Well, you could rig it up with a light dimmer, or a ceiling-fan/motor control, as a practical test and see how that works - before working out an Arduino-included plan.
[Some light dimmers may not be good with inductive loads1 (those "rated" as fan controllers are.)]
Anyway, I don't anticipate joy to result from the rectification of a TRIAC output.
http://www.ilight.co.uk/downloads/iLIGHT%20Binder-HowDimmers.pdf
1 OK, right, a transformer is not a motor, but it is an inductive load.