Systems And Controls Engineering Question Paper

Systems And Controls Engineering

Course:Bachelor Of Science In Manufacturing Engineering And Technology

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
OF SCIENCE (MANUFACTURING)
SET 410: SYSTEMS AND CONTROL ENGINEERING

DATE: TUESDAY, 2ND DECEMBER 2008
TIME: 11.00 A.M. – 1.00 P.M.

INSTRUCTIONS:

(i)
There are a total of Five questions.
(ii)
Select any Three questions.
(iii)
Define all symbols used.
(iv)
Marks will be awarded for procedure, methodologies used and not necessarily the
final answer.

1.
A system has the following open loop Transfer Function:-

K
G(s) =

S(S ? )(
1 S ? )
6
(i)
If it is operated with unity feedback, determine:-
(a)
The closed loop Transfer Function. (2 Marks)
(b)
The angles of asymptotes. (2 Marks)
(c)
The breakaway points. (4 Marks)
(d)
The points of intersection of the asymptotes with the imaginary axis. (7 Marks)
(ii)
Plot the root locus. (5 Marks)

2.
The open loop Transfer Function of a unity feedback system is given by:-
K
G(s) =

(S ? 5
.
0 S)(S ? 25
.
0
S)
Design a suitable lead compensator for this system for the following specifications:-
(i)
Phase Margin =
o
45 .
(ii)
Steady State error should be less than 0.5 for a step function of 1,000 units. Draw the Bode Plots of uncompensated and compensated system in a semi log sheet and obtain the Transfer Function of the compensator. (20 Marks)

3.
Consider a unity feedback system with the open loop Transfer Function:-
K
G(s) =
S(S ? a)
(i)
The given frequency domain specifications are M = 1.04 and ? =11.55
P
P
radians/sec. Find the value of:-
a. ‘K’.
(7 Marks)
b. ‘a’.
(6 Marks)
(ii)
For the values of K and a, calculate the system:-
a.
Settling time.
(3 Marks)
b. Bandwidth.
(3 Marks)

4.
(a)
Demonstrate thorough understanding of:-
(i)
AC Servomechanisms.
(5 Marks)
(ii)
Position Servomechanisms.
(5 Marks)
(b)
Consider an armature controlled dc motor, given in Fig. Q4.
(i)
Derive an expression for Torque in terms of the angular velocity of the shaft. (3 Marks)
(ii)
Obtain its Transfer Function in terms of the angular shaft position and armature voltage. (8 Marks)

5
A specific closed loop control system is to be designed for an under damped response to a step input. The specifications for the system are:-
(i)
30% > percentage overshoot > 10%.
(ii)
Settling time < 0.4 seconds.

(a)
Identify the desired area for the determinant roots of the system. (8 Marks)
(b)
Determine the smallest value of a third root, r , if the complex roots are to represent the dominant response.
(4 Marks)
(c)
The closed loop system Transfer Function, T(s), is third order and the feedback has unity gain. Determine the forward Transfer Function
C(s)
G(s) =

E(s)
When the settling time is 0.4s and percentage overshot is 30%. (8 Marks)

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