As an "outsider" to both approaches, there's not much I can say or add beyond comments from an (retired) electrical engineer. With a VFD, there are a number of "side" benefits, such as a soft start. I'm old school and not too much up to date on technology of the last 15 years or so. But I have worked with VFDs in the past. Big ones, high horsepower ones, 50 HP ones.
VFDs work as desired, as well as designed, for frequency shifts of plus or minus 30 CPS.(+/- 50%) They cannot maintain good regulation as you approach zero speed. Speed is controlled with frequency. Higher, over "base" speed, could have deliterious effects, I don't know. A lot depends on the actual characteristics of the motor. And that can vary from one to another.
A DC motor with a "permanant magnet field" has better speed regulation at lower speeds. But also has a severe loss of torque as speed approaches zero. Speed is regulated with voltage, the most common method being "Pulse Width Modulation". More modern DC motors have little capacity for running above "base" speed, beyond what can be accomplished with increased voltage. I guess "field weakening" on a "compound" motor is a lost art. . .
Each method has pluses and minuses. Much depends on how much time and effort the end user will invest in setting up and maintaining the machine.
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