speed control of single phase induction motor
If you are asking wether or not you can control the speed of a single phase motor, many other questions arise, To keep it simple...shaded pole, psc (your common furnace motors) and ceiling fans, as well as your universal (your common electric drill and portable hand saws) the kind that use brushes...yes they can be speed controlled, usually not very smooth.
If it is a split phase or a capacitor start,(like your compressor motors or your machine motors) that need a constant torque application, and usually start under a heavy load, no way no how will these be controlled.
Only in a three phase world will these heavier loads be speed controlled and never cheapily
The smaller shaded pole and psc motors can be controlled with something as simple as a dimmer switch (provided your amp draw is not exceeded) or a dehummer switch,(specially made dimmers for fans).
Sparky