Exact noise cancellation for 1D-acoustic propagation systems

Jérôme Lohéac (1) , Chaouki Nacer Eddine Boultifat (2, 3) , Philippe Chevrel (3, 2) , Mohamed Yagoubi (3, 2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 IMT Atlantique - DAPI - Département Automatique, Productique et Informatique
3 LS2N - équipe CODEx - Commande, Observation, Diagnostic et Expérimentation

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.

Mots clés: Active noise control; noise cancellation; one-dimensional wave equation; Boundary control; D'Alembert formula

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Jérôme Lohéac, Chaouki Nacer Eddine Boultifat, Philippe Chevrel, Mohamed Yagoubi. Exact noise cancellation for 1D-acoustic propagation systems. Mathematical Control and Related Fields, 2022, 12 (1), pp.1-16. ⟨10.3934/mcrf.2020055⟩. ⟨hal-02500391v2⟩