LINEAR CONTROL SYSTEM ANALYSIS AND DESIGN WITH MATLAE Fifth Edition, Revised and Expanded John J. D’Azzo and Constantine H. Houpis Air Force Institute of Technology Wright-Patterson Air Force Base, Ohio, U.S.A. Stuart N. Sheldon US. Nuclear Regulatory Commission Lisle, Illinois, U.S.A. MARCEL MARCEL DEKKER, INC. 9% DEKKER NEW YORK BASEL Copyright © 2003 Marcel Dekker, Inc. ThefourtheditionwaspublishedasLinearControlSystemAnalysisandDesign: ConventionalandModern,byJohnJ.D’AzzoandConstantineH.Houpis(McGraw-Hill, 1995). Althoughgreatcarehasbeentakentoprovideaccurateandcurrentinformation,neither theauthor(s)northepublisher,noranyoneelseassociatedwiththispublication,shallbe liableforanyloss,damage,orliabilitydirectlyorindirectlycausedorallegedtobecaused bythisbook.Thematerialcontainedhereinisnotintendedtoprovidespecificadviceor recommendationsforanyspecificsituation. Trademarknotice:Productorcorporatenamesmaybetrademarksorregisteredtrade- marksandareusedonlyforidentificationandexplanationwithoutintenttoinfringe. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress. ISBN:0-8247-4038-6 Thisbookisprintedonacid-freepaper. Headquarters MarcelDekker,Inc.,270MadisonAvenue,NewYork,NY10016,U.S.A. tel:212-696-9000;fax:212-685-4540 DistributionandCustomerService MarcelDekker,Inc.,CimarronRoad,Monticello,NewYork12701,U.S.A. tel:800-228-1160;fax:845-796-1772 EasternHemisphereDistribution MarcelDekkerAG,Hutgasse4,Postfach812,CH-4001Basel,Switzerland tel:41-61-260-6300;fax:41-61-260-6333 WorldWideWeb http://www.dekker.com The publisher offers discounts on this book w hen ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright ß 2003 by Marcel Dekker, Inc. Ali Rights Reserved. N either t his book nor any part may be reproduced or transmitted in any form or by any means, electronic or m ec hanical, including photocopying, m i crofilming, and recording, or by any informa tion storage and retrieval system, without permis sion in writing fr om the publisher. Current printing (last digit): 10987654321 PRINTED IN UNITED STATES OF AMERICA Copyright © 2003 Marcel Dekker, Inc. A Series of Reference Books and Textbooks I. 2. 3. 4. 5. 6. 7. a. 9. 10. 11. 12. 13. Editors NEIL MUNRO, PH.D., D.Sc. Professor Applied Control Engineering University of Manchester Institute of Science and Technology Manchester, United Kingdom FRANK L. LEWIS, PH.D. Moncrief-O'Donnell Endowed Chair and Associate Director of Research Automation & Robotics Research Institute University of Texas, Arlington Nonlinear Control of Electric Machinery, Damn M. Dawson, Jun Hu, and Timothy C. Burg Computational Intelligence in Control Engineering, Robert E. King Quantitative Feedback Theory: Fundamentals and Applications, Con- stantine H. Houpis and Steven J. Rasmussen Self-Learning Control of Finite Markov Chains, A. S. Poznyak, K. Najim, and E. Gomez-Ramirez Robust Control and Filtering for Time-Delay Systems, Magdi S. Mah- moud Classical Feedback Control: With MATLAB, Boris J. Luhe and Paul J. Enright Optimal Control of Singularly Perturbed Linear Systems and Applications: High-Accuracy Techniques, Zoran Gajic' and Myo-Taeg Lim Engineering System Dynamics: A Unified Graph-Centered Approach, Forhes T. Brown Advanced Process Identification and Control, Enso lkonen and Kaddour Najim Modem Control Engineering, P. N. Paraskevopoulos Sliding Mode Control in Engineering, edited by Wilfrid Pwrugueffi and Jean Pierre Barhot Actuator Saturation Control, edited by Vikram Kapila and Karolos M. Gng oria dis Nonlinear Control Systems, Zoran VukiC, Ljubomir KuQaCa, Dali DonlagiC, Sejid Tesnjak Copyright © 2003 Marcel Dekker, Inc. 14. Linear Control System Analysis and Design with MATLAB: Fifth Edition, Revised and Expanded, John J. D’Azzo, Consfanfine H. Houpis, and Sfuatt N. Sheldon Additional Volumes in Preparation Robot Manipulator Control: Theory and Practice, Second Edition, Re- vised and Expanded, Frank L. Lewis, Damn M. Dawson, and Chaouki T. Abdallah Robust Control System Design: Advanced State Space Techniques, Second Edition, Revised and Expanded, Chia-Chi Tsui Copyright © 2003 Marcel Dekker, Inc. Series Introduction Many textbooks have been writt en on control engineeri n g, describing new techniques for co ntrolling systems, or new and better ways of mathematically formulating existing methods to solve the ever-increasing complex problems faced by p racticing engineers. H owever, few of these books fully addres s the applications aspects of control engineering. It is the intention of this new series to redress this situation. The series will stress applications issues, and not just the mathematics of control engineeri ng . It will provi de texts that present not onl y both new and well-established techniques, bu t also detailed examples of the application of these methods to the solution of real-world problems. The authors will be drawn from both the academic world and the relevant applications sectors. There are already many exciting examples of the application of control techniques in the established fie l ds of electrical , mechani cal (including aero- space), and chemical engineering.We have only to look around in today’s highly automated soci ety to see the use o f advanced robotics techniques in the manufacturing industries; the use of automated control and navigation systems in air and surface transport systems; the increasing use of intelligent control systems in the many artifacts available to the domestic consumer market; and the reliable supply of water, gas, and electrical power to the domestic consumer and to industry. However, there are currently many challenging problems that could benefit from wider exposure to the applicability of control methodolo- gies, and the systematic systems-oriented basis inherent in the application of control techniques . Copyright © 2003 Marcel Dekker, Inc. This series presents books that draw on expertise from both the academic world and the applications domains, and will be useful not only as academically recommended course texts but also as handbook s for practit i on ers in many applications domains. Linear Control System Analysis and De sign wi th MATLAB is another outstanding entry in Dekker’s Control Engineering series. Neil Munro Copyright © 2003 Marcel Dekker, Inc. Preface The countless technological advances of the twentieth century require that future engineering education emphasize bridging the gap between theory and the real world.This edition has been prepared with particular attention to the needs of undergraduates, especially those who seek a solid foundation in control theory as w ell as an ability to bri dge the gap between control theory and its real- world applications. To help the reader achieve this goal, computer-aided design accuracy checks (CADAC) are used throughout the text to encourage good habits of computer literacy. Each CADAC uses fundamental concepts to ensure the viability of a computer s olution. This edition has been enhanced as a solid undergraduate and first-year graduate text; it emphasizes applying control theory fundamentals to both ana- log and sampled-data single-input single-output (SISO) feedback control sys- tems. At the same time, the coverage of digital control systems is greatly expan ded. Extensive referenc e is made to computer -aided design (CAD) packages to simplify the design process. The result is a comprehensive pre- sentation of control theory and designöone that has been thoroughly class- tested, ensuring its value for classroom and se lf-study use. This book features extensive use of explan a tions, diagrams , calculat i ons, tables, and symbols. Such mathematical rigor is necessary for design applica- tions and advanced control work. A solid foundation is built on concepts of modern control theory as well as those elements of conventional control theory that are relevant in analysis and design of control systems. The presentation of various techniques helps the reader understand what A. T. Fuller has called Copyright © 2003 Marcel Dekker, Inc. ‘‘theenigmaticcontrolsystem.’’Toprovideacoherentdevelopmentofthesub- ject,weeschewformalproofsandlemmas,insteadusinganorganizationthat drawstheperceptivestudentsteadilyandsurelytothedemandingtheoryof multivariablecontrolsystems.Designexamplesareincludedthroughouteach chaptertoreinforcethestudent’sunderstandingofthematerial.Astudentwho hasreachedthispointisfullyequippedtoundertakethechallengesofmore advancedcontroltheories,aspresentedinadvancedcontroltheorytextbooks. Chapter2setsforththeappropriatedifferentialequationstodescribethe performanceofphysicalsystems,networks,anddevices.Theblockdiagram,the transferfunction,andthestatespace(theessentialconceptofmodern controltheory)arealsointroduced.Theapproachusedforthestatespaceis thesimultaneousderivationofthestate-vectordifferentialequationwiththe SISOdifferentialequationforachosenphysicalsystem.Thechapteralsoshows howtoderivethemathematicaldescriptionofaphysicalsystemusing LaGrangeequations. Chapter3presentstheclassicalmethodofsolvingdifferentialequations. Oncethestate-variableequationhasbeenintroduced,acarefulexplanationof itssolutionisprovided.Therelationshipofthetransferfunctiontothestate equationofthesystemispresentedinChapter14.Theimportanceofthestate transitionmatrixisdescribed,andthestatetransitionequationisderived. Theideaofeigenvaluesisexplainednext;thistheoryisusedwiththeCayley^ HamiltonandSylvestertheoremstoevaluatethestatetransitionmatrix. TheearlypartofChapter4presentsacomprehensivedescriptionof Laplacetransformmethodsandpole-zeromaps.Somefurtheraspectsofmatrix algebraareintroducedasbackgroundforsolvingthestateequationusing Laplacetransforms.Finally,theevaluationoftransfermatricesisclearly explained. Chapter5beginswithsystemrepresentationbytheconventionalblock- diagramapproach.Thisisfollowedbyadiscussionofsimulationdiagramsand thedeterminationofthestatetransitionequationusingsignalflowgraphs.The chapteralsoexplainshowtoderiveparallelstatediagramsfromsystemtransfer functions,establishingtheadvantagesofhavingthestateequationinuncoupled form. Chapter6introducesbasicfeedbacksystemcharacteristics.Thisincludes therelationshipbetweensystemtypeandtheabilityofthesystemtofollowor trackpolynomialinputs. Chapter7presentsthedetailsoftheroot-locusmethod.Chapters8and9 describethefrequency-responsemethodusingbothlogandpolarplots.These chaptersaddressthefollowingtopics:theNyquiststabilitycriterion;thecorre- lationbetweenthes-plane,frequencydomain,andtimedomain;andgainset- tingtoachieveadesiredoutputresponsepeakvaluewhiletrackingpolynomial commandinputs.Chapters10and11describethemethodsforimproving Copyright © 2003 Marcel Dekker, Inc. systemperformance,includingexamplesofthetechniquesforapplyingcascade andfeedbackcompensators.Boththeroot-locusandfrequency-response methodsofdesigningcompensatorsarecovered. Chapter12developstheconceptofmodelingadesiredcontrolratiowith figuresofmerittosatisfysystemperformancespecifications.Thesysteminputs generallyfallintotwocategories:(1)desiredinputthatthesystemoutputisto track(atrackingsystem)and(2)anexternaldisturbanceinputforwhichthe systemoutputistobeminimal(adisturbance-rejectionsystem).Forbothtypes ofsystems,thedesiredcontrolratioissynthesizedbytheproperplacement ofitspolesandinclusionofzeros,ifrequired.Chapter12alsointroducesthe Guillemin-Truxaldesignprocedure,whichisusedfordesigningatracking controlsystemandadesignprocedureemphasizingdisturbancerejection. Chapter13explainshowtoachievedesiredsystemcharacteristicsusing completestate-variablefeedback.Twoimportantconceptsofmoderncontrol theoryöcontrollabilityandobservabilityöaretreatedinasimpleandstraight- forwardmanner. Chapter14presentsthesensitivityconceptsofBode,asusedinvariation ofsystemparameters.Othertoolsincludethemethodofusingfeedbacktransfer functionstoformestimatesofinaccessiblestatesforuseinstatefeedback,and atechniqueforlinearizinganonlinearsystemaboutitsequilibriumpoints. Chapter15presentsthefundamentalsofsampleddata(S-D)control systems.Chapter16describesthedesignofdigitalcontrolsystems,demonstrat- ing,forexample,theeffectivenessofdigitalcompensation.Theconceptofa pseudo-continuous-time(PCT)modelofadigitalsystempermitstheuseof continuous-timemethodsforthedesignofdigitalcontrolsystems. Thetexthasbeenpreparedsothatitcanbeusedforself-studyby engineersinvariousareasofpractice(electrical,aeronautical,mechanical, etc.).Tomakeitvaluabletoallengineers,weusevariousexamplesoffeedback controlsystemsandunifythetreatmentofphysicalcontrolsystemsbyusing mathematicalandblock-diagrammodelscommontoall. Therearemanycomputer-aideddesign(CAD)packages(e.g., MATLAB Õ [seeApp.C],Simulink,andTOTAL-PC)availabletohelpstudents and practicing engineers analyze, design, and simulate control systems. The use of MATLAB is emphasized throughout the book, and many MATLAB m- fil es are presented as examples . We thank the students who have used this book in its previous editions and the instructors who have reviewed this edition for their helpful comments and recommendations. We thank especially Dr. R. E. Fontana, Professor Emeritus of Electrical Engineering, Air Force Institute of Technology, for the encouragement he provided for the previous editions. This edition is dedicated to the memory of Dr. T. J. Higgins, Professor Emeritus of Electrical Engineer- ing,University of Wisconsin, for his thorough review of the earlier manuscripts. Copyright © 2003 Marcel Dekker, Inc. We also express our appreciation to Professor Emeritus Donald McLean of the Univ ersity of Southampton, England, formerly a visiting profes sor at the Air Force Institute of Technology. Our association wi th him has been an enlightening and refreshing experience. The personal relationship with him has been a source of inspiration and deep respect. John J. D’Azzo Constantine H. Houpis Stuart N. She ldon Copyright © 2003 Marcel Dekker, Inc. [...]... position,velocity, and acceleration may represent the state variables of a position control system The definition of state variables and their use in representing systems are contained in Chaps 2, 3, and 5 The use of state-variable methods for the design of control systems is presented in Chaps 13 and 14 The design methods presented in Chaps 7 to 16 require knowledge of a fixed mathematical model of the system. .. simulations demonstrated the viability of a QFT design approach in producing flight-worthy aircraft control systems It illustrated the benefits of designing flight control systems with the QFT robust control system design technique in contrast to the brute force approach of optimizing a flight control system for performance in expected configurations and then scheduling the gains 1.3 DEFINITIONS From... also be assigned to this definition of the word system Thus, the study of feedback control systems is essentially a study of an important aspect of systems engineering and its application Command input.The motivating input signal to the system, which is independent of the output of the system and exercises complete control over it (if the system is completely controllable) Reference selector (reference... the system In another form of discontinuous control system the actuating signal must reach a prescribed value before the system dynamics reacts to it; i.e., the control action is discontinuous in amplitude rather than in time This type of discontinuous control system is commonly called an on-off or relay feedback control system Both forms may be present in a system In this text continuous control systems... readily to a basic understanding of feedback control systems The fundamentals of sampled-data (S-D) control systems are given in Chap 15 Digital control systems are introduced in Chap 16 With the above introductory material, it is proper to state a definition [1] of a feedback control system: ‘‘A control system that operates to achieve prescribed relationships between selected system variables by comparing... slave) and mechanism Black’s important paper on feedback amplifiers appeared [15] in the same year After World War II, control theory was studied intensively and applications have proliferated Many books and thousands of articles and technical papers have been written, and the application of control systems in the industrial and military fields has been extensive This rapid growth of feedback control systems... form of discontinuous control the input and output quantities are periodically sampled and discontinuous Continuous control implies that the output is continuously fed back and compared with the reference input compared; i.e., the control action is discontinuous in time This is commonly called a digital, discrete-data or sampled-data feedback control system A discretedata control system may incorporate... Error Analysis for Stable Systems 15.11 Root-Locus Analysis for Sampled-Data Control Systems 15.12 Summary 16 Digital Control Systems 16.1 Introduction 16.2 Complementary Spectra 16.3 Tustin Transformation: s to z Plane Transformation 16.4 z-Domain to the w- and w0-Domain Transformations 16.5 Digitization (DIG) Technique 16.6 Digitization (DIG) Design Technique 16.7 The Pseudo-Continuous-Time (PCT) Control. .. the twentieth century, which was accelerated by the advent of computers and control systems, has resulted in tremendous advances in the field of science Thus, automatic control systems and computers permeate life in all advanced societies today These systems and computers have acted and are acting as catalysts in promoting progress and development, propelling society into the twenty-first century Technological... implementation Design methods for analog SISO control systems shown in Fig 1.3 are covered in Chaps 6 to 16 Some systems require a precision in their performance that cannot be achieved by the structure of Fig 1.3 Also, systems exist for which there are multiple inputs and/ or multiple outputs They are discussed in References 3 and 8 The design methods for such systems are often based on a representation of the system . LINEAR CONTROL SYSTEM ANALYSIS AND DESIGN WITH MATLAE Fifth Edition, Revised and Expanded John J. D’Azzo and Constantine H. Houpis Air Force. 2003 Marcel Dekker, Inc. 14. Linear Control System Analysis and Design with MATLAB: Fifth Edition, Revised and Expanded, John J. D’Azzo, Consfanfine H. Houpis, and Sfuatt N. Sheldon Additional. Inc. ThefourtheditionwaspublishedasLinearControlSystemAnalysisandDesign: ConventionalandModern,byJohnJ.D’AzzoandConstantineH.Houpis(McGraw-Hill, 1995). Althoughgreatcarehasbeentakentoprovideaccurateandcurrentinformation,neither theauthor(s)northepublisher,noranyoneelseassociatedwiththispublication,shallbe liableforanyloss,damage,orliabilitydirectlyorindirectlycausedorallegedtobecaused bythisbook.Thematerialcontainedhereinisnotintendedtoprovidespecificadviceor recommendationsforanyspecificsituation. Trademarknotice:Productorcorporatenamesmaybetrademarksorregisteredtrade- marksandareusedonlyforidentificationandexplanationwithoutintenttoinfringe. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress. ISBN:0-8247-4038-6 Thisbookisprintedonacid-freepaper. Headquarters MarcelDekker,Inc.,270MadisonAvenue,NewYork,NY10016,U.S.A. tel:212-696-9000;fax:212-685-4540 DistributionandCustomerService MarcelDekker,Inc.,CimarronRoad,Monticello,NewYork12701,U.S.A. tel:800-228-1160;fax:845-796-1772 EasternHemisphereDistribution MarcelDekkerAG,Hutgasse4,Postfach812,CH-4001Basel,Switzerland tel:41-61-260-6300;fax:41-61-260-6333 WorldWideWeb http://www.dekker.com The