Poles and zeros are based on the transfer function, which relates the output to the input. So in addition to the output signal, you'll also need to use the input signal. And you need to make sure that the frequency content of the input covers the frequencies that are relevant to your system, which you'll need to have some idea about.
One option is to try a single run with a Chirp Signal as the input, which might be difficult to use if you have low frequency poles or zeros.
Another approach would be to generate a single signal that is a series of sine waves.
Or you an run a loop over frequency stimulating the model with a single sine wave.
Once you have the input and output signals, then you can try ot use a function like tfest(), to estimate the transfer function, from which you can extract the poles and zeros.