PID control

A PID controller computes its output from three terms. Proportional acts on the current error: bigger error, bigger push. Integral adds up error over time so small persistent offsets eventually get corrected. Derivative reacts to how fast the error is changing, which damps overshoot. Many practical loops use only P and I, because the derivative term amplifies sensor noise and has to be filtered.

PID is everywhere (temperature, pressure, flow, motor speed) because it needs no detailed model and can be tuned on real hardware. Classic tuning rules such as Ziegler–Nichols date to the 1940s; modern practice usually starts from a step test or a model and refines on the bench.

Where it bites: a PID tuned at one operating point can be sluggish or oscillatory at another (different load, temperature or flow). Real implementations also need anti-windup, output limits, derivative filtering, smooth switching between manual and automatic modes, and a sensible sample rate. Those details, not the three-term formula, are where most field problems come from.