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Standard Form for second order systems.

  1. Nov 17, 2012 #1
    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.
     
  2. jcsd
  3. Nov 17, 2012 #2

    NascentOxygen

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    Staff: Mentor

    Parentheses, please!!

    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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