# A conjugate gradient least square based method for sound field control.

Authors: Libianchi, Pierangelo; Agerkvist, Finn T.; Shabalina, Elena

Publication Date: 01.08.2021

Permalink: orbit.dtu.dk/en/activities/a-conjugate-gradient-least-square-based-method-for-sound-field-co

**Abstract:**

In sound field control, a set of control sources is used to match the pressure field generated by noise sources but with opposite phase to reduce the total sound pressure level in a defined area commonly referred to as dark zone. This is usually an ill-posed problem. The approach presented here employs a subspace iterative method where the number of iterations acts as the regularization parameter and controls unwanted side radiation, i.e. side lobes. More iterations lead to less regularization and stronger side lobes. The number of iterations is controlled by problem-specific stopping criteria. Simulations show the increase of lobing with increased number of iterations. The solutions are analysed through projections on the basis provided by the source strength modes corresponding to the right singular vector of the transfer function matrix. These projections show how higher order pressure modes (left singular vectors) become dominant with larger number of iterations. The method proposed here not only allows to control the energy of the side lobes but also to explicitly apply constraints over the amplitude of the solution using an active set-type method which is crucial to avoid non linearities in the control sources.