Steady-State Error

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.