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for most AC motors, varying the voltage will only change the torque.

To vary the speed of an AC motor Vary the frequency not the voltage.
Voltage will change torque if varied.
Other than Brushless DC motors.
DC motors do vary speed with variable voltage.
If the normal motor RPM is 1750 (1800).
Anything above 2600 RPM would be overspeed.
And could be hazardous.

Comemnts...
The M/G arrangement is a case of overkill. It is just way too involved for this job.
Increasing the voltage, on a properly loaded synchronous motor, just increases the current and torque not the speed.

Thanks,
Len

You may be able to hack a DC to AC converter.
Using a variable frequency i.e. 555 timer, driving an audio power amp.
with an output transformer to increase the voltage.
Since you are only driving a fractional HP motor.

Your post piqued my interest for two reasons: 1) AC servo motors are plentiful, but hobby-grade AC servo drivers are not, 2) off-grid inverters are pricey. I searched high and low for a decent pure-sine-wave inverter design that someone had open-sourced before conceding defeat and buying one off-the-shelf a couple of years ago (my inverter experience post is hear somewhere). Likewise, I bought new DC motors and Gecko drivers for my CNC mill after much (fruitless) research on a DIY solution with AC motors/drivers.

Turns out very few have gone through the trouble of designing/testing an inverter with a smooth waveform and appreciable output power. Even fewer have shared their experience with the rest of us. This particular "special-sauce" appears to be well-guarded.

In my travels, I found lots of references to Magic Sine Waves. Googling on "open source inverter" now yields more hits than I remember, too.

Looking forward to hearing what you come up with.

Another way might be to use a sine wave oscillator
driving an audio amplifier.
You get to keep a sine wave drive.
You will need a fairly powerful amp.
At a guess about 400 Watts.
And a suitable transformer on its output.
Careful of the top frequency (speed).
Yes some small motors do turn some very high speeds.

We never asked what type of winding is the motor?
True AC motors only can vary the RPM by varying the frequency.
The universal motor will vary with voltage change and will run on DC as well.
A good Dc power supply tracking positive and negative could be adapted to
power an AC motor. You would need to use an oscillator to vary the power supply
control voltages (?) and maybe a transformer to adapt to the desired voltage.

Did you ever solve the problem.
I spotted an AC drive in packages from 1/2 KW to 18 1/2 KW single phase drives
at120 Volt. And others for 3 phase for higher power.
The brand was "Vacon" They may or may not be variable speed / frequency.
The name Kaman was or is the North American distributor.
Good Luck.

Just to close this issue, I hacked a Triad 12V inverter years ago to get 50hz.. I went back in and added an external pot to trim the frequency up to about 175hz., nearly 3x. It was simply a test setup and would be way too expensive and bulky for a finished application .
The customer used it for a few weeks and decided that it wasn't worth the effort and cost for the benefit of the increased speed.
Project was disassembled and put back as original...

Got to move on!
Thanks all,

Len

Lenp, I work for the U.S. Postal Service and we usually use speed controls on our powered roller conveyors. There was only one case where we had to do what you were attempting and we did it by mounting the single phase drive roller under the rest of the idler rollers in the conveyor section.

The original drive roller position was replaced with an idler roller and O-ring attached to it and the powered roller. On the powered roller, we added a round clamp and grooved it to accept the o-ring that attaches to the rest of the idler rollers in that section. The larger clamp allowed the powered roller to move that section of the conveyor faster and solved our problem.

Just thought might want to know the 'Postal' method.

If you really need variable speed AC drive Single Phase. Here's one although for 230 Volt.
It is 0.75HP,3.5A,230V,1Ph:
Model No. 5WJK1
Grainger Industrial Supply. I believe it Covers 10Hz to 400Hz and has acceleration and? deceleration
timer/s.

I stumbled upon this one. It is close to your spec.