A Kalman filter-based active control algorithm for non-stationary vibration with time-varying secondary paths

This paper proposes a perturbed-weight mirror Filtered-x Kalman filter (PwMFxKF) algorithm for active vibration control (AVC) under time-varying operating conditions. The existing perturbed-weight mirror Filtered-x Least Mean Square (PwMFxLMS) algorithm handles time-varying secondary paths effectively. However, like all LMS-based methods, it cannot track rapid frequency variations under non-stationary excitations such as engine acceleration and deceleration due to the inherent limitation of fixed step-sizes. To overcome this drawback, the proposed algorithm integrates a standard controller-weight Kalman filter (KF) and the Joseph-form covariance update into the PwMFxLMS online path-modeling framework. A time-varying discrete Riccati solver with Joseph-form covariance update is employed to ensure numerical stability during real-time implementation. The algorithm is evaluated under three secondary path scenarios, including time-invariant, sudden change, and slow drift, using experimentally measured non-stationary reference signals. Results show that the proposed algorithm outperforms ideal Filtered-x Least Mean Square (FxLMS ∞ ) and PwMFxLMS, and achieves performance comparable to the ideal Filtered-x Kalman filter (FxKF ∞ ), in convergence speed and vibration attenuation, particularly under time-varying secondary paths. Experimental validation on a laboratory marine cabin test rig further confirms that the proposed algorithm successfully suppresses vibrations under acceleration and deceleration profiles.