Maybe I should add more context. I have specifically tried applying PID style feedback systems to computational problems, not controllers that interface with hardware, circuits, etc. My undergrad was in math and electrical engineering, I "pivoted" to software as a grad student (though I was always very involved in the software side of my department; I was a coder from when I was a kid.) The place I found it to work the best is with designing a homegrown autoscaler years before k8s ever became a viable thing for a company to play with [1]. Most of the problem domains I applied it to do not have linear models that can effectively model the theory. Yes I know that a PID is only proven to be stable when working with linear systems, but this is the reality of the problems I've worked with.

Eventually when if statements stop working I found that decision trees work great and XGBoost continues to be a great iteration of a decision tree.

[1]: I was an early hire at a tech unicorn and we built an autoscaler pretty early into the company's tenure. While it was a great success for a long time once k8s became established in the industry we had a really hard time training new talent to it and I left as we began a massive company-wide effort to move our workloads onto k8s.