class test 2008

ZITE 3203 Control Theory 2 Class Test 1

ZITE 3203 Control Theory 2Class Test

All answers must be written in ink. Pencils may only be used for drawing, sketching orgraphical work.

Question 1

K G(s)+

Figure 1: The control system for Question 1.

In the control system shown in Figure 1 the transfer function G(s) is given to be

G(s) =0.5(s + 11)

(s + 1)3,

and K > 0 is a positive gain parameter. The Bode plot of G(s) is shown below in Figure 3 onpage 2.(a) For the case of K = 1, sketch the Nyquist plot for this system. From the Nyquist plot sketch,

determine the range of values of K for which the closed loop system is stable.

(b) For the case of K = 1, determine the gain margin of the system.(c) For the case of K = 1, predict the steady-state error of the response of the closed loop system

to a unit step input.

Question 2

K G(s)+

Figure 2: The control system for Question 2.

(a) For the system in Figure 2G(s) =

1

s(s + 1)(s + 2), K > 0,

sketch the root-locus diagram for the closed loop system.

(b) Using the sketch, determine, whether the closed loop system is stable for all K > 0.

17 September 2008

ZITE 3203 Control Theory 2 Class Test 2

100

80

60

40

20

0

20M

agni

tude

(dB)

102 101 100 101 102225

180

135

90

45

0

Phas

e (de

g)Bode Diagram

Frequency (rad/sec)

Figure 3: The Bode plot for Question 1.

17 September 2008