Event-triggered vibration control for a class of flexible mechanical systems with bending deformation and torsion deformation based on PDE model

Abstract

Most of the research on event-triggered control method is aimed at the traditional ordinary differential equation (ODE) system, which neglects the high-order mode of the system and lacks precision. There are also a few researches on event-triggered control for simple single-degree-of-freedom flexible mechanical systems. This paper focuses on the more complex multi-degree of freedom coupling flexible beams. There are two kinds of deformation of the flexible beam, namely bending deformation and torsion deformation. Based on the coupled partial differential equation (PDE) model of the flexible beam, an event-triggered control algorithm is designed in this paper to address the vibration control problem of the mechanical system. The stability and convergence of the closed-loop system are proved via Lyapunov’s direct method while the Zeno phenomenon is avoided. The simulation results clearly and directly show the effectiveness and superiority of this method, which are consistent with the theoretical analysis. Overall, the proposed event-triggered control method is feasible for PDE models and has good control effect while reduce signal transmission.