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Unexpected Zeta and Overshoot relation

  1. Mar 15, 2015 #1
    I have a designed feedback control system trying to minimize the overshoot and the setting time. The zeta I (think) ended up with is 0.94. According to this formula:
    8058482ea4375b100288947a97eba5d3.png
    I am supposed to have a very small overshoot. However the step response of the system looks like this:
    ZGlafdw.png
    The poles are:
    0.0000 + 0.0000i (0 is also a zero, so do they cancel?)
    -2.0000 + 0.0000i
    -0.5313 + 0.1740i
    -0.5313 - 0.1740i
    -0.5600 + 0.0000i
    -0.0600 + 0.0000i

    Does that formula apply only for second order system? Or must I have miscalculated something?
     
  2. jcsd
  3. Mar 15, 2015 #2

    rude man

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    Homework Helper
    Gold Member

    Yes, the pole & zero at the origin cancel.
    Leaving you with a whopping 5th-order system. I wouldn't know any other way than to compute the actual response to a step input, eschewing any and all a priori formulas.
     
  4. Mar 15, 2015 #3
    Great, thanks.
     
  5. Mar 16, 2015 #4

    LvW

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    Your 5th order system has only one dominant complex pole pair with a pole-Q of app. Qp=0.52. The remaining poles are negative-real.
    Hence, I agree with you that we can expect a rather small overshoot only (assuming that the mentioned poles apply to closed-loop conditions).
     
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