Transfer Function and Response Analysis

NAME:
NUMBER:

Q. 1. 1. 1.
Transfer Function (G) Poles Overshoots
(Mp) %
Peak Time (tp)
(Seconds)
Damping
Ratio (ζ)
933.6
---------------------
s^2 + 6.111 s + 933.6
-3.0555
+30.4018i
-3.0555 -30.4018i
72.9 0.103 0.1
933.6
---------------------
s^2 + 18.33 s + 933.6
-9.1665
+29.1476i
-9.1665 -29.1476i
37.1 0.106 0.3
933.6
---------------------
s^2 + 30.56 s + 933.6
-15.2775
+26.4614i
-15.2775 -
26.4614i
16.3 0.118 0.5
933.6
--------------------
s^2 + 43.2 s + 933.6
-21.6024
+21.6089i
-21.6024 -
21.6089i
4.33 0.145 0.707
933.6
---------------------
s^2 + 51.94 s + 933.6
-25.9717
+16.0958i
-25.9717 -
16.0958i
0.629 0.195 0.85
933.6
---------------------
s^2 + 61.11 s + 933.6
-30.5550 +
0.0000i
-30.5550 -
0.0000i
0 >3.5 1.0
933.6
---------------------
s^2 + 183.3 s + 933.6
-178.0876
-5.2424
0 >3.5 3.0
933.6
---------------------
s^2 + 366.7 s + 933.6
-364.0958
-2.5642
0 >3.5 6.0
Step Response: For constant Wn and varying Zt
Step Response
Time (seconds)
Amplitude
0 0.5 1 1.5 2 2.5 3 3.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
System: G
Peak amplitude: 1.73
Overshoot (%): 72.9
At time (seconds): 0.103
System: G
Peak amplitude: 1.37
Overshoot (%): 37.1
At time (seconds): 0.106
System: G
Peak amplitude: 1.16
Overshoot (%): 16.3
At time (seconds): 0.118
System: G
Peak amplitude: 1.04
Overshoot (%): 4.33
At time (seconds): 0.145
System: G
Peak amplitude: 1.01
Overshoot (%): 0.629
At time (seconds): 0.195
System: G
Peak amplitude: >= 1
Overshoot (%): 0
At time (seconds): > 3.5