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

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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: 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 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 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 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?

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 (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 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 sampled-data response, y(k), of the closed-loop system shown in Figure Q4(b). In this system,

2 2 20 (s+275) (s-17)( )

(s + 16s + 571) (s + 8s + 6354) G s =

0.2( ) 1 zC z

z = −

and the set-point 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) (s-17)e( )

(s + 16s + 571) (s + 8s + 6354) G s =

Evaluate how this delay effects the performance and stability of the closed-loop 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 closed-loop 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 steady-state 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 set-point

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]