Ac Booster Fan Control?

I have an ac booster fan (inline) installed in a duct. It is controlled by a pressure switch attached to the plenum. It works 90% of the time. However, the switch acts up when it gets real cold. It sometimes won’t shut off or it will continue running for a long time. I only want it to run when the AC is on (ac/heat - same thing here). Any ideas? The fan is 120AC. I thought about monitoring the temperature in the plenum and looking for a delta, but that might not work well becuase the plenum temp will take a while after the cycle to cool off or heat up.

Thanks,

Tony