(9) The Bode diagram of the open-loop transfer function G(s) of a unity feedback control system is obtained experimentally and is shown below when its loop gain K is set at its nominal value, Ko. 1. Find the gain and phase margins of the system from the diagram as best you can read. Also find the gain and phase crossover frequencies. Gain crossover frequency @1 =, Phase crossover frequency @2 =, GM = PM = 2. Repeat part (1) if the loop gain K is 10 times its nominal value (i.e., K = 10 Ko). Gain crossover frequency oi = Phase crossover frequency @2 = GM = PM =

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(9) The Bode diagram of the open-loop transfer function G(s) of a unity feedback control system
is obtained experimentally and is shown below when its loop gain K is set at its nominal
value, Ko.
1. Find the gain and phase margins of the system from the diagram as best you can read.
Also find the gain and phase crossover frequencies.
Gain crossover frequency @ị
Phase crossover frequency O2
GM =
PM =
2. Repeat part (1) if the loop gain K is 10 times its nominal value (i.e., K = 10 Ko).
Gain crossover frequency wi =,
Phase crossover frequency @2
GM =
PM =
Find out how much the loop gain K must be changed from its nominal value Ko (i.e., K =
a Ko) if the gain margin is to be 40 dB. (5 points)
3
a =
Find out how much the loop gain K must be changed from its nominal value Ko (i.e., K =
BKo) if the phase margin is to be 45°. (5 points)
4
B =
60
40
20
-20
40
-60
-80
-100
-120
0.01
0.1
1.0
10
100
1000
w (rad/sec)
-45
-90
-135
-180
-225
-270
0.01
0.1
1.0
10
100
1000
w (rad/sec)
(8op) (mf)D7
G(Jw)I (dB)
Transcribed Image Text:(9) The Bode diagram of the open-loop transfer function G(s) of a unity feedback control system is obtained experimentally and is shown below when its loop gain K is set at its nominal value, Ko. 1. Find the gain and phase margins of the system from the diagram as best you can read. Also find the gain and phase crossover frequencies. Gain crossover frequency @ị Phase crossover frequency O2 GM = PM = 2. Repeat part (1) if the loop gain K is 10 times its nominal value (i.e., K = 10 Ko). Gain crossover frequency wi =, Phase crossover frequency @2 GM = PM = Find out how much the loop gain K must be changed from its nominal value Ko (i.e., K = a Ko) if the gain margin is to be 40 dB. (5 points) 3 a = Find out how much the loop gain K must be changed from its nominal value Ko (i.e., K = BKo) if the phase margin is to be 45°. (5 points) 4 B = 60 40 20 -20 40 -60 -80 -100 -120 0.01 0.1 1.0 10 100 1000 w (rad/sec) -45 -90 -135 -180 -225 -270 0.01 0.1 1.0 10 100 1000 w (rad/sec) (8op) (mf)D7 G(Jw)I (dB)
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