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IIIIII Examination Paper SEMESTER: FIRST SEMESTER EXAMINATIONS 2008 UNIT: ENB30‘I INSTRUMENTATION AND CONTROL  THEORY 1 DURATION OF EXAMINATION: PERUSAL: 10 MINUTES
WORKING: 2 HOURS EXAMINATION MATERIAL SUPPLIED BY THE UNIVERSITY: EXAMINATION BOOKLETS  TWO (2) PER STUDENT
GRAPH PAPER MM  TWO (2) PER STUDENT
FORMULA SHEET  ONE (1) PAGE ATTACHED EXAMINATION MATERIAL SUPPLIED BY THE STUDENT: WRITING IMPLEMENTS
DRAWING IMPLEMENTS
CALCULATORS — ANY TYPE INSTRUCTIONS TO STUDENTS: Students are prohibited from having mobile phones or any other device capable of communicating information
(either verbal or written) in their possession during the examination NOTES MAY BE MADE ONLY ON THE EXAMINATION PAPER DURING PERUSAL TIME FOUR (4) QUESTIONS ONLY ARE TO BE ATTEMPTED, OF WHICH QUESTION ‘I IS COMPULSORY ATTEMPT QUESTION 1 IN A SEPARATE EXAMINATION BOOKLET ALL QUESTIONS ARE OF EQUAL VALUE Queensland University of Technology GUT GUT Kelvin Grove Carseldine Question 1 (COMPULSORY "ANSWER IN A SEPARATE BOOKLET) (a) Name one type of sensor that can be used for each of the following parameters
and, for each sensor, brieﬂy describe how it works:
(i) pressure
(ii) rotary motion
(iii)mechanical strain
(7 marks) (b) By sketching a diagram, describe how the 4terminal microohmmeter is used to measure low value resistances.
(5 marks) (c) By sketching a diagram, describe ONE of the following measuring equipment:
(i) a permanent magnet moving coil meter
(ii) a moving iron meter
(iii)an induction disc kWh meter
(5 marks) ((1) A PCbased displacement measurement system uses a 10bit (210 = 1024 steps)
ADC (analoguetodigital converter) to measure the output of a linear
displacement potentiometer. The DC output voltage of the linear displacement
potentiometer varies from 2.00 V to 8.00 V when the potentiometer is extended
from 0 mm to 500 mm. (i) What is the output voltage when the potentiometer is extended to a position of 100 mm? (4 marks)
(ii) What is the smallest displacement that can be detected by the displacement measurement system?
(4 marks) ENB301T1.081 cont./...... Question 2 (a) Consider the spring mass system shown in Figure 1. Determine a transfer function
between the applied force F , and the displacement of the mass x. (6 marks) (b) What are the poles of this system and what effect does the size of the mass and the
spring constant have on the frequency of oscillation of the system? (5 marks) (c) The transfer function of a motor is
6(8) 2 20 = Y(s)
S(s +10) no) position of the rotor and armature voltage respectively. Determine a differential
equation relating the angular position to the .armature voltage. (5 marks) where Y (3), R6?) are the Laplace transforms of the angular (d) Draw a block diagram of the motor in 1(c) being used in a closed loop negative feedback conﬁguration with a position sensor whose transfer function is TK 1 being s +
used in the feedback path. (3 marks)
(e) Determine the closed loop transfer function for the system in 1(0) (3 marks) (f) Write Matlab code to plot a root locus for the system of 1(c) as the gain on the sensor
varies. (3 marks) 17;. I
I
I
I
I
I
I
—> H Figure l ENB301T1.081 cont] .... .. \\\\\\\ Question 3 (a) Consider the system whose characteristic equation is KC? +1) ) = 0. Find the range of gain K for which this system is stable. 1 ____._____________
+s(s+l)(s+2Xs+3 (10 marks) (b) State the Nyquist stability criterion for the case where two right half plane poles exist
in the open loop transfer function. (3 marks) (c) Draw a Nyquist plot for a system whose open loop transfer function is 6(3) = K and comment on the effect K has on stability. (7 marks) 52(5 +1) (d) In constructing a compensator using op amps and discrete components what steps are
needed to take account of variations in component values and non—standard component values. (5 marks) ENB301T1.081 cont./...... Question 4 Consider the system shown in Figure 2 below. (a) Determine the location of the closed loop poles and hence the damping ratio, natural
frequency. (6 marks) (b) Determine the static velocity error constant (3 marks) (0) Determine the position the closed loop poles would need to be in order for the 5%
settling time to be halved. (3 marks) (d) Using the geometrical technique given in lectures design a lead compensator of the l
S + E
form GC (s) = KC 1 which when placed in the feedforward path will cause the
+ ﬁ.
S aT
root locus of the system to pass through the positions calculated in (c). (13 marks) Figure 2 ENB301T1.081 cont./ .... .. Question 5 (a) Deﬁne the terms gain and phase margin (2 marks) (b) Using Bode diagrams obtain the gain and phase margins for the system shown in
Figure 3 for the two cases K =1 & K:100. (16 marks) (0) In designing a lead compensator using a Bode plot according to a speciﬁcation of
phase margin why is it necessary to increase the maximum lead angle above the
difference between the existing phase margin and the desired value. (3 marks) (d) In designing a lag compensator what is the usual objective of such a compensator and
where must the compensator pole and zero be placed relative to the other poles? Give reasons. (4 marks) Figure 3 END OF PAPER ENB301T1.081 (0
Formula Sheet
0’
Lam} = ms) — f( *) L{:7f(r)} = ﬁns) —— sf( + )—f'(0*) F (s) Luo f(t)dt}= S
L{f(t — a)u(t — a)} = was) L{ 1(1)} = aF(as)
a
a)“. = a)” ‘II — g2 air—ﬂ, ﬂ=cos"lg 4 cw”
= i180°(2k +1) n—m I; (2%) = 6 H ENB301T1.081 ...
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 MCGREGOR
 Nyquist plot, Nyquist stability criterion, Queensland University of Technology

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