A novel adaptive algorithm with an IIR filter and a variable step size for active noise control in a short duct

The intake system in an automotive engine has a short duct compared with that of the exhaust system. The filtered-x LMS (FX-LMS) algorithm has been applied to the active noise control (ANC) system in a short acoustic duct. This algorithm design is based on the FIR (finite impulse response) filter; however, it has a slow convergence issue due to a large number of zero coefficients. To improve the convergence performance, the step size of the LMS algorithm was modified from fixed to variable. However, this algorithm is still not suitable for the ANC system of a short acoustic duct because the reference signal is affected by the backward acoustic wave propagated from a secondary source. Therefore, the recursive filtered-u LMS algorithm (FU-LMS) based on the infinite impulse response (IIR) is developed to consider backward acoustic propagation. Generally, this algorithm has a stability problem. The stability issue was improved using an error-smoothing filter. In this paper, the recursive LMS algorithm with a variable step size and smoothing error filter is designed. This recursive LMS algorithm, the FU-VSSLMS algorithm, uses an IIR filter. With fast convergence and good stability, this algorithm is suitable for the ANC system in a short acoustic duct, such as the intake system of an automotive engine. This algorithm is applied to the ANC system of a short acoustic duct. The disturbance signals used as primary noise source are a sinusoidal signal embedded in white noise and the chirp signal, which has a variable instantaneous frequency. The test results demonstrate that the FU-VSSLMS algorithm has a superior convergence performance when compared with the FX-LMS and FX-LMS algorithms. The algorithm can be successfully applied to the ANC system in a short duct, such as the intake duct.