Sun, G., Feng, T., Xu, J., Li, M. et al., "Modified FxLMS Algorithm with Equalized Convergence Speed for Active Control of Powertrain Noise," SAE Int. J. Passeng. Cars - Mech. Syst. 8(3):868-872, 2015, doi:10.4271/2015-01-2217.
Current powertrain active noise control (ANC) systems are not sufficient enough to track the fast engine speed variations, and yield consistent convergence speeds for individual engine order such that a balanced noise reduction performance can be achieved over a broad frequency range. This is because most of these ANC systems are configured with the standard filtered-x least mean squares (FxLMS) algorithm, which has an inherent limitation in the frequency-dependent convergence behavior due to the existence of secondary path model (electro-acoustic path from the input of control loudspeaker to the output of monitoring error microphone) in the reference signal path. In this paper, an overview is given first to compare several recently modified FxLMS algorithms to improve the convergence speed for harmonic responses such as eigenvalue equalization FxLMS (EE-FXLMS) and normalized reference LMS (NX-LMS) algorithms. Then, a novel modified FxLMS algorithm, termed as the inverse model LMS (IMLMS) algorithm, is proposed as the basis for active powertrain noise control. The proposed algorithm is realized by utilizing the inverse model of the secondary path, either cascading at the output of adaptive filter or adding in the reference signal generator, to minimize the effect of its dynamic on the algorithm's convergence. To validate the effectiveness of the proposed algorithm, numerical simulations using measured powertrain noise responses are also performed. Results show comparable convergence speeds at individual engine order and appreciable noise reductions over a broad engine rotational speed range.