Electronic – arduino – RC Snubber For Phase Angle Controller

While the answers above are excellent, you have failed to identify the types of AC motors you are using.

Are they brushed motors? Or squirrel cage types or?

If your motors do not have brushes, then you should not realistically be looking to control speed, as they will naturally try to assume the speed of the windings/armature ratio versus frequency of the supply, and under a real load, you could end up cooking the windings and the triac.

If your motors have brushes, (ie, like vacuum cleaner motors, blenders, drills and saws use brushed motors), then it's a lot easier, since you're dealing with a commutator that chops the voltage to something like pulsed dc.

Let's talk order magnitude for ease of understanding. Say your high voltage side is 50Hz mains power. In that case the reactance of the capacitor is:

\$X_C = \dfrac{1}{2\pi fC} = \dfrac{1}{2\pi\cdot50\cdot 47\cdot10^{-9}} \approx 68\text{k}\Omega\$

As the capacitor's reactance is much higher than R3 and therefore we can safely ignore R3 for sake of this discussion. Also the maximum gate voltage will be in the order of 1V, which can again be ignored with respect to eg. 100V mains voltage.

If the mains power is 100V then the gate current of the TRIAC will be approximately:

\$I = \dfrac{U}{X} = \dfrac{100}{68\text{k}}\approx 1.5\text{mA}\$

For an average TRIAC 1.5mA is sufficient gate current to trigger it and the photo-TRIAC has no part in it at all. When using a 230V mains, the current will even peak at approximately 5mA. As Wouter mentions in his answer aswell, the current calculated is shifted in phase with respect to the voltage across the TRIAC, causing the TRIAC to reliably trigger.

I am unsure why C1 was included in the circuit. The TRIAC doesn't act as an inductive or capacitive load, so there is little need for a snubber arounc C1 anyway. The other snubber C2/R4 can be much more benificial, although a snubber should ideally be dimensioned for a specific load.