Find poles & zeros by looking at graph of step response

Question

If I am given a graph like the following:

How would I be able to find the poles and zeros with no other information given? Is it even possible to laplace transform it?

Answer 1

Well the derivative of the step response would be the impulse response, from which we can obtain the system function(inverse Laplace). We can roughly approximate the function in the graph, by looking at the time constant(approx, .002) and the asymptote(.75) $$c(t)=0.75(1- e^{-\frac{t}{0.002}})$$ and hence the derivative would be, $$h(t)=\frac{0.75}{0.002}e^{-\frac{t}{0.002}}$$ whose inverse would be $$H(s)=\frac{0.75/0.002}{s+\frac{1}{0.002}}$$ Which is the transfer function. So there's one pole at s= -500