Speed Control in Single Phase Motor

What format?

What type of single phase AC motor do you have, synchronous, universal, shaded pole, capacitor start or capacitor run. This will determine if you need to vary the voltage or frequency. Thus a pulse width modulation circuit approach or variable frequency approach will be needed. I presume that you have experience in power circuitry prototype work so that you will not burn your facility down from an insulation fire or insufficient cooling of the power electronics.

It also would be helpful to specify the speed range and mechanical load applied to this motor.

It probably will be just much easier to hire somebody to install and select the proper driver.