An Auxiliary Function-Based Active Vibration Control Scheme for Flexible Cantilever Beams Using Piezoelectric Actuators

This paper presents a new control scheme for suppressing the flexible cantilever beam vibration by using the piezoelectric actuator. Based on the Hamiltonian principle, partial differential mathematical models of the flexible beam active vibration control system are characterized. Considering the complexity of the partial differential control system design, the Galerkin method is employed to decompose the partial differential dynamics model of the system into an ordinary differential model for the design of active vibration controllers. With an auxiliary function and the simplified ordinary differential mathematical model, a new active vibration controller is proposed to achieve fast vibration suppression. The stability of the closed-loop control system studied in this paper is demonstrated by means of the Lyapunov theory. Finally, numerical simulations are constructed in order to verify the effectiveness of the control strategy proposed in this paper. The results show that the proposed control method can reduce the vibration of the flexible cantilever beam effectively, making it a promising technique for active vibration control of flexible structures.