The waveform may be sine, triangular or square, and the pole count may
be between 3 and 9
Pole count in motors generally refers to magnetic poles. Since there is a N pole for every S pole, pole count is always an even number.
- Is the requested motor speed respected, at least on average with the drive, or does it slip?
Induction motors have slip synchronous motors don't.
- How much angular misalignment might be expected between the achieved position/phase and speed versus the requested position and speed?
There is an angular relationship between the magnetic fields of the stator and rotor. Torque is proportional to the sine of the angle. The average speed error for a synchronous motor will be zero with respect to frequency or as close to matching the request as the resulting frequency.
- What would I expect for the output of a continually varying speed request against a varying load? Is the error on the order of a few degrees or a few revolutions?
That depends on the multiple factors that are involved.
- What motor layouts, permanent magnet etc. are compatible with vector control?
As far as I know, any valid structural motor design is compatible.
- What influence does waveform shape and pole count have on the positional accuracy?
Higher pole count results in fewer degrees of magnetic field displacement "electrical degrees" per mechanical rotation degree "mechanical degrees."
Relative position control is usually performed based on the moving components of driven machines that need to maintain alignment. It usually requires encoder feedback from the alignment points. The machine alignment point will probably need to tolerate an error due to the motor's torque angle variation for the expected load variation.