A recursive least squares based control algorithm for the suppression of tonal disturbances

Mitigation of the effects of tonal noise and vibration has importance across a wide range of application domains. For low frequency disturbances, active control methodologies have proven to be highly effective when coupled with harmonic algorithms that target specific problematic frequencies. In this paper a novel harmonic control approach is presented that combines a classical exponential forgetting recursive least squares (ExF-RLS) estimator with an optimal gradient descent update law. The paper provides a rigorous proof that with a sinusoidal reference, the ExF-RLS estimator can be approximated by a fixed parameter filter and that the accuracy of the approximation is dependent upon the values of both the forgetting factor and the sampling frequency. With this approximation it is also proven that the complete iterative frequency domain harmonic control algorithm, when used with an instantaneous update, can be accurately represented by a linear time-invariant (LTI) feedback compensator. Such representations have clear importance since the stability, performance, convergence and robustness properties of the adaptive system can thereby be examined using well-established LTI analysis tools. The algorithm and the analytical results described above are illustrated in the paper using an experimental active vibration isolation mount that has been developed for marine systems application.