The issue with Dougs is that as soon as the door closes again then the fan starts up again, which the way I'm reading it is not supposed to happen.
What about a time off delay timer (I think off delay - time starts on break and then maintains contact until X amount of seconds) on the doors? So that they can start the fan up but if the doors stay open for more then say 10 seconds then the fan shuts down.
This setup would allow them to start the motor with their start/stop station, the fan would start up, they could walk in as normal and the system would still run smoothly with proper airflow. If someone proped the door open or if it didn't close correclty, after 10 seconds the fan would shut down and then the system would have to be restarted from the start/stop station again.
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I was rereading original post - if the door contacts are Open when the door is closed then you would need to do a "time starts on make" instead of time starts on break...