Adaptive vibration control of piezoelectric cantilever beams with uncertainties

Abstract

Considering the stiffness characteristics of piezoelectric layer, the bending stiffness of piezoelectric cantilever beam is obtained by applying the first-order shear deformation theory. The finite element model of piezoelectric cantilever beam is established by Hamilton variation principle. At the maximum strain point, the sensors/actuators are equipped in pairs. Based on the uncertain dynamic model of piezoelectric cantilever beam, an adaptive sliding mode controller (ASMC) is designed by using backstepping technique. The correctness of the finite element model of cantilever beam established is verified by comparing the calculation results of ANSYS software. The effectiveness and superiority of the proposed the ASMC method are verified by the numerical simulations, in comparison with traditional linear quadratic regulator (LQR) control method.