Actuator saturation
= Actuator saturation
{title2=$u_{\mathrm{applied}}=\min(u_{\max},\max(u_{\min},u_{\mathrm{requested}}))$}
<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. https://www.fbswiki.org/wiki/index.php/PID_Control[Åström and Murray, PID Control: saturation and integral windup]{ref}