PID works well for most industrial controls, but it's a blunt instrument. Its mainly valuable because it's simple and doesn't really require much knowledge of t

PID works well for most industrial controls, but it's a blunt instrument. Its mainly valuable because it's simple and doesn't really require much knowledge of the plant to implement. No 'model' is really required, other than the vaguest knowledge of first order dynamics. Instead of model knowledge you just iteratively tune it until it works. If you need a really optimal control trajectory minimizing or maximizing for some parameter, you are willing to do the system identification necessary for it to work, and you don't much care whether an electrician can understand how it works model-based controls are much better. as /u/Communitivity mentioned so called 'model based control' (which is an umbrella of techniques) is a much more powerful tool.