Control Theory and Marks

ME2142/ME2142E

NATIONAL UNIVERSITY OF SINGAPORE

ME2142/ME2142E – FEEDBACK CONTROL SYSTEMS
(Semester II : AY2009/2010)
Time Allowed : 2 Hours

INSTRUCTIONS TO CANDIDATES:

1.

This examination paper contains FOUR (4) questions and comprises FOUR (4) printed pages.

2.

Answer ALL FOUR (4) questions.

3.

All questions carry equal marks.

4.

This is a CLOSED-BOOK EXAMINATION with authorized materials: each student is allowed to bring in ONE (1) A4-sheet of personal notes for his/her own use. No stick-ons are allowed on this one sheet of personal notes.

PAGE 2

ME2142/ME2142E

QUESTION 1 (25 MARKS)
(a)

Ω( s )
2
,
=
V ( s ) (0.01s + 1)(0.1s + 1) where Ω(s ) and V (s ) are the Laplace transforms of the motor speed, ω (t ) , and the applied voltage, v(t ) , respectively. Determine the time response the motor speed, ω (t ) , when the applied input voltage, v(t ) , is a unit step. Sketch the response for ω (t ) .
(10 marks)
The transfer function of a motor is determined to be

Motor

(b)
R +

E

+

K

2
( s + 1)

5

-

-

Ω

1 s θ

Figure P1.1

The position feedback control system shown in Figure P1.1 has a proportional controller with gain, K, and an inner speed feedback loop.
(i)

Determine the value of the proportional gain, K, for the system to have a damping ratio of 0.5. Determine the corresponding damped natural frequency.
(7 marks)

(ii)

For the proportional gain obtained in (i) above, determine the steady-state error to a unit ramp input and sketch the likely response when the input r (t ) has the form shown in Figure P1.2 below.
(8 marks) r(t) 3

2

1

t, sec
0

1

2

3

4

5

6

Figure P1.2
Continue on next page….

PAGE 3

ME2142/ME2142E

QUESTION 2 (25 MARKS)
R

C

+
-

Figure P2.1


1 
A proportional-plus-integral controller, Gc ( s ) = K p 1 +
 T s  , is employed to control an

i 

unstable plant.
(a)