Extract information about zeros of system from step response

Is there any way to know whether or not an unknown system has positive or negative zeros just from looking at the step response? This is the step response: • If I remember correctly, then if the step response initially moves in the opposite direction, then your system is non-minimum phase (has an right half plane zero(s)). But I do not know the formal proof for this. Apr 8 '17 at 0:00

Here is my approach to identifying this system.

Because the steady-state response to a step input is a nonzero constant, we can infer that the system must not have a zero at the origin (because the steady-state response to a step would be zero), and it must not have a pole at the origin (because the steady-state response to a step would be a ramp).

Typically, when systems start off in the "wrong" direction, we can infer the presence of a right-half-plane (or "nonminimum phase") zero. The location of the zero determines the degree of "undershoot". I started off by guessing the zero was at +1.

Next, I estimated the location of the poles. The dominant time constant appears to be about a second. Playing around with the transfer function in MATLAB suggested that a better estimate would be s = -1.5.

The nonzero initial condition suggested to me that there might be another zero. To keep the transfer function proper, I increased the order of the pole to 2.

I found that I got a reasonable fit with the transfer function $G_p(s) = \frac{(s-1)^2}{(s+1.5)^2}$, though you could obviously do better by tweaking parameters. 