Static Shape Determination and Control for Large Space Structures: I. The Flexible Beam

Abstract

A shape control or determination problem for a large space structure involves a linear partial differential equation representing shape displacements with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green’s functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Static shape control and determination algorithms are developed for one dimensional models, and illustrated with simulations of flexible beam examples. Solutions reduce to the solution of systems of linear equations of dimension less than or equal to the number of observations, or control forces. Approximations to solution elements in terms of modal expansions are presented.