix Fraction DescriptionMIMOMulti-Input, Multi-OutputMISOMulti-Input, Single-OutputMLMaximum LikelihoodMPCModel Predictive ControlNEVNNormalised Error Variance NormNLPVNon-Linear Parameter VaryingNMSSNon-Minimal State SpaceNSRNoise–Signal RatioNVRNoise Variance RatioPACFPartial AutoCorrelation FunctionPBHPopov, Belevitch and HautusPEMPrediction Error MinimisationPIProportional-IntegralPIDProportional-Integral-DerivativePIPProportional-Integral-PlusPRBSPseudo Random Binary SignalRBFRadial Basis FunctionRIVRefined Instrumental VariableRIVARRefined Instrumental Variable with Auto-Regressive noiseRIVBJRefined Instrumental Variable for Box–Jenkins modelsRIVCBJRefined Instrumental Variable for hybrid Continuous-time Box–Jenkins modelsRLSRecursive Least SquaresRMLRecursive Maximum LikelihoodRWRandom WalkRWPRectangular-Weighting-into-the-PastSDStandard DeviationSDARXState-Dependent Auto-Regressive eXogenous variablesSDPState-Dependent ParameterSEStandard ErrorSISOSingle-Input, Single-OutputSPSmith PredictorSRIVSimplified Refined Instrumental VariableSRIVCSimplified Refined Instrumental Variable for hybrid Continuous-time modelsSRWSmoothed Random WalkSVFState Variable FeedbackTDCTrue Digital ControlTFTransfer FunctionTFMTransfer Function MatrixTVPTime Variable ParameterYICYoung Information CriterionList of Examples, Theorems and Estimation Algorithms
Examples
Theorems
Estimation Algorithms
