A data-driven neural model predictive controller for multi-layer nonlinear vibration isolation system

For an active multi-layer nonlinear vibration isolation system (MNVIS) with quasi-zero-stiffness (QZS) characteristics, this paper proposes a data-driven method to train the controller based on model predictive control (MPC) theory, which combines the identification of the prediction model with the solution of the optimal control law. Inspired by the framework of neural ordinary differential equations (NODEs), the substructure physics-informed neural network (PINN) is designed to establish the surrogate dynamic model (SDM) of the controlled object for the predictive controller. Instead of solving the optimal control force online, the neural network controllers are trained by minimizing the cost functions of MPC. Final results indicate that the identified SDMs accurately capture the dynamic characteristics of the true dynamic models, and the trained neural network controllers can approximate the optimal control laws. Moreover, these controllers are capable of achieving an outstanding vibration isolation performance specified by the cost functions, and further enhancing the low-frequency vibration isolation of the MNVIS.