Design of Frequency-Adaptive Flux Observer in PMSM Drives Robust to Discretization Error

This article analyzes the effect of discretization in the frequency-adaptive flux observer (FAO). Although FAO has structural simplicity and ease of implementation, the discrete-time FAO has phase and gain errors in fundamental flux estimation. As a result, the estimated flux might be erroneous, especially in the high-speed region. For accurate flux estimation, this article analyzes how the voltage synthesis in the pulsewidth-modulation affects the stator flux. Through the analysis, the backward Euler method is selected for the primitive stator flux estimation. To mitigate the FAO's discretization error, the proposed FAO utilizes the integrators constructed at the rotor reference frame (RRF). Since the discretization error comes from the approximation error of the continuous-time integrator at the operating frequency, the proposed FAO conducts the fundamental flux extraction at the RRF, where the operating frequency components are treated as a dc signal. Thanks to the coordinate transformation, the FAO can be discretized with no error while keeping the structure of double integrators. The proposed method is verified through the computer simulation and experimental test.