I am trying to figure out how to have a microcontroller control the speed of a low power AC motor. Does the gate of a triac operate off of AC or DC or is that even the right question to ask (I am new to this)? The idea would be to use the PWM pins on a microcontroller to trigger the gate of a triac to vary the speed of the motor. The motor runs off of 120V (wall outlet) and probably quite a bit less than 1 amp. It is just an aquarium powerhead.

 

Yes you can control it with a Triac.Triac operation is like this; triacs can switch both AC or DC. If you use the Triac to switch AC then the Triac stays on only when the gate receives current. Remove the gate currents and it switches off when the AC waves passes though the 0 volts transition. Contrary to SCRs that stay always on when triggered even if you remove the gate current, you must disconect all power to swith SCRs off when triggered.
If you have fish in the aquarium I do not recommend you the wave effect. If this is why you want to control the speed of the motor. This will create unnecessary stress on the fish. If you have only corals then it is great in order to pass diferent nutrients constantly through them changing the water currents. I used to breed/grow soft corals in a 60 gallons aquarium.

 

The tank just has soft corals, Large Polyp Stony corals, and a maroon clown which stays close to the rocks where the currents are fairly stable. The random currents were to benefit the corals.

So if a triac stays on once it is triggered all the way until the AC wave passes through 0v, that would suggest PWM on the gate won't be successful because the output from the triac will not pulse on and off other than perhaps pulsing off when the wave passes through 0v which doesn't do me any good. How can I use the triac to control the speed or is there a different direction that I need to look in?

 

You'll want a zero-crossing detector and a variable monostable. Trigger the monostable with the zero-crossing detector, and trigger the triac at the end of the monostable cycle. Or you could just use a commercial lamp dimmer, which works on this same idea.

Note: AC motors don't generally respond well to this kind of input. They respond better when we change both voltage and frequency together.

I know nothing about aquaria.