Optimal control of a beam with discontinuously distributed piezoelectric sensors and actuators

Abstract

Because of its light weight, broadband, and adaptable properties, smart material has been widely applied in the active vibration control (AVC) of flexible structures. Based on a first-order shear deformation theory, by coupling the electrical and mechanical operation, a 4-node quadrilateral piezoelectric composite element with 24 degrees of freedom for generalized displacements and one electrical potential degree of freedom per piezoelectric layer was derived. Dynamic characteristics of a beam with discontinuously distributed piezoelectric sensors and actuators were presented. A linear quadratic regulator (LQR) feedback controller was designed to suppress the vibration of the beam in the state space using the high precise direct (HPD) integration method.

Keywords

smart material / first-order shear deformation / high precise direct (HPD) / linear quadratic regulator (LQR) / beam / piezoelectric sensor / piezoelectric actuator