Shape control of composite material plates using piezoelectric actuators

This paper concerns the shape control of composite material plates using piezoelectric actuators. A finite element formulation is developed for modeling a laminated composite plate that has piezoelectric actuators and sensors. To improve the accuracy of the prediction of the plate deformation, a simple higher-order deformation theory is used. The electrical potential is treated as a generalized coordinate, allowing it to vary over the element. For the shape control, an optimization algorithm, based on finite element techniques, is developed to determine optimal actuator voltages to minimize the surface error between the desired shape and actual deformed shape. The error function for a plate element is determined by calculating the mean square of the surface error over the surface, instead of determining it only at the node points of the element. Based on these techniques, Matlab codes were developed. Analyses were performed to determine optimum actuator voltages. The analytical results demonstrate the feasibility of using piezoelectric actuators for the active shape control of spacecraft reflectors.