|Nov17-12, 06:45 PM||#1|
Standard Form for second order systems.
Suppose there's a system with given uncertain parameters. And I would like to obtain certain Rise time, max. over shoot, settling time by adjusting those parameters.
Let's say this is the second order system;
T(s) = (ks + c) / (s2 + as + b)
First of all; for a second order system there is a standard form which is;
Wn2 / s2 + 2ζωns + ωn2
As we have to have the Wn2 in the numerator, it's not that way always. Just like in the example. So, what am I suppose to do at that point ?
If the transfer function T(s) looks like exactly the standard form, I could get the desired values by changing parameters. I think.
|Nov17-12, 08:53 PM||#2|
ωn2 / ( s2 + 2ζωns + ωn2 )
The constant in the numerator doesn't affect ζ, nor ωn, nor parameters such as % overshoot, rate of gain fall-off, etc., since these are calculated as ratios. The numerator is just a scaling factor for the plots.
The general expression is: A.ωn2 / ( s2 + 2ζωns + ωn2 )
where A can be seen to be the low frequency gain of this system.
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