Active vibration control (AVC) can solve many vibration problems. However, structural vibration in underwater vehicles often involves other factors such as complex excitation and path coupling, etc. At present, the traditional algorithm (e.g., multi Filtered-x Least Mean Square, M-FxLMS) usually cannot effectively process the multi-frequency excitation and the coupling effects of the multi-secondary path, which will affect its convergence and stability to a certain extent. Consequently, a novel strategy is presented in this paper, namely, the wavelet packet transformation decentralized decoupling M-FxLMS algorithm (WPTDDM-FxLMS), which can solve the structural vibration problems mentioned above. The multi-frequency control is converted into a single-frequency line spectrum control, and the feedback compensation factor is introduced in the identification of the secondary path, both of which can simplify the multi-path control system to the parallel single-path systems. Furthermore, the WPTDDM-FxLMS algorithm is applied to the AVC in a multi-input and multi-output system (MIMO) vibration platform. Finally, the simulation and experiments show that the wavelet packet can decompose the multi-frequency excitation into a line spectrum signal, and the improvement of the decentralized decoupling and the variable step-size can effectively reduce the computation amount and increase the convergence speed and accuracy. Overall, the novel algorithm is significant for multi-path coupling vibration control. It will have certain engineering application value in underwater vehicles.

Active control is an effective way to suppress low‐frequency mechanical vibration. However, with applications to submarine equipment, there are still some shortcomings due to vibration coupling and multifrequency complex excitation. In this paper, a novel hybrid improved adaptive control strategy, feedback and online identification filtered‐x LMS, namely, FOFxlms, is proposed, which introduces the residual errors to correct variable step‐size, uses the estimated primary path to improve online identification, and applies internal feedback to compensate for the feedforward control. Then the FOFxlms algorithm is applied to a double‐layer vibration isolation system of submarine rotating equipment, and the simulation results show that the normalized variable step‐size with residual error can effectively improve convergence speed, the internal feedback can efficaciously compensate for steady‐state control accuracy, and the online identification can dynamically identify the time‐varying characteristics of the secondary path. The vibration reduction efficiency of Fxlms, FFxlms, and FOFxlms increases for the fundamental frequency vibration; the control effect and convergence speed are also enhanced in turn.

The giant magnetostrictive actuator has great use in vibration control, but the linear model cannot fully describe its dynamic characteristics. In this chapter, based on the domain wall theory and piezomagnetic theory, a hysteresis nonlinear model is established to fully describe the actuator dynamic characteristics. In combination with the regularisation method, a sliding mode controller has been designed, and the giant magnetostrictive actuator is also studied in the application of active control. Experimental results show that the hysteresis nonlinear model proposed in the chapter can fully describe the actuator’s dynamic characteristics in a wider frequency band and the active control also has a much better isolation effect than the passive vibration; it can significantly attenuate the external incentives.