---

FWIW, this is the AC controller I use for manual heating element control of my hacked popcorn popper:

https://www.amazon.com/gp/product/B00MFEA5AE/

Take a look at the pictures, and you'll notice that the control element is a small panel with a digital display (of duty cycle, 0-100), with a 4-conductor ribbon cable connecting to the driver board.

I got mine, gave some thought to how to wire it for controlling 120V, tried it with a lamp test load and it worked; so I had no need to try and figure out how the control head was signalling the driver. If you have the tools to understand it (a DMM might do it, scope would probably be better), you might (or might not) find you could use an analog-out from an Arduino or Pi in place of the control head. More complicated (I suspect) would be to keep the control element as a visible duty-cycle display, and hack it to allow an Arduino/Pi to "push the buttons" using digital output pins.

I don't really trust the power ratings of parts like this, but provided you have some airflow over the heat sink it seems like it would control a lot of fan.