First, check this out:
SPACE VECTORS
You use PWM to control the red, green and blue vectors (voltages). The net result is the rotating black vector.
Here's a graphical representation relating to the field oriented control:
Field oriented control
The upper left animation represents the vector sum of the 3 phase voltages. Notice that Xa and Xb change with time. Now, you do a transformation so that you are rotating with the rotor. That is the upper right animation. Now, Xd and Xq do not change with time. You can now use a PI loops with those values since they don't change with time. Then you do an inverse transform and modify the pwm duties accordingly. I'm still trying to understand it. I will soon.