The write-up is very hard to understand.
Let's mention a couple of things.
The actuator needs to have limit switches.
The actuator might coast.
The relay would not be my choice. An automotive relay would be better.
I believe the ON time has to be greater than how long it takes to open/close the door respectively.
External limit switches are preferred. When limit switches are used, they have to be rated for the relay current. Automotive relay coild currents are fairly large. the contact ratings are like 40 A. You can buy two relays and a harness essentially configured for this application.
There is a suggested polarity because SOME have built in diodes. MOST schematics IGNORE this. there are a couple of different terminal arrangements as well. Even with limit switches, the system does not consume power when th\e door is either open or closed.
Simplisticly, one relay is OPEN and the other is CLOSE. If they are both on at the same time, the motor stops. The way the relays should be arranged, you will get an instantaneous stop but because there are nolimit switches, the actuator might coast.
Wiring is easy to describe and it;s mostly an automotive door lock type circuit. You can make the relay use a switched positive voltage to activate or a switched negative one.
The basic idea is to have the commons of the two relays connect to the motor and the NC contacts of both relays go to ground. In the unenergised state, the motor is shorted. Thinking a little far ahead. when the motor is commanded to stop via an external limit switch, the motor acts as a generator into a short. This can be a problem. When the actuator starts, you have a 2-5x surge in current. Again a problem. A 40 A rated.
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