Motor Speed Controller Voltage Regulator
No that will not work.

That "voltage regulator" is not really a voltage regulator, it is a dimmer circuit, something like this:



These circuits work very well with resistive loads like lightbulbs and heaters.

They do not work very well with motors.

The simplest dimmer circuits which are better optimized for motor loads usually have a large inductor which I do not see on this "regulator".

But the main issue is that your motor is 3 phase and this dimmer is not, it is strictly 2 phase only.

You will need a proper 3-phase motor controller to adjust the speed of your 3-phase motor. If you use something else, it will either not work, blow up and generally end in tears.