Optimal shape control of a beam using piezoelectric actuators with low controlvoltage

Abstract

This paper deals with the shape control of a cantilever beam structure by using laminatedpiezoelectric actuators (LPAs) with a low control voltage. The shape control equation ofthe cantilever beam partially covered with LPAs is derived based on the constitutiverelations of the elastic material and piezoelectric material and shear deformation beamtheory (Timoshenko theory). The actuating forces produced by the LPAs areformulated as well. It reveals how the actuating forces depend on the number ofpiezoelectric layers, the thickness of piezoelectric layers and the position of theactuators. The driving voltages of the LPAs are then determined by a geneticoptimization algorithm. The shape control of the cantilever beam from applying theoptimal voltage to the LPAs is simulated. The simulation results show that anLPA of large layer number is able to diminish effectively the pre-deflection of thebeam under a low control voltage. The voltage applied to the LPA of five layerswas almost five times smaller than that of one layer. In addition, increasing thenumber of LPA layers can significantly improve the control performance as theacting forces of the LPA are a quadratic function of the LPA layer number. TheL2 norm of the displacement array of all nodes is diminished about 30% after optimization.Also with the same low control voltage, the LPA can obtain a better control performancethan the conventional single layer piezoelectric actuator.