[YuechenLi]

I think the more valuable topic to study is feedback control loop in general as a part of control theory: gain, stability/oscillation damping, overshoot, hysteresis/minimum commit, and noise filtering strategies (low pass, Kalman, etc). Those are just very useful general concepts applicable to any kind of long running systems.

The actual PID controllers ,however, are actually really finicky to tune, and hard to reason about directly. Good for simple linear systems, but it falls apart as real life systems tend to be complex and nonlinear.