COLLEGE OF ENGINEERING
PUTRAJAYA CAMPUS
FINAL EXAMINATION
SEMESTER II 2013/2014
PROGRAMME
: Bachelor of Mechanical Engineering (Honours)
SUBJECT CODE
: MESB313/ MESB323
SUBJECT
:Modeling and Analysis of Dynamic Systems
:Modeling and Control of Dynamic Systems
DATE
: January 2014
TIME
: 3 Hours
Instruction to candidates:
1. DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE INSTRUCTED TO DO
SO
2. All answer and rough work must be done on the answer booklet. Use both sides of the
paper
3. There are total EIGHT questions in this paper
4. Answer ALL the questions
5. Questions are individually marked
6. Total marks are 100
_______________________________________________________________________
THIS QUESTION PAPER CONSISTS OF 10 PRINTED PAGES INCLUDING THIS
COVER PAGE.
MESB313 /MESB323, Semester II, 2013/2014
PART A
QUESTION 1. [15 marks]
A fixed disc is free to rotate on mass. Force f(t) is applied to the mass which is held by a spring as
shown in Figure 1. The force f(t) on the mass is considered as input and the output is the rotation θ(t)
of the disc. Find the transfer function 𝐺 (𝑠) =
𝛩(𝑠)
𝐹(𝑠)
[15 marks]
Figure 1
QUESTION 2. [15 marks]
A gears wheel system is shown in Figure 2. The input torque τ(t) is applied to the driver wheel 1 on
left and the output is the rotation θ3(t) of driven wheel 3. Find the transfer function 𝐺(𝑠) =
𝛩3 (𝑠)
𝑇(𝑠)
[15 marks]
Figure 2
Page 2 of 10
MESB313 /MESB323, Semester II, 2013/2014
QUESTION 3. [10 marks]
An operation amplifier circuit in Figure 3 derives an electromagnetic coil L on a servo valve. Write a
transfer function 𝐺 (𝑠) =
𝐼𝑣 (𝑠)
𝐸𝑖 (𝑠)
[10 marks]
Figure 3
QUESTION 4. [10 marks]
A hot metal piece is quenched at controlled bath temperature Tb, which is maintained by heat flow qin
in the tank. The process is shown in Figure 4. Model the process and find the transfer function
𝐺 (𝑠 ) =
𝑇(𝑠)
𝑄𝑖𝑛 (𝑠)
[10 marks]
qin
[marks 10]
Figure 4
Page 3 of 10
MESB313 /MESB323, Semester II, 2013/2014
PART B
QUESTION 5. [15 marks]
Closed loop temperature control system is shown in Figure 5. The capacitance of heating chamber C
= 0.1 Kcal/°C , R =40 °C sec/Kcal. Input is the heat added to the chamber Qi (s) and output is the
temperature of the chamber T(s). Find the followings:
𝑇(𝑠)
i)
Closed loop transfer function
[5 marks]
ii)
Find the steady state error ess (t) for step input 1/s
iii)
Find ess (t) with integral controller
𝑄𝑖 (𝑠)
𝐾𝐼 = 0.1
𝑠
for step input 1/s
[5 marks]
[5 marks]
Figure 5
QUESTION 6. [15 marks]
Closed loop system time response shown in Figure 6 belongs to temperature control system in
Figure 6 for Ki = 0.1. Find the followings:
i)
The oscillation frequency ωd rad/sec of responses
[5 marks]
ii)
Peak time Tp
[5 marks]
iii)
Find ζ, given 𝜍 =
1
𝑥
𝑙𝑛 1
𝑛−1 𝑥𝑛
2
1
𝑥
√4𝜋+[
(𝑙𝑛 1 )]
𝑛−1
𝑥𝑛
Page 4 of 10
[5 marks]
MESB313 /MESB323, Semester II, 2013/2014
Figure 6. Closed loop system response
QUESTION 7. [10 marks]
One second order and one first order bode plots are shown in Figure 7. Find two transfer functions
from the two plots.
Hint: Make use of second order response in appendix IV
[10 marks]
Figure 7. Closed loop system frequency response
Page 5 of 10
MESB313 /MESB323, Semester II, 2013/2014
QUESTION 8. [10 marks]
Add the two frequency plot shown in Figure 7. Use the bode plot given in appendix 1 and attach it
with your answer script.
[10 marks]
-END OF QUESTION PAPER-
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MESB313 /MESB323, Semester II, 2013/2014
APPENDIX I
Bode Plot Graph paper
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MESB313 /MESB323, Semester II, 2013/2014
APPENDIX II
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MESB313 /MESB323, Semester II, 2013/2014
APPENDIX III
tr 
 
d
  tan  1
d  n
1
2

1
2
1
n1
 
4
x
ln
x
1
n
 1 

n  1
 ln


x
x
1
2




2
Page 9 of 10
MESB313 /MESB323, Semester II, 2013/2014
APPENDIX IV
Second Order System Frequency Response
Page 10 of 10