Absolutely - I've done this in industrial facilities and it's very common with LED's where it's generally called PWM (Pulse Width Modulation). Somewhat obviousl

Absolutely - I've done this in industrial facilities and it's very common with LED's where it's generally called PWM (Pulse Width Modulation). Somewhat obviously, you'd generally use a "hidden layer" converting the % output of the PID algorithm to % duty cycle. This works if your device can have a short enough cycle time for the PID algorithm to receive reasonable response feedback to its output. Ideally for PID to duty cycle conversions, your system should be low frequency (large "inertia") and the physical actuator/device you're controlling should have a high frequency (able to turn on/off rapidly, as LED's can with PWM). The difficulty for home HVAC is that you'd like to start/stop it as rarely as possible to extend the life of the motors. The cycle frequency ends up being in the same order of magnitude relative to the frequency that the house heats and cools. Obviously you can tune these things until the cows come home, and eventually you'll probably find some good settings. In reality, most people/installers/technicians will improperly tune a PID loop, especially if it converts to % duty cycle. Hysteresis will almost always work better for home HVAC. Alternatively, you can install (somewhat expensive) variable speed AC units and then happily use PID. You'll probably save a bit of energy and be more comfortable overall with more precise management of not only temperature, but also humidity.