It was discovered early in the process of finding good
weights for the controllers that a typical failing of a classic
PID controller was a significant issue: integrator saturation
and/or wind-up. Since the integrator function of the PID is
constantly accumulating the system error in an effort to force
the controller to respond to small errors that persist over time,
it acts as if it has a long memory. This can cause problems
as a large but temporary error is not forgotten or neglected
by the integrator and causes its output to skew heavily in one
direction for a long period of time, even past the point where
such a skew is beneficial. Similarly, if conditions exist where
a small error persists over a long period of time (such as
an actuator at its mechanical limit or other control weights
dominating the response of the system), the integrator will
accumulate this error and its output will attempt to correct all
of this error even if the conditions that originated in the error
have passed. If it is not possible to keep the error signal into
the integrator at a low value, the integrator can easily come
to have a significant negative impact on the overall control
effectiveness.