Modern control systems (12th edition) richard c dorf and robert h bishop

© 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.

MODERN CONTROL SYSTEMS
SOLUTION MANUAL

Richard C. Dorf

Robert H. Bishop

University of California, Davis

Marquette University

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



© 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.

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 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
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.

www.elsolucionario.org

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

iii


© 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.

T A B L E - O F - C O N T E N T S

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.

iv

Introduction to Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mathematical Models of Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
State Variable Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Feedback Control System Characteristics . . . . . . . . . . . . . . . . . . . . . . . 133

The Performance of Feedback Control Systems . . . . . . . . . . . . . . . . . 177
The Stability of Linear Feedback Systems . . . . . . . . . . . . . . . . . . . . . . 234
The Root Locus Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Frequency Response Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Stability in the Frequency Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
The Design of Feedback Control Systems . . . . . . . . . . . . . . . . . . . . . . . 519
The Design of State Variable Feedback Systems . . . . . . . . . . . . . . . . 600
Robust Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
Digital Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714


© 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.

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

www.elsolucionario.org
Desired
power
output

Error

-

Microprocessor

Laser

Power
Sensor

power

A driver controlled cruise control system:
Controller

Process

Foot pedal
Desired
speed

Power
out

Measurement

Measured

E1.2

Current i(t)

-

Driver

Car and
Engine

Actual
auto
speed

Measurement

Visual indication of speed

E1.3

Speedometer

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 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 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 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 camera control 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


© 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.

3

Exercises

E1.5

Tacking a sailboat as the wind shifts:

Error

Desired
sailboat
direction

-

Controller

Actuators

Sailor

Rudder and
sail adjustment

Wind

Process

Sailboat

Actual
sailboat
direction

Measurement
Measured sailboat direction

Gyro compass

E1.6

An automated highway control system merging two lanes of traffic:
Controller

Error

Desired
gap

-

Embedded
computer

Actuators

Brakes, gas or
steering

Process

Active
vehicle

Actual
gap

Measurement

www.elsolucionario.org
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

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 to Control Systems

Human 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
Optimal
flight path
Meteorological
data

Desired
Flight
Path

E1.10

Specified
Flight
Trajectory

Health
Parameters

Corrections to the
flight path

Gc(s)

G(s)

Controller

Aircraft

Location
and speed

Flight
Path

Unmanned aerial vehicle used for crop monitoring in an autonomous
mode:
Trajectory
error

-

Controller

UAV

Gc(s)

G(s)

Flight
Trajectory

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 pendulum control system using an optical 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

Optical
encoder

In the video game, the player can 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

Actuator

Process

www.elsolucionario.org
Desired
game
objective

Error

-

Player

Joystick

Measurement

Player
(eyesight, tactile, etc.)

Video game

Game
objective


© 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.

6

CHAPTER 1

Introduction to Control Systems

Problems
P1.1

Desired
temperature
set by the
driver

An automobile interior cabin temperature control system block diagram:

Error

-

Controller

Process

Thermostat and
air conditioning
unit

Automobile
cabin

Automobile
cabin temperature

Measurement
Measured temperature

P1.2

Temperature
sensor

A human operator controlled 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 composition control block diagram:
Controller

Process

Error
Desired
chemical
composition

-

Mixer tube

Valve

Measurement
Measured chemical
composition

Infrared analyzer

Chemical
composition


© 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.

7

Problems

P1.4

A nuclear reactor control block diagram:
Controller

Process

Error
Desired
power level

Reactor
and rods

Motor and

amplifier

-

Output
power level

Measurement
Measured chemical
composition

P1.5

A light seeking control system to track the sun:

Measurement

Light
source

Dual
Photocells

Ionization chamber

Controller

Ligh
intensity

Trajectory
Planner

Desired
carriage
position

Controller

-

Process

Motor
inputs

Error

Motor,
carriage,
and gears

K

Photocell
carriage
position

www.elsolucionario.org
P1.6

If you assume that increasing worker’s wages results in increased prices,
then by delaying or falsifying cost-of-living data you could reduce or eliminate the pressure to increase worker’s wages, thus stabilizing prices. This
would work only if there were no other factors forcing the cost-of-living
up. Government price and wage economic guidelines would take the place
of additional “controllers” in the block diagram, as shown in the block
diagram.
Controller

Process
Market-based prices

Initial
wages

-

Industry

Government
price
guidelines

Controller

Wage increases

Government
wage
guidelines

Cost-of-living

K1

Prices


© 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.

8

CHAPTER 1

P1.7

Introduction to Control Systems

Assume that the cannon fires initially at exactly 5:00 p.m.. We have a
positive feedback system. Denote by ∆t the time lost per day, and the
net time error by ET . Then the follwoing relationships hold:
∆t = 4/3 min. + 3 min. = 13/3 min.
and
ET = 12 days × 13/3 min./day .
Therefore, the net time error after 15 days is
ET = 52 min.

P1.8

The student-teacher learning process:
Process

Controller

Lectures

Error
Desired
knowledge

-

Teacher

Knowledge

Student

Measurement

Exams

Measured knowledge

P1.9

A human arm control system:
Process

Controller
u
Desired
arm
location

e

y

s
Brain

Nerve signals

z
Measurement

Visual indication of
arm location

Pressure
Eyes and
pressure
receptors

Arm &
muscles

d

Arm
location


© 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.

9

Problems

P1.10

An aircraft flight path control system using GPS:
Controller

Desired
flight path
from air traffic
controllers

Actuators

Computer
Auto-pilot

Error

-

Process

Ailerons, elevators,
rudder, and
engine power

Flight
path

Aircraft

Measurement
Measured flight path

P1.11

Global Positioning
System

The accuracy of the clock is dependent upon a constant flow from the
orifice; the flow is dependent upon the height of the water in the float
tank. The height of the water is controlled by the float. The control system
controls only the height of the water. Any errors due to enlargement of
the orifice or evaporation of the water in the lower tank is not accounted
for. The control system can be seen as:

www.elsolucionario.org

Desired
height of
the water
in float tank

P1.12

-

Controller

Process

Float level

Flow from
upper tank
to float tank

Actual
height

Assume that the turret and fantail are at 90◦ , if θw = θF -90◦ . The fantail
operates on the error signal θw - θT , and as the fantail turns, it drives the
turret to turn.

y

Wind

qW = Wind angle
qF = Fantail angle
qT = Turret angle

Controller

*

qW
qF
qT

qW

*

Turret

x

-

Process
Torque

Error

Fantail

Fantail

Gears & turret

qT


© 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.

10

CHAPTER 1

P1.13

Introduction to Control Systems

This scheme assumes the person adjusts the hot water for temperature
control, and then adjusts the cold water for flow rate control.
Controller

Error

Desired water
temperature

Process

Hot water

system

Valve adjust

-

Hot
water

Actual
water temperature
and flow rate
Desired water
flow rate

Cold water
system

Valve adjust

-

Cold
water

Measurement

Measured water flow
Measured water temperature

P1.14

Human: visual
and touch

If the rewards in a specific trade is greater than the average reward, there
is a positive influx of workers, since
q(t) = f1 (c(t) − r(t)).
If an influx of workers occurs, then reward in specific trade decreases,
since
c(t) = −f2 (q(t)).
Controller

Average
rewards
r(t)

P1.15

Desired
Fuel
Pressure

Error

-

f1(c(t)-r(t))

Process

q(t)

- f2(q(t))

Total of
rewards
c(t)

A computer controlled fuel injection system:

-

Controller

Process

Electronic
Control Unit

High Pressure Fuel
Supply Pump and
Electronic Fuel
Injectors

Measurement
Measured fuel pressure

Fuel Pressure
Sensor

Fuel
Pressure


© 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.

11

Problems

P1.16

With the onset of a fever, the body thermostat is turned up. The body
adjusts by shivering and less blood flows to the skin surface. Aspirin acts
to lowers the thermal set-point in the brain.
Controller

Desired temperature
or set-point from body
thermostat in the brain

Process

Adjustments
within the
body

-

Body
temperature

Body

Measurement
Measured body temperature

P1.17

Internal sensor

Hitting a baseball is arguably one of the most difficult feats in all of sports.
Given that pitchers may throw the ball at speeds of 90 mph (or higher!),
batters have only about 0.1 second to make the decision to swing—with
bat speeds aproaching 90 mph. The key to hitting a baseball a long distance is to make contact with the ball with a high bat velocity. This is
more important than the bat’s weight, which is usually around 33 ounces
(compared to Ty Cobb’s bat which was 41 ounces!). Since the pitcher can
throw a variety of pitches (fast ball, curve ball, slider, etc.), a batter must
decide if the ball is going to enter the strike zone and if possible, decide
the type of pitch. The batter uses his/her vision as the sensor in the feedback loop. A high degree of eye-hand coordination is key to success—that
is, an accurate feedback control system.

www.elsolucionario.org
P1.18

Define the following variables: p = output pressure, fs = spring force
= Kx, fd = diaphragm force = Ap, and fv = valve force = fs - fd .
The motion of the valve is described by yă = fv /m where m is the valve

mass. The output pressure is proportional to the valve displacement, thus
p = cy , where c is the constant of proportionality.

Constant of
proportionality

Spring

Screw
displacement
x(t)

K

fs

-

Valve position

fv

Valve

c

y

Diaphragm area

fd

A

Output
pressure
p(t)


© 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.

12

CHAPTER 1

P1.19

Introduction to Control Systems

A control system to keep a car at a given relative position offset from a
lead car:

Throttle

Position of
follower

Follower

car

Actuator

u

-

Controller

Relative
position

-

Position
of lead

Lead car

Fuel
throttle
(fuel)

Video camera
& processing
algorithms

Reference
photo

Desired relative position

P1.20

A control system for a high-performance car with an adjustable wing:

Desired
road
adhesion

-

Process

Actuator

Controller

Computer

Adjustable
wing

Road
conditions

Race Car

Road

adhesion

Measurement

Measured road adhesion

P1.21

K

Tire internal
strain gauges

A control system for a twin-lift helicopter system:
Measurement
Measured separation
distance

Desired separation
distance

-

Controller

Process
Separation distance

Pilot
Desired altitude

Radar

Helicopter
Altitude

Measurement
Measured altitude

Altimeter


© 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.

13

Problems

P1.22

The desired building deflection would not necessarily be zero. Rather it
would be prescribed so that the building is allowed moderate movement
up to a point, and then active control is applied if the movement is larger
than some predetermined amount.
Process
Controller

Desired

deflection

Hydraulic
stiffeners

-

Building

Deflection

Measurement

Measured deflection

P1.23

Strain gauges
on truss structure

K

The human-like face of the robot might have micro-actuators placed at
strategic points on the interior of the malleable facial structure. Cooperative control of the micro-actuators would then enable the robot to achieve
various facial expressions.

www.elsolucionario.org
Controller

Process

Error
Desired
actuator
position

-

Voltage

Electromechanical
actuator

Amplifier

Actuator
position

Measurement

Position
sensor

Measured position

P1.24

We might envision a sensor embedded in a “gutter” at the base of the
windshield which measures water levels—higher water levels corresponds
to higher intensity rain. This information would be used to modulate the

wiper blade speed.
Process

Controller

Desired
wiper speed

Wiper blade
and motor

Electronic
Control Unit

-

Measurement

K

Measured water level

Water depth
sensor

Wiper
blade
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.

14

CHAPTER 1

Introduction to Control Systems

A feedback control system for the space traffic control:

P1.25

Controller

Error

Desired
orbit position

Control
law

-

Actuator
Jet
commands

Process
Applied
forces

Reaction
control jets

Satellite

Actual

orbit position

Measurement
Measured orbit position

Radar or GPS

Earth-based control of a microrover to point the camera:

P1.26

Microrover
Camera position
command

Receiver/
Transmitter

Controller

G(s)

Gc(s)

Rover
position

Camera

Camera
Position

m
Ca
ap
er

Sensor

ea

iti
os

M

Measured camera
position

on

d
re
su

d
an

m
m
co

ap
er

m
ca

on

iti
os

P1.27

Desired
Charge
Level

Control of a methanol fuel cell:

-

Controller

Recharging
System

Gc(s)

GR(s)

Methanol water
solution

G(s)
Sensor

Measured charge level

Fuel Cell

H(s)

Charge
Level


© 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.

15

Advanced Problems

Advanced Problems
AP1.1

Control of a robotic microsurgical device:

Microsurgical
robotic manipulator

Controller
Desired
End-effector
Position

-

G(s)

Gc(s)

End-effector
Position

Sensor

H(s)

AP1.2

An advanced wind energy system viewed as a mechatronic system:
AERODYNAMIC DESIGN
STRUCTURAL DESIGN OF THE TOWER
ELECTRICAL AND POWER SYSTEMS

www.elsolucionario.org

SENSORS
Rotor rotational sensor
Wind speed and direction sensor
ACTUATORS
Motors for manipulatiing the propeller pitch

Physical System Modeling

CONTROL SYSTEM DESIGN AND ANALYSIS
ELECTRICAL SYSTEM DESIGN AND ANALYSIS
POWER GENERATION AND STORAGE

Sensors and Actuators
WIND ENERGY
SYSTEM

Software and
Data Acquisition

CONTROLLER ALGORITHMS
DATA ACQUISTION: WIND SPEED AND DIRECTION
ROTOR ANGULAR SPEED
PROPELLOR PITCH ANGLE

AP1.3

Signals and Systems

Computers and
Logic Systems

COMPUTER EQUIPMENT FOR CONTROLLING THE SYSTEM
SAFETY MONITORING SYSTEMS

The automatic parallel parking system might use multiple ultrasound
sensors to measure distances to the parked automobiles and the curb.
The sensor measurements would be processed by an on-board computer
to determine the steering wheel, accelerator, and brake inputs to avoid
collision and to properly align the vehicle in the desired space.


© 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.

16

CHAPTER 1

Introduction to Control Systems

Even though the sensors may accurately measure the distance between
the two parked vehicles, there will be a problem if the available space is
not big enough to accommodate the parking car.
Controller

Desired
automobile
position

Error

Actuators

On-board
computer

-

Steering wheel,
accelerator, and
brake

Process

Actual
automobile
position

Automobile

Measurement

Position of automobile
relative to parked cars
and curb

Ultrasound

There are various control methods that can be considered, including placing the controller in the feedforward loop (as in Figure 1.3). The adaptive
optics block diagram below shows the controller in the feedback loop, as
an alternative control system architecture.

AP1.4

Process

Astronomical
object
Uncompensated
image

Astronomical
telescope
mirror

Compensated
image

Measurement

Wavefront
reconstructor

Wavefront
corrector

Wavefront
sensor

Actuator & controller

AP1.5

Desired
floor

Error

-

The control system might have an inner loop for controlling the acceleration and an outer loop to reach the desired floor level precisely.

Controller #2

Outer
Loop

Desired
acceleration

Error

-

Controller #1

Elevator
motor,
cables, etc.

Inner
Loop
Measured acceleration

Acceleration
Measurement

Elevator

Floor


© 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.

17

Advanced Problems

An obstacle avoidance control system would keep the robotic vacuum
cleaner from colliding with furniture but it would not necessarily put the
vacuum cleaner on an optimal path to reach the entire floor. This would
require another sensor to measure position in the room, a digital map of
the room layout, and a control system in the outer loop.

AP1.6

Process
Desired
distance
from
obstacles

Error

-

Controller

Measured distance from obstacle

Motors,
wheels, etc.

Robotic
vacuum

cleaner

Infrared
sensors

www.elsolucionario.org

Distance
from
obstacles


© 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.

18

CHAPTER 1

Introduction to Control Systems

Design Problems
CDP1.1

The machine tool with the movable table in a feedback control configuration:
Controller

Error

Desired
position
x

Amplifier

-

Actuator

Process

Machine
tool with
table

Positioning
motor

Actual
position
x

Measurement

Position sensor

Measured position

DP1.1

Use the stereo system and amplifiers to cancel out the noise by emitting
signals 180◦ out of phase with the noise.
Process

Controller
Noise
signal
Desired
noise = 0

Shift phase
by 180 deg

-

Machine
tool with
table

Positioning
motor

Noise in
cabin

Measurement

Microphone

DP1.2

Desired
speed
of auto
set by
driver

1/K

An automobile cruise control system:
Controller

Desired
shaft
speed

-

Electric
motor

Process

Automobile
and engine

Valve

Measurement

Measured shaft speed

Shaft speed
sensor

Drive shaf t speed

K

Actual
speed
of auto


© 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.

19

Design Problems

DP1.3

An automoted cow milking system:
Measurement
Cow location

Vision system

Motor and
gears

-

Desired cup
location

Process

Actuator

Controller

Location
of cup

Robot arm and
cup gripper

Cow and
milker

Milk

Measurement

Vision system

Measured cup location

DP1.4

A feedback control system for a robot welder:
Controller

Process

Computer and
amplifier

Error

Voltage

Motor and
arm

www.elsolucionario.org
Desired
position

-

Weld
top
position

Measurement

Vision camera

Measured position

DP1.5

A control system for one wheel of a traction control system:
Antislip
controller

Engine torque

+

-

Wheel
dynamics

+

-

Wheel
speed

Sensor

+

Actual slip

1/Rw

Vehicle
dynamics

Brake torque

+

Vehicle speed

Antiskid
controller

Rw = Radius of wheel

Sensor

Measured
slip


© 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.

20

CHAPTER 1

Introduction to Control Systems

A vibration damping system for the Hubble Space Telescope:

DP1.6

Controller
Desired
jitter = 0

Error

Computer

-

Actuators

Gyro and
reaction wheels

Process
Signal to
cancel the jitter

Spacecraft
dynamics

Jitter of
vibration

Measurement

Measurement of 0.05 Hz jitter

DP1.7

A control system for a nanorobot:
Controller

Desired
nanorobot
position

Rate gyro
sensor

Error

-

Biocomputer

Actuators

Plane surfaces
and propellers

Process

Nanorobot

Actual
nanorobot
position

Measurement

External beacons

Many concepts from underwater robotics can be applied to nanorobotics
within the bloodstream. For example, plane surfaces and propellers can
provide the required actuation with screw drives providing the propulsion. The nanorobots can use signals from beacons located outside the
skin as sensors to determine their position. The nanorobots use energy
from the chemical reaction of oxygen and glucose available in the human
body. The control system requires a bio-computer–an innovation that is
not yet available.
For further reading, see A. Cavalcanti, L. Rosen, L. C. Kretly, M. Rosenfeld, and S. Einav, “Nanorobotic Challenges n Biomedical Application,
Design, and Control,” IEEE ICECS Intl Conf. on Electronics, Circuits
and Systems, Tel-Aviv, Israel, December 2004.
DP1.8

The feedback control system might use gyros and/or accelerometers to
measure angle change and assuming the HTV was originally in the vertical
position, the feedback would retain the vertical position using commands
to motors and other actuators that produced torques and could move the
HTV forward and backward.

© 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.

21

Design Problems

Process
Desired angle
from vertical (0o)

Error

-

Controller

Measured angle from vertical

Motors,
wheels, etc.

HTV

Gyros &
accelerometers

www.elsolucionario.org

Angle from
vertical