Actuator saturation ($u_{\mathrm{applied}}=\min (u_{\max },\max (u_{\min },u_{\mathrm{requested}}))$)

Actuator saturation means the applied control input reaches a device limit even if the controller requests a larger or smaller command. In the heater interpretation, the applied command is bounded between $0$ and $100\%$. If integral action continues accumulating a persistent tracking error beyond that limit, its stored integral can grow without producing the requested physical correction, delaying recovery when the goal changes. The unconstrained steady-state tracking error formulas require that the necessary command can actually be applied. ^[ref]