An unregulated power supply will be sufficient and is recommended for most applications because of its simplicity. If a motor with a large inertial load decelerates quickly it will act as an alternator and send voltage back to the drive which then sends it back to the power supply. Because many regulated power supplies feature protection circuitry this may cause the power supply to fault or reset; however, if the supply is unregulated it will simply get absorbed by the filter capacitor.
The drive is a current source in the constant torque region and adds no additional phase lag. In the constant power region however, the drive is a voltage source so it introduces an additional 90 degree phase lag. The total phase lag now is 180 degrees, which is a setup for a sustained and building motor oscillation. This oscillation is commonly called mid-band instability or mid-band resonance.
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