I think in the general case, say you made a black box PID controller then attach it to some system it is supposed to control then you have to tune it, which isn

I think in the general case, say you made a black box PID controller then attach it to some system it is supposed to control then you have to tune it, which isn't so much "guessing" but a specific refining process. If you have a model for the system under control, then sure, it's math