I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to have the sample rate considerably faster than the plant dynamics, but the physics of this system are such that this is inherently impossible. I can get some control of the system by hand-tuning a PID, but it seems considerably sub-optimal.
Is there a strategy for developing a controller like this?
Edit: I should add that the plant is this situation is a relatively complex LTI plant with reverberations caused by pure time delays. The delay cycles are a bit slower than the Nyquist frequency. The plant is stable.