Sluggish step response of control loop
If the control signal is at maximum and you are still not getting the system performance you want than the problem would be an under sized actuator.

Consider a controls engineer sitting in their car at a stop light that just turned green.  The engineer would like to reach a speed of 40 Mph as soon as possible.  So the engineer floors the peddle.  You can consider a floored peddle a saturated command signal.  At this point it is no longer up to the engineer to affect the acceleration of the vehicle.  The only way to improve the cars performance is by changing the car it self.  Not the control system (The driver in this case)