class test 2007
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test2007TRANSCRIPT
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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.
A plant G has the Bode plot shown in Figure 2. It is known that all of the plants poles orzeros are located in the left half-plane of the complex plane, and possibly on the imaginary axis,and there are no poles or zeros in the right half-plane. It is proposed to control this plant usinga negative feedback control system shown in Figure 1; here K > 0 is the adjustable gain of anamplifier.
PSfrag replacementsK G(s)
+
Figure 1: The control system for Questions 1-3.
Q 1. For the case of K = 1, determine whether the closed loop system is stable. Assume nocrossover frequencies outside the frequency range shown in Figure 2. Explain the answer.
Q 2. Propose a value of the gain K such that the loop gain of the control system has a phasemargin of no less than 45. What will the gain margin of the control system in Figure 1 befor this value of K? Comment on stability and robustness of the closed loop system in thiscase.
Q 3. Suppose K is selected so that the closed loop system is stable. What will the steady stateerror of the closed loop system be when the reference input is a unit step?
19 September 2007
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ZITE 3203 Control Theory 2 Class Test 2
Bode Diagram
Frequency (rad/sec)
Pha
se (d
eg)
Mag
nitu
de (d
B)
100
80
60
40
20
0
20
40
60
80
100
100 101 102 103270
225
180
135
90
20 dB/decade
Figure 2: The Bode plot for the plant in Questions 1-3.
19 September 2007
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ZITE 3203 Control Theory 2 Class Test 3
Q 4. This question is not related to the previous questions.
Which of the figures shown in Figure 3 may represent positive root loci of a closed-loopcontrol system? Explain your answers.
Figure 3: Root loci for Question 4.
19 September 2007