Nice. But... why not make the levitation field coil a three-phase array, producing a controlled frequency rotating field, with the levitation feedback via overall field strength? Then you can levitate the object AND spin it invisibly. You could also provide power to the levitated object by a higher frequency modulation of the same field (via separate coil, if easiest.)
It seems to be an obvious 'next step' nobody I've ever seen takes. Has anyone?
For instance
I wish someone would do it. It's one of those projects I want to do, but know I'm never going to get time to do myself.
The rotational component of the field doesn't have to fully invert as in a generator or motor, just include variations in the amplitude. Any conductive disk in the levitated object will then have induced eddy currents proportional to the varying field, that will drag it around following the external field rotation. Does not have to be much force, since there's no friction.