Standing-Wave Notch Filters With Improved Signal-Processing Response Considering Misalignment-Induced Harmonics in PMSM

Owing to the assembly tolerances in practical mechanical systems, the permanent-magnet synchronous machines (PMSMs) may inevitably encounter misalignment with the load shafts. As a result, harmonics at mechanical frequencies may be introduced into the signals of PMSMs, thus degrading the overall signal quality. To filter out these harmonics, notch filters (NFs) are traditionally utilized. However, existing NFs often suffer from noticeable response delays when trying to remove these mechanical harmonics at low-speed conditions. Accordingly, this article develops a standing-wave NF to reduce the response delay. It utilizes the mechanism of standing waves to linearize the temporal variations of the signals being processed. In this way, it becomes feasible to acquire the necessary linearly independent equations to calculate each component within the signals individually. As a result, the harmonics can be directly identified and eliminated, thereby accelerating the signal-processing procedure. Moreover, the Vandermonde matrix is utilized to rearrange these calculation equations, providing feasible analytical solutions even for high-order matrices and ensuring robust scalability. The accelerated dynamic performance and harmonic-removal performance of the proposed filters have been validated experimentally.