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MODERN CONTROL SYSTEMS
SOLUTION MANUAL
Richard C. Dorf Robert H. Bishop
University of California, Davis The University of Texas at Austin
A companion to
MODERN CONTROL SYSTEMS
ELEVENTH EDITION
Richard C. Dorf
Robert H. Bishop
Prentice Hall
Upper Saddle River, NJ 07458
Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. Bishop.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material 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 07458.
c
2008 by Prentice-Hall, Inc .
Upper Saddle River, New Jersey 0745 8
All rights reserved. No part of this book may be reproduced, in any form o r by any means, without
permission in writing from the publisher.
The author and publisher of this book have used their b e st efforts in preparing this book. These
efforts include the development, research, and testing of the theories a nd programs to determine their
effectiveness. The author and publisher shall not be liable in any event for incidental or consequential
damages in connection with, or arising out of the furnishing, performance, or use of these programs.
Camera-ready copy for this manual was prepared by the author using L
A
T
E
X 2
ε
.
MATLAB is a registered trademark of The MathWorks, Inc.
24 Prime Park Way, Natick, MA 0 1760-1520.
Phone. (508) 653-1415, Fax: (508) 653- 2997
Email: info@mathwor k.com
LabVIEW MathScript is a registered trademark of the National Instruments Corporation
11500 N Mopa c Expwy, Austin, TX 78759-35 04
Phone. (800) 531-5066, Fax: (512) 683- 8411
E-mail: info@ni.com
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
ISBN 0-13-227029-3
Pearson Education Limited (UK)
Pearson Education Australia Pty Ltd
Prentice Hall Canada Ltd
Pearson Educacion de Mexico, S.A. de C.V.
Pearson Education Japan KK
Pearson Education China Ltd
Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. Bishop.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material 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 07458.
P R E F A C E
In each chapter, there are five problem types:
Exercises
Problems
Advanced Problems
Design Problems/Continuous Design Problem
Computer Problems
In total, there are over 850 problems. The abundance of problems of in-
creasing complexity gives students confidence in their problem-solving
ability as they work their way f rom the exercises to the design and
computer-based problems.
It is assumed that instructors (and students) have access to MATLAB,
the Control System Toolbox or the LabVIEW and MathScript. All of the
comptuer solutions in this Solution Manual were developed and tested on
a Window XP platform using MATLAB 7.3 Release 2006b and the Control
System Toolbox Version 7.1 and LabVIEW 8.2. It is not possible to verify
each solution on all the available computer platforms that are compatible
with MATLAB and LabVIEW MathScript. Please forward any incompati-
bilities you encounter with the scripts to Prof. Bishop at the email address
given below.
The authors and the staff at Prentice Hall would like to establish an
open line of communication w ith the instructors using Modern Control
Systems. We encourage you to contact Prentice Hall with comments and
suggestions for this and future editions.
Robert H. Bishop rhbishop@mail.utexas.edu
iii
Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. Bishop.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material 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 07458.
T A B L E - O F - C O N T E N T S
1. Introduction to Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Mathematical Models of Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3. State Variable Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4. Feedback Control Sys tem Characteristics . . . . . . . . . . . . . . . . . . . . . . . 126
5. The Performance of Feedback Control Systems . . . . . . . . . . . . . . . . . 166
6. The Stability of Linear Feedback Systems . . . . . . . . . . . . . . . . . . . . . . 216
7. The Root Locus Metho d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
8. Frequency Response Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
9. Stability in the Frequency Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
10. The Design of Feedback Control Systems . . . . . . . . . . . . . . . . . . . . . . . 492
11. The Design of State Variable Feedback Systems . . . . . . . . . . . . . . . . 574
12. Robust Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
13. Digital Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691
iv
Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. Bishop.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material 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 07458.
C H A P T E R 1
Introduction to Control Systems
There are, in general, no un ique solutions to the following exercises and
problems. Other equally valid block diagrams may be submitted by the
student.
Exercises
E1.1 A microprocessor controlled laser system:
Controller
Error
Current i(t)
Power
out
Desired
power
output
Measured
power
-
Laser
Process
processor
Micro-
Power
Sensor
Measurement
E1.2 A driver controlled cruise control system:
Desired
speed
Foot pedal
Actual
auto
speed
Visual indication
of speed
Controller
-
Process
Measurement
Driver
Car and
Engine
Speedometer
E1.3 Although the principle of conservation of momentum explains much of
the process of fly-casting, there does not exist a comprehensive scientific
explanation of how a fly-fisher uses the small backwar d and forward mo-
tion of the fly rod to cast an almost weightless fly lure long distances (the
1
Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. Bishop.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
This material 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 07458.
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