That’s actually a neat idea. You could use a microcontroller with a small vibration sensor to pick up the cat’s purring frequency, then time the motor that opens the food compartment with a few milliseconds of delay so it clicks just when the cat’s ears are perked up. Keep the motor low‑current, maybe a tiny stepper or even a servo with a low torque rating, and run it from a 5 V regulator so the whole thing stays under a few watts. If you add a tiny OLED display you can log the feeding times and tweak the algorithm later. The key is smoothing the motor ramp‑up and making the sound output a gentle click instead of a loud whir. Sounds doable, and the cat will thank you by not batting at the feeder.