Dear customer, I understand your problem but there is a very important characteristic in your query and that is that the engine loses RPMs, there is a very important part of the operation of the minimum/idle, this component is known as the throttle potentiometer, the Minimum valve is the valve in the throttle body and it is in charge of regulating the minimum rpm load at which the engine is located.
For example, the minimum of an average engine is between 700 and 800 rpm, when the compressor is activated, this increases. The load of the engine and the valve of the minimum potentiometer now tends to open the acceleration a little more so that it can compensate this load and continue maintaining the rpm at these values of 700 and 800.
When the potentiometer has problems, when activating the air compressor, the load can cause the motor to decrease the rpm, sometimes it can even turn off, and obviously this causes vibration and noise in the motor due to this load difference.
I recommend you disassemble the throttle body and perform complete maintenance including the potentiometer, there is the possibility that it must be replaced, you will have to verify it before doing it, as well as its connections and wiring.