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Leaky partial updates to control a real device casing

Bismor Dariusz

Vibrations in Physical Systems

2022

Vol. 33, nr 3

art. no. 2022304

Structural active noise control (ANC) is one of few solutions applicable when global noise reduction is required: control of a whole device casing allows to lower the acoustic energy emitted by this device. Unfortunately, structural ANC usually requires a large number of sensors and actuators, making the control system multichannel with large dimensionality. This in turn presents a huge computational power demands. There are several ways to lower this demand, the partial updates being one of them. The goal of this paper is to show applicability of the leaky partial update LMS algorithms in structural ANC of a washing machine casing. The transfer functions of the numerous device paths were identified using a real washing machine in the ANC laboratory. The identified transfer functions allowed to create a simulation system, where different algorithms could be easily tested. The results of the simulations confirm effectiveness of the proposed solution.

Stability Conditions for the Leaky LMS Algorithm Based on Control Theory Analysis

Bismor D., Pawelczyk M.

Archives of Acoustics

2016

Vol. 41, No. 4

731--739

The Least Mean Square (LMS) algorithm and its variants are currently the most frequently used adaptation algorithms; therefore, it is desirable to understand them thoroughly from both theoretical and practical points of view. One of the main aspects studied in the literature is the influence of the step size on stability or convergence of LMS-based algorithms. Different publications provide different stability upper bounds, but a lower bound is always set to zero. However, they are mostly based on statistical analysis. In this paper we show, by means of control theoretic analysis confirmed by simulations, that for the leaky LMS algorithm, a small negative step size is allowed. Moreover, the control theoretic approach alows to minimize the number of assumptions necessary to prove the new condition. Thus, although a positive step size is fully justified for practical applications since it reduces the mean-square error, knowledge about an allowed small negative step size is important from a cognitive point of view.