Sensorless Control of PMSMs at Ultralow Speed: An Adaptive Position Estimation Strategy Based on Reconstructed Flux Linkage

Model-based sensorless control of permanent magnet synchronous motors (PMSMs) faces challenges at ultralow speeds and during smooth zero-speed crossing. This is primarily attributed to insufficient utilization of model information and inherent stability defect. To address these issues, a position error estimation method is proposed based on gradient descent adaptation. First, a hybrid current–voltage stator flux observer is designed as a reference model under a convergence assumption. To fully utilize the model information, the estimated position error is incorporated into both the permanent magnet and the saliency terms via a reconstructed flux linkage. A quadratic flux-error cost function is then minimized by an Massachusetts Institute of Technology (MIT)-rule-based adaptive law to yield the estimated position error, while speed and position are recovered by a phase-locked loop. The coupled observer–adaptation dynamics are analyzed, and input-to-state stability is established in the presence of nonlinearities and disturbances. Practical enhancements, including integral leakage and virtual signal injection, are incorporated, and concise tuning guidelines are provided to enhance the reproducibility. Experiments on a 2.2-kW PMSM test rig include step transients, ultralow-speed operation, and motoring-generating transition. The proposed method maintains dynamic characteristics and delivers improved ultralow-speed performance over two representative model-based methods.