PID get real fun when you model physical systems, like say filling a tank while trying to maintain liquid depth and temperature or maintaining a constant reacti

PID get real fun when you model physical systems, like say filling a tank while trying to maintain liquid depth and temperature or maintaining a constant reaction rate. You get to start taking laplace transforms. I had a ChemE professor who’d tell stories from the 30’s when chemical engineering was forming as a discipline. Common practice back in the day (before the theory) was to manually adjust parameters until things went unstable, then back off 5%. Turns out the optimum point is the inflection between stable and unstable behavior.