# CONTROL SYSTEMS ENGINEERING - wiley.com · PDF fileBlock Diagram Parameters V n K K a R J D K...

### Transcript of CONTROL SYSTEMS ENGINEERING - wiley.com · PDF fileBlock Diagram Parameters V n K K a R J D K...

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Calif rnia State P lytechnic University,P m na

Fourth Edition

JOHN WILEY & SONS, INC.

Norman S. Nise

CONTROLSYSTEMSENGINEERING

Motor

i(t)

Desiredazimuth angle

input

Differential amplifierand power amplifier

Potentiometer

θ

Potentiometer

θo(t)Azimuth

angleoutput

θ

Antenna

JL kg-m2

Ja kg-m2

Da N-m s/radKb V-s/radKt N-m/A

n-turn potentiometer

Azimuth angleoutput

o(t)θ

DL N-m-s/rad

vi(t)vo(t) K

K1s + a

+

–

vp(t) ea(t)Ra

MotorFixedfield–V

+V

θm(t)θ

Poweramplifier

Differentialpreamplifier

Desiredazimuth angle

inputθi(t)θ

n-turn potentiometer

Armature

+V

–V

N1Gear

N2Gear

N3Gear

Layout

Schematic

Antenna Azimuth Position Control System

–

+θi(s) Vi(s) Ve(s) Vp(s) Ea(s) θm(s)

Potentiometer PreamplifierPower

amplifierMotor

and load Gears

Kpot KK1 Km Kg

Kpot

Potentiometer

Desiredazimuth

angleAzimuth

angle

θo(s)

s + a s(s + am)

θ θ θ

Parameter Configuration 1 Configuration 2 Configuration 3

Parameter Configuration 1 Configuration 2 Configuration 3

1

1

2

3

pot

1

10 10 1010 1 1— — —

100 150 100100 150 100

8 5 50.02 0.05 0.050.01 0.01 0.010.5 1 10.5 1 125 50 50

250 250 250250 250 250

1 5 51 3 3

0.318

—

100

100

2.083

1.71

0.1

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N te: reader may fill in C nfigurati n 2 and C nfigurati n 3 c lumns after c m-pleting the antenna c ntr l Case Study challenge pr glems in Chapters 2 and 10,respectively.

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Block Diagram

Schematic Parameters

Block Diagram Parameters

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Library of Congress Cataloging-in-Publication Data:

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EXECUTIVE EDITOR Bill Z brist

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Nise, N rman S.C ntr l Systems Engineering/N rman S. Nise.—4 ed.

Includes bibli graphical references.1. Aut matic c ntr l. 2. Systems engineering. I. Title.

TJ213 .N497 2004 629.8-dc21ISBN 0-471-44577-0WIE ISBN 0-471-45243-2

Printed in the United States f America

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To my wife, Ellen;sons, Benjamin and Alan;daughter, Sharon;and to the memory ofmy mother-in-love,Bobby Manashil,whose love of reading hasbeen an inspiration.

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Examples, Skill-Assessment Exercises, Case Studies

Cyber Exploration Laboratory

Control Systems Engineering

Key Features

Preface

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This b k intr duces students t the the ry and practice f c ntr l systemsengineering. The text emphasizes the practical applicati n f the subject t theanalysis and design f feedback systems.

The study f c ntr l systems engineering is essential f r students pursuingdegrees in electrical, mechanical, aer space, r chemical engineering. C ntr lsystems are f und in a br ad range f applicati ns within these disciplines, fr maircraft and spacecraft t r b ts and pr cess c ntr l systems.

is suitable f r upper-divisi n c llege and uni-versity engineering students and f r th se wh wish t master the subject matterthr ugh self-study. The student using this text sh uld have c mpleted typical l wer-divisi n c urses in physics and mathematics thr ugh differential equati ns. Otherrequired backgr und material, including Laplace transf rms and linear algebra, isinc rp rated in the text, either within chapter discussi ns r separately in the ap-pendixes r n an acc mpanying CD-ROM. This review material can be mittedwith ut l ss f c ntinuity if the student d es n t require it.

The key features f this f urth editi n are

Standardized chapter rganizati n

Qualitative and quantitative explanati ns

and thr ugh ut the text

C ntr l S luti ns P wered by JustAsk!

experiments

Abundant illustrati ns

Numer us end- f-chapter pr blems

Emphasis n design

Flexible c verage

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Preface vii

Standardized Chapter Organization

Qualitative and Quantitative Explanations

Examples, Skill-Assessment Exercises, and Case Studies

Examples Skill-Assessment Exercises

Case Studies

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Emphasis n c mputer-aided analysis and design

Ic ns identifying maj r t pics

CD-ROM c ntaining additi nal material

Let us l k at each feature in m re detail.

Each chapter begins with a list f chapter bjectives, f ll wed by a list f casestudy bjectives that relate the chapter bjectives t specific student perf rmancein s lving a practical case study pr blem, such as an antenna azimuth p siti nc ntr l system.

T pics are then divided int clearly numbered and labeled secti ns c ntainingexplanati ns, examples, and, where appr priate, skill-assessment exercises withanswers. These numbered secti ns are f ll wed by ne r m re case studies, as willbe utlined in a few paragraphs. Each chapter ends with a brief summary, severalreview questi ns requiring sh rt answers, and a set f h mew rk pr blems.

Explanati ns are clear and c mplete and, where appr priate, include a brief reviewf required backgr und material. T pics build up n and supp rt ne an ther in a

l gical fashi n. Gr undw rk f r new c ncepts and termin l gy is carefully laid tav id verwhelming the student and t facilitate self-study.

Alth ugh quantitative s luti ns are bvi usly imp rtant, a qualitative r intu-itive understanding f pr blems and meth ds f s luti n is vital t pr ducing theinsight required t devel p s und designs. Theref re, whenever p ssible, new c n-cepts are discussed fr m a qualitative perspective bef re quantitative analysis anddesign are addressed. F r example, in Chapter 8 the student can simply l k atthe r t l cus and describe qualitatively the changes in transient resp nse that willccur as a system parameter, such as gain, is varied. This ability is devel ped with

the help f a few simple equati ns fr m Chapter 4.

Explanati ns are clearly illustrated by means f numer us numbered and labeledthr ugh ut the text. Where appr priate, a secti n c ncludes with

. These are c mputati n drills, m st with answers, that testc mprehensi n and pr vide immediate feedback. C mplete s luti ns can be f undn the acc mpanying CD-ROM.

Br ader examples in the f rm f can be f und after the last num-bered secti n f every chapter, with the excepti n f Chapter 1. These case studiesare practical applicati n pr blems that dem nstrate the c ncepts intr duced in thechapter. Each case study c ncludes with a “Challenge” pr blem that students mayw rk in rder t test their understanding f the material.

One f the case studies, c ncerning an antenna azimuth p siti n c ntr l system,is carried thr ugh ut the b k. The purp se is t illustrate the applicati n f newmaterial in each chapter t the same physical system, thus highlighting the c ntinuityf thedesignpr cess.An ther,m rechallengingcase study, inv lvinganUnmanned

Free-Swimming Submersible Vehicle, is devel ped ver the c urse f five chapters.

DesignDesign

Prefaceviii

Control Solutions Powered by JustAsk!

Cyber Exploration Laboratory Experiments

Cyber Exploration Laboratory

Abundant Illustrations

Numerous End-of-Chapter Problems

Emphasis on Design

Design ProblemsProgressive Analysis and

The Control SolutionsCompanion

The Control Solutions Companion

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C ntr l S luti ns is a Web site that is essentially a tut r serving the needs f b ththe student and the pr fess r. A t tal f ver 150 end- f-chapter pr blems andSkill-Assessment Exercises fr m the b k will have step-by-step s luti ns. Thesepr blems are w rked in detail and explanati ns f every facet f the s luti ns arepr vided. As such, this Web site is a valuable t l in the use f this b k. This siteis passw rd pr tected and can be accessed by purchasing

, ISBN 0471483885. This c mpani n supplies y u with an access c det the C ntr l S luti ns Web site as well as instructi ns n h w t use the Web site.

can be purchased n the b k c mpani n Website, www.wiley.c m/c llege/nise.

C mputer experiments using MATLAB, Simulink, and the C ntr l System T l-b x are f und at the end f the Pr blems secti n f Chapters 4 thr ugh 13 under thesubheading . The experiments all w the readert verify the c ncepts c vered in the chapter via simulati n. The reader als canchange parameters and perf rm ”what if” expl rati n t gain insight int the effectf parameter and c nfigurati n changes. The experiments are written with stated

Objectives, Minimum required s ftware packages, as well as Prelab, Lab, and P st-lab tasks and questi ns. Thus, the experiments may be used f r a lab rat ry c ursethat acc mpanies the class.

The ability t visualize c ncepts and pr cesses is critical t the student’s under-standing. F r this reas n appr ximately 750 ph t s, diagrams, graphs, and tablesappear thr ugh ut the b k t illustrate the t pics under discussi n.

Each chapter ends with a variety f h mew rk pr blems that all w students ttest their understanding f the material presented in the chapter. Pr blems varyin degree f difficulty and c mplexity, and m st chapters include several practical,real-life pr blems t help maintain students’ m tivati n. Als , the h mew rk pr b-lems c ntain a pr gressive analysis and design pr blem that uses the same practicalsystem t dem nstrate the c ncepts f each chapter.

This textb k places a heavy emphasis n design. Chapters 8, 9, 11, 12, and 13f cus primarily n design. But even in chapters that emphasize analysis, simpledesign examples are included wherever p ssible.

Thr ugh ut the b k, design examples inv lving physical systems are identi-fied by a ic n. End- f-chapter pr blems that inv lve the designf physical systems are included under the separate heading and

als , in chapters c vering design, under the heading

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Preface ix

Design Problem

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. In these examples and pr blems, a desired resp nse is specified,and the student must evaluate certain system parameters, such as gain, r specifya system c nfigurati n al ng with parameter values. In additi n, the text includesnumer us design examples and pr blems (n t identified by an ic n) that inv lvepurely mathematical systems.

Because visualizati n is s vital t understanding design, this text carefullyrelates indirect design specificati ns t m re familiar nes. F r example, the lessfamiliar and indirect phase margin is carefully related t the m re direct and famil-iar percent versh t bef re being used as a design specificati n.

F r each general type f design pr blem intr duced in the text, a meth d l gyf r s lving the pr blem is presented—in many cases in the f rm f a step-by-steppr cedure, beginning with a statement f design bjectives. Example pr blemsserve t dem nstrate the meth d l gy by f ll wing the pr cedure, making simpli-fying assumpti ns, and presenting the results f the design in tables r pl ts thatc mpare the perf rmance f the riginal system t that f the impr ved system.This c mparis n als serves as a check n the simplifying assumpti ns.

Transient resp nse design t pics are c vered c mprehensively in the text. Theyinclude

Design via gain adjustment using the r t l cus

Design f c mpensati n and c ntr llers via the r t l cus

Design via gain adjustment using sinus idal frequency resp nse meth ds

Design f c mpensati n via sinus idal frequency resp nse meth ds

Design f c ntr llers in state space using p le-placement techniques

Design f bservers in state space using p le-placement techniques

Design f digital c ntr l systems via gain adjustment n the r t l cus

Design f digital c ntr l system c mpensati n via -plane design and the Tustintransf rmati n

Steady-state err r design is c vered c mprehensively in this textb k andincludes

Gain adjustment

Design f c mpensati n via the r t l cus

Design f c mpensati n via sinus idal frequency resp nse meth ds

Design f integral c ntr l in state space

Finally, the design f gain t yield stability is c vered fr m the f ll wingperspectives:

R uth-Hurwitz criteri n

R t l cus

Nyquist criteri n

B de pl ts

State SpaceState Space

State SpaceState Space

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Prefacex

1

Flexible Coverage

Emphasis on Computer-Aided Analysis and Design

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The material in this b k can be adapted f r a ne-quarter r a ne-semester c urse.The rganizati n is flexible, all wing the instruct r t select the material that bestsuits the requirements and time c nstraints f the class.

Thr ugh ut the b k state-space meth ds are presented al ng with the classi-cal appr ach. Chapters and secti ns (as well as examples, exercises, review ques-ti ns, and pr blems) that c ver state space are marked by aic n and can be mitted with ut any l ss f c ntinuity. Th se wishing t add abasic intr ducti n t state-space m deling can include Chapter 3 in the syllabus.

In a ne-semester c urse, the discussi ns f state-space analysis in Chapters 4,5, 6, and 7, as well as state-space design in Chapter 12, can be c vered al ng withthe classical appr ach. An ther pti n is t teach state space separately by gather-ing the appr priate chapters and secti ns marked with the ic nint a single unit that f ll ws the classical appr ach. In a ne-quarter c urse, Chap-ter 13, “Digital C ntr l Systems,” c uld be eliminated.

C ntr l systems pr blems, particularly analysis and design pr blems using the r tl cus, can be tedi us, since their s luti n inv lves trial and err r. T s lve thesepr blems, students sh uld be given access t c mputers r pr grammable calcu-lat rs c nfigured with appr priate s ftware. In this f urth editi n, MATLABc ntinues t be integrated int the text as an pti nal feature.

Many pr blems in this text can be s lved with either a c mputer r a hand-held, pr grammable calculat r. F r example, students can use the pr grammablecalculat r t (1) determine whether a p int n the -plane is als n the r t l -cus, (2) find magnitude and phase frequency resp nse data f r Nyquist and B dediagrams, and (3) c nvert between the f ll wing representati ns f a sec nd- rdersystem:

P le l cati n in p lar c rdinates

P le l cati n in Cartesian c rdinates

Characteristic p lyn mial

Natural frequency and damping rati

Settling time and percent versh t

Peak time and percent versh t

Settling time and peak time

Handheld calculat rs have the advantage f easy accessibility f r h mew rk andexams. Please c nsult Appendix G, l cated n the encl sed CD-ROM, f r a dis-cussi n f c mputati nal aids that can be adapted t handheld calculat rs.

Pers nal c mputers are better suited f r m re c mputati n-intensive applica-ti ns, such as pl tting time resp nses, r t l ci, and frequency resp nse curves,as well as finding state-transiti n matrices. These c mputers als give the student

Simulink

MATLAB

Symbolic Math

State Space

GUI Tool

Preface xi

Icons Identifying Major Topics

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a real-w rld envir nment in which t analyze and design c ntr l systems. Th sen t using MATLAB can write their wn pr grams r use ther pr grams, such asPr gram CC. Please c nsult Appendix G, n the acc mpanying CD-ROM, f r adiscussi n f c mputati nal aids that can be adapted f r use n c mputers that dn t have MATLAB installed.

With ut access t c mputers r pr grammable calculat rs, students cann tbtain meaningful analysis and design results and the learning experience will

be limited.

Several ic ns identify c verage and pti nal material. The ic ns are summarizedas f ll ws:

The C ntr l S luti ns ic n identifies pr blems included n the C ntr l S -luti ns Web site p wered by JustAsk! These pr blems are w rked in detail andexplanati ns f every facet f the s luti n are pr vided.

The MATLAB ic n identifies MATLAB discussi ns, examples, exercises, andpr blems. MATLAB c verage is pr vided as an enhancement and is n t requiredt use the text.

The Simulink ic n identifies Simulink discussi ns, examples, exercises, andpr blems. Simulink c verage is pr vided as an enhancement and is n t required tuse the text.

The GUI T l ic n identifies MATLAB GUI T ls discussi ns, examples, ex-ercises, and pr blems. The discussi n f the t ls, which includes the LTI Viewer,the Simulink LTI Viewer, and the SISO Design T l, is pr vided as an enhance-ment and is n t required t use the text.

The Symb lic Math ic n identifies Symb lic Math T lb x discussi ns,examples, exercises, and pr blems. Symb lic Math T lb x c verage is pr videdas an enhancement and is n t required t use the text.

The State Space ic n highlights state-space discussi ns, examples, exercises,and pr blems. State-space material is pti nal and can be mitted with ut l ss fc ntinuity.

Design

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Prefacexii

1 2

3

Control Solutions

CD-ROM Containing Additional Material

End-of-chapter problems

Control Solutions

MATLAB

MATLAB’s Simulink?

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P werP int is a registered trademark f Micr s ft C rp rati n.

Acr bat is a registered trademark f Ad be Systems Inc rp rated.

Simulink is a registered trademark f The MathW rks, Inc

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The Design ic n clearly identifies design pr blems inv lving physical systems.

C ntr l S luti ns p wered by JustAsk! is a Web site that c n-tains step-by-step s luti ns t ver 150 end- f-chapter pr blems. Details are de-scribed under Key Features earlier in this Preface.

A CD-ROM disk acc mpanies the textb k. The disk c ntains the f ll wing:

P werP int and Acr bat files c ntaining m st figures fr m the textb k.The files may be used as a c nvenient meth d t pr ject graphics n a screent enhance lectures.

S luti ns t skill-assessment exercises

All M-files used in the MATLAB, Simulink, GUI T ls, and Symb lic MathT lb x tut rials

Additi nal c mputer pr grams that can be used by readers with ut access tMATLAB

C pies f Cyber Expl rati n Lab rat ry experiments f r c nvenience in print-ing, f r the purp se f including the experiment questi ns and tasks as a c versheet f r the lab rep rts

Additi nal appendixes; t pics in Table f C ntents

A link t the JustAsk! Website

The f ll wing list describes the key changes in this f urth editi n.

There is at least a 10% change in the pr blems at theend f the chapters.

C ntr l S luti ns p wered by JustAsk! is a Web site that c n-tains step-by-step s luti ns t ver 150 end- f-chapter pr blems. Details are de-scribed under Key Features earlier in this Preface.

The use f MATLAB f r c mputer-aided analysis and design c n-tinues t be integrated int discussi ns and pr blems as an pti nal feature in thef urth editi n. The MATLAB tut rial has been updated t MATLAB Versi n 6.5 theC ntr l System T lb x Versi n 5.2, and the Symb lic Math T lb x Versi n 3.0.

The use f Simulink t sh w the effects f n nlineari-ties up n the time resp nse f pen-l p and cl sed-l p systems appears again in

Preface xiii

MATLAB’s GUI Tools

Cyber Exploration Laboratory

Topics moved to CD-ROM

Book Organization by Chapter

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this f urth editi n. We als c ntinue t use Simulink t dem nstrate h w t sim-ulate digital systems. In additi n, Simulink has been added t the new subsecti ndescribed bel w—the Cyber Expl rati n Lab rat ry. Finally, the Simulink tut rialhas been updated t Simulink 5.

The MATLAB’s GUI T ls tut rial has been updated tinclude new and revised versi ns f the LTI Viewer, the Simulink LTI Viewer, andthe SISO Design T l, which replaces the R t L cus Design GUI.

New t this editi n are c mputer experimentsusing MATLAB, Simulink, and the C ntr l System T lb x. These experimentsare f und at the end f the Pr blems secti n f Chapters 4 thr ugh 13 under thesubheading, “Cyber Expl rati n Lab rat ry.” The experiments may be used f r alab rat ry c urse that acc mpanies the class. C pies f these experiments can bef und n the acc mpanying CD-ROM and can be printed f r c nvenience.

Derivati ns in Chapters 4 and 5 were m ved t theacc mpanying CD-ROM. In particular, the derivati n f the time d main s luti nf state equati ns, in Secti n 4.11, in the third editi n, n w ccupies Appendix In the acc mpanying CD-ROM. Als , the derivati n f similarity transf rmati ns,

previ usly in Secti n 5.8, is n w in Appendix K n the acc mpanying CD-ROM.Secti ns 4.11 and 5.8 still c ntain the results f the derivati ns as well as examples.Finally, the derivati n f a schematic f r a dc m t r, previ usly in Appendix F inthe third editi n, has been m ved t Appendix H n the acc mpanying CD-ROM.

Many times it is helpful t understand an auth r’s reas ning behind the rganiza-ti n f the c urse material. The f ll wing paragraphs h pefully shed light n thist pic.

The primary g al f Chapter 1 is t m tivate students. In this chapter studentslearn ab ut the many applicati ns f c ntr l systems in everyday life and ab utthe advantages f study and a career in this field. C ntr l systems engineeringdesign bjectives, such as transient resp nse, steady-state err r, and stability, areintr duced, as is the path t btaining these bjectives. New and unfamiliar termsals are included in the Gl ssary.

Many students have tr uble with an early step in the analysis and designsequence: transf rming a physical system int a schematic. This step requiresmany simplifying assumpti ns based n experience the typical c llege studentd es n t yet p ssess. Identifying s me f these assumpti ns in Chapter 1 helps tfill the experience gap.

Chapters 2, 3, and 5 address the representati n f physical systems. Chapters 2and 3 c ver m deling f pen-l p systems, using frequency resp nse techniquesand state-space techniques, respectively. Chapter 5 discusses the representati n andreducti n f systems f rmed f interc nnected pen-l p subsystems. Only a rep-resentative sample f physical systems can be c vered in a textb k f this length.Electrical, mechanical (b th translati nal and r tati nal), and electr mechanicalsystems are used as examples f physical systems that are m deled, analyzed, anddesigned. Linearizati n f a n nlinear system— ne technique used by the engineert simplify a system in rder t represent it mathematically—is als intr duced.

Prefacexiv

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Chapter 4 pr vides an intr ducti n t system analysis, that is, finding anddescribing the utput resp nse f a system. It may seem m re l gical t reversethe rder f Chapters 4 and 5, t present the material in Chapter 4 al ng withther chapters c vering analysis. H wever, many years f teaching c ntr l systems

have taught me that the s ner students see an applicati n f the study f systemrepresentati n, the higher their m tivati n levels remain.

Chapters 6, 7, 8, and 9 return t c ntr l systems analysis and design with thestudy f stability (Chapter 6), steady-state err rs (Chapter 7), and transient resp nsef higher- rder systems using r t l cus techniques (Chapter 8). Chapter 9 c vers

design f c mpensat rs and c ntr llers using the r t l cus.Chapters 10 and 11 f cus n sinus idal frequency analysis and design. Chap-

ter 10, like Chapter 8, c vers basic c ncepts f r stability, transient resp nse, andsteady-state err r analysis. H wever, Nyquist and B de meth ds are used in placef r t l cus. Chapter 11, like Chapter 9, c vers the design f c mpensat rs, but

fr m the p int f view f sinus idal frequency techniques rather than r t l cus.An intr ducti n t state-space design and digital c ntr l systems analysis and

design c mpletes the text in Chapters 12 and 13, respectively. Alth ugh these chap-ters can be used as an intr ducti n f r students wh will be c ntinuing their studyf c ntr l systems engineering, they are useful by themselves and as a supplement

t the discussi n f analysis and design in the previ us chapters. The subject mat-ter cann t be given a c mprehensive treatment in tw chapters, but the emphasisis clearly utlined and l gically linked t the rest f the b k.

The f ll wing materials c mprise the teaching package f r C ntr l Systems Engi-neering, f urth editi n. Be sure t peri dically check www.wiley.c m/c llege/nisef r up-t -date inf rmati n n this publicati n.

is a website that is essentially atut r serving the needs f b th the student and the pr fess r. A t tal f ver 150end- f-chapter pr blems and Skill Assessment Exercises c vering numer us t p-ics within the chapter will have step-by-step s luti ns. These pr blems are w rkedin detail, and explanati ns f every facet f the s luti n are pr vided. As such, thiswebsite is a valuable t l in the use f this b k. This site is passw rd-pr tectedsite but can be accessed by purchasing theISBN 0471483885. This c mpani n supplies y u with access c de t the C ntr lS luti ns website as well as instructi ns n h w t use the website.

can be purchased n the b k’s c mpani n website,www.wiley.c m/c llege/nise.

Key figures fr m the text are available as full-c l r electr nic graphics in Micr s ft’s P werP int. These files can be f und nthe acc mpanying CD-ROM and at www.wiley.c m/c llege/nise.

All MATLAB M-files and Simulinkfiles used in the appendixes f this textb k can be f und n the acc mpanying CD-ROM and at www.wiley.c m/c llege/nise.

by N rmanS. Nise, this manual c ntains detailed s luti ns t m st f the pr blems in the text.The S luti ns Manual is available nline nly t qualifying faculty.

Preface xv

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Acknowledgments

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The auth r w uld like t ackn wledge the c ntributi ns f faculty and students,b th at Calif rnia State P lytechnic University, P m na and acr ss the c untry,wh se suggesti ns thr ugh all editi ns have made a p sitive impact n the newediti n. I particularly want t thank the Electrical and C mputer Engineering De-partment and Kathleen Hayden, Chair, as well as the C llege f Engineering andEdward H hmann, Dean. Their supp rt and enc uragement was vital t the c m-pleti n f this v lume.

I w uld like t express my appreciati n t reviewers wh ffered valuable sug-gesti ns f r this 4 editi n. The reviewers include J hn G lzy, Devry University,C lumbus Ohi ; Frank Owen, Cal P ly University, San Luis Obisp ; and EliasStrangas, Michigan State University.

The auth r w uld like t thank J hn Wiley & S ns, Inc. and its staff f r nceagain pr viding pr fessi nal supp rt f r this pr ject thr ugh all phases f its de-vel pment. Specifically, the f ll wing are due rec gniti n f r their c ntributi ns:Bruce Spatz, Publisher, wh gave full executive supp rt and enc uragement t thewh le pr ject; Bill Z brist, Executive Edit r, wh pr vided a high level f pr -fessi nal guidance, as well as g d hum r, thr ugh ut the 3 and 4 editi ns;Heather Olszyk, Assistant Edit r, J van Yglecias, Pr gram Assistant, and Jen-nifer Welter, Ass ciate Edit r, wh pr vided excellent edit rial supp rt early inthe pr ject; Catherine Mergen, Assistant Edit r, wh c ntinued with the excellentlevel f supp rt and pr vided answers t my numer us questi ns; Ailsa Manny,Edit rial Assistant, wh did an excellent j b securing permissi ns assistance; andKatherine Hepburn, Seni r Marketing Manager, f r letting y u kn w f this b k’sexistence. I w uld als like t thank Patricia McFadden, Seni r Pr ducti n Edit r,wh saw the b k thr ugh all phases f pr ducti n; Harry N lan, Design Direc-t r, Karin Kinchel e, Seni r Designer, and Lisa Gee, Ph t Edit r wh guided theappearance f the final pr duct. My sincere appreciati n is als expressed t T mKulesa, New Media Edit r, f r his hard w rk and expertise in pr ducing the CD-ROM that acc mpanies this b k.

Finally, kud s g ut t Publicati n Services and its staff f r pr ducing the fi-nal versi n f the b k in a timely fashi n. Specifically, I want t thank Jan Fisher,Pr ject Manager, f r pr viding answers t my questi ns and s luti ns t my c n-cerns and Brand n M. Warga, Pr ducti n C rdinat r, f r putting the pieces fthis puzzle t gether. Finally, I want t express my appreciati n t Peter Nels n andAlysia C ley, C pyedit rs, wh se keen eyes and attenti n t details c ntinuallyamazed me.

N rman S. Nise

xvi

1.1 Introduction, 2

1.2 A History of Control Systems, 4

1.3 The Control Systems Engineer, 9

1.4 Response Characteristics and System Configurations, 10

1.5 Analysis and Design Objectives, 14

Introduction to a Case Study, 17

1.6 The Design Process, 21

1.7 Computer-Aided Design, 26Summary, 28Review Questions, 29Problems, 29Bibliography, 35

2.1 Introduction, 38

2.2 Laplace Transform Review, 39

2.3 The Transfer Function, 49

1

37

Contents

1. Introduction

2. Modeling in the Frequency Domain

Contents xvii

2.4 Electric Network Transfer Functions, 52

2.5 Translational Mechanical System Transfer Functions, 68

2.6 Rotational Mechanical System Transfer Functions, 76

2.7 Transfer Functions for Systems with Gears, 82

2.8 Electromechanical System Transfer Functions, 87

2.9 Electric Circuit Analogs, 94

2.10 Nonlinearities, 97

2.11 Linearization, 99

Case Studies, 105Summary, 109Review Questions, 109Problems, 110Bibliography, 125

3.1 Introduction, 128

3.2 Some Observations, 129

3.3 The General State-Space Representation, 133

3.4 Applying the State-Space Representation, 136

3.5 Converting a Transfer Function to State Space, 144

3.6 Converting from State Space to a Transfer Function, 151

3.7 Linearization, 154

Case Studies, 157Summary, 162Review Questions, 163Problems, 163Bibliography, 172

4.1 Introduction, 175

4.2 Poles, Zeros, and System Response, 175

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3. Modeling in the Time Domain

4. Time Response

Contentsxviii

4.3 First-Order Systems, 179

4.4 Second-Order Systems: Introduction, 182

4.5 The General Second-Order System, 188

4.6 Underdamped Second-Order Systems, 191

4.7 System Response with Additional Poles, 202

4.8 System Response with Zeros, 206

4.9 Effects of Nonlinearities upon Time Response, 212

4.10 Laplace Transform Solution of State Equations, 216

4.11 Time Domain Solution of State Equations, 219

Case Studies, 227Summary, 230Review Questions, 232Problems, 233Design Problems, 244Cyber Exploration Laboratory, 248Bibliography, 251

5.1 Introduction, 253

5.2 Block Diagrams, 253

5.3 Analysis and Design of Feedback Systems, 263

5.4 Signal-Flow Graphs, 266

5.5 Mason’s Rule, 269

5.6 Signal-Flow Graphs of State Equations, 272

5.7 Alternative Representations in State Space, 275

5.8 Similarity Transformations, 286

Case Studies, 293Summary, 299Review Questions, 300Problems, 301Design Problems, 318

2525. Reduction of Multiple Subsystems

Contents xix

Cyber Exploration Laboratory, 321Bibliography, 322

6.1 Introduction, 325

6.2 Routh-Hurwitz Criterion, 329

6.3 Routh-Hurwitz Criterion: Special Cases, 332

6.4 Routh-Hurwitz Criterion: Additional Examples, 340

6.5 Stability in State Space, 348

Case Studies, 351Summary, 353Review Questions, 354Problems, 354Design Problems, 362Cyber Exploration Laboratory, 365Bibliography, 366

7.1 Introduction, 369

7.2 Steady-State Error for Unity Feedback Systems, 373

7.3 Static Error Constants and System Type, 379

7.4 Steady-State Error Specifications, 384

7.5 Steady-State Error for Disturbances, 386

7.6 Steady-State Error for Nonunity Feedback Systems, 389

7.7 Sensitivity, 393

7.8 Steady-State Error for Systems in State Space, 396

Case Studies, 400Summary, 403Review Questions, 404Problems, 405Design Problems, 419Cyber Exploration Laboratory, 422Bibliography, 423

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6. Stability

7. Steady-State Errors

Contentsxx

8.1 Introduction, 425

8.2 Defining the Root Locus, 429

8.3 Properties of the Root Locus, 432

8.4 Sketching the Root Locus, 435

8.5 Refining the Sketch, 440

8.6 An Example, 451

8.7 Transient Response Design via Gain Adjustment, 454

8.8 Generalized Root Locus, 460

8.9 Root Locus for Positive-Feedback Systems, 461

8.10 Pole Sensitivity, 465

Case Studies, 467Summary, 472Review Questions, 473Problems, 474Design Problems, 489Cyber Exploration Laboratory, 496Bibliography, 497

9.1 Introduction, 500

9.2 Improving Steady-State Error via Cascade Compensation, 503

9.3 Improving Transient Response via Cascade Compensation, 514

9.4 Improving Steady-State Error and Transient Response, 531

9.5 Feedback Compensation, 547

9.6 Physical Realization of Compensation, 558

Case Studies, 564Summary, 570Review Questions, 571Problems, 572Design Problems, 582Cyber Exploration Laboratory, 588Bibliography, 589

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8. Root Locus Techniques

9. Design via Root Locus

Contents xxi

10.1 Introduction, 591

10.2 Asymptotic Approximations: Bode Plots, 598

10.3 Introduction to the Nyquist Criterion, 619

10.4 Sketching the Nyquist Diagram, 624

10.5 Stability via the Nyquist Diagram, 631

10.6 Gain Margin and Phase Margin via the Nyquist Diagram, 635

10.7 Stability, Gain Margin, and Phase Margin via Bode Plots, 638

10.8 Relation between Closed-Loop Transientand Closed-Loop Frequency Responses, 641

10.9 Relation between Closed- and Open-Loop Frequency Responses, 645

10.10 Relation between Closed-Loop Transientand Open-Loop Frequency Responses, 651

10.11 Steady-State Error Characteristics from Frequency Response, 655

10.12 Systems with Time Delay, 660

10.13 Obtaining Transfer Functions Experimentally, 665

Case Study, 670Summary, 672Review Questions, 673Problems, 674Cyber Exploration Laboratory, 687Bibliography, 688

11.1 Introduction, 691

11.2 Transient Response via Gain Adjustment, 692

11.3 Lag Compensation, 696

11.4 Lead Compensation, 700

11.5 Lag-Lead Compensation, 707

Case Studies, 713Summary, 715

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10. Frequency Response Techniques

11. Design via Frequency Response

Contentsxxii

Review Questions, 716Problems, 716Design Problems, 721Cyber Exploration Laboratory, 724Bibliography, 728

12.1 Introduction, 727

12.2 Controller Design, 728

12.3 Controllability, 735

12.4 Alternative Approaches to Controller Design, 740

12.5 Observer Design, 745

12.6 Observability, 753

12.7 Alternative Approaches to Observer Design, 757

12.8 Steady-State Error Design via Integral Control, 764

Case Study, 768Summary, 773Review Questions, 775Problems, 776Design Problems, 781Cyber Exploration Laboratory, 783Bibliography, 784

13.1 Introduction, 786

13.2 Modeling the Digital Computer, 790

13.3 The -Transform, 793

13.4 Transfer Functions, 799

13.5 Block Diagram Reduction, 802

13.6 Stability, 805

13.7 Steady-State Errors, 813

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12. Design via State Space

13. Digital Control Systems

Contents xxiii

13.8 Transient Response on the -Plane, 818

13.9 Gain Design on the -Plane, 820

13.10 Cascade Compensation via the -plane, 824

13.11 Implementing the Digital Compensator, 828

Case Studies, 831Summary, 836Review Questions, 837Problems, 838Design Problems, 844Cyber Exploration Laboratory, 845Bibliography, 847

G.1 Matrix Definitions and Notations

G.2 Matrix Operations

G.3 Matrix and Determinant Identities

G.4 Systems of Equations

Bibliography

G.1 Step Response of a System Represented in State Space

G.2 Root Locus and Frequency Response

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Appendix A List of Symbols

Appendix B MATLAB Tutorial

Appendix C MATLAB’s Simulink Tutorial

Appendix D MATLAB’s GUI Tools Tutorial

Appendix E MATLAB’s Symbolic Math Toolbox Tutorial

Glossary

Answers to Selected Problems

Credits

Index

Appendix F Matrices, Determinants, and Systems of Equations CD-ROM

Appendix G Control System Computational Aids CD-ROM

Contentsxxiv

L.1 Behavior of the Root Locus at Infinity

L.2 Derivation of Transition Method for Breakawayand Break-in Points

t 0 �

Appendix H Derivation of a Schematic for a DC Motor CD-ROM

Appendix I Derivation of the Time Domain Solution of State Equations CD-ROM

Appendix J Solution of State Equations for 0 CD-ROM

Appendix K Derivation of Similarity Transformations CD-ROM

Appendix L Root Locus Rules: Derivations CD-ROM

Solutions to Skill-Assessment Exercises CD-ROM

Control Systems Engineering Toolbox CD-ROM

Lecture Graphics CD-ROM

Cyber Exploration Laboratory Experiments CD-ROM