focdetails.txt

How FOC works:
You capture the amperage at each of the three phases (well, first two is all thats required)
Take those amperages and apply clarke transform. This decomposes the three phase current to two
phase current - Ia and Ib which are time variant direct and quadrature current (90 degrees apart)
These currents are then rotated with the park transform to be time invariant Id and Iq which are 
the actual direct and quadrature currents. Now, we know the D and Q currents and can figure out
if they're what we hoped they'd be or not. A PI loop controls a correlated set of variables Vd and Vq that
track output voltage in direct and quadrature. Those variables set the output PWM intensity but they're
also time invariant. We need to rotate them to time variant via the inverse park transform. Now we've
got Va and Vb which are the two voltages perpendicular to each other in time variant space. From these
two voltages we need to get back to the three phases currents. This could be done via an inverse
clarke transform that turns them into three phase currents again.