Field-oriented control (FOC)
Field-oriented control is the clever maths that lets a complicated three-phase AC motor be controlled as easily as a simple DC motor. Recall that torque is greatest when the rotor and stator fields are exactly 90° apart; FOC's whole job is to hold that 90° angle no matter how fast the motor spins. It does this with a coordinate transform (the Clarke and Park transforms) that mathematically 'rides along' with the spinning rotor, freezing the rotating quantities into two steady knobs: one that sets the magnetic field, and one that sets the torque.
With those two decoupled controls, software can independently command 'how much magnetising flux' and 'how much twist' instant by instant, giving smooth torque, full pulling power even from a dead stop, and razor-sharp response. FOC is what makes a modern EV launch instantly and silently and a robot arm move with grace; it runs thousands of times per second on the microcontroller inside every premium motor drive, fed by rotor-position feedback and current measurements.
The breakthrough idea, dating to the early 1970s, was to transform the motor's three fixed-axis currents into a frame that rotates with the rotor — once you do that, the messy AC quantities look like simple DC values you can regulate with ordinary loops.