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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: Answer any FOUR questions. 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 openloop control
system and a closedloop control system. Include a block diagram illustrating the
difference between an openloop system and a closedloop system. Give one
example of an openloop system and one example of a closedloop 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 T t U t 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 timeconstant?
[5 marks]
(c) Calculate the closedloop transfer function for the system illustrated in Figure Q1(c)
for a value of controller gain K = 10. Is the closedloop system stable for this value
of gain? Generate the response to a unit step input and measure (i) the steadystate
error and (ii) the percentage overshoot. How would you eliminate the steadystate
error in this case?
PlantControlle R(s) U(s)+

Y(s)
K 2 0.6
0.4 0.4s s+ +
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 (firstorder, secondorder, 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 proportionalonly controller, as illustrated in Figure Q3(b). Determine the maximum value of proportional gain that can be used before the closedloop system becomes unstable.
Figure Q3 (b).
[8 marks]
Industrial ProcessController
R(s) U(s)+

Y(s)
K
G(s)
Q4. (a) Consider the sampled data control system illustrated in Figure Q4(b). List the steps
that need to be performed to analyze this system.
[5 marks]
(b) Determine the first four points of the sampleddata response, y(k), of the closedloop system shown in Figure Q4(b). In this system,
2 2 20 (s+275) (s17)( )
(s + 16s + 571) (s + 8s + 6354) G s =
0.2( ) 1 zC z
z = −
and the setpoint sequence, R(z), is a unit step. The sampling period is
T = 0.01 seconds.
Plant
Controller
R(z) U(s)
+

Y(s)
C(z)
ZOH
Y(z)
U(z)E(z)
T
G(s)
Figure Q4(b): Sampled data control system
[12 marks]
(c) A time delay of 0.1seconds is added to the transfer function G(s) of Q4 (b) i.e 0.1s
2 2 20 (s+275) (s17)e( )
(s + 16s + 571) (s + 8s + 6354) G s =
Evaluate how this delay effects the performance and stability of the closedloop system.
[8 marks]
Q5. (a) Your laboratory practice required you to interface a HP printer to a data acquisition card and design a controller to controller the position of the print cartridge carriage. Draw a block diagram of the print cartridge control loop, clearly identifying the most important elements of this control loop.
[5 marks]
(b) Describe how you interfaced both the motor and the sensor of the print cartridge carriage system to the computer. Describe how you tested this interface to ensure that it was working correctly.
[10 marks]
(c) With reference to your experience in DLX3 with the HP printer, describe (from start to finish) how you would design a controller for the HP printer. If you were part of a team of four engineers, describe how you would manage the project and allocate work to different individuals.
[10 marks]
Q6. (a) Design a PI controller for the system 82( )
10 1
seG s s
−
= +
to achieve a closedloop response
with a settling time of approximately 30seconds and a percent overshoot of less than 5%.
[15 marks]
(b) Determine the controller gain required to yield a steadystate error of 2% for the
system illustrated in Figure Q6(b). In this system,
5( ) (s+2) (s + 3)
G s =
the sampling period, T is equal to 0.05sec, ( 0.5)( ) 0.6
K zC z z +
= −
and the setpoint
sequence, R(z), is a unit step.
Plant
Controller
R(z) U(s)
+

Y(s)
C(z)
ZOH
Y(z)
U(z)E(z)
T
G(s)
Figure Q6(b): Sampled data control system
[10 marks]