Optimal shape control of adaptive structures for performance maximization

Abstract

Shape control of deformable structures has been studied for various performance-enhancing adaptive structures. In this paper, a new optimal shape control methodology is proposed for performance maximization of deformable structures. Using finite element modeling, deformation caused by a set of actuators is expressed in terms of actuation values. Then, a cost function is defined based on a given performance metric of the structure, and necessary and sufficient conditions for the cost function to be minimized are derived. Using the necessary condition, an analytical solution for actuation values that produce the maximum performance is obtained, and the sufficient condition is used to verify that the solution actually leads to the minimum cost. As an example, application of the proposed methodology is demonstrated by using a simple longitudinally actuated one-dimensional bar. The same methodology is also applied to a mechanically deformable one-dimensional structure with an array of radiating elements. The results show that the optimal shape control methodology developed in this study can be applied to certain types of performance maximization problems for adaptive deformable structures.