how to characterise a rotary inverted pendulum ?

Hi all, I did a PID control to control a rotary inverted pendulum, but now I have to characterise it, overshoot, settling time, those stuff, in few words (the time response).

How I send and step unit , or impulse signal through arduino?, How I find natural frequency undamped, relative damped factor, etc.

Thanks in advance.

ingeoswaldo: How I find natural frequency undamped, relative damped factor, etc.

Presumably you know (or are expected to know) what those terms mean in terms of the behaviour of a dynamic system. By measuring the behaviour, you can estimate those values. If you know enough about the behaviour to describe it mathematically, you can calculate those characteristics instead. If you were expected to do this, obviously you would already have been shown how.