Solution Manual For Modern Control Systems 12th Edition By Richard C. Dorf Robert H. Bishop | All Chapters | Complete Guide A+

© 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, photocopyin
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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, photocopyin
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.

It is assumed that instructors (and students) have access to MATLAB
www.elsolucionario.org
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 MATLAB 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 MATLAB 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, photocopyin
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

, © 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, photocopyin
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 unique 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 Process


www.elsolucionario.org
Desired
power
output
-
Error
Micro-
processor
Current i(t)


Measurement
Laser Power
out


Measured
Power
power
Sensor



E1.2 A driver controlled cruise control system:

Controller Process

Foot pedal Car and
Desired Actual
Driver
speed - Engine auto
speed
Measurement



Visual indication of speed
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 backward and forward mo-
tion of the fly rod to cast an almost weightless fly lure long distances (the

1