Incorrect integrator result with saturation

Hello,

I am implementing a PID loop where the input signal will be an acceleration signal that will be fed into a double integrator plant. As I have a limitation on my plant's ability to accelerate, I have placed a saturation on the PID block.

When I plot out acceleration signal and velocity signal after all this, I see something weird: when acceleration signal gets saturated, velocity signal does not change at all... which makes no sense as I expect to see output signal from integrator to keep increasing if what goes into it is held at constant.

What could possibly be causing this problem?

[Arkadiy Turevskiy]

can you attach the model? Hard to diagnose otherwise.