Maneuver simulations of flexible spacecraft by solving TPBVP

Abstract

The optimal control of 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. 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 (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response