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Homework Help: Performance Characterisitics Given a Zero in the System

  1. Mar 8, 2013 #1
    I have the equations to determine the rise time, peak time, percent overshoot, and settling time for a generic second-order system with no zeros in the system. Given a unit step input for the open-loop transfer function G(s)=(s+1)/(s2+2s+1) how do I analytically determine the performance characteristics (aside from using MATLAB)?

    Thanks in advance!
  2. jcsd
  3. Mar 8, 2013 #2

    rude man

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    You can split your transfer function into two parts. One part has no zeros so you an apply your time-response function directly.

    The second function is the same as the first except there is a zero in it - at the origin. A clever way to get the time response to this part is to realize that if F(s) → f(t) then sF(s) → df(t)/dt.
  4. Mar 8, 2013 #3

    Thank you, this certainly helps!
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