LEROTHOLI POLYTECHNIC
SCHOOL OF ENGINEERING AND TECHNOLOGY
COURSE & YEAR:
SUBJECT
:
SUBJECT CODE :
ASSESSMENT :
DATE
:
DURATION
:
TOTAL MARKS :
ELECTRICAL ENGINEERING YEAR 3
CONTROL SYSTEMS II
CYS 322
SUPPLEMENTARY EXAMS
AUGUST 2021
3 HOURS
100 MARKS
EXAMINER
INTERNAL MODERATOR
:
:
L.MASUPHA
INSTITUTIONAL MODERATION PANEL
REQUIREMENTS
1.
Calculators
2.
Writing utilities
INSTRUCTIONS
1.
2.
3.
4.
5.
6.
Answer ANY FOUR questions.
Draw a line at the end of every question answer, before you start the next one.
Do not write in the margins, margins must be reserved for examiners
No communication is allowed during the examination, except with the invigilator.
Show all your working where calculations are involved.
Failure to follow any of the instructions 2 to 5 above may result in loss of marks.
PAPER CONSISTS OF:
Five(5) typed pages cover page inclusive.
DO NOT TURN THE PAGE BEFORE PERMISSION IS GRANTED.
USE OF MOBILE PHONES IS STRICTLY PROHIBITED
1
QUESTION ONE
a) i. What is control system?
[3 Marks]
ii. What are the two major types of control systems?
[2 Marks]
b) Identify the basic control loop elements to control the speed of a DC motor.
[16 Marks]
c) The output speed of a motor (ω rad/s) is related to the angle of the input sensor (θ radians) by the
transfer function
[4 Marks]
(ω(s) / θ(s)) = Km / (Tms + 2)
Where Km = 15s-1 and Tm = 4s
Determine the DC gain and time constant of the system.
QUESTION TWO
a) Define
i.
Mathematical model of a system,
ii.
Linear time invariant system,
iii.
[3 Marks]
[3 Marks]
Transfer function.
[3 Marks]
b) i. For the passive electrical network shown in figure Q2 ( b), determine the transfer function
relating V2(s) and V1(s)
[8 Marks]
ii. When C = 2µF and R1 =R2 = 1MΩ, determine the steady-state gain K and the time constant τ.
[4 Marks]
iii. Find an expression for the unit step response.
[4 Marks]
R1
C
V1(t)
R2
Figure Q2 (b) Passive electrical network.
2
V2(t)
QUESTION THREE
a) An automatic control system for the temperature of a room consists of a reference voltage fed into
a differential amplifier. This is connected to a solenoid valve which then manages gas flow into the
gas heater to heat the room. Negative feedback is provided by a measurement system which feeds a
differential voltage amplifier. Sketch the schematic diagram of the system and explain how the error
signal is detected.
[12 Marks]
b) Consider the control system in figure Q3 (b) and explain its operation.
[8 Marks]
Figure Q3 (b)
b) c) A temperature measurement system has a thermometer which produces a resistance change of
0.007Ω/°C connected to a Wheatstone bridge which produces a current change of 20mA/ Ω.
What is the overall transfer function of the system?
QUESTION FOUR
a) For an under damped system define:
i.
Rise time.
ii.
Delay time.
iii.
Overshoot
3
[5 Marks]
iv.
v.
Damped period
Settling time
[10 Marks]
b) Find the rise and 2% settling time and damped natural frequency of the second order system step
input response in figure Q4 (b)
[10 Marks]
Figure Q4 (b)
c) What will be the state of damping of a system having the following transfer function and subjected
to a unit step input?
[5 Marks]
1
𝐺(𝑠) = 𝑠2 +8𝑠+16
4
QUESTION FIVE
a) Derive the transfer function for the system in figure Q 5 (a)
[7Marks]
Figure Q 5 (a)
b) Is the driving of an automobile best described as a servomechanism or a process control system?
Why?
[5 Marks]
c) The parts of the process we are trying to control are referred to as________________ [2Marks]
i. Process control
ii. Process variables
iii. Process deviation
d) _______________ is a desired pre-determined threshold
i. Set point
ii. Warning indicator
iii. Feedback loop
[2 Marks]
e) _______________ signals represent unwanted random signal in the measuring device or in the
process.
[2 Marks]
i. Disturbance
ii. Noise
iii. Error
f) Regulation control objective has a ____________ set point in the control loop.
i. Variable
ii. Small
iii. Constant
[2 Marks]
g) What is the difference between the second order system which is over damped and that which is
critically damped?
[4 Marks]
h) Name one test signal used in time response analysis.
5
[1 Mark]