Varying the speed could be as simple as triac phase control of the AC input
to your motor.
Is there a triac or scr/bridge on the old controller?

When the voltage is dropped, there is more slipage in the magnetic field,
so the motor spins slower.

I think what you may have is a normal capacitor run INDUCTION motor.
Can you feel any cogging of magnetic poles when no power is applied?
If you spin the rotor by hand, do you get anything out of the input leads?
If not, its more likely and simple induction motor, as commonly used for
fans, garage door openers, etc.

Borrow or buy a 'fan speed control' commonly used for ceiling fans to see
if the
motor slows down smoothly. A fan dimmer is just like a like light dimmer,
except that the pot starts out at max voltage instead of minimum,
and often has a trimpot adjustment to set the minimum speed to
something other than zero output.

R
--=20
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