Iterative learning approach to active noise control of highly autocorrelated signals with applications to machinery noise

This study describes an iterative learning approach to the active control of machinery noise with high autocorrelation properties. In contrast to typical active noise control solutions, which work by adapting the transfer function of the controller, in the iterative learning control one adapts the control signal itself. Special care was taken to develop a generic solution that can handle different sorts of secondary path models including very long and non‐minimum phase finite impulse response filters. To achieve that, the authors used spectral factorisation and exploit the fact that, for non‐minimum phase systems, a stable inverse can be constructed if the causality constraint is relaxed and later restored by taking advantage of the periodicity of the attenuated signal. The resulting controller can be efficiently implemented on a sample‐to‐sample calculation basis. The behaviour and the performance of the proposed scheme are studied using computer simulations and real‐world experiments on noises from an electric transformer and functional magnetic resonance imaging device. The proposed solution was also compared to normalised feedforward filtered‐X least mean squares algorithm and performed much better in terms of attenuation, convergence, and robustness.