# Identify transfer funtion given step response

This is the system with its step response below.

I'm asked to find the transfer function. Note that this is a question from an exam sheet and a computer can't be used.

I can say that it has to do with an underdamped system but will my transfer function have a zero as well? More specifically, will b1 in the following be zero? $$T(s)=\frac{b_1s+b_0}{s^2+2ζω_ns+ω_n^2}=\frac{b_1s+b_0}{(s+a)^2+ω^2}$$

I can also tell that b0 is equal to ωn^2 since the steady state error is zero and that ω=2.

To sum up, I'm having trouble with b1 and a if my speculations are correct.

• What's the input step size? – Chu Jul 23 '17 at 22:36
• 1 but I guess it's multiplied by that 2 in the diagram. – John Katsantas Jul 23 '17 at 22:37
• Ok, so r(t)= unit step. The initial slope of the response is not zero (at least, as far as I can see), so there may well be a zero. But I would try to fit a standard (no zeros) 2nd order using the log_dec method first and check the goodness of fit. – Chu Jul 23 '17 at 22:54