MODERN CONTROL SYSTEMS

1 MODERN CONTROL SYSTEMSSOLUTION MANUALR ichard C. DorfRobert H. BishopUniversity of California, DavisMarquette UniversityA companion toMODERNCONTROLSYSTEMSTWELFTHEDITIONR ichard C. DorfRobert H. BishopPrentice HallUpper Saddle River Boston Columbus San Francisco New YorkIndianapolis London Toronto Sydney Singapore Tokyo Montreal DubaiMadrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

2 For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 's Solutions ManualRichard C. Dorf, University of California, DavisRobert H. Bishop, University of Texas at AustinISBN-10: 013602498 XISBN-13: 9780136024989 Publisher: Prentice HallCopyright: 2011 Format: On-line SupplementPublished: 08/16/2010 Educator Home | eLearning & Assessment | Support/Contact Us | Find your rep | Exam copy bookbag 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

3 For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ MODERN CONTROL SYSTEMS , 12/EP R E F A C EIn each chapter, there are five problem types:ExercisesProblemsAdvanced ProblemsDesign Problems/Continuous Design ProblemComputer ProblemsIntotal, there are over 1000 problems. The abundance of problems of in-creasing complexity gives students confidence in their problem-solvingability as they work their way from the exercises to the design andcomputer-based is assumed that instructors (and students) have access to MATLABand the CONTROL System Toolbox or to LabVIEW and the MathScript RTModule.

4 All of the computer solutions in thisSolution Manualwere devel-oped and tested on an Apple MacBook Pro platform using 2008a and the CONTROL System Toolbox Version and LabVIEW2009. It is not possible to verify each solution on all the available computerplatforms that are compatible with MATLABand LabVIEW MathScriptRT Module. Please forward any incompatibilities you encounter with thescripts to Prof. Bishop at the email address given authors and the staff at Prentice Hall would like to establish anopen line of communication with the instructors usingModern ControlSystems. We encourage you to contact Prentice Hall with comments andsuggestions for this and future H.

5 Bishop 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ A B L E - O F - C O N T E N T S1. Introduction to CONTROL SYSTEMS .. 12. Mathematical Models of SYSTEMS .

6 223. State Variable Models .. 854. Feedback CONTROL System Characteristics .. 1335. The Performance of Feedback CONTROL SYSTEMS .. 1776. The Stability of Linear Feedback SYSTEMS .. 2347. The Root Locus Method .. 2778. Frequency Response Methods .. 3829. Stability in the Frequency Domain .. 44510. The Design of Feedback CONTROL SYSTEMS ..51911. The Design of State Variable Feedback SYSTEMS .. 60012. Robust CONTROL SYSTEMS .. 65913. Digital CONTROL SYSTEMS ..714iv 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

7 For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ H A P T E R 1 Introduction to CONTROL SystemsThere are, in general, no unique solutions to the following exercises andproblems. Other equally valid block diagrams may be submitted by microprocessor controlled laser system:ControllerErrorCurrent i(t)PoweroutDesiredpoweroutputMeasuredpo wer-LaserProcess driver controlled cruise CONTROL system:DesiredspeedFootpedalActualautosp eedVisual indicationof speedController-ProcessMeasurementDriver Car the principle of conservation of momentum explains much ofthe process of fly-casting, there does not exist a comprehensive scientificexplanation of how a fly-fisher uses the small backward and forward mo-tion of the fly rod to cast an almost weightless fly lure long distances (the1 2011 Pearson Education, Inc.)

8 , Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 1 Introduction to CONTROL Systemscurrent world-record is 236 ft). The fly lure is attached to a short invisibleleader about 15-ft long, which is in turn attached to a longer and thickerDacron line.

9 The objective is cast the fly lure to a distant spot with dead-eye accuracy so that the thicker part of the line touches the water firstand then the fly gently settles on the water just as an insect ofthe !yActualpositionof the !yVisual indicationof the position of the !yFly-"sherWind disturbanceController-ProcessMeasurement Mind and body of the!y-"sher Rod, line,and castVision of the !y-" autofocus camera CONTROL system:One-way trip time for the beamDistance to subjectLens focusingmotorK 1 LensConversion factor(speed of light or sound)Emitter/ReceiverBeamBeam returnSubject 2011 Pearson Education, Inc.

10 , Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ a sailboat as the wind shifts:DesiredsailboatdirectionActualsai lboatdirectionMeasured sailboat directionWindError-ProcessMeasurementAct uatorsControllerSailboatGyro compassRudder andsail automated highway CONTROL system merging two lanes of traffic:DesiredgapActualgapMeasured gapError-ProcessMeasurementActuatorsCont rollerActivevehicleBrakes, gas the speedometer, the driver calculates the difference between themeasured speed and the desired speed.