Operating Systems Chapter 1 Homework With Sensor Such The One Depicted The

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1000

Solutions Manual: Chapter 1

7th 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’s incubator

(d) Watt’s steam engine with ‡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 desired output signal

the sensor

the actuator

the actuator output signal

the controller

the controller output signal

the reference signal

the error signal

Notice that in a number of cases the same physical device may per-

form more than one of these functions.

Solution:

(a) A manual steering system for an automobile:

1001

1002CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

(b) Drebbel’s incubator:

(d) Fly-ball governor:

1.1. PROBLEMS AND SOLUTIONS 1003

2. Identify the physical principles and describe the operation of the thermo-

stat 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

1004CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

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:

1.1. PROBLEMS AND SOLUTIONS 1005

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 the variable, the actuator that

causes it to increase and/or decrease, the information path that completes

the feedback path, and the disturbances that upset the variable. You may

need to consult an encyclopedia or textbook on human physiology for

information on this problem.

(a) blood pressure

(b) blood sugar concentration

(d) eye-pointing angle

(e) eye-pupil diameter

Solution:

Feedback control in human body:

Variable Sensor Actuator Inform ation path Disturbances

a) Blood pressure –Arterial –Cardiac output –A¤erent nerve –Bleeding

dilation –Stress,Pain

b) Blo od sugar –Pancreas –Pancreas secreting –Blo od ‡ow to –Diet

5. Draw a block diagram of the components for temperature control in a

refrigerator or automobile air-conditioning system.

Solution:

1006CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

6. Draw a graph of the components for an elevator-position control. Indi-

cate how you would measure the position of the elevator car. Consider a

combined coarse and …ne measurement system. What accuracies do you

suggest for each sensor? Your system should be able to correct for the

fact that in elevators for tall buildings there is signi…cant cable stretch as

a function of cab load.

Solution:

A coarse measurement can be obtained by an electroswitch located before

7. Feedback control requires being able to sense the variable being controlled.

Because electrical signals can be transmitted, ampli…ed, and processed

easily, often we want to have a sensor whose output is a voltage or current

proportional to the variable being measured. Describe a sensor that would

give an electrical output proportional to:

1.1. PROBLEMS AND SOLUTIONS 1007

(a) temperature

(b) pressure

(d) ‡ow of liquid along a pipe (or blood along an artery) force

(e) linear position

(f) rotational position

(g) linear velocity

(h) rotational speed

(i) translational acceleration

(j) torque

Solution:

Sensors for feedback control systems with electrical output. Exam-

ples

(a) Temperature: Thermistor- temperature sensitive resistor with resis-

(b) Pressure: Strain sensitive resistor mounted on a diaphragm which

bends due to changing pressure

1008CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

(e) Position.

When direct mechanical interaction is possible and for “small” dis-

(h) Speed: Any toothed wheel or gear on a rotating part may be used to

(i) Acceleration: A mass movement restrained by a spring measured by

1.1. PROBLEMS AND SOLUTIONS 1009

8. Each of the variables listed in Problem 7 can be brought under feedback

control. Describe an actuator that could accept an electrical input and be

used to control the variables listed. Give the units of the actuator output

signal.

Solution:

(a) Resistor with voltage applied to it or mercury arc lamp to generate

9. Feedback in Biology

(a) Negative Feedback in Biology: When a person is under long term stress

(say a couple of weeks before an exam!), hypothalamus (in the brain) se-

cretes a hormone called CRF (Corticotrophin Releasing Factor) which

binds to a receptor in the pituitary gland stimulating it to produce ACTH

(Adrenocorticotropic hormone), which in turn stimulates the adrenal cor-

tex (outer part of the adrenal glands) to release the stress hormone Glu-

cocorticoids (GC). This in turn shuts down (turns o¤ the stress response)

for both CRF and ACTH production by negative feedback via the blood-

stream until GC returns to its normal level. Draw a block diagram of this

closed-loop system.

(b) Positive Feedback in Biology: This happens in some unique circum-

stances. Consider the birth process of a baby. Pressure from the head

of the baby going through the birth canal causes contractions via secre-

tion of a hormone called Oxytocin which causes more pressure which in

turn intensi…es contractions. Once the baby is born, the system goes back

to normal (negative feedback). Draw a block diagram of this closed-loop

system.

Solution:

1010CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

(a) Negative Feedback in Biology – Stress

(b) Positive Feedback in Biology – Child birth