Is the Double Acting Hydraulic Cylinder also adapted to usage where a velocity is given to the rod and it builds pressure in the hydraulic chambers which is then used in a hydraulic system?

Double acting Hydraulic Cylinders are mostly used with a hydraulic motor building the pressure in the chambers which then creates a movement on the rod depending on the pressure difference on each side of the piston.

Can the hydraulic cylinder be used the other way around, meaning can we impose a movement on the rod which will build a pressure in the chambers. I am planning on doing this with forces that greatly vary and I am often getting the Pressure Drop Below Zero error in the piston chamber.

Is the hydraulic cylinder model built for this type of usage?