Math is rusty, but I was thinking about a transformer with the low voltage side having an RC network.
If you have any run or start caps lying around, it could be a place to start, I would not go out and buy one.
Find the biggest non-polarized cap you cna find and a resonable low voltage. Speaker crossover caps usually are rated at 100 V. e.g.
https://www.parts-express.com/cat/non-polarized-electrolytic-capacitors/1385
Otherwise 1 uF's Metalized polyester are common at say 50 to 100 V. Whatever low voltage you have and somewhere between 100 and 1000 ohms.
Look at the voltage either across the cap or resistor with an AC voltmeter.
I would suppose that if stuff worked and you looked at the voltage across the resistor or cap, there would be no discontinuities.
This really doesn't give you something to control, except 0-100% should not give discontinuities.
With an C circuit, you should be able to monitor the voltage across the cap and the voltage across the resistor (current) and see the phase angle.
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so, see where your "junk box" leads.
Some low voltage transformer
Some R
Some C that likes AC
Monitor V across Cap and I (Voltage across resistor) with scope, It will be isolated at that point.
Adjust R and C until you can see a phase difference.
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You won;t be controlling anything, just outputting a "% power" %(V^2) (if you use your table) and watching the waveform/
Meanwhile, try to find a universal motor for a final test. These are found in drills and will operate on AC and DC. Just don't use it in the beginning.