Exact noise cancellation for 1d-acoustic propagation systems

IF 0.9 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2020-10-19 DOI:10.3934/MCRF.2020055

Jérôme Lohéac, C. Boultifat, P. Chevrel, M. Yagoubi

引用次数: 0

Abstract

This paper deals with active noise control applied to a one-dimensional acoustic propagation system. The aim here is to keep over time a zero noise level at a given point. We aim to design this control using noise measurement at some point in the spatial domain. Based on symmetry property, we are able to design a feedback boundary control allowing this fact. Moreover, using D'Alembert formula, an explicit formula of the control can be computed. Even if the focus is made on the wave equation, this approach is easily extendable to more general operators.

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一维声传播系统的精确噪声消除

本文研究了应用于一维声传播系统的主动噪声控制。这里的目标是随着时间的推移，在给定的点保持零噪声水平。我们的目标是在空间域中的某个点使用噪声测量来设计这种控制。基于对称特性，我们能够设计一个允许这一事实的反馈边界控制。此外，利用达朗贝尔公式可以计算出控制的显式公式。即使重点放在波动方程上，这种方法也很容易扩展到更一般的算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.