I've used desks with motorized faders! (and spent a couple days a week in high school running, maintaining, and programming a small half million dollar lighting setup for a big theater. ) Recently I've done some firmware programming on for theatrical/stage LEDs.

All this to say, did you ever consider writing a test sequence of various position and rate changes, and then analyze the actual vs commanded data offline to get an equation for the response? I've had some success doing that for a similar control problem.