Download Closed Loop Transfer Function - Electrical Control Engineering - Exam and more Exams Electrical Engineering in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Summer Examination 2001/
Module Title: Electrical Control Engineering
Module Code: ELEC 7003
School: Electrical and Electronic Engineering
Programme Title: Bachelor of Engineering in Electrical Engineering – Year 3
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: Summer 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 RLC 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;
itdt dt c
dit vi t Rit L ()
(a) Show that the system transfer function can be given by the following equation;
LC
s L
R
s
LC
V s
V s
i
o 1
2
10 marks
(b) Given that the value of the circuit components are as follows; R = 15Ω, L = 5H and C = 0.02F,
evaluate the system transfer function. 5 marks
(c) Draw a pole-zero diagram to show the location of the system poles and zeros 5 marks
Fig.
vi t
vo t
Q
(a)
Sketch the location of the poles and zeros on pole-zero diagrams for the following transfer functions;
(i) 5
s
s (ii) 2 5
2 ss 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)
1
H(s)
s
12
C(s)
Q
Consider the closed loop control system shown below in Fig. 4 where C(s) is a PI Controller.
Fig. 4
(a) Show that the closed loop transfer function is given by
7
2 p i
p i
K K
s s
K s K
Rs
Ys
10 marks
(b) Determine values for Kp and Ki such that the closed loop system will have a critically
damped response with a 1% settling time, Ts 1 %= 18 seconds. Assume
n
Ts
10 marks
R(s) (^) U(s) Y(s)
E(s)
C(s) G(s)
1
H(s)
s
K
K
i p 7 1
s
Laplace Transform Pairs
f(t) F(s)
1 Unit impulse^ t 1
2 Unit Step^1 t s
3 t 2
s
4 1 !
1
n
t
n
( n^ = 1,2,3,…) n s
5
n t ( n = 1,2,3,…) 1
n s
n
6
at e
s a
7
at te
2
s a
8
n at t e n
1
1!
( n^ = 1,2,3,…)
n s a
9
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 s a
2
(^20) e t
at
sin
(^22)
s a
21 e t
at
cos
2 2
s a
s a
22
e (^) n t
n (^) nt 2 2
sin 1 1
2 2
2
(^2) n n
n
s s
23
e (^) n t nt^2 2
sin 1 1
2 1 1 tan
0 ^ )
2 2 s (^2) ns n
s
24
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
30
1 t 2 t
2 1
2 2
cos cos
2 2
2
2 2
2 2 1
2
s s
s
31 ^ t t^ t
sin cos 2
2 22
2
s
s
