# Feedback Control Dynamic System

Topics: Control theory, Trigraph, Control system Pages: 825 (58216 words) Published: February 25, 2013
100

Solutions Manual
6th Edition

Feedback Control of Dynamic
Systems
.
.

Gene F. Franklin
.

J. David Powell
.

Abbas Emami-Naeini
.
.
.
.

Assisted by:
H.K. Aghajan
H. Al-Rahmani
P. Coulot
P. Dankoski
S. Everett
R. Fuller
T. Iwata
V. Jones
F. Safai
L. Kobayashi
H-T. Lee
E. Thuriyasena
M. Matsuoka

Chapter 1

An Overview and Brief
History of Feedback Control
1.1

Problems and Solutions

1. Draw a component block diagram for each of the following feedback control systems.
(a) The manual steering system of an automobile
(b) Drebbel’ incubator
s
(c) The water level controlled by a ‡ and valve
oat
(d) Watt’ steam engine with ‡
s
y-ball governor
In each case, indicate the location of the elements listed below and give the units associated with each signal.
the process
the process output signal
the sensor
the actuator
the actuator output signal
The reference signal
Notice that in a number of cases the same physical device may perform more than one of these functions. Solution:
(a) A manual steering system for an automobile:
101

102CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

(b) Drebbel’ incubator:
s

(c) Water level regulator:

(d) Fly-ball governor:

1.1. PROBLEMS AND SOLUTIONS

103

(e) Automatic steering of a ship:

2. Identify the physical principles and describe the operation of the thermostat in your home or o¢ ce. Solution:
A thermostat is a device for maintaining a temperature constant at a desired value. It is equipped with a temperature sensor which detects deviation from the desired value, determines whether the temperature setting is exceeded or not, and transmits the information to a furnace or air conditioner so that the termperature in the room is brought back

104CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL S to ra g e
chest

R e f in e r

S creen s
a n d c le a n e rs

M a c h in e
chest

P re sse s

D r y in g
s e c tio n

R eel

W ire
T h ic k
s to c k

CV
W h ite
w a te r

C o n s is te n c y
m e te r

C o n tro lle r

Figure 1.1: A paper making machine From Karl Astrom, (1970, page 192) reprinted with permission.

to the desired setting.
Examples: Tubes …lled with liquid mercury
are attached to a bimetallic strip which tilt the tube and cause the mercury to slide over electrical contacts. A bimetallic strip consists of two strips of metal bonded together, each of a di¤erent expansion coe¢ cient so that temperature changes bend the metal. In some cases, the bending of bimetallic strips simply cause electrical contacts to open or close directly. In most cases today, temperature is sensed electronically using,for example, a thermistor, a resistor whose resistance changes with temperature. Modern computer-based thermostats are programmable, sense the current from the thermistor and convert that to a digital signal. 3. A machine for making paper is diagrammed in Fig. 1.12. There are two main parameters under feedback control: the density of …bers as controlled by the consistency of the thick stock that ‡

ows from the headbox onto the
wire, and the moisture content of the …nal product that comes out of the dryers. Stock from the machine chest is diluted by white water returning from under the wire as controlled by a control valve (CV). A meter supplies a reading of the consistency. At the “dry end” of the machine, there is a moisture sensor. Draw a signal graph and identify the seven components listed in Problem 1 for

(a) control of consistency
(b) control of moisture
Solution:
(a) Control of paper machine consistency:

M o is tu re
m e te r

1.1. PROBLEMS AND SOLUTIONS

105

(b) Control of paper machine moisture:

4. Many variables in the human body are under feedback control. For each of the following controlled variables, draw a graph showing the process being controlled, the sensor that measures...