Cross-posted from signal processing stack exchange:
Consider the following approach for de-rating proportional feedback gains to account for a measurement delay by controlling a future-projected response:
In practice, I've found this works pretty well for the simple case of controlling the velocity of a DC motor whose position is measured by a rotary encoder. However, position control is troublesome, because typically we don't have the same phase lag in the position and the velocity measurements due to the need to compute velocity via some form of finite differencing (which has some inherent lag).
Given optimal PD gains for such a position-velocity system (e.g. as computed via LQR or pole-placement), is there comparably simple way to "de-rate" the gains in the above manner, but reflecting this difference? A naive attempt to divide the future-projection into "chunks" quickly devolved into calculus/algebra soup, and I admit such things are not my forte.
Any advice, including fundamentally different approaches to the problem, are welcome!
