My understanding is that neither frequency nor voltage regulation are used. The fan speed is actually controlled by air friction across the blades (if you were to remove the blades from the fan and turn it on, it will spin very fast, even on low speed).
The control module uses capacitors in series in order to add reactance to the circuit, which reduces the current to the motor (reduces torque). The reduced current + the air friction from spinning results in a slower speed.
The module switches between 2 different capacitors depending on the speed you select. It works the same way as using the pull-chain on a 3-speed ceiling fan.
- Capacitor 1 for low speed
- Capacitor 2 for medium
- No capacitor for high speed
Note: I am not an electrician. This is just my understanding of how things work, and I may be mistaken.