Rise time and overshoot for second-order system with a zero

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Kuriger9
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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!
 

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Kuriger9 said:
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!

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.
 
rude man said:
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.



Thank you, this certainly helps!