Identification of a nonlinear PMSM model using symbolic regression and its application to current optimization scenarios

Gerd Bramerdorfer, Wolfgang Amrhein, Stephan M. Winkler, Michael Affenzeller

Research output: Chapter in Book/Report/Conference proceedingsConference contributionpeer-review

22 Citations (Scopus)


This article presents the nonlinear modeling of the torque of brushless PMSMs by using symbolic regression. It is still popular to characterize the operational behavior of electrical machines by employing linear models. However, nowadays most PMSMs are highly utilized and thus a linear motor model does not give an adequate accuracy for subsequently derived analyses, e.g., for the calculation of the maximum torque per ampere (MTPA) trajectory. This article focuses on modeling PMSMs by nonlinear white-box models derived by symbolic regression methods. An optimized algebraic equation for modeling the machine behavior is derived using genetic programming. By using a Fourier series representation of the motor torque a simple to handle model with high accuracy can be derived. A case study is provided for a given motor design and the motor model obtained is used for deriving the MTPA-trajectory for sinusoidal phase currents. The model is further applied for determining optimized phase current waveforms ensuring zero torque ripple.

Original languageEnglish
Title of host publicationIECON Proceedings (Industrial Electronics Conference)
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479940325
Publication statusPublished - 24 Feb 2014

Publication series

NameIECON Proceedings (Industrial Electronics Conference)


  • Brushless machines
  • cogging torque
  • MTPA
  • symbolic regression
  • torque ripple


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