Today I was visiting a chemical industry and I had some time to ask the guide leader what control systems they are used here.
The answer was: Adaptive PID's and MPC.
I have heard that LQ-technique such as LQG or LQR are also used, most in robotics.
So then I asking the question: Why are robust control techniques such as $\mu$ synthesis , $H_2$ control and $H_{\infty}$ not applied in industries? I know...they are very advanced and difficult, but adaptive and predective are even more advanced. I also know that adaptive controllers have autotuning and predective controlers, such as MPC, is more like a LQG which can predict the future behavior of the system.
Most of the masters programme and Phd programme at universities are teaching robust control techniques and robust control techniques are not a new thing. But why aren't they applied practical in the industry?
Chemical processes are really slow (very long time constants) and the models are not that difficult either. Therefore, MPC is not that hard to implement. MPC gets hard when your process is difficult to model and you need very fast computation of the next control signal. The same reasons apply for adaptive PIDs.
Furthermore, as I already explained in some previous questions you had here. Focus to understand the real problem and not what the fanciest solution is from theory. $H_{\infty}$ and $\mu$ synthesis are nice but very difficult to apply, the gain to be won by it is simply too small if there even is one...