Analysis and compensation of reference frequency mismatch in multiple-frequency feedforward active noise and vibration control system

In the field of active noise and vibration control (ANVC), a considerable part of unwelcome noise and vibration is resulted from rotational machines, making the spectrum of response signal multiple-frequency. Narrowband filtered-x least mean square (NFXLMS) is a very popular algorithm to suppress such noise and vibration. It has good performance since a priori-knowledge of fundamental frequency of the noise source (called reference frequency) is adopted. However, if the priori-knowledge is inaccurate, the control performance will be dramatically degraded. This phenomenon is called reference frequency mismatch (RFM). In this paper, a novel narrowband ANVC algorithm with orthogonal pair-wise reference frequency regulator is proposed to compensate for the RFM problem. Firstly, the RFM phenomenon in traditional NFXLMS is closely investigated both analytically and numerically. The results show that RFM changes the parameter estimation problem of the adaptive controller into a parameter tracking problem. Then, adaptive sinusoidal oscillators with output rectification are introduced as the reference frequency regulator to compensate for the RFM problem. The simulation results show that the proposed algorithm can dramatically suppress the multiple-frequency noise and vibration with an improved convergence rate whether or not there is RFM. Finally, case studies using experimental data are conducted under the conditions of none, small and large RFM. The shaft radial run-out signal of a rotor test-platform is applied to simulate the primary noise, and an IIR model identified from a real steel structure is applied to simulate the secondary path. The results further verify the robustness and effectiveness of the proposed algorithm.