An incremental algorithm for static shape control of smart structures with nonlinear piezoelectric actuators

Abstract

Optimum control voltage design for static shape control of structures with nonlinear piezoelectric actuators is studied in this paper. In order to perform static shape control, the finite element equations of plates with nonlinear piezoelectric actuator patches is formulated using an eight-node adhesive element which combines a pair of collocated four-node quadrilateral elements for the upper and lower plates and a pseudo-adhesive layer element. An iteratively calibrated incremental method is presented to find the optimal control voltages that can actuate a shape best matching the desired shape. In this method, the desired shape is expressed by the sum of a number of small incremental desired shapes, and the control voltages to achieve each incremental desired shape are calculated step by step. The control voltages in each step are then calibrated by using the accumulated intermediate desired shape iteratively. Finally, a simulation example is given to illustrate that the present algorithm is effective in finding the optimal control voltage distribution for shape control of nonlinearly actuated structures. The results show that the present method can give satisfactory control voltages with a reasonable number of incremental steps.