Dynamic event-triggered piecewise vibration control for the piezoelectric cantilever beams

The main objective of this paper is to suppress vibrations while reducing the communication burden for a class of piezoelectric cantilever beams. Different from the existing partial differential equation (PDE)-based vibration control methods, which typically employ periodic or static event-triggering mechanisms, a dynamic event-triggered piecewise controller is proposed, and its practical feasibility is verified through experiments on a physical platform. Initially, a second-order PDE model is developed for a cantilever beam equipped with multiple macro-fiber composite (MFC) actuators, explicitly accounting for the spatially distributed and piecewise inputs. Subsequently, a sufficient condition is derived using the Lyapunov direct method to ensure the convergence of the spatiotemporal deformation of the closed-loop system under bounded external disturbances. Then, to further improve communication efficiency, a dynamic event-triggered mechanism is incorporated into the piecewise controller, effectively reducing the triggering frequency while rigorously avoiding Zeno behavior. Furthermore, the construction procedure of the piezoelectric cantilever beam-based control experimental platform is presented in detail. Experimental results clearly demonstrate that the proposed approach effectively achieves vibration attenuation while significantly reducing communication overhead compared with existing methods.