Analysis of PMSM Torque Waveform Discrepancies in a Hardware-in-the-Loop Environment

This paper compares Permanent-Magnet Synchronous Motor (PMSM) torque waveforms measured on a dynamometer test bench and generated by a real-time Hardware-in-the-Loop (HiL) simulation. A nonlinear PMSM model, parameterised using measurements from the physical motor and incorporating magnetic saturation through Look-Up Tables, was implemented on a dSpace HiL platform. Torque signals were evaluated at steady-state operating points of 20, 100, and 200 rpm using time-domain errors, Pearson and Spearman correlations, and FFT-based spectral analysis. An affine gain–offset transformation was applied to separate calibration-related discrepancies from differences caused by dynamic behaviour and unmodelled physical effects. The maximum observed initial discrepancy between dynamometer-measured and HiL-estimated torque was 0.638 Nm. Affine calibration reduced the maximum error by up to 85%, demonstrating that gain and offset mismatches were major contributors to the original error. However, correlation values remained low, and spectral analysis identified substantial differences in harmonic content. The dynamometer signals contained speed-dependent components, including a component near the 24th mechanical harmonic, whereas the HiL signals were dominated by the first mechanical harmonic. The proposed workflow supports mean-torque-oriented HiL validation and identifies priorities for improving model representation, channel scaling, and dynamic testing procedures.