Optimal large angle maneuvers of a flexible spacecraft

Abstract

The optimal control of three-dimensional large-angle rapid maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two-point boundary-value problem is then solved by using the quasilin-earization algorithm and the method of particular solutions. The numerical results for the flexible nonlinear system, the flexible linearized system, and the rigidized nonlinear system are presented to compare the differences in their time responses.