Here are responses of two plants, when you give a constant input 5unit(t) to the
ID: 2268291 • Letter: H
Question
Here are responses of two plants, when you give a constant input 5unit(t) to them Please find approximate TFs for the two plants. Test your answers in MATLAB by command step (5*TF) d. System: untitled1 System: untitled1 se Time (seconds): 1.29 Amplitude: 5.01 System: untitled1 Step F Time (seconds): 2.67 Time (seconds): 2.16 Amplitude: 0.5 Amplitude: 0.547 0.5 System: untitled 1 Time (seconds): 4.19 Amplitude: 0.489 4 0.4 System: untitled1 Time (seconds): 2.86 Amplitude: 3.79 0.2 4 6 4 Time (cerondel Time (cerondeExplanation / Answer
a ) From the plot the percentage OS is 25% which implies gheta = 0.4
the settling time is 2.86 = 4 / (gheta * Wn)
Wn= 3.49
The close loop poles are (s+1.39+2.77i)*(s+1.39-2.77i) = s^2 + 2.78 s + 9.605
The transfer function = 1
--------------------
s^2 + 2.78 s + 9.605
Matlab code for step response:
s=tf('s');
g= 1/(s^2+2.78*s+9.605);
step(feedback(g,1))
b)
From the plot the percentage OS is 10% which implies gheta = 0.46
the settling time is 4.19 = 4 / (gheta * Wn)
Wn= 1.6
The close loop poles are (s+0.95+1.28i)*(s+0.95-1.28i) = s^2 + 1.9 s + 2.541
The transfer function = 1
--------------------
s^2 + 1.9 s + 2.541
Matlab code for step response:
s=tf('s');
g= 1/(s^2+1.9*s+2.541);
step(feedback(g,1))
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