Modern Control Systems (11th Edition)

730 Pages·2007·4.82 MB·english

by  Richard C. Dorf

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.
c2008 by Prentice-Hall, Inc.
(cid:13)
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 programsto 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-readycopy for this manual was prepared by the author using LATEX2ε.
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Phone. [phone],Fax: [phone]
Email: [email protected]
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Phone. [phone],Fax: [phone]
E-mail: [email protected]
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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
aWindow XP platformusingMATLAB7.3 Release 2006b andtheControl
System Toolbox Version 7.1 andLabVIEW8.2. Itis not possibleto verify
each solution on all the available computer platforms that are compatible
with MATLAB and LabVIEW MathScript. Please forward any incompati-
bilitiesyouencounterwiththescriptstoProf.Bishopattheemailaddress
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 [email protected]
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.
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 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
Error Micro- Currenti(t)
Dpoewsiererd - processor Laser Pouotwer
output
Measurement
Measured Power
power Sensor
E1.2 A driver controlled cruise control system:
Controller Process
Footpedal Car and
Dspeeseirded - Driver Engine Aaucttoual
speed
Measurement
Speedometer
Visualindicationof speed
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 flylure long distances (the
1
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.
2 CHAPTER 1 Introduction to Control Systems
currentworld-record is 236 ft). Theflylureis attached toashortinvisible
leader about 15-ft long, which is in turn attached to a longer and thicker
Dacron line. Theobjective is cast the fly lure to a distant spot with dead-
eye accuracy so that the thicker part of the line touches the water first
and then the fly gently settles on the water just as an insect might.
Wind
Fly-fisher disturbance
Controller Process
Dpthoeess iifltrieyodn of - Mbflyoi-ndfidys hoaenf rdt h e Ranodd ,c lainset, Apofoc tsthiuteiao fllny
Measurement
Vision of
Visual indication the fly-fisher
of the position of
the fly
E1.4 An autofocus camera control system:
One-way trip time for the beam
K Conversion factor
1 (speed of light or
sound)
Beam
Emitter/ Distance to subject
Receiver
Beam return Subject
Lens focusing
motor
Lens
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.
Exercises 3
E1.5 Tacking a sailboat as the wind shifts:
Controller Actuators Wind Process
Error
Dsaeilsbiroeadt - Sailor Rsauidl addejru asntmdent Sailboat Asacitlbuoalat
direction direction
Measurement
Measured sailboat direction
Gyro compass
E1.6 An automated highway control system merging two lanes of traffic:
Controller Actuators Process
Dgaepsired -Error Ecommbpeudtdeerd Bstreaekreins,g gas or Avechtiivcele Agacptual
Measurement
Measured gap
Radar
E1.7 Using the speedometer, the driver calculates the difference between the
measured speed and the desired speed. The driver throotle knob or the
brakes as necessary to adjust the speed. If the current speed is not too
much over the desired speed, the driver may let friction and gravity slow
the motorcycle down.
Controller Actuators Process
Error
Dspeeseirded - Driver Tbhrarokettsle or Motorcycle Amcottuoarlcycle
speed
Measurement
Visual indication of speed
Speedometer
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.
4 CHAPTER 1 Introduction to Control Systems
E1.8 Human biofeedback control system:
Controller Process
Message to
Desired - Hypothalumus blood vessels Human body Actual
body body
temp temp
Measurement
Visual indication of
body temperature TV display Body sensor
E1.9 E-enabled aircraft with ground-based flight path control:
Corrections to the Controller Aircraft
flight path
Desired Flight
- Gc(s) G(s)
Flight Path
Path
Meteorological Health Location
data Parameters and speed
Optimal
flight path
Ground-Based Computer Network
Optimal
flight path Location
and speed
Meteorological Health
data Parameters
-
Desired Flight
Corrections to the Gc(s) G(s)
Flight Path
flight path
Path Controller Aircraft
E1.10 Unmanned aerial vehicle used for crop monitoring in an autonomous
mode:
Trajectory Controller UAV
error
Specified Flight
- Gc(s) G(s)
Flight Trajectory
Trajectory
Sensor
Location with Map Ground
respect to the ground photo
Correlation Camera
Algorithm
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.
Exercises 5
E1.11 Aninvertedpendulumcontrolsystemusinganopticalencodertomeasure
the angle of the pendulum and a motor producing a control torque:
Actuator Process
Error Voltage Torque
Desired - Controller Motor Pendulum Angle
angle
Measurement
Measured Optical
angle encoder
E1.12 Inthevideogame, theplayer can serveasboththecontroller andthesen-
sor. The objective of the game might be to drive a car along a prescribed
path. The player controls the car trajectory using the joystick using the
visual queues from the game displayed on the computer monitor.
Controller Actuator Process
Error
Desired - Player Joystick Video game Game
game objective
objective
Measurement
Player
(eyesight, tactile, etc.)
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.
6 CHAPTER 1 Introduction to Control Systems
Problems
P1.1 An automobile interior cabin temperature control system block diagram:
Controller Process
Error Thermostat and Automobile
Dteemsipreedrature - air conditioning cabin Acaubtoinm teombipleerature
set by the unit
driver
Measurement
Measured temperature Temperature
sensor
P1.2 A human operator controlled valve system:
Controller Process
Error *
Dflueisdired - Valve Tank Foluutipdut
output *
Measurement
Visual indication
of fluid output *
Meter
* = operator functions
P1.3 A chemical composition control block diagram:
Controller Process
Error
Dcheesmireicdal - Valve Mixer tube Ccohmempoicsaitlion
composition
Measurement
Measured chemical
composition Infrared analyzer
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For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.