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The Open University of Sri LankaDiploma in Technology - Level
04Academic Year 2012/13MEX4243 - CONTROL SYSTEMS ENGINEERING - TMA
1
(1) Answer all questions.(2) Write your registration number
clearly on your answer script.(3) Send your answer scripts under
registered cover to the address given below or put it into the
assignment box available at the Department of Mechanical
Engineering (Block 17), Nawala.
THE COURSE CO-ORDINATOR - MEX4243DEPARTMENT OF MECHANICAL
ENGINEERINGTHE OPEN UNIVERSITY OF SRI LANKAP.O. BOX 21,
NAWALANUGEGODA.
(4) Last date of submission3rd August, 2012(5) No late
submissionswill be accepted.
Q1. Select one physical quantity from the list given in Table
Q1, corresponding to yourregistration number.
First digit of the Reg. No. Physical quantity
1 , 2 Temperature3 , 4 Linear velocity5 , 6 Position
7 Fluid level
Table Q1
(a) Describe how the selected quantity may be measured using a
transducer.
(b) Now, suggest a real situation/ application within your
experience, where you wouldlike to control this quantity.
(c) Sketch a complete block diagram to show how you would use
the transducer (withother elements) in a feedback control system to
achieve your objective.
(d) Describe the function of each block of your control
system.(e) Obtain a transfer function to represent the
transducer.(f) Creating a model of the system that can be analyzed
with linear system methods.
(This mathematical model will be used in your TMA 2 & TMA
3)
State clearly the assumptions made in simplifying the model.
Note: K eep your model simple and closed loop system being only
of the second or thirdorder, at most fourth order.
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Question 02
Figure Q2 shows the block diagram of a control system, where
R(s) is the reference signaland C(s) is the output. Find the
transfer function C(s)/ R(s) of the system by
(a)simplifying the block diagram. Show all the steps
clearly.(b)Applying the Masons gain formula. Show all the steps
clearly.
Figure Q2
Q3.Figure Q3 shows a second order control system.
Figure Q3
Select G(s) according to your registration number from Table
Q2.
1st digit of the Registration number
1 2 3 4 5 6 7
G(s)
)17(
92
++ ss
)16(
112
++ ss
3
)2(
)1(
+
+
s
s
)14(
32
++ ss
)2(
3
+ss
)3)(2(
3
++ ss
)6(
12+s
Table Q3
(a)(i) Obtain the characteristic equation and calculate the
following when aunit step inputis applied to the system.
(I) Damping ratio (II) Natural frequency (III) Peak time(IV)
Rise time (V) Settling time
_R(s) + + + + + C(s)
-
G1 G3
H1
G4
H2
G2
R(s) + C(s)_
G(s)
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(ii) Use MATLAB to plot the step response of your system and
verify the answers in a(i).(iii) Comment on the nature of the step
response (damped, undamped . etc.) of your
system.
(b) (i) How would your system respond when aunitramp input is
applied? Explain how the
above characteristics in part a(i) of your system change with
this new input.
(ii) Plot your system with ramp response by using MATLAB and
verify the above answerin part b(i).
Note: For all MATLAB/ Other programs you have to attach both
scripts (code) and plots.
