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.
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
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.
, 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.
c 2008 by Prentice-Hall, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without
permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing this book. These
efforts include the development, research, and testing of the theories and 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 LATEX 2ε .
MATLAB is a registered trademark of The MathWorks, Inc.
24 Prime Park Way, Natick, MA 01760-1520.
Phone. (508) 653-1415, Fax: (508) 653-2997
Email:
LabVIEW MathScript is a registered trademark of the National Instruments Corporation
11500 N Mopac Expwy, Austin, TX 78759-3504
Phone. (800) 531-5066, Fax: (512) 683-8411
E-mail:
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
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.
, 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.
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 from 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 with 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
iii
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.
, 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.
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 System Characteristics . . . . . . . . . . . . . . . . . . . . . . . 126
5. The Performance of Feedback Control Systems . . . . . . . . . . . . . . . . . 166
6. The Stability of Linear Feedback Systems . . . . . . . . . . . . . . . . . . . . . . 216
7. The Root Locus Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
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.
ISBN-13: 9780132270298. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.
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
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.
, 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.
c 2008 by Prentice-Hall, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without
permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing this book. These
efforts include the development, research, and testing of the theories and 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 LATEX 2ε .
MATLAB is a registered trademark of The MathWorks, Inc.
24 Prime Park Way, Natick, MA 01760-1520.
Phone. (508) 653-1415, Fax: (508) 653-2997
Email:
LabVIEW MathScript is a registered trademark of the National Instruments Corporation
11500 N Mopac Expwy, Austin, TX 78759-3504
Phone. (800) 531-5066, Fax: (512) 683-8411
E-mail:
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
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.
, 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.
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 from 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 with 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
iii
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.
, 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.
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 System Characteristics . . . . . . . . . . . . . . . . . . . . . . . 126
5. The Performance of Feedback Control Systems . . . . . . . . . . . . . . . . . 166
6. The Stability of Linear Feedback Systems . . . . . . . . . . . . . . . . . . . . . . 216
7. The Root Locus Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
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.
