# Closed-Loop control system - Control Systems - Exam, Exams for Control Systems. Aligarh Muslim University

## Control Systems

Description: Main points of this past exam are: Closed-Loop Control System, Open-Loop System, Differential Equation, Domestic Central Heating, Electric, Transfer Function, Time-Constant
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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering
- Stage 3
(EELXE_8_Y3)
Autumn 2008
CONTROL SYSTEMS
(Time: 3 Hours)
INSTRUCTIONS:
Each question is worth 25 marks.
You MUST include a list of all MATLAB commands or Simulink diagrams used to
answer a question. Marks will be lost if you fail to do this.
Examiners: Dr. T O' Mahony
Prof. G. Hurley
Dr. S. Foley
Q1. (a) In your own words clearly explain the difference between an open-loop control
system and a closed-loop control system. Include a block diagram illustrating the
difference between an open-loop system and a closed-loop system. Give one
example of an open-loop system and one example of a closed-loop system.
[5 marks]
(b) The thermal response of a domestic central heating system is defined by the
differential equation () 0.003 ( ) 0.02 ( )
dT t Tt Ut
dt
+=
where T(t) is the building
temperature and U(t) is the input signal that switches on/off the electric/gas boiler.
Apply the Laplace Transform to determine a transfer function for this system. What
is the gain of the domestic heating system and what is the time-constant?
[5 marks]
(c) Calculate the closed-loop transfer function for the system illustrated in Figure Q1(c)
for a value of controller gain K = 10. Is the closed-loop system stable for this value
of gain? Generate the response to a unit step input and measure (i) the steady-state
error and (ii) the percentage overshoot. How would you eliminate the steady-state
error in this case?
Plant
Controlle
R(s) U(s)
+
-
Y(s)
K
2
0.6
0.4 0.4ss++
Figure Q1(c)
[15 marks]
Q2. (a) Consider the frequency responses illustrated in Figure Q2(a) and Figure Q2(b).
Figure Q2(a)
Figure Q2(b)
Estimate transfer functions from these data sets, giving reasons to support the type
of model you choose (first-order, second-order, etc) and clearly explaining how the
parameters were determined. Subsequently, use MATLAB to generate the Bode
diagrams for the functions you estimated and compare these responses with Figures
Q2(a) and (b). Comment on the accuracy of your estimates and describe how the
accuracy could be improved.
[20 marks]
(b) Explain how you would attempt to determine the frequency response of the printer
apparatus that you used in your laboratory practice.
[5 marks]
Q3. (a) Load the data file Aut08Q3.mat from the accompanying diskette to the MATLAB
workspace to generate the variables time input output that represent the
step response of an industrial process. Identify a transfer function for the system
from this data. Examine the accuracy of your model by comparing the response of
your transfer function with the variable output. In your opinion, is the model
sufficiently accurate for control purposes and how could the model be improved?
[17 marks]
(b) The transfer function G(s) identified from part (a) is to be controlled using a
proportional-only controller, as illustrated in Figure Q3(b). Determine the
maximum value of proportional gain that can be used before the closed-loop system
becomes unstable.
Figure Q3 (b).
[8 marks]
Industrial Process
Controlle
r
R(s)
U(s)
+
-
Y(s)
K
G(s)