Optimal virtual sensing for active noise control in a rigid-walled acoustic duct

Abstract

The performance of local active noise control systems is generally limited by the small sizes of the zones of quiet created at the error sensors. This is often exacerbated by the fact that the error sensors cannot always be located close to an observer’s ears. Virtual sensing is a method that can move the zone of quiet away from the physical location of the transducers to a desired location, such as an observer’s ear. In this article, analytical expressions are derived for optimal virtual sensing in a rigid-walled acoustic duct with arbitrary termination conditions. The expressions are derived for tonal excitations, and are obtained by employing a traveling wave model of a rigid-walled acoustic duct. It is shown that the optimal solution for the virtual sensing microphone weights is independent of the source location and microphone locations. It is also shown that, theoretically, it is possible to obtain infinite reductions at the virtual location. The analytical expressions are compared with forward difference prediction techniques. The results demonstrate that the maximum attenuation, that theoretically can be obtained at the virtual location using forward difference prediction techniques, is expected to decrease for higher excitation frequencies and larger virtual distances.