Active vibration isolation of a monostable nonlinear electromagnetic actuator using machine learning adaptive feedforward control

In the realm of nonlinear vibration systems, the control of periodic low-frequency vibrations presents a formidable challenge due to the intricate nature of nonlinear dynamics. This paper proposes a novel machine learning adaptive feedforward active control method tailored for suppressing periodic low-frequency vibrations. Leveraging a monostable nonlinear electromagnetic actuator with an elastic boundary (MAEB), our method harnesses the power of a back-propagation neural network (BPNN) to accurately identify the driving model of the MAEB. This model is then integrated into the adaptive control loop for continuous parameter updating of the controller BPNN. Our approach demonstrates high proficiency in eliminating harmonic frequency components and ensuring robust control stability, thereby surpassing traditional filtered-x least mean square (Fx-LMS) algorithm. Specifically, our approach enhances overall vibration isolation performance by an impressive 7.13 dB compared to the Fx-LMS algorithm. Furthermore, our study validates the efficacy of the proposed method in accommodating variations in excitation, including low-frequency single-line and dual-line spectrums. A detailed parametric study underscores the pivotal role of neural network hyperparameters in enhancing active control performance, with adjustments to the number of hidden layer nodes and the learning rate offering notable improvements in convergence speed.