Modern Control Systems 12th Edition Dorf Solutions Manual Full Download: http://testbankreal.com/down http://testba nkreal.com/download/modern-con © 2011 Pearson Education, Inc., Upper Saddle River, NJ. Allload/modern-control-systems-12th-ed rights reserved. Thistrol-systems-12th-edition-dorf-solutio publication is protected by ition-dorf-solutions-manual/ Copyright and written ns-manual/ 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 MOD ERN CON CONTR TROL OL SYS SYSTEM TEMS S SOLUTION SOLUT ION MANUA MANUAL L
Richard C. Dorf
Rob ert H. Bishop
Unive Un iversit rsityy of Ca Califo liforni rnia, a, Dav Davis is
Marqu Ma rquett ettee Un Unive iversi rsity ty
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
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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 increasing crea sing compl complexit exity y giv gives es stude students nts confid confidence ence in their proble problem-sol m-solving ving abil ab ilit ity y as th they ey wor ork k th thei eirr wa way y fr from om th thee ex exer erci cise sess to th thee de desi sign gn an and d computer-based problems. It is assumed that instructors (and students) have access to MATLAB and the Control System Toolbox or to LabVIEW and the MathScript RT Module. All of the computer solutions in this Solution Manual were developed 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 Modern Control Systems . We encourage you to contact Prentice Hall with comments and suggestions for this and future editions. Robert Robe rt H. Bis Bishop hop
rhbis rh bishop hop@ma @marqu rquett ette.e e.edu du
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T A B L E - O
F - C O N T
E N T S
1. Introduction to Control Systems .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. 1 2. Mathematical Mo Models of of Sy Systems . .. . .. . .. .. . .. . .. .. . .. . .. .. . .. . . 22 3. State Va Variable Mo Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4. Fee eedb dbac ack k Co Con ntr trol ol Sy Syst steem Ch Char araact cteeri rist stic icss . . . . . . . . . . . . . . . . . . . . . . . 13 1333 5. Th Thee Per erfo form rman ance ce of Fee eedb dbac ack k Con Contr trol ol Sy Syst stem emss . . . . . . . . . . . . . . . . . 17 1777 6. Th Thee St Staabi bili litty of of Lin ineear Fee eedb dbac ack k Sy Syst steems . . . . . . . . . . . . . . . . . . . . . . 23 2344 7. The Root Locus Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8. Frequency Respo pon nse Method odss . .. .. . .. . .. .. . .. . .. .. . .. . .. .. . .. . . 382 9. Stability in in th the Fr Frequency Do Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 10. The Design of Feedback Control Systems .......................519 11.. Th 11 Thee Des Desig ign n of Sta State te Var Varia iabl blee Fee Feedb dbac ack k Syst System emss . . . . . . . . . . . . . . . . 60 6000 12. Robust Control Systems ........................ ............... 659 13. Digital Control Systems ....................... .................714
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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
Desired power output
Error
-
Micro- processor
Currenti(t)
Laser
Power Sensor
power
A driver controlled cruise control system: Controller
Desired speed
Power out
Measurement
Measured
E1.2
Process
Process
Foot Fo ot ped pedal al
-
Driver
Car and Engine
Actual auto speed
Measurement
Visual Visu al indica indication tion of speed speed
E1.3
Speedometer
Although the princi Although principle ple of conservation conservation of momen momentum tum explains much 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 motion of the fly rod to cast an almost weightless fly lure long distances (the 1
© 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.
2
CHAPTER 1
Introduction Introduc tion to Contro Controll Syste Systems ms
current world-record is 236 ft). The fly lure is attached to a short invisible leader about 15-ft long, which is in turn attached to a longer and thicker Dacron line. The objective is cast the fly lure to a distant spot with deadeye 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. Fly-fisher Desired position of the fly
Controller
-
Wind disturbance
Mind and body of the fly-fisher
Process
Rod, line, and cast
Actual
position of the fly
Measurement
Visual indication of the position of the fly
E1.4
Vision of the fly-fisher
An autofocus autofocus camera camera control control system: system: One-way trip time for the beam
Conversion factor (speed of light or sound)
K1 Beam Emitter/ Receiver Beam return
Distance to subject
Subject Lens focusing motor
Lens
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3
Exercises
E1.5
Tack acking ing a sailboat as the wind shifts shifts::
Error
Desired ailboat irection
-
Controller
Actuators
Sailor
Rudder and sail adjustment
Wind
Process
Sailboat
Actual sailboat direction
Measurement Measured sailboat direction
Gyro compass
E1.6
An automated highway highway control control system merging two two lanes of traffic: Controller
Error
Desired gap
-
Embedded computer
Actuators
Brakes, gas or steering
Process
Active vehicle
Actual gap
Measurement Measured gap
Radar
E1.7
Using the speedometer, speedometer, the driv driver er calculates calculates the differ difference ence between 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
Desired speed
Error
-
Driver
Actuators
Throttle or brakes
Measurement Visual indication of speed
Speedometer
Process
Motorcycle
Actual motorcycle speed
© 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.
4
CHAPTER 1 E1.8
Introduction Introduc tion to Contro Controll Syste Systems ms
Human biofeedback biofeedback control system: Controller
Desired body temp
Process
Hypothalumus
-
Message to blood vessels
Actual body temp
Human body
Measurement Visual indication of body temperature
E1.9
TV display
Body sensor
E-enabled aircraft with ground-based flight path control: Corrections to the flight path
Desired Flight Path
-
Controller
Aircraft
Gc(s)
G(s)
Flight Path Health Parameters
Meteorological data
Location and speed
Optimal flight path
Ground-Based Computer Network
Desired Flight Path
E1.10
Specified Flight Trajectory
Optimal flight path Health Parameters
Meteorological data
Corrections to the flight path
Gc(s)
G(s)
Controller
Aircraft
Location and speed
Flight Path
Unmanned Unmann ed aerial aerial ve vehic hicle le use used d for crop mon monito itorin ringg in an aut autono onomou mouss mode: Trajectory error
UAV UA V
Controller
-
Gc( s s))
Flight Trajectory
G( s s))
Sensor Location with respect to the ground
Map Correlation Algorithm
Ground photo
Camera
© 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.
5
Exercises
E1.11
An inverted inverted pendulum control control system using an optical encoder encoder to measure the angle of the pendulum and a motor producing a control torque: Actuator
Voltage
Error
Desired angle
-
Controller
Process
Torque
Motor
Pendulum
Angle
Measurement
Measured angle
E1.12
In the video game, the player player can serve serve as both the controller and the sensor. 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
Desired game objective
Optical encoder
Error
-
Player
Actuator
Joystick
Measurement
Player (eyesight, tactile, etc.)
Process
Video game
Game objective
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6
CHAPTER 1
Introduction Introduc tion to Contro Controll Syste Systems ms
Problems P1.1
Desired temperature set by the driver
An automobile interior interior cabin temperature temperature control system system block diagram:
Error
-
Controller
Process
Thermostat and air conditioning unit
Automobile cabin
Automobile cabin temperature
Measurement Measured temperature
P1.2
Temperature Temp erature sensor
A human operator controlled valve valve system: Controller
Process
Error *
Desired fluid output *
-
Tank
Valve
Fluid output
Measurement Visual indication of fluid output *
Meter * = operator functions
P1.3
A chemical chemical composition composition control control block diagram: diagram: Controller
Process
Error Desired chemical composition
-
Mixer tube
Valve
Measurement Measured Mea sured chemical composition
Infrared analyzer
Chemical composition
