Active Shielding based on implicit control: a one dimensional approach

In order to apply an active noise control system, the sensors position is one of the most important variables to obtain a desired silent zone. This is due to the fact that the attenuation is achieved at the same location where the noise is measured. As a consequence, sensors become obstacles inside the silent zone. This issue produces several solutions which highly increase the computational cost, e.g. the estimation in virtual sensing. The aim of this article is to present a new method to generate a silent zone only controlling the noise at its boundaries for one dimensional enclosure, which eliminates the computational cost of the estimation. The principle of the method and its conditions is defined in this document as implicit control. Afterward, the new method is proven using a discrete model of the wave equation. Next, the required condition for applying implicit control is empirically proven for one dimensional duct through output error method for system identification. At the end, a simulation of the control scheme for one dimensional enclosure is shown.