Order Tracking based Least Mean Squares Algorithm

This paper presents a novel least mean squares approach for active control of structural mechanic systems. Order tracking is used to estimate the gradient for a steepest descent approach more precisely than the standard narrow-band filtered-x least mean squares (FxLMS). The derivation for the new order tracking based least mean square (OLMS) algorithm is presented for a single-input single-output system. The update equations of the OLMS are then compared with an FxLMS algorithm, leading to an interpretation that the FxLMS incorporates order tracking properties. Both algorithms are compared in simulations to show their different convergence performances at multiple frequencies. If only one frequency is present, the OLMS shows similar performance. However, in the case of multiple frequencies being present, the OLMS shows a significant performance increase. The presence of multiply frequencies lowers the performance of the FxLMS. This is analogous to the performance of the OLMS with an improper order tracking filter. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.