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Amplitude
The unit step response can be shown as:
Model Order Reduction By Mixed...
1
Step Response
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Reducing the denominator by utilising the characteristics of the system, like damping ratio (ξ), undamped
natural frequency of oscillations (ω n ) etc.
For an aperiodic or almost periodic system, ξ = 0.99, number of oscillations before the system settles = 1
Since, ω n = 4/ξ*T s
Therefore, ω n = 4/ (0.99*3.93) = 1.0281
Reduced denominator:
D 2 (s) = s 2 + 2ξω n s + ω n
2
Therefore, D 2 (s) = s 2 + 2.0356s + 1.0569
Now, reducing numerator by Padé Approximation:
b 0 = 1.0569
b 1 = 2.0356
c 0 = 1
c 1 = - 1.08333
Now, reduced model representation:
Hence, final reduced model:
a 0 = b 0 c 0 = 1.0569
a 1 = b 0 c 1 + b 1 c 0 = 0.891
Its characteristics can be given as:
Rise Time: 2.3589
Settling Time: 4.1169
Settling Min: 0.9021
Settling Max: 1.0000
Overshoot: 0
Undershoot: 0
Peak: 1.0000
Peak Time: 10.3072
0
0 1 2 3 4 5 6
G s =
G s =
Time (sec)
a 0 + a 1 s
s 2 + 2.0356s + 1.0569
1.0569 + 0.891s
s 2 + 2.0356s + 1.0569
www.ijceronline.com ||May ||2013|| Page 92