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

TL;DR

This paper demonstrates that permanent magnet synchronous motors can be globally stabilized using a PI current control under certain conditions, leveraging passivity properties and Lyapunov theory for a broad audience.

Contribution

It proves that industry-standard PI control can achieve global asymptotic stabilization of PMSMs with viscous friction, a novel theoretical insight.

Findings

PI control stabilizes PMSMs with viscous friction

Passivity of the voltage-current map is key

Lyapunov theory confirms global stability

Abstract

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.