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IIIII. Examination Paper SEMESTER: FIRST SEMESTER EXAMINATIONS 2009 UNIT: ENBBO’I INSTRUMENTATION AND CONTROL  THEORY 1 DURATION OF EXAMINATION: PERUSAL: 10 MINUTES
WORKING: 2HOURS EXAMINATION MATERIAL SUPPLIED BY THE UNIVERSITY: EXAMINATION BOOKLETS — TWO (2) PER STUDENT
FORMULA SHEET  ONE (1) PAGE ATTACHED
GRAPH PAPER MM  THREE (3) PER STUDENT 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 SECTION A — QUESTION 1 IS TO BE ATTEMPTED SECTION B — THREE (3) QUESTIONS ONLY ARE TO BE ATTEMPTED ATTEMPT EACH SECTION IN A SEPARATE EXAMINATION BOOKLET MARKS FOR EACH QUESTION ARE AS INDICATED 1
SECTION A Question 1 (COMPULSORY —ANSWER IN A SEPARATE BOOKLET) (a) The following questions related to the ladder program below: gang M0001
(i) Explain the deﬁnition of SOTU (Single Output Up). (2 marks)
(ii) What is the difference between output of LEDl and LEDZ after SW1 is toggled on? (2 marks)
(iii)What is the output of LED3 after the following operations (in order of occurrence)?
A SW1 is toggled on
B SW1 is toggled off
C SW2 is toggled on
(4 marks) Question 1 continued overleaf... ENB301Tl.09l cont./ ...... Question 1 (cont) (iv) Describe the condition that triggers the adding counter (CNT) C001 to reset.
(9marks) (b) A PC—based displacement merriment system uses a 10bit (210 = 1024 steps) ADC
(analogueto—digital 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) ENB301T1.091 cont./ ...... 3
SECTION B Question 2 A shock absorber in a road vehicle can alter road comfort by providing a “soft” ride for
highway driving and a “stiff” ride for offroad work. Figure 1 below simulates the
suspension of a car with M, B, and K values. (a) Determine a transfer function between the force exerted by the road f and the
vertical displacement x (5 marks) (b) Determine the pole locations as functions of B and K if M=10. (3 marks) (0) Determine values of B and K that would provide for poles at (i) —10 an d 2.5 ( stiff ride) (4 marks)
(ii) 5 and 5 (less stiff ride) (4 marks)
(iii) — 3 i j4 (soft ride) (4 marks) ((1) In the case of poles at — 3 i j 4 ,determine the expected overshoot and settling
time for a unit step of road force. (5 marks) Road Surface Figure 1 ENB301Tl .091 cont./ ...... Question 3 (a) A DC motor is to be used as an angular positioning device in a unit gain closed
loop conﬁguration as shown in Figure 2. (i) Determine the closed loop transfer function for this system (2 marks) (ii) Determine the characteristic equation (2 marks)
(iii) Determine the damping ratio and natural frequency as a function of the
constants K & a (4 marks)
(iV) Determine the steady state error expected from the system in ﬁgure 2 for a
unit ramp input (2 marks)
(V) Comment on how varying K & or might affect the steady state error to a
unit ramp input (2 marks) (b) Regarding the example in question 3(a) an engineer suggests placing an integrator
in feedforward path in order to reduce the steady state error to a unit ramp input
to zero, see Figure 3.
(i) Why would an engineer suggest such an action? (4 marks)
(ii) Determine the characteristic equation for the system in Figure 3
(4 marks)
(iii) Using a Routh test investigate the stability of the system in Figure 3 (5 marks) Figure 3 ENB301T1.091 cont./ ...... Question 4 Consider the system shown in Figure 4 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) (c) Determine the position the closed loop poles would need to be in order for the 5%
settling time to be halved while maintaining the same overshoot. (3 marks) (d) Using the geometrical technique given in lectures design a lead compensator of the s + 1
form GC (s) 2 KC ? which when placed in the feedforward path will cause the
s + ~—
aT
root locus of the system to pass through the positions calculated in (c). (l 3 marks) R(s) + . 6 0(5)
S(s + l) Figure 4 ENB301T1.091 cont./. ..... Question 5 (a) Deﬁne the terms gain and phase margin. (2 marks) (b) Consider a system with the open loop transfer function GH(s) = Wig—‘1‘) Using a
s 1s + Nyquist plot determine the stability of this system in closed loop. (5 marks) (0) Conﬁrm your ﬁndings in Question 5(b) by performing a root locus plot. (5 marks) (d) Using a Nyquist plot show the effect on system stability of adding a PD compensator with transfer function G6 (s) = K 2 (l + T25) in the feedforward path. (7 marks)
(6) Consider a system with the open loop transfer function GH(s) = ——————S—:—1————— s(s + 4) (s + 20)
Write a MATLAB program which will
(i) Perform a Bode plot
(ii) Perform a Root Locus plot
(iii) Determine the gain and phase margins (6 marks) END OF PAPER ENB301T1.091 (0
Formula Sheet
L{"— m} = sF<s> — f( +)
ﬂ
L{:;':—2f(t)} = s2F<s> —sf( + )—f'(0*) Lmﬂmﬁ}: Ff) L{f(t — a)u(t — a)} = e"‘”F(s) L{f(.;.j}=ap(as) ab‘: nV1”§2 ﬂ— 4 g0)"
_ i180°(2k + 1) n—m n m
219: * Z Z:
__ '=1 i=1 __l
0H n—m sin¢m :tﬁ
1+a 1
_«/ZT Z=N+P we ENB30YFL091 ...
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