Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies

This paper presents a numerical study concerning the active vibration control of smart piezoelectric beams. 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 acting as sensors or actuators. A one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized. A partial layerwise theory, with three discrete layers, and a fully coupled electro-mechanical theory is considered. 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 collocated asymmetric piezoelectric sensor/actuator pair bonded on the surface. The transverse 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 closed-loop classical and optimal control systems. The case studies allow the comparison of their performances demonstrating some of their advantages and disadvantages.