system response

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shalipse
shalipse 2012-5-8
Hi everyone, i am trying to obtain a response of a first order system to a step input, however the output the graph depicts doesn't match with what i expected. would someone be kind enough to give me a push in the right direction. the script for the program is thus:
clear all clc k1 = 2e4; k2 = 2e7; k3 = 2e4; c = 2e10; num= [(k1*c) (k1*k2)]; den= [(c*k1*k3) (k1*k2*k3)]; P=tf(num,den); display (P) step (P), grid title('y3 with a step input') %ylim([0 1])
Regards

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采纳的回答

Arkadiy Turevskiy
Your system P, as defined, is simply a gain. You can see that if you do
zpk(P)
ans =
5e-05 (s+0.001)
---------------
(s+0.001)
You can even see it if you look carefully at your num and den formulas:
num = k1*c*s+k1*k2 =k1*(c*s+k2)
den = c*k1*k3*s+k1*k2*k3 = k1*k3*(c*s+k2)
Therefore
num/den = k1* (c*s+k2) / (k1*k3* (c*s+k2)) = 1/k3
This is exactly what you see when you look at step response.
In short, recheck your formulas.
Arkadiy
  2 个评论
shalipse
shalipse 2012-5-8
Thank you Arkadiy for providing me with a good hint. but does this implies that the system is unstable? and what further analysis can be made to the system?.
kind regards
Arkadiy Turevskiy
Arkadiy Turevskiy 2012-5-9
the system is simply a gain, so it is stable. You need to recheck your formulas, most likely there is an error in how you calculate num and den.

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