A Parallelized Input Matching LMS Adaptive Filter for the Rejection of Spatially Cyclic Disturbances

Spatially cyclic disturbances exist widely in rotating machines. They usually have fixed spatial cycles rather than constant time periods, which affect the stationarity of angular speed tracking. An input matching least mean square (LMS) adaptive filter (IMLMS-AF) is proposed to cope with the effects of spatially cyclic disturbances. The IMLMS-AF sets a part of the inputs as spatially cyclic signals for disturbance rejection and forms another part as a time-dependent function for reference tracking. Furthermore, an updated law and convergence of the pending weights are given. The system's stability is proved by combining the instantaneous gradient with Lyapunov theory. Moreover, the IMLMS-AFs are parallelized to reject disturbance with multiple components and reference tracking. The effectiveness and superiority of the proposed control method are verified and compared with other methods by simulations and experiments.