Solutions Manual
Solutions Manual
, 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
, 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 Current i(t)
Desired Micro- Power
Laser
power - processor out
output
Measurement
Measured
Power
power
Sensor
E1.2 A driver controlled cruise control system:
Foot pedal
Desired Actual
speed - auto
speed
Visual indication of 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 fly lure long distances (the
1
, 2 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
(speed of light or
Emitter/
Solutions Manual
, 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
, 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 Current i(t)
Desired Micro- Power
Laser
power - processor out
output
Measurement
Measured
Power
power
Sensor
E1.2 A driver controlled cruise control system:
Foot pedal
Desired Actual
speed - auto
speed
Visual indication of 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 fly lure long distances (the
1
, 2 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
(speed of light or
Emitter/
