Optimal current waveforms for brushless permanent magnet motors

Abstract

In this paper, we give energy-optimal current waveforms for a permanent magnet synchronous motor that result in a desired average torque. Our formulation generalises previous work by including a general back-electromotive force (EMF) wave shape, voltage and current limits, an arbitrary phase winding connection, a simple eddy current loss model, and a trade-off between power loss and torque ripple. Determining the optimal current waveforms requires solving a small convex optimisation problem. We show how to use the alternating direction method of multipliers to find the optimal current in milliseconds or hundreds of microseconds, depending on the processor used, which allows the possibility of generating optimal waveforms in real time. This allows us to adapt in real time to changes in the operating requirements or in the model, such as a change in resistance with winding temperature, or even gross changes like the failure of one winding. Suboptimal waveforms are available in tens or hundreds of microseconds, allowing for quick response after abrupt changes in the desired torque. We demonstrate our approach on a simple numerical example, in which we give the optimal waveforms for a motor with a sinusoidal back-EMF, and for a motor with a more complicated, nonsinusoidal waveform, in both the constant-torque region and constant-power region.

Keywords:

• brushless DC motors
• permanent magnet synchronous motors
• optimal control
• convex optimization
• ADMM

Disclosure statement

No potential conflict of interest was reported by the authors.