Freeze the integral whenever the output is saturated and the error would drive it further in. One condition, no new parameter, and it cannot destabilise the loop.
On a first-order plant with a PI controller and an actuator clipped well below what a large step demands, the unguarded loop overshoots 12.8% and takes 49 seconds to settle. With clamping the overshoot is zero and it settles in 25 — with identical gains. Back-calculation, which bleeds the integral by the amount that was clipped, is smoother and tunable: it reaches setpoint in about half the time clamping takes at the cost of roughly one percent overshoot.
It is not a substitute for tuning and it is not an improvement to a healthy loop. Give the same loop an actuator with plenty of headroom and all three behaviours produce the same response to within a fraction of a percent — which is the test that this is a saturation effect rather than a tuning one. Lengthening the integral time would also reduce the overshoot, and that is the wrong fix: it degrades every ordinary correction the loop makes for the rest of its life in order to protect against the exceptional one.
Estimate with the rule, then check it against the calculator that models it properly.
Open Integral Windup & Anti-Windup →Freeze the integral whenever the output is saturated and the error would drive it further in. One condition, no new parameter, and it cannot destabilise the loop. On a first-order plant with a PI controller and an actuator clipped well below what a large step demands, the unguarded loop overshoots 12.8% and takes 49 seconds to settle.