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Active vibration control for the time-varying systems with a new adaptive algorithm

This paper proposes a new adaptive algorithm for the active vibration control of time-varying systems in the presence of broadband or narrowband disturbances. The new algorithm combines the conventional filtered-x least mean square algorithm with the recursive prediction error (RPE) algorithm after the gradient modification of the RPE algorithm. The modified RPE algorithm is used to estimate the model of the control path online. The well-known filtered-x least mean square (FxLMS) algorithm is effective for the uncertain or time-varying systems, and adopts an auxiliary white noise approach to estimate the model of the control path online. However, the auxiliary excitation will degrade the control performance to some extent. In the new algorithm, the auxiliary excitation is eliminated at the expense of a larger computational burden. The influence of the estimated finite impulse response series on the convergence is also discussed. A propulsion shafting model with the time-varying dynamics is established by frequency response function synthesis. Numerical simulation for the established model is presented to demonstrate the superior performance of the proposed algorithm as compared with the FxLMS algorithm.