Active noise control in encapsulated structures with non-minimum phase characteristics using a Kalman filter approach

This paper studies the problem of active broadband noise control for an encapsulated structure. The structure is analyzed using the finite element method (FEM) to capture the interactions within the multi-physical domains of vibro-acoustic systems, allowing a detailed investigation of the propagation of sound waves and their interaction with the structural components. The frequency response function (FRF) of each control path, such as primary path and secondary path, is identified to quantify the dynamic behavior of the system across different frequencies. A complex identification method is used to calculate the state-space representations of each path for implementing an effective active noise control (ANC) algorithm. It is shown that the system under investigation exhibits non-minimum phase characteristics, a challenging aspect in ANC due to phase delays and inverted dynamics that complicate achieving precise noise cancellation. Traditional ANC algorithms, such as the Filtered-x Normalized Least Mean Squares (FxNLMS), struggle in dealing with non-minimum phase (NMP) characteristics, resulting in limited noise reduction with significant delays and undershoot effects. To overcome these limitations, this paper proposes the application of a Kalman filter approach in the ANC system, which offers enhanced efficiency and robustness in controlling the system under consideration. In comparison, the performance of the Kalman filter approach for noise reduction in the frequency band from 0 to 450 Hz can be quantified as 16.92 dB, compared to 2.72 dB for the FxNLMS approach.