Dynamic Instability and ARBF Neural Network Control of Piezoelectric Microlaminates

This paper investigates the nonlinear vibration control and dynamic instability of cantilevered piezoelectric microlaminates with geometric imperfections, taking into account an unknown time-varying delay and external disturbances. The dynamic equations for the microlaminates are derived using the MCST, FSDT, nonlinear von Karman equation, and Hamilton’s principle. The Galerkin method is applied to discretize these nonlinear partial differential equations. It is found that initial imperfections can trigger the dynamic phenomenon. To control the vibrations, two control strategies are implemented: The adaptive radial basis function (ARBF) feedback linearization controller and the ARBF sliding mode controller. A comparative analysis of the time histories, control voltage, and adaptive parameter responses of the two controllers under four different external conditions is conducted. The results indicate that both controllers effectively suppress the vibration of the system, thereby mitigating the risk of dynamic instability. Additionally, the findings suggest that, although both controllers meet the targeted control objectives, the ARBF sliding mode controller not only demonstrates enhanced control performance but also necessitates lower energy consumption in comparison to the ARBF feedback linearization controller.