Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control

This note shows that the industry standard desired equilibrium for permanent magnet synchronous motors (i.e., maximum torque per Ampere) can be globally asymptotically stabilized with a PI control around the current errors, provided some viscous friction (possibly small) is present in the rotor dynamics and the proportional gain of the PI is suitably chosen. Instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties. The analysis relies on basic Lyapunov theory making the result available to a wide audience.