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THE INSTITUTION OF ENGINEERS SRI LANKAENGINEERING COURSE

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PART ITI

323 - Control Systems Engineering

DATE: 7 November 2012 FROM: 0900 HRS to 1200HRS

DURATION: THREE HOURS

READ THE FOLLOWING INSTRUCTIONS CAREFULLY BEFORE ANSWERINGTHE QUESTION PAPER

1 Answer only five (05) questions and all questions carry equal marks. Themark assigned to each part of a question is given against that part.

2 All answers to the given questions should be underlined for the purpose ofeasy identification.

3 Write the question Number to which you answer on the cover pageappropriately.

1

Question 01

Figure Q 1 shows an industrial process temperature control system, which needs to becontrolled for temperature ( B) in the tank heated by an electric coil.

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Boiler Valveq

.....-- Tank/' "- ~

~ " >--r\\ ix r- ~-" L-

~'.# \ ..•.. I ••. 3 g:~t ;t 'x"-"'- t I 41- iHeating Coil

t Amp I , 0,. r / e e1 I ~- I (

I I • I I .~tI Steam/ ... I 8<, ,~ I L......< I exhaust

j~/'

L ___ J<,T/ b Solenoid Armature

I <,Amp Thermocouple

BB

Figure QI

(a) What is the block that marked as BB? What is the purpose of it? [2]

(b) What is the main purpose of Solenoid Armature? [3]

(c) Draw a complete functional block diagram for the closed loop system thatincludes the transducer, the controller, the plant and other entities. [6]

(d) Identify each output signal for each block/component (in given terms) on thediagram. [3]

(e) Describe the operation of the control system that you have drawn in (c). [6]

Question 02

(a) What is bandwidth? [2](b) Why negative feedback is invariably preferred in closed loop system? [2](c) What are the main advantages of Bode Plot? [2](d) What are the advantages of Nichols chart? [2](e) What are the two types of compensation? [2](f) What are the three types of compensators? [2](g) What is the significance of integral controller and derivative controller in a PID

controller? [3](h) Why derivative controller is not used in control systems? [2](i) What is the effect of PI controller on the system performance? [3]

2

Question 03

(a) Briefly explain (sketches can only be used to explain the answer) following for a2nd order control system: [8]

i) Peak time ii) Maximum overshootiii) Rise time iv) Delay time

(b) Figure Q3 shows the block diagram of a control system, and the response of thesystem output when apply a unit-step input. Assume that J = 1 kgnr',

Find the following:

i) Damping ratio ii) Natural frequencyiii) Values of K and L [12]

R(s)- qs)KJs

1s

L

c(t)

o 2 tFigure Q3

Question 04

(a) What is meant by system stability?[3]

(b) What are the conditions that should be satisfied for stability of a linear time-invariant system?[5]

(d) Determine the range of K for stability of the following characteristicequations.[12]

i. S4 + 3s3 + 6s2 + 18s + K = 0ii. S4 +10Ks3 +4S2 +12s+18=0

3

Question OS

(a) Define the following terms.[4]

i) Complementary Root Loci (CRL)ii) Root contours (RC)

(b) A unity negative feedback control system has an open loop transfer function given byKG(s) = --,---------

S(S2 + 4s + 13)Sketch the root locus plot of the system by determining the following. [16]

i) Centroid, number and angle of asymptotes.ii) Angle of departure of root loci from the poles.iii) Breakaway points if any.iv) The value of K and the frequency at which the root loci crosses the imaginary

axIS.

Question 06

(a) Defme following terms. [4]i. Phase marginii. Gain marginiii. Phase crossover pointiv. Gain crossover point

(b) Sketch the asymptotic bode plot for a unity feedback system characterized by looptransfer function,

G(s) = K(l + 0.5s)(1 + O.025s)S3 (1 + O.002s)(1 + O.005s)

Show that the system is continuously stable. Find the range of values for whichthe system is stable. [16]

4

~

Question 07

A feedback system is represented by a signal flow graph shown in figure Q4.

(a) Construct a state model of the system. [5]

(b) Find the coefficient matrix A of the state space model of part (a). [5]

(c) Determine the stability of the system. [5]

(d) Determine the transfer function of C(s)jU(s) from the state model of part (a). [5]

Figure Q7

Question 08

A machine is being designed to wrap boxes of chocolate. The boxes arrive at the machine on aconveyor belt. The list below shows the process steps in sequence.

i) The box arrives and is detected by an optical sensor (P). After this the conveyor (C)is stopped and the box is clamped by a gripper (H) in place, where it was stopped.

ii) A wrapping mechanism (W) is turned on for 2 seconds.

iii) A sticker cylinder (S) is turned on for 1 second to put consumer labeling on the box.

iv) The gripper (H) is turned off and the conveyor (C) is turned on.

v) After the box leaves the system returns to an idle state.

Develop ladder logic programs for the system using the following methods. [20]i) Timing diagramii) Process sequence bit.

It is extremely important that you include regular start and stop inputs.

5

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