This discussion focuses on analytically determining the performance characteristics of a second-order system with a specific open-loop transfer function G(s)=(s+1)/(s²+2s+1) given a unit step input. The key performance metrics include rise time, peak time, percent overshoot, and settling time. Participants suggest splitting the transfer function into two parts: one without zeros, where standard time-response functions apply, and another with a zero at the origin, utilizing the relationship between F(s) and its time derivative. This method allows for a comprehensive analysis without relying on MATLAB.
PREREQUISITESControl system engineers, students studying control theory, and anyone interested in the analytical performance analysis of second-order systems.
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!
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.