Imagine for a moment that you keep the input velocity fixed throughout the identification experiment, then you might inject into the system a sudden change in the final commanded position set-point while measuring as feedback the current position of your equipment (e.g. joint encoders). You will thus come up with a bunch of profiles of commanded vs. feedback positions for your identification goal. To this end you can profitably rely on the ident tool of the MATLAB System Identification Toolbox.
Explore the system response against different input position steps and remember to validate any result over profiles sets that you did not use during identification.
Finally, you could assume that varying the input velocity will have an impact on the internal controller responsivity, since of course what you're going to model is the whole apparatus made up of the internal actuators, controller, etc. In theory, you should repeat the identification experiment over a range of different input velocities.