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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examination 2011
Module Title: Electrical Control Engineering
Module Code: ELEC
School: Electrical and Electronic Engineering
Programme Title: Bachelor of Engineering in Electrical Engineering – Award
Programme Code: EELEC_7_Y
External Examiner(s): Mr G. Beecher, Dr M. Duffy
Internal Examiner(s): Mr N. Canty
Instructions: Answer any three questions
Duration: 2 Hours
Sitting: Autumn 2011
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the
correct examination.
If in doubt please contact an Invigilator.
Q
Consider the RC circuit shown in Fig. 1 below, where the input voltage, vi t , is the DC supply
voltage. The output voltage, vo t , is the voltage across the capacitor C. The circuit can be
represented by the following differential equation;
v t dt
dv t v t RC o
o i
(a) Show that the system transfer function can be given by the following equation;
1
V s RCs
V s
i
o
7 marks
(b) Given that the value of the circuit components are as follows; R = 40Ω, and C = 0.05F, evaluate
the system transfer function. 6 marks
(c) Draw a pole-zero diagram to show the location of the system poles and zeros 7 marks
Fig.
vi t vo t
R
C
i
Q
(a)
Sketch the location of the poles and zeros on pole-zero diagrams for the following transfer functions;
(i) 3
s
s (ii) 3 4
2
ss s
s 6 marks
(b) Consider the closed loop control system shown below in Fig. 3.
Fig. 3
(i) Calculate the closed loop transfer function
R s
Ys 10 marks
(ii)Assuming s
R s
, calculate the steady state value of the output, yss , using the Final Value
Theorem (FVT) 4 marks
R(s) (^) U(s) Y(s)
E(s)
G(s)
H(s)
s
C(s)
Q
Consider the closed loop control system shown below in Fig. 4 where C(s) is a PD Controller.
Fig. 4
(a) Determine that the closed loop transfer function is given by
2
2 d p
p d
K^ K
s s
K K s
Rs
Ys
^
10 marks
(b) Determine values for Kp and Kd such that the closed loop system will have a critically
damped response with a 1% settling time, Ts 1 %= 6 seconds. Assume
n
Ts
10 marks
R(s) (^) U(s) Y(s)
E(s)
C(s) G(s)
H(s)
K (^) p sKd 2 1
s s
Laplace Transform Pairs
f(t) F(s)
1 Unit impulse^ t 1
2 Unit Step^1 t s
3 t 2
s
1 !
1
n
t
n
( n^ = 1,2,3,…) n s
n t ( n = 1,2,3,…) 1
n s
n
at e
s a
at te
2
s a
n at t e n
1
1!
( n^ = 1,2,3,…)
n s a
n at t e
( n = 1,2,3,…)
1
n s a
n
10 sin t 2 2
s
11 cos t 2 2
s
s
12 sinh t 2 2
s
13 cosh t 2 2
s
s
14 ^
at e a
1
s s a
15 ^
at bt e e b a
s a s b
16 ^
bt at be ae b a
s a s b
s
17 ^
at bt be ae ab a b
s s a s b
18 ^
at at e ate a
1
2
2
s s a
19 ^
at at e a
1
2 s^2 s a
20 e t
at sin
(^22)
s a
21 e t
at
cos
(^22)
s a
s a
e (^) n t
n (^) n t 2 2
sin 1 1
(^)
2 2
2
(^2) n n
n
s s
e (^) n t nt^2 2
sin 1 1
2 1 1 tan
0 ^ )
2 2 s (^2) n s n
s
e (^) n t nt^2 2
sin 1 1
2 1 1 tan
0 ^ )
2 2
2
(^2) n n
n
ss s
25 1 cos t
2 2
2
ss
26 t sin t
2 2 2
3
s s
27 sin t t cos t
2 22
3 2
s
28 t^ t
sin 2
2 22
s
s
29 t cos t
2 22
2 2
s
s
1 t 2 t
2 1
2 2
cos cos
2 2
2 1
2 2
2 2 1
2 s s
s
31 ^ t t^ t
sin cos 2
2 22
2
s
s
