Making the door move is simple. Making the door close with a natural movement however is where a little more curriculum is needed. The mechanics where the actuator meets the door, is where you will achieve this. Along with the door hinge itself. They make a cabinet door hinge that is starting to get more and more popular, as some of you already know. It has built in tiny air piston that allows the door to shut nice and slow, and soft. Some can be adjusted.

If it were me, I would make a fastener that allows play in the connection between a rod and the door. The rod being the one connecting to the actuator. Setting the actuator back from the door X amount of inches. The play will let the door free fall, allowing the hinge to slowly shut the door. On the hinge side, were talking less than a half an inch.

Yet again, the depletion of the center of the door, replaced by grill cloth, would look nice, and save a ton of work, and act more functional. In reality, No client wants to see a cabinet door open while using the system.

My 2 pesos