Filtered-X LMS vs repetitive control for active structural acoustic control of periodic disturbances

This paper presents a comparison of repetitive control and narrowband filtered-X LMS feedforward control, both applicable in the field of active structural acoustic control (ASAC) and active noise control (ANC) of periodic disturbances. This can be useful for example in rotating machinery, where the disturbance is often determined by the rotational speed. A frequency domain relation between the disturbance and the error signal is presented for the filtered-X LMS algorithm. This relation leads to a frequency domain convergence criterion which is consistent with existing literature and experimental observations. Furthermore, both control strategies are compared based on these frequency domain relations. The comparison shows that an inverse based repetitive controller behaves as an harmonic canceler, while the filtered-X LMS algorithm deviates from this behaviour at frequencies between the harmonics. Finally, the paper suggests the possibility to further match the behaviour of both algorithms, and to improve the performance for ASAC of periodic disturbances.