vector control

And no English either.

-- Ferme le Bush

Basic difference is that V/Hz just varies the applied ac voltage amplitude in proportion to the variation in frequency. Vector control uses a PWM voltage.

This should do it for you. FOC is the same as Closed Loop Vector as mentioned in that FAQ.

At its simplest. Volts per hertz control is just that, you adjust the voltage input in proportion to the frequency as you change speed. The V/Hz ratio is proportional to the flux in the motor, so you are assuming that by doing this you are keeping the flux constant in the motor. Vector control is like controlling a DC motor. You take the motor currents and by doing some reference frame transformations you can separate the current into two components: field or flux component and torque component. By performing this transformation, you are actually creating decoupled sets of currents and by controlling each component separately you get much more precise control over the machine. The main drawback is that vector or field oriented control requires either position feedback or state estimation for the position.