Brushless Motors and Field-Oriented Control

A brushless motor has magnets on the spinning rotor and coils in the fixed stator. The controller must switch the coils so the magnetic field always pulls the rotor forward. Field-oriented control keeps that field exactly 90 degrees ahead of the rotor, for smooth, efficient torque.

Commutation Rotor speed Field lead angle (FOC)

Torque from field angle

The torque on the rotor depends on the angle $\delta$ between the stator field and the rotor magnet. It is largest when the field leads by 90°:

$$\tau \propto \lvert \mathbf{B}_s \rvert \sin\delta$$

Field-oriented control measures the rotor angle $\theta$, transforms the three phase currents into a rotating frame aligned with the rotor (the Clarke and Park transforms), and sets the currents so the field leads by exactly 90°. The phase currents come out as smooth sine waves:

$$i_a = I\cos(\theta + 90^\circ) \quad i_b = I\cos(\theta + 90^\circ - 120^\circ) \quad i_c = I\cos(\theta + 90^\circ + 120^\circ)$$

What to notice

Six-step commutation jumps the field in 60° hops, so the lead angle swings between 60° and 120°. That causes torque ripple you can feel and hear. FOC holds the field steady at 90° ahead, so the torque line is flat. Change the lead angle away from 90° and the same current makes less torque. With the field fixed, the rotor just swings to line up with it and stops, like a compass.

FOC is why drone motors, robot joints, and electric scooters can be smooth and quiet. It needs a good rotor angle, from an encoder or estimated from the motor's back voltage.