class test 2008
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test 2008TRANSCRIPT
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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
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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