Nick Kirkby

Field Oriented Control (FOC) is a method of control (typically torque) for polyphase electric machines.  I made the following post to get more comfortable with the rotating vectors that are at the heart of FOC. Most of the pictures in this post are animated GIFs, so you should be able to click on them and see them move.

For a real explanation of how FOC works, read Shane Colton or James Mevey.

This animation (made with GeoGebra) shows three scalars labeled A, B, and C.  In the animation they range from -1 to 1.  These scalars represent the currents through the three phases of the motor.


Their magnitudes change sinusoidally and look like this when plotted versus time:


When the three current scalars are summed, they look like a single rotating vector with constant magnitude.


Because Freedom is Slavery, War is Peace and Current is Torque, it makes sense to imagine the rotating summed current vector as a rotating magnetic field, one which drags the already magnetized rotor around to create torque.


3phase-rmf-noadd-60f-airopt“. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

For the purpose of doing motor control, it makes sense to express the sum of the three stator currents as two orthogonal components in the rotor frame, d and q.  Here’s what that looks like.  This is called the clarke, or 3-to-2 transformation.  It takes the three (120 degree spaced) phase currents and expresses them as two (90 degree spaced) components.


**d – direct

q – quadrature**

d is the direction that the magnets point in, and q is 90 degrees offset from that.

for a plain old 3 phase permanent magnet motor (think RC plane motor), controllers usually put current on the q axis because it is the torque producing axis.  Creating a magnetic field 90 degrees from the rotor’s magnetic field will drag the rotor into alignment


The image above is from James Mevey’s masters thesis.  It is an excellent description of just about everything about theory behind three phase motor control (READ IT).  Unlike most other papers on motors and motor control, it is surprisingly readable.  While much of the math is beyond me (or makes me fall asleep), I have still been able to learn from it because it contains tasty hand drawn diagrams and a healthy disgruntlement with the stuffiness of other learning resources related to electric motors.



It shows how the (fictional but still useful) d and q axes rotate with the rotor.  The alpha and beta axes (also fictional and useful) are fixed in the stator frame with the windings that transform current into flux.  In a permanent magnet motor, torque is produced by pushing current through coils in the stator to make a magnetic field perpendicular to the rotor magnetic field.  The rotor tries to align itself with the stator field, producing torque.  To continuously produce torque, the direction of the stator current vector must always lead the rotor.

Didn’t click  the links at the top?

Shane Colton or James Mevey tell how FOC works with unparalleled clarity.