Hi @fadafido, welcome to the community! I see you posted a few questions, and that’s great. Hopefully you can find all the answers you need.
If you think about it, technically the projector screen is like a motorized window blind. Depending upon the power requirements of the screen’s motor, perhaps you can incorporate Somfy’s solution, like this:
I think you could also use a set of relays, or something like FortrezZ Mimo2+:
Motorized window shades
Low Voltage Lighting