Your motor sounds like it might be a split phase motor as shown in fig9 which shows a fan type motor application.
What is your actual application? If this is a lightly loaded application such as the fan shown, it might work, but i would be inclined to look at at other options if the application is more demanding.
These type of controllers do work in the likes of ceiling fans etc, you could pick one of those up and try it.
1ph induction motor speed control can be very touchy in some applications so more would have to be known before definite recommendation can be made.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.