Modern control systems

Design Examples and Design Problems (DP)

CHAPTER
Example
Example
Example
COP I. 1
DPI.I
DP1.2
DP1.3
DPI.4
DP 1.5
DP1.6

I
Turntable Speed Control
Insulin Delivery Control System
Disk Drive Read System
Traction Drive Motor Control
Automobile Noise Control
Automobile Cruise Control
Dairy Farm Automation
Welder Control
Automobile Traction Control
Huhble Telescope Vibration
Reduction

CHAPTER
Example
Example
Example

Example
Example
CDP2.1
DP2.1
DP2.2
DP2.3
DP2.4

2
Electric Traction Motor Control
Mechanical Accelerometer
Laboratory Robot
Low-Pass Filter
Disk Drive Read System
Traction Drive Motor Control
Selection of Transfer Functions
Television Beam Circuit
Transfer Function Determination
Op Amp Diffcrentiating Circuit

CHAPTER
Example
Example
CDP3.1
DP3.1
DP3.2

3
Printer Belt Drive
Disk Drive Read System

Traction Drive Motor Control
Shock Absorher for Motorcycle
Diagonal Matrix Differential
Equation
Aircraft Arresting Gear
Bungi Jumping System

DP3.3
DP3.4

CHAPTER 4
English Channel Boring
Example
Machines
Mars Rover Vehicle
Example
Disk Drive Read System
Example
Traction Drive Motor Control
CDP4.1
Speed Control System
DP4.1
Airplane Roll Angle Control
DP4.2
Velocity Control System
DP4.3
Laser Eye Surgery
DP4.4
Pulse Generating Op Amp
DP4.5

Circuit

PAGE
21
22
23
30
30
30
30
30
30
31

72
75
77
78
94
115
116
116
116
116

147
155
170
170
170

171
17l

191
194
202
218
218
218
218
219
220

CHAPTER 5
Hubble Telescope Pointing
Example
Control
Disk Drive Read System
Example
Traction Drive Motor Control
CDP5.1
Jet Fighter Roll Angle Control
DP5.1
Welding Arm Position Control
DP5.2
Automobile Activc Suspension
DP5.3
System
Space Satellite Orientation
DP5.4

Control
Deburring Rohot for Machined
DP5.5
Parts
DC Motor Position Control
DP5.6
CHAPTER
Example
Example
CDP6.1
DP6.1
DP6.2
DP6.3
DP6.4
DP6.5
Dpo.6

6
Tracked Vehicle Turning Control
Disk Drive Read System
Traction Drive Motor Control
Automohile Ignition Control
Mars Guidcd Vehicle Control
Parameter Selection
Space Shuttle Rocket
Tratlic Control System
Robot Steered Motorcycle

CHAPTER 7
Laser Manipulator Control"

Example
System
Rohot Control System
Example
Disk Drive Read System
Example
Traction Drive Motor Control
CDP7.1
Pitch Rate Aircraft Control
DP7.1
Two-Rotor Helicopter Velocity
DP7.2
Control
Mars Rover
DP7.3
Remotely Controlled Welder
DP7.4
High-Performance Jet Aircraft
DP7.5
Automatic Control of Walking
DP7.o
Motion
OP Amp Control System
DP7.7
Robot Arm Elbow Joint Actuator
DP7.8
Four- Wheel-Steered Automobile
DP7.9
Pilot Crane Control
DP7.1O

Planetary RO\u Vehicle
DP7.11
AutoIllobile Distance Control
DP7.12
Roll Angle Aircraft Autopilot
DP7.13

259
271
285
285
286
286
286
287
287

307
317
328
328
328
328
328
328
329

368
371
379

398
398
398
398
399
399
399
400
400
400
401
401
402
403


CHAPTER 8
Example
Engraving Machine Control
System
Example
Disk Drive Read System
CDP8.]
Traction Drive Motor Control
DP8.1
Automobile Steering System
DP8.2
Autonomous Planetary ExplorerAmbler
DPS.3
Vial Position Control Under a

Dispenser
DP8.4
Automatic Anesthesia Control
System
CHAPTER 9
Example
Remotely Controlled
Reconnaissance Vehicle
Example
Disk Drive Read System
CDP9.1
Traction Drive Motor Control
DP9.1
Mobile Robot for Toxic Waste
Cleanup
DP9.2
Control of a Flexible Arm
DP9.3
Automatic Blood Pressure
Regulator
DP9.4
Robot Tennis Player
DP9.5
Electrohydraulic Actuator
DP9.6
Steel Strip-Rolling Mill
DP9.7
Lunar Vehicle Control
DP9.8
High-Speed Steel-Rolling Mill

DP9.9
Two- Tank Temperature Control
DP9.10
Hot Ingot Robot Control
CHAPTER
Example
Example
Example
CDP10.1
DPIO.I
DPIO.2
DPIO.3
DPIO.4
DPIO.5
DPIO.6
DPIO.7
DPIO.S
DPIO.9

10
Rotor Winder Control System
The X- Y Plotter
Disk Drive Read System
Traction Drive Motor Control
Two Cooperating Robots
Heading Control of a Bi- Wing
Aircraft
Mast Flight System
Robot Control Using Vision
High-Speed Train Tilt Control

Large Antenna Control
Tape Transport Speed Control
Automobile Engine Control
Aircraft Roll Angle Control

CHAPTER II
Example
Automatic Test System
Example
Disk Drive Read System

435
444
484
464

CDPI1.l
DPl1.l
DPIl.2
DPI \.3
DPIl.4
DPIl.5
DPI1.6

Traction Drive Motor Control
Levitation of a Steel Ball
Automobile Carburetor Control
Diesel-Electric Locomotive
Helicopter Control
Manufacturing of Paper

Coupled-Drive Control

CHAPTER
Example
Example
Example
Example

12
Aircraft Autopilot
Space Telescope Control System
Robust Bobbin Drive
Ultra-Precision Diamond
Turning Machine
Disk Drive Read System
Traction Drive Motor Control
Turntable Position Control
Control of a DAT Player
Pointing Accuracy of the GRID
Device
Dexterous Hand Master
Microscope Control
Microscope Control
Artificial Control of Leg
Articulation
Elevator Position Control
Electric Ventricular Assist
Device
Space Robot Control
Solar Panel Pointing Control

Magnetically Levitated Train
Control
Mars Guided Vehicle Control
with PID
Benchmark Mass-Spring System

674
674
674
674
675
676
676

464
465
466

505
519
546
546
546
546
548
54S
548
549
549
549

550

592
595
605
624
624
624
625
625
626
627
627
627
627

655
666

Example
CDPI2.1
DP12.1
DP12.2
DP12.3
DPI2.4
DP12.5
DP12.6
DP12.7
DP12.8
DP12.9

DP12.10
DP12.11
DP12.12
DP12.13
DP12.14

CHAPTER 13
Example
Worktable Motion Control
System
Example
Disk Drive Read System
CDPl3.1
Traction Drive Motor Control
DPI3.1
Temperature Control System
DP13.2
Disk Drive Read-Write HeadPositioning System
DP13.3
Vehicle Traction Control
DPI3.4
Machine-Tool System
DP13.5
Polymer Extruder Control

702
703
705
710
719

733
733
733
735
735
736
737
737
738
738
739
739
740
740
740

762
774
782
782
782
782
782
782


Modem
Control Systems
NINTH

EDITION

Richard C. Dorf
University of California, Davis

.;

Robert H. Bishop

_

The University of Texas at Austin


Library of Congress Cataloging-in-Publication

Data

Dorf Richard C.
Modern control systems / Richard C. Dorf and Robert H. Bishop.-9th ed.
p.cm.
Includes bibliographical references and index.
ISBN 0-13-030660-6
1. Feedback comol systems. 2. Control theory. L Bishop, Robert H., 1957-11.Title.
TJ21 .D67 2000
629.8'3-dc21

00-039967

Vice-president and Editorial Director: Marcia Horton

Acquisitions editor: Eric Frank
Editorial assistant: Jennie Diblasi •
Executive managing editor: Vince O'Brien
Managing editor: David A. George
Vice-President of production and manufacturing: David l¥. Riccardi
Editorial supervision: Scott Disanno
Cover director: Carole Anson
Cover: John Christiana
Marketing manager: Danny Hoyt
Manufacturing buyer: Pat Brown
Peter Menzel Photography/Mark Tilden's Robots-Analog
Nervous Net-"Unibug
1.0" Walking Past Desert
Flowers at Great Sand Dunes National Monument in Colorado. Image is from upcoming photography book
"Robo sapiens," by Peter Menzel and Faith D' Aluisio. Material World Books. M.LT. Press. Fall, 2000.
©2001 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 nqt 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.
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:

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1
ISBN 0-13-030660-6
Pearson
Pearson
Prentice
Pearson
Pearson
Pearson
Pearson
Prentice

Education Limited (UK)
Education Australia Pty Ltd
Hall Canada Ltd
Educaci6n de Mexico, S.A. de C.V.
Education Japan KK
Education China Ltd
Education Asia Pte Ltd
Hall, Upper Saddle River, New Jersey


Of the greater teacherswhen they are gone,
their students will say:
we did it ourselves.
Dedicated to:
Lynda Ferrera Bishop
and
Joy MacDonald Darf
In grateful appreciation

Contents
CHAPTER

1

Introduction to Control Systems
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12

CHAPTER

2

Introduction
2
History of Automatic Control 4
Two Examples of the Use of Feedback 7
Control Engineering Practice 8
Examples of Modern Control Systems 9

Automatic Assembly and Robots 16
The Future Evolution of Control Systems 16
Engineering Design 18
Control System Design 19
Design Example: Turntable Speed Control 21
Design Example: Insulin Delivery Control System 22
Sequential Design Example: Disk Drive Read System 23
Exercises 24
Problems 25
Design Problems 30
Terms and Concepts 31

Mathematical Models of Systems
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12

1

32

Introduction
33
Differential Equations of Physical Systems 33
Linear Approximations of Physical Systems 38
The Laplace Transform 41
The Transfer Function of Linear Systems 47
Block Diagram Models 62
Signal-Flow Graph Models 66
Computer Analysis of Control Systems 71
Design Examples 72
The Simulation of Systems Using MATLAB 80
Sequential Design Example: Disk Drive Read System
Summary 97
Exercises 98
Problems 104
Advanced Problems 115
Design Problems 115
MATLABProblems 116
Terms and Concepts 118

94

v


vi
CHAPTER

Contents

3

State Variable Models
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12

CHAPTER

4

119

Introduction
120
The State Variables of a Dynamic System 121
The State Differential Equation
123
Signal-Flow Graph State Models 126
Alternative Signal-Flow Graph State Models 132
The Transfer Function from the State Equation

136
The Time Response and the State Transition Matrix 138
A Discrete-Time Evaluation of the Time Response 142
Design Example: Printer Belt Drive 147
Analysis of State Variable Models Using MATLAB 152
Sequential Design Example: Disk Drive Read System 155
Summary 159
Exercises 159
Problems 161
Advanced Problems 168
Design Problems 170
MATLABProblems 171
Terms and Concepts 172

Feedback Control System Characteristics
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11

173

Open- and Closed-Loop Control Systems 174

Sensitivity of Control Systems to Parameter Variations 176
Control of the Transient Response of Control Systems 179
Disturbance Signals in a Feedback Control System 183
Steady-State Error 187
The Cost of Feedback 190
Design Example: English Channel Boring Machines 191
Design Example: Mars Rover Vehicle 194
Control System Characteristics Using MATLAB 196
Sequential Design Example: Disk Drive Read System 202
Summary 205
Exercises 207
Problems 209
Advanced Problems 215
Design Problems 218
MATLABProblems 220
Terms and Concepts 222


vii

ix

Contents

:5
-

The Performance of Feedback Control Systems
5.1
5.2

5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.U
5.13

•...

5.14

The Stability of Linear Feedback Systems

~6

l--

6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

#---

l

224
Introduction
Test Input Signals 225
Performance of a Second-Order System 227
Effects of a Third Pole and a Zero on the Second-Order
Response 233
Estimation of the Damping Ratio 238
The s-Plane Root Location and the Transient Response
The Steady-State Error of Feedback Control Systems
The Steady-State Error of Nonunity Feedback Systems
Performance Indices 247
The Simplification of Linear Systems 256
Design Example: Hubble Telescope Pointing Control
System Performance Using MATLAB 262
Sequential Design Example: Disk Drive Read System
Summary 277
Exen;~=,es 275
Problems 279
Advanced Problems 284
Design Problems 285
287
MATLAB Problems
Terms and Concepts 289

--

223

System
239
240
245

259
271

-

290

The Concept of Stability 291
The Routh-Hurwitz Stability Criterion 295
The Relative Stability of Feedback Control Systems 303
The Stability of State Variable Systems 304
Design Example: Tracked Vehicle Turning Control 307
System Stability Using MATLAB 309
317
Sequential Design Example: Disk Drive Read System
Summary 320
Exercises 321
Problems 322
Advanced Problems 326
Design Problems 328
329
MATLAB Problems
Terms and Concepts 330

viii

Contents

CHAPTER

7

The Root Locus Method
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12

331

Introduction
332
The Root Locus Concept 332
The Root Locus Procedure 339

An Example of a Control System Analysis and Design Utilizing the
Root Locus Method 351
Parameter Design by the Root Locus Method 354
Sensitivity and the Root Locus 359
Three-Term (PID) Controllers 366
Design Example: Laser Manipulator Control System 368
The Design of a Robot Control System 371
The Root Locus Using MATLAB 373
Sequential Design Example: Disk Drive Read System 379
Summary 380
Exercises 384
Problems 386
-Advanced Problems 396
Design Problems 398
MATLABProblems 404
Terms and Concepts 405

/--

CHAPTER

8

Frequency Response Methods
8.1
8.2
8.3
8.4
8.5
8.6

8.7
8.8
8.9
8.10

CHAPTER

9

406

Introduction
407
Frequency Response Plots 409
An Example of Drawing the Bode Diagram 426
Frequency Response Measurements
430
Performance Specifications in the Frequency Domain
Log Magnitude and Phase Diagrams 435
Design Example: Engraving Machine Control System
Frequency Response Methods Using MATLAB 439
Sequential Design Example: Disk Drive Read System
Summary 446
Exercises 451
Problems 454
Advanced Problems 462
Design Problems 464
MATLABProblems 466
Terms and Concepts 468

Stability in the Frequency Domain
9.1
9.2

Introduction
470
Mapping Contours in the s-Plane

471

--

469

432
435
444


ix

Contents

9.3
9.4
9.5
9.6
9.7
9.8
9.9

9.10
9.11
9.12

aMPTER

.

The Nyquist Criterion 476
Relative Stability and the Nyquist Criterion 487
Time-Domain Performance Criteria Specified in the Frequency
Domain 493
System Bandwidth 500
The Stability of Control Systems with Time Delays 501
Design Example: Remotely Controlled Reconnaissance
Vehicle 505
PID Controllers in the Frequency Domain 508
Stability in the Frequency Domain Using MATLAB 509
Sequential Design Example: Disk Drive Read System 519
Summary 521
Exercises 528
Problems 534
Advanced Problems 544
Design Problems 546
MATLABProblems 551
Terms and Concepts 552

10 The Design of Feedback Control Systems
10.1
10.2

10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
10.15
10.16

553

554
Introduction
Approaches to System Design 555
Cascade Compensation Networks 557
Phase-Lead Design Using the Bode Diagram 561
Phase-Lead Design Using the Root Locus 567
System Design Using Integration Networks 573
Phase-Lag Design Using the Root Locus 576
Phase-Lag Design Using the Bode Diagram 580
System Design on the Bode Diagram Using Analytical and
Computer Methods 585
Systems with a Prefilter 586
Design for Deadbeat Response 589

Design Example: Rotor Winder Control System 592
Design Example: The X- Y Plotter 595
System Design Using MATLAB 598
Sequential Design Example: Disk Drive Read System 605
Summary 606
Exercises 608
Problems 610
Advanced Problems 621
Design Problems 624
MATLABProblems 628
Terms and Concepts 630


X

CHAPTER

Contents

11 The Design of State Variable Feedback Systems
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10

11.11
11.12

CHAPTER

Introduction
631
Controllability 632
Observability 634
Optimal Control Systems 636
Pole Placement Using State Feedback 645
Ackermann's Formula 651
Limitations of State Variable Feedback 652
Internal Model Design 652
Design Example: Automatic Test System 655
State Variable Design Using MATLAB 658
Sequential Design Example: Disk Drive Read System
Summary 668
Exercises 668
Problems 669
Advanced Problems 672
Design Problems 674
MATLABProblems 677
Terms and Concepts 679

12 Robust Control Systems
12.1
12.2
12.3
12.4

12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
12.13
12.14
12.15
12.16

631

666

680

Introduction
681
Robust Control Systems and System Sensitivity 682
Analysis of Robustness 685
Systems with Uncertain Parameters
688
The Design of Robust Control Systems 690
PID Controllers 695
The Design of Robust PID Controlled Systems 697
Design Example: Aircraft Autopilot 702
The Design of a Space Telescope Control System 703

The Design of a Robust Bobbin Drive 705
The Robust Internal Model Control System 708
The Design of an Ultra-Precision Diamond Turning Machine
The Pseudo-Quantitative Feedback System 714
Robust Control Systems Using MATLAB 716
Sequential Design Example: Disk Drive Read System 719
Summary 721
Exercises 723
Problems 724
Advanced Problems 730
Design Problems 733
MATLABProblems 741
Terms and Concepts 742

710


xi

Contents

CHAPTER

13

Digital
13.1
13.2
13.3
13.4

13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14

Control Systems

743

744
Introduction
Digital Computer Control System Applications 744
Sampled- Data Systems 746
The z-Transform 749
Closed-Loop Feedback Sampled-Data Systems 754
Stability Analysis in the z-Plane 756
Performance of a Sampled-Data, Second-Order System 757
760
Closed-Loop Systems with Digital Computer Compensation
The Design of a Worktable Motion Control System 762
The Root Locus of Digital Control Systems 764
Implementation of Digital Controllers 768
Digital Control Systems Using MATLAB 769
Sequential Design Example: Disk Drive Read System 774

Summary 776
Exercises 776
Problems 778
Advanced Problems 780
Design Problems 782
MATLABProblems 783
Terms and Concepts 784

787

APPENDIX

A

.MATLABBasics

APPENDIX

B

Simulink Basics

APPENDIX

C

Symbols, Units, and Conversion Factors
On WWW

APPENDIX

0

An Introduction
On WWW

APPENDIX

E

Decibel Conversion

APPENDIX

F

Complex Numbers

APPENDIX

G

z- Transfer Pairs
References
Index

825

813

805

to Matrix Algebra
On WWW
On WWW
On WWW


ABOUT THE AUTHORS
Richard C. Dorf is a Professor of Electrical and Computer Engineering at the
University of California, Davis. Known as an instructor who is highly concerned with
the discipline of electrical engineering and its application to social and economic
needs, Professor Dod has written and edited several successful engineering text books
and handbooks, including the best selling Engineering Handbook and the Second
Edition of the Electrical Engineering Handbook. Professor Dorf is a Fellow of the
IEEE and is active in the fields of control system design and robotics. Dr. Dod holds
a patent for the PIDA controller.
Robert H. Bishop holds the Myron L. Begeman Fellowship in Engineering in the
Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin. A talented educator, Professor Bishop has been recognized for
his contributions in the classroom with the coveted Lockheed Martin Tactical Aircraft
Systems Award for Excellence in Engineering Teaching. An active member of AIAA,
IEEE, and ASEE, he recently received the John Leland Atwood Award from the
American Society of Engineering Educators and the American Institute of Aeronautics and Astronautics which is given periodically to "a leader who has made lasting and significant contributions to aerospace engineering education." Dr. Bishop is
a distinguished researcher with an interest in guidance, navigation, and control of
aerospace vehicles.

ABOUT THE COVER
"Unibug 1.0" walking past desert flowers at Grand Sand Dunes National Monument
in Colorado. This Image is from the upcoming Photography book entitled "Robo
sapiens" by Peter Menzel and Faith D'Aluisio. Material World Books. M.LT. Press,

Fall, 2000. Photography provided by Peter Menzel and Mark TIlden's robots-Analog
Nervous Net .

.

xiii


Preface
MODERN CONTROL SYSTEMS-

THE BOOK

The Mars Pathfinder spacecraft was sent aloft aboard a Delta II expendable
launch vehicle on December 4, 1996 to begin a seven-month journey to the Red Planet. The Pathfinder mission, one of the first of the NASA Discovery-class missions,
was the first mission to land on Mars since the successful Viking spacecraft over two
decades ago. After traveling over 497,418,000 km, the spacecraft impacted the Martian surface on July 4, 1997 with a velocity of about 18 m/s. Upon impact the spacecraft bounced up approximately 15 meters, then continued to bounce another 15
times and rolled to a stop about 1 km from the initial impact point. The landing site
is known as the Sagan Memorial Station and is located in the Ares Vallis region at 19.33
N, 33.55 W. Pathfinder deployed the first-ever autonomous rover vehicle, known as
the Sojourner, to explore the landing site area. The mobile Sojourner had a mass of
10.5 kilograms and was designed to roam in a 300-m2 area for around 30 days. The
0.25-m2 solar array provided 16 watt-hours of peak power and the primary battery
provided about 150 watt-hours of power. The steering control of this vehicle had to
be accurate and had to limit the power consumption. Control engineers playa critical role in the success of the planetary exploration program. The role of autonomous
vehicle spacecraft control systems will continue to increase as flight computer hardware and operating systems improve. In fact, Pathfinder used a commercially produced, multitasking computer operating system hosted in a 32-bit radiation-hardened workstation with 1-gigabyte storage, programmable in C. This is quite an
advancement over the Apollo computers with a fixed (read-only) memory of 36,864
words (one word was 16 bits) together with an erasable memory of 2,048 words. The
Apollo "programming language" was a pseudocode notation encoded and stored as
1

a list of data words "interpreted" and translated into a sequence of subroutine links.
Interesting real-world problems, such as planetary mobile rovers like Sojourner, are
used as illustrative examples throughout the book. For example, a mobile rover design problem is discussed in the Design Example in Section 4.8.
Control engineering is an exciting and a challenging field. By its very nature, control engineering is a multidisciplinary subject, and it has taken its place as a core
course in the engineering curriculum. It is reasonable to expect different approaches to mastering and practicing the art of control engineering. Since the subject has a
strong mathematical foundation, one might approach it from a strictly theoretical
point of view,emphasizing theorems and proofs. On the other hand, since the ultimate
objective is to implement controllers in real systems, one might take an ad hoc approach relying only on intuition and hands-on experience when designing feedback
I For further reading on the Apollo guidance, navigation, and control system, see R. H. Battin, "An
Introduction to the Mathematics and Methods of Astrodynamics," AIAA Education Series, 1.S.
pzemieniecki/Series Editor-in-Chief, 1987.

XV


xvi

Preface

control systems. Our approach is to present a control engineering methodology that,
while based on mathematical fundamentals, stresses physical system modeling and
practical control system designs with realistic system specifications.
We believe that the mQst important and productive approach to learning is for
each of us to rediscover and recreate anew the answers and methods of the past.
Thus the ideal is to present the student with a series of problems and questions and
point to some of the answers that have been obtained over the past decades. The traditional method-to confront the student not with the problem but with the finished
solution-is to deprive the student of all excitement, to shut off the creative impulse,
to reduce the adventure of humankind to a dusty heap of theorems. The issue, then,
is to present some of the unanswered and important problems that we continue to
confront, for it may be asserted that what we have truly learned and understood, we

discovered ourselves.
The purpose of this book is to present the structure of feedback control theory and to provide a sequence of exciting discoveries as we proceed through the text
and problems. If this book is able to assist the student in discovering feedback control system theory and practice, it will have succeeded.
THE AUDIENCE
This text is designed for an introductory undergraduate course in control systems for
engineering students. There is very little demarcation between aerospace, chemical,
electrical, industrial, and mechanical engineering in control system practice; therefore
this text is written without any conscious bias toward one discipline. Thus it is hoped
that this book will be equally useful for all engineering disciplines and, perhaps, will assist in illustrating the utility of control engineering. The numerous problems and examples represent all fields, and the examples of the sociological, biological, ecological,
and economic control systems are intended to provide the reader with an awareness
of the general applicability of control theory to many facets of life.We believe that exposing students of one discipline to examples and problems from other disciplines will
provide them with the ability to see beyond their own field of study. Many students pursue careers in engineering fields other than their own. For example, many electrical
and mechanical engineers find themselves in the aerospace industry working alongside
aerospace engineers. We hope this introduction to control engineering will give students a broader understanding of control system design and analysis.
In its first eight editions, Modern Control Systems has been used in senior-level
courses for engineering students at more than 400 colleges and universities. It also
has been used in courses for engineering graduate students with no previous background in control engineering.
THE NINTH EDITION
A companion website has been developed for students and faculty using the ninth
edition. The website contains practice exercises and exam problems, all the MATLAB
m-files and Simulink simulations in the book, Laplace and z-transform tables, written materials on matrix algebra, complex numbers, and symbols, units, and conver-


Preface

xvii

sion factors. An icon will appear in the book margin whenever there is additional related material on the website. Also, since the website provides a mechanism for continuously updating and adding control related materials of interest to students and
professors, it is advisable to visit the,website regularly during the semester or quarter when taking the course. The MCS website address is Jdorf.
With the ninth edition we continue to evolve the design emphasis that historically has characterized Modern Control Systems. Using the real-world engineering problems associated with designing a controller for a disk drive read system, we present

the Sequential Design Example (identified by an arrow icon in the text), which is considered seqentially in each chapter using the methods and concepts in that chapter.
Disk drives are used in computers of all sizes and they represent an important application of control engineering. Various aspects of the design of controllers for the disk
drive read system are considered in each chapter. For example, in Chapter 1 we identify the control goals, identify the variables to be controlled, write the control specifications, and establish the preliminary system configuration for the disk drive. Then in
Chapter 2 we obtain models of the process, sensors, and actuators. In the remaining
chapters we continue the design process, stressing the main points of the chapters.

In the same spirit as the Sequential Design Example, we present a design problem that we call the Continuous Design Problem (identified by a triple arrow icon in
the text) to give students the opportunity to build upon a design problem from chapter to chapter. High-precision machinery places stringent demands on table slide systems. In the Continuous Design Problem, students apply the techniques and tools
presented in each chapter to the development of a design solution that meets the
specified requirements.


Preface

The computer-aided design and analysis component of the book continues to evolve
and improve. The MATLAB* end-of-chapter problem set are identified by the graphical
icon in the text. Also, many of the solutions to various components of the Sequential Design Example utilize MATLAB with corresponding scripts included in the figures.
In the ninth edition, we introduce the use of Simulink as an efficient way for
MATLAB users to model, simulate, and analyze feedback control systems. Since
Simulink is an interactive tool utilizing graphical interfaces effectively, we believe
that the best way to learn about it is to jump right in and use it. Appendix B is devoted to the basics of Simulink where the student can walk through a sequence of
steps to construct and simulate a simple system. We attempt to provide basic information about Simulink that is as loosely tied to specific releases of the software as
possible. At the time of this ninth edition, the latest version is Simulink 3.0. As different versions of Simulink are released, previous introductions to Simulink Basics
will be posted on the MCS website-check there if you are having compatibility
problems with the Simulink models in this book.
Simulink examples are presented in Chapters 5 and 11. In Chapter 5, aircraft
roll control is investigated using Simulink. In Chapter 11, a Simulink simulation is developed to study a system in state variable form.

PEDAGOGY
The book is organized around the concepts of control system theory as they have been

developed in the frequency and time domains. A real attempt has been made to make
the selection of topics, as well as the systems discussed in the examples and prob* MATLABis a registered trademark of The MathWorks, Inc.


xix

Preface

lems, modern in the best sense. Therefore this book includes discussions on robust
control systems and system sensitivity, state variable models, controllability and observability, computer control systems, internal model control, robust PID controllers,
and computer-aided design and analysis, to name a few. However, the classical
topics of control theory that have proved to be so very useful in practice have been
retained and expanded.
Building Basic Principles: From Classical to Modern.
Our goal is to present a
clear exposition of the basic principles of frequency- and time-domain design techniques. The classical methods of control engineering are thoroughly covered: Laplace
transforms and transfer functions; root locus design; Routh-Hurwitz stability analysis;
frequency response methods, including Bode, Nyquist, and Nichols; steady-state error
for standard test signals; second-order system approximations; and phase and gain
margin and bandwidth. In addition, coverage of the state variable method is significant.
Fundamental notions of controllability and observability for state variable models
are discussed. Full state feedback design with Ackermann's formula for pole placement
is presented, along with a discussion on the limitations of state variable feedback.
Upon this strong foundation of basic principles, the book provides many
opportunities to explore topics beyond the traditional. Advances in robust control
theory are introduced in Chapter 12. The implementation of digital computer control systems is discussed in Chapter 13. Each chapter but the first uses a MATLAB
section to introduce the student to the notion of computer-aided design and analysis.The book concludes with an extensive References section, divided by chapter, to
guide the student to further sources of information on control engineering.
Development of Problem-Solving Skills.
Reading the chapters,

attending lectures and taking notes, and working through the illustrated examples are
all part of the learning process. But the real test comes at the end of the chapter with
the problems. The book takes the issue of problem solving seriously. In each chapter, there are five problem types:

Progressive

o
o
o
o
o

Exercises
Problems
Advanced Problems
Design Problems
MATLAB

Problems

For example, the problem set for State Variable Models, Chapter 3 (see page 159) includes 19 exercises, 36 problems, 6 advanced problems, 5 design problems, and 7 MATLABproblems. The exercises permit the students to utilize readily the concepts and
methods introduced in each chapter by solving relatively straightforward exercises
before attempting the more complex problems. Answers to one-third of the exercises are provided. The problems require an extension of the concepts of the chapter to
new situations. Introduced in the seventh edition to the problem set, the advanced
problems represent problems of increasing complexity. The design problems
emphasize the design task; the MATLABproblems give the student practice with
problem solving using computers. In total, the book contains more than 800 problems. Also, the MCS website contains practice exercises that are instantly graded
providing quick feedback for students. The abundance of problems of increasing

XX

Preface

complexity gives students confidence in their problem-solving ability as they work
their way from the exercises to the design and MATLABproblems. A complete instructor manual, available for all adopters of the text for course use, contains complete solutions to all end-of-chapter problems.
A set of M-files,the Modern Control Systems Toolbox, has been developed by the
authors to supplement the text. The M-files contain the scripts from each MATLABand
Simulink example in the text. You may retrieve the M-files from Prentice Hall at
www.prenhall.com/dorf.
Design Emphasis Without Compromising Basic Principles. The all-important
topic of design of real-world, complex control systems is a major theme throughout
the text. Emphasis on design for real-world applications addresses interest in design
byABET and industry. Each chapter contains at least one design example, including the following:

o

insulin delivery control (Sec. 1.11, page 22)

U low-pass filter (Sec. 2.9, page 72)

o
o
o
o
o

printer belt drive (Sec. 3.9, page 147)
Mars rover vehicle (Sec. 4.8, page 194)
Hubble Space Telescope pointing control (Sec. 5.11, page 259)

tracked vehicle turning control (Sec. 6.5, page 307)
laser manipulator control system (Sec. 7.8, page 368)

o engraving machine control system (Sec. 8.7, page 435)

o
o
o
o

remotely controlled reconnaissance vehicle (Sec. 9.8, page 505)
x-y plotter (Sec. 10.13, page 595)

automatic test system (Sec. 11.9, page 655)
ultra-precision diamond turning machine (Sec. 12.12, page 710)

U worktable motion control system (Sec. 13.9, page 762)

The MATLABsections assist students in utilizing computer-aided design and analysis
concepts and rework many of the design examples. In Chapter 5, the Sequential Design Example: Disk Drive Read System is analyzed using MATLAB.A MATLABscript
that can be used to analyze the design is presented in Figure 5.53, p. 274. In general,
each script is annotated with comment boxes that highlight important aspects of the
script. The accompanying output of the script (generally a graph) also contains comment boxes pointing out significant elements. The scripts can also be utilized with
modifications as the foundation for solving other related problems.


Learning Enhancement.
Each chapter begins with a chapter Preview describing
the topics the student can expect to encounter. The chapters conclude with an endof-chapter Summary and Terms and Concepts. These sections reinforce the important concepts introduced in the chapter and serve as a reference for later use.
A second color is used to add emphasis when needed and to make the graphs

and figures easier to interpret. Problem 12.4, page 726, asks the student to determine
the value of Ka to meet specified design goals. The associated Figure 12.4, p. 726,
assists the student with (a) visualizing the problem, and (b) taking the next step to
develop the transfer function model:


xxii

Preface

THE ORGANIZATION
Chapter 1 provides an introduction
to the basic history of control theory and practice. The purpose of this chapter is to
describe the general approach to designing and building a control system.

Chapter 1 Introduction to Control Systems.

Mathematical models of physical
systems in input-output
or transfer function form are developed in Chapter 2. A
wide range of systems, including mechanical, electrical, and fluid, are considered.
Chapter 2 Mathematical Models of Systems.

Mathematical models of systems in state variable form are developed in Chapter 3. Using matrix methods, the transient response
of control systems and the performance of these systems are examined.
Chapter 3 State Variable Models.

Chapter 4 Feedback Control System Characteristics.
The characteristics of
feedback control systems are described in Chapter 4. The advantages of feedback

are discussed, and the concept of the system error signal is introduced.
Chapter 5 The Performance of Feedback Control Systems. In Chapter 5, the per-

formance of control systems is examined. The performance of a control system is
correlated with the s-plane location of the poles and zeros of the transfer function of
the system.
The stability of feedback
systems is investigated in Chapter 6. The relationship of system stability to the characteristic equation of the system transfer function is studied. The Routh-Hurwitz
stability criterion is introduced.
Chapter 6 The Stability of Linear Feedback Systems.

Chapter 7 The Root Locus Method. Chapter 7 deals with the motion of the roots
of the characteristic equation in the s-plane as one or two parameters are varied.
The locus of roots in the s-plane is determined by a graphical method. We also introduce the popular PID controller.
Chapter 8 Frequency Response Methods.
In Chapter 8, a steady-state sinusoida input signal is utilized to examine the steady-state response of the system as the
frequency of the sinusoid is varied. The development of the frequency response plot,
called the Bode plot, is considered.

System stability utilizing frequency
response methods is investigated in Chapter 9. Relative stability and the Nyquis criterion are discussed.
Chapter 9 Stability in the Frequency Domain.

Several approaches to designing and compensating a control system are described and developed in Chapter
10.Various candidates for service as compensators are presented and it is shown how
they help to achieve improved performance.
Chapter 10 The Design of Feedback Control Systems.

The main topic of
Chapter 11 is the design of control systems using state variable models. Tests for con-

Chapter 11 The Design of State Variable Feedback Systems.


xxiii

Preface

troll ability and observability are presented, and the concept of an internal model design is discussed.
Chapter 12 deals with the design of highly accurate control systems in the presence of significant uncertainty. Five methods
for robust design are discussed, including root locus, frequency response, ITAE methods for robust PID controllers, internal models, and pseudo-quantitative feedback.
Chapter 12 Robust Control Systems.

Chapter 13 Digital Control Systems. Methods for describing and analyzing the
performance of computer control systems are described in Chapter 13.The stability
and performance of sampled-data systems are discussed.
Appendixes.

The appendixes are:

A

MATLABBasics

B

Simulink Basics

ACKNOWLEDGMENTS
We wish to express our sincere appreciation to the following individuals who have

assisted us with the development of this ninth edition as well as all previous editions:
Mahmoud A. Abdallah, Central Sate University (OH); John N. Chiasson, University of Pittsburgh; Samy EI-Sawah, California State Polytechnic University, Pomona;
Peter 1. Gorder, Kansas State University; Duane Hanselman, University of Maine;
Ashok Iyer, University of Nevada, Las Vegas; Leslie R. Koval, University of
Missouri-Rolla; L. G. Kraft, University of New Hampshire; Thomas Kurfess, Georgia Institute of Technology; Julio C. Mandojana, Mankato State University; Jure
Medanic, University of Illinois at Urbana-Champaign; Eduardo A. Misawa, Oklahoma State University; Medhat M. Morcos, Kansas State University; Mark Nagurka,
Marquette University; Carla Schwartz, The MathWorks, Inc.; D. Sybbaram Naidu,
Idaho State University; Ron Perez, University of Wisconsin-Milwaukee; Murat
Tanyel, Dordt College; Hal Tharp, University of Arizona; John Valasek, Texas A &
M University; Paul P.Wang, Duke University; and Ravi Warrier, GMI Engineering
and Management Institute.
OPEN LINES OF COMMUNICATION
The authors and the staff at Prentice Hall would like to establish a line of communication with the users of Modern Control Systems. We encourage all readers to send
Prentice Hall your e-mail address and pass along comments and suggestions for this
and future editions. By doing this, we can keep you informed of any general-interest
news regarding the textbook and pass along interesting comments of other users.
Keep in touch!
Richard C. Dorf·
Robert H. Bishop
Prentice Hall






1.1

Introduction

2

1.2

History of Automatic Control

1.3

Two Examples of the Use of Feedback

4

1.4

Control Engineering Practice

1.5

Examples of Modern Control Systems

7

8
9

1.6

Automatic Assembly and Robots

1.7

The Future Evolution of Control Systems

16

1.8

Engineering Design

16

18

1.9

Control System Design

1.10

Design Example: Turntable Speed Control

19

1.11

Design Example: Insulin Delivery Control System

1.12

Sequential Design Example: Disk Drive Read System

21
22
23

PREVIEW
In this chapter we describe a general process for designing a control system. A con-

trol system consisting of interconnected components is designed to achieve a desired
purpose. To understand the purpose of a control system, it is useful to examine examples of control systems through the course of history. These early systems incorporated many of the same ideas of feedback that are in use today.
Modern control engineering practice includes the use of control design strategies
for improving manufacturing processes, the efficiency of energy use, advanced automobile control, including rapid transit, among others. We will examine these very interesting applications of control engineering.
We also discuss the notion of a design gap. The gap exists between the complex
physical system under investigation and the model used in the control system synthesis. The iterative nature of design allows us to handle the design gap effectively
while accomplishing necessary trade-offs in complexity, performance, and cost in
order to meet the design specifications.
Finally, we introduce the Sequential Design Example: Disk Drive Read System.
This example will be considered sequentially in each chapter of this book. It represents a very important and practical control system design problem while simultaneously serving as a useful learning tool.

1


2

Chapter 1

Introduction

to Control Systems

1.1 INTRODUCTION
Engineering is concerned with understanding and controlling the materials and forces
of nature for the benefit of humankind. Control system engineers are concerned with
understanding and controlling segments of their environment, often called systems,
to provide useful economic products for society. The twin goals of understanding and
control are complementary because effective systems control requires that the systems be understood and modeled. Furthermore, control engineering must often consider the control of poorly understood systems such as chemical process systems. The
present challenge to control engineers is the modeling and control of modern, complex, interrelated systems such as traffic control systems, chemical processes, and robotic systems. Simultaneously, the fortunate engineer has the opportunity to control
many very useful and interesting industrial automation systems. Perhaps the most
characteristic quality of control engineering is the opportunity to control machines
and industrial and economic processes for the benefit of society.
Control engineering is based on the foundations of feedback theory and linear
system analysis, and it integrates the concepts of network theory and communication
theory. Therefore control engineering is not limited to any engineering discipline but
is equally applicable to aeronautical, chemical, mechanical, environmental, civil, and
electrical engineering. For example, quite often a control system includes electrical,
mechanical, and chemical components. Furthermore, as the understanding of the dynamics of business, social, and political systems increases, the ability to control these
systems will increase also.
A control system is an interconnection of components forming a system configuration that will provide a desired system response. The basis for analysis of a system
is the foundation provided by linear system theory, which assumes a cause-effect relationship for the components of a system. Therefore a component or process to be
controlled can be represented by a block, as shown in Fig. 1.1. The input-output relationship represents the cause-and-effect relationship of the process, which in turn
represents a processing of the input signal to provide an output signal variable, often
with a power amplification. An open-loop control system utilizes a controller or control actuator to obtain the desired response, as shown in Fig. 1.2. An open-loop system is a system without feedback.
Aij()p¢n-166p

c()ntl'otsystel1lutili~~saijactuating«leViceto control the process
directlywitl)Qllt usjng feedback.


FIGURE 1.3
Closed-loop

feedback control
system (with
feedback).

In contrast to an open-loop control system, a closed-loop control system utilizes
an additional measure of the actual output to compare the actual output with the desired output response. The measure of the output is called the feedback signal. A simple closed-loop feedback control system is shown in Fig. 1.3.A feedback control system is a control system that tends to maintain a prescribed relationship of one system
variable to another by comparing functions of these variables and using the difference
as a means of control.
A feedback control system often uses a function of a prescribed relationship between the output and reference input to control the process. Often the difference between the output of the process under control and the reference input is amplified and
used to control the process so that the difference is continually reduced. The feedback
concept has been the foundation for control system analysis and design.

A closed~I~~pcontrolsysteJlluses a measurement of the output and feedback of
thissigl\al~o~oOlP~re it with the desired output (reference or command).
Due to the increasing complexity of the system under control and the interest in
achieving optimum performance, the importance of control system engineering has
grown in the past decade. Furthermore, as the systems become more <;omplex,the interrelationship of many controlled variables must be considered in the control scheme.
A block diagram depicting a multivariable control system is shown in Fig. 1.4.
A common example of an open-loop control system is an electric toaster in the
kitchen. An example of a closed-loop control system is a person steering an automobile (assuming his or her eyes are open) by looking at the auto's location on the
road and making the appropriate adjustments.
The introduction of feedback enables us to control a desired output and can improve accuracy, but it requires attention to the issue of stability of response.

FIGURE 1.4
Multivariable
control system.