Overshoot

Thermal control often has a contradictory feel: temperature rises slowly at first, then overshoots near the target.

The heater is at full power, but temperature takes a long time to rise. Increasing gains makes warm-up faster, but overshoot appears near the target. Integral action removes offset, but overshoot becomes larger. Filtering makes the display smoother, but control reacts late.

This is often blamed on bad PID tuning.

The core issue is not the three gains alone. Heat transfer is slow, heat storage is significant, and feedback is often delayed.

With proportional control alone, many systems get close to the target but remain slightly off.

Temperature stays 1°C below the target while the environment keeps removing heat. Motor speed stays a little low because load torque is always present. Liquid level remains slightly below target because leakage or outflow requires a baseline pump flow.

That long-lasting offset is steady-state error.

Integral action is valuable because it keeps accumulating as long as error persists. It slowly pushes output higher until the system can compensate for the long-term load.