Integral windup was more of a problem in analog controllers.

This type of controller does work properly in an open loop situation which causes integral windup with an integral function.

In this case integral windup can actually involve the integrator being turned off for periods of time until the response falls back into an acceptable range.

This also achieves a control error of zero in the steady-state, but avoids integral windup and can give a significantly improved control action compared to an optimized PID controller.

Integral windup particularly occurs as a limitation of physical systems, compared with ideal systems, due to the ideal output being physically impossible (process saturation: the output of the process being limited at the top or bottom of its scale, making the error constant).