PD control of a rotating smart beam with an elastic root

The paper is aimed at the proportional and derivative controls of vibration of a rotating beam by using a pair of piezoelectric sensor and actuator layers. Using Hamiltonʹs principle derives the governing differential equations and the boundary conditions for the coupled axial-bending vibration of a piezoelectric rotating beam with elastically restrained root. The analytical method given by Lin et al. is used to determine the transient response of a piezoelectric rotating beam. The influences of the proportional and derivative control gain factors on the performance of the first two modes of an elastically constrained beam are investigated. It is found that considering the proportional control law only is not helpful to the active damping of a rotating beam. Moreover, considering the proportional and derivative controls suitably and simultaneously enhances the active damping of a rotating beam with an elastic root.