© 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 07458.
MODERN CONTROL SYSTEMS
SOLUTION MANUAL
Richard C. Dorf Robert H. Bishop
University of California, Davis Marquette University
A companion to
MODERN CONTROL SYSTEMS
TWELFTH EDITION
Richard C. Dorf
Robert H. Bishop
Prentice Hall
Upper Saddle River Boston Columbus San Francisco New York
Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai
Madrid 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. 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 1000 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.
www.elsolucionario.org
It is assumed that instructors (and students) have access to M ATLAB
and the Control System Toolbox or to LabVIEW and the MathScript RT
Module. All of the computer solutions in this Solution Manual were devel-
oped and tested on an Apple MacBook Pro platform using M ATLAB 7.6
Release 2008a and the Control System Toolbox Version 8.1 and LabVIEW
2009. It is not possible to verify each solution on all the available computer
platforms that are compatible with M ATLAB and LabVIEW MathScript
RT Module. Please forward any incompatibilities 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
, © 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 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........................................................... 22
3. State Variable Models ............................................................................. 85
4. Feedback Control System Characteristics ............................................ 133
5. The Performance of Feedback Control Systems ................................. 177
6. The Stability of Linear Feedback Systems .......................................... 234
7. The Root Locus Method....................................................................... 277
8. Frequency Response Methods .............................................................. 382
9. Stability in the Frequency Domain ...................................................... 445
10. The Design of Feedback Control Systems .......................................... 519
11. The Design of State Variable Feedback Systems ............................... 600
12. Robust Control Systems ..................................................................... 659
13. Digital Control Systems ..................................................................... 714
iv
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.
MODERN CONTROL SYSTEMS
SOLUTION MANUAL
Richard C. Dorf Robert H. Bishop
University of California, Davis Marquette University
A companion to
MODERN CONTROL SYSTEMS
TWELFTH EDITION
Richard C. Dorf
Robert H. Bishop
Prentice Hall
Upper Saddle River Boston Columbus San Francisco New York
Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai
Madrid 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. 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 1000 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.
www.elsolucionario.org
It is assumed that instructors (and students) have access to M ATLAB
and the Control System Toolbox or to LabVIEW and the MathScript RT
Module. All of the computer solutions in this Solution Manual were devel-
oped and tested on an Apple MacBook Pro platform using M ATLAB 7.6
Release 2008a and the Control System Toolbox Version 8.1 and LabVIEW
2009. It is not possible to verify each solution on all the available computer
platforms that are compatible with M ATLAB and LabVIEW MathScript
RT Module. Please forward any incompatibilities 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
, © 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 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........................................................... 22
3. State Variable Models ............................................................................. 85
4. Feedback Control System Characteristics ............................................ 133
5. The Performance of Feedback Control Systems ................................. 177
6. The Stability of Linear Feedback Systems .......................................... 234
7. The Root Locus Method....................................................................... 277
8. Frequency Response Methods .............................................................. 382
9. Stability in the Frequency Domain ...................................................... 445
10. The Design of Feedback Control Systems .......................................... 519
11. The Design of State Variable Feedback Systems ............................... 600
12. Robust Control Systems ..................................................................... 659
13. Digital Control Systems ..................................................................... 714
iv
