Over-determined Fx-Newton algorithm for active control of low-frequency sinusoids in the vibration and noise radiated by a cylindrical shell

An over-determined multi-channel Fx-Newton algorithm is proposed for active control of structural vibration. The theoretical principle of this algorithm is first derived in the frequency domain and the implementation of the algorithm is then introduced in the time domain. Analytical results show that the rate of convergence of this algorithm is close to that of the Fx-Newton algorithm, and faster than that of the Fx-LMS algorithm. Experiments are also conducted on a raft mounted in a cylindrical shell to test the effects of active-passive vibration isolation with the Fx-Newton algorithm and the proposed over-determined Fx-Newton algorithm. The effects of attenuation of both algorithms are also evaluated on the sinusoids in the radiated noise. The results reveal that at some frequencies where the sinusoids are not suppressed by the Fx-Newton algorithm, the over-determined Fx-Newton algorithm, however, can effectively suppress their presence both in the vibration of the base plate and in the normal vibration of the cylindrical shell. Hence the over-determined Fx-Newton algorithm has excellent effect of global vibration control, and can well attenuate the sinusoids in the noise radiated by the cylindrical shell.