Is there really a Motor in your refrigerator?
Most of them has an self interruptor inside like an old door bell.
So the membrane will go forward and back by an Electro magnet steered by an switch to compress the cooling fluid.
In series to that "motor" is an Overload Switch and an interruptor ( PTC ) for starting the process.
So an PWM would not work, also like frequency shifting.
Check this out, before start developing.
Compressors for cooling rooms has a normal motor. That needs the full voltage for startig up. The RPM can be steered by controlling the phase frequency. But i guess that will not work in a wide range, because the phase shifting in such a motor is done by an capacitator.