Grey-box Modeling for IPMSMs Considering Nonlinearity of Torque and Current

This paper proposes a grey-box model for IPMSMs (Interior Permanent Magnet Synchronous Motors) that accounts for the nonlinear relationship between currents and torque directly. IPMSMs with high power density typically exhibit complex torque characteristics due to the effects of magnetic saturation and spatial harmonics, necessitating the introduction of various nonlinear compensation tables based on magnetic field analysis to ensure control performance. However, inputting data without considering the physical properties can lead to many variables and increased memory usage, which does not necessarily improve control performance. Consequently, models representing magnetic saturation characteristics with a reduced number of parameters, as well as torque estimation methods, are under investigation. Moreover, advancements in high-precision and rapid-response torque sensors, along with magnetic field analysis technologies, have enabled detailed offline measurements of IPMSM torque, with promising prospects for control applications. In this study, we propose an Extended Torque Coefficient (ETC) matrix to express the grey-box model for control purposes, utilizing accurate map data reflective of the actual machine. In addition, the proposed model can be applied to calculate torque gradient in the current vector space, which is maximize torque control performance, while maintaining the ETC matrix.