Actuator saturation influence

I need to design a controller for a physical plant which is inherently stable. I am simply trying to control it to a reference value and make the response quick enough. Sadly, but as in most cases my control actuator is saturating. I have modeled the saturation effect on Simulink software but my suspicion remains. When saturating I am no longer in linear regime. I would like to add that my controller includes only gain and no integrators which may wind up.

I will gladly read your thought on the subject.
Thanks,
Vlad