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.
It is necessary to cut off all vibration transmission paths for an active vibration isolation system. A greater suppression of local responses will result in a better overall attenuation. In order to realize impediment at possible transmission paths, a new scenario of multi-axis transmission control is proposed, in which the active/passive isolator attenuates vibration transmission at multi-degrees of freedom by vertical and horizontal actuators mounted orthogonally on the intermediate inertial mass. This scenario is able to weaken the cross-coupling of control action between isolators by the passive parts. In order to investigate the characteristics of multi-axis transmission control, the dynamic model of a partitioned isolation system with one active/passive isolator is established and the involved transmission control is analyzed. The numerical results show that the foundation vibration can be attenuated along with the decrease of vibrations of the intermediate inertial mass. It is further revealed by experimental results that the multi-axis transmission control at the intermediate inertial mass is necessary to achieve sufficient vibration attenuation in the foundation, whereas the control in a single axis is ineffective. These verified results imply that the active/passive isolation with local transmission path control makes it possible to apply decentralized control in a large active vibration isolation system.
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