Classical and optimal active vibration control of smart piezoelectric beams

Abstract

In this paper a numerical study concerning the active vibration control of smart piezoelectric beams is presented. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches with sensing and actuating capabilities. As a mathematical model, a one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized and briefly presented. The mathematical model considers a partial layerwise theory, with three discrete-layers, and a fully coupled electro-mechanical theory. The finite element model equations of motion and electric charge equilibrium are presented and recast into a state variable representation in terms of the physical modes of the beam. The analyzed case studies concern the vibration reduction of a cantilever aluminum beam with a pair of collocated piezoelectric patches mounted on the surface. The displacement time history, for an initial displacement field and white noise force disturbance, and point receptance at the free end are evaluated with the open- and closedloop classical and optimal control systems. The case studies allow to compare their performances and demonstrate their advantages and disadvantages.