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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: enter image description here

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  • $\begingroup$ 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. $\endgroup$
    – fibonatic
    Apr 8 '17 at 0:00
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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.

Step response.

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