A PMSM digital twin that relearns its own step: FPGA runs the network, and a shifted machine is re-approached in 94 seconds
Synopsis
Real-time digital twins of permanent magnet synchronous machines have relied on offline-identified parameters or finite-element flux look-up tables, which must be regenerated when the machine changes. The Inferencer-in-the-Loop architecture has a field-programmable gate array execute a physics-guided network while a GPU retrains it from reference data, switching weights only after validation. Across damper circuits, shifted parameters and an FEA-calibrated saturated machine, one kernel form reaches average normalized mean absolute errors of 0.19%–0.67% at measured kernel latencies of 0.30–0.34 microseconds; on a 200-W drive, a residual form gives errors of 5.9%–9.4% of measured RMS over six held-out runs.
Interpretation
The executed step of the real-time digital twin itself becomes learnable: a field-programmable gate array runs a compact network mapping present state and voltages to the next current increment and torque, so a machine change means new weights rather than new controller interfaces or real-time schedules. Twin models previously rested on identified parameters or finite-element flux look-up tables, with maps regenerated offline when the machine changed and online estimators tracking only a few parameters such as resistance and PM flux. For damper circuits, shifted parameters and an FEA-calibrated saturated machine, one kernel form gives average normalized mean absolute errors of 0.19%–0.67% at measured FPGA kernel latencies of 0.30–0.34 microseconds, and retraining for a shifted machine nears its final loss within 94 seconds.
Against a measured drive, the network instead corrects an analytical step and learns its physical parameters from operating data, covering effects outside the equations such as inverter nonlinearity and thermal drift. Analytical and look-up models are more accurate but need known parameters or an accurate flux map, and must be rebuilt offline when the machine changes. On the 200-W drive, over six held-out runs totaling 1193 seconds, this residual form's error is 5.9%–9.4% of measured RMS against 10.4%–13.2% for an independently fitted grey-box model, and each step takes under 2.5 microseconds, 20 times faster than real time even at 20-kHz sampling.
During heating, online-updated heads follow the winding-resistance rise so the twin stays aligned with the machine while it runs. The frozen model drifts to normalized mean absolute errors of 0.57% and 1.12% by the last segment, while the grey-box model stays at 1.32%–1.43% and 1.35%–1.41%. Over 30 minutes of loading, standstill probes measure resistance rising from 71.28 to 74.18 milliohms, and the online head tracks that 2.91-milliohm rise with an RMS error of 0.44 milliohms, about 15% of the rise.
Perspective
The demonstrated scope covers four closed-loop simulation stages, a transient study including damper and ground faults, and a 200-W surface-mounted PMSM bench that is magnetically linear; the bench exercises inverter nonlinearity and temperature-dependent parameters rather than saturation. The authors propose future work on testing the twin on a saturated machine, triggering updates automatically over full thermal cycles on the FPGA, and coupling it to external controllers for closed-loop HIL and fault tests.
The authors note that where exact equations or maps exist, analytical and look-up models are up to 0.33 percentage points more accurate, so the network trades accuracy for coverage and update convenience. The learned step deviates most during braking after a speed step, where it leaves the training trajectory's range. The bench is magnetically linear between 300 and 2000 rpm with load currents up to 6 A, so saturation is examined only in simulation. The online heads are command-referred and lump winding, magnet and inverter changes together.