I did a simulation of a cavity, feedback signal was calculated using LQG controller. I assumed that there is not length -> angle coupling and 2 mirrors that form the cavity have the same equation of motions (Q and eigen frequencies are the same). Cost functional was chosen in such a way that frequencies below 15 Hz contribute much more then other frequencies.

Gains in the controller are calculated to minimize the cost functional.

This technique works well, but it requires full information about the system states. If we do not assume that cavity mirrors have the same equations of motion then we need to apply Kalman filter to approximate the position of one of the mirrors.