Modern Control Systems – Solution Manual for Core Control Theory and System Analysis (Comprehensive Worked Solutions)

MODERN CONTROL SYSTEMS
SOLUTION MANUAL

PREFACE

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 a Window XP platform using MATLAB 7.3 Release 2006b and the
Control System Toolbox Version 7.1 and LabVIEW 8.2. It is not
possible to verify each solution on all the available computer platforms that
are compatible with MATLAB and LabVIEW MathScript. Please
forward any incompati- bilities 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

,Table of Content

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




Chapter 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 Current i(t)
Desired Micro- Power
Laser
power
output
- processor out
Measurement

Measured
Power
power
Sensor

,E1.2 A driver controlled cruise control system:


Foot pedal
Desired Actual
speed - auto
speed




Visual indication




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

, CHAPTER 1 Introduction to Control Systems

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 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



Actual

fly
of - position
of the fly




E1.4 An autofocus camera control system:

One-way trip time for the beam


Conversion factor




Emitter/