Attitude control of Earth-pointing spacecraft using nonlinear H ∞ control

Abstract

The attitude control of an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque, is explored. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear ${\mathcal{H}}_{\infty }$ control methodology and are subsequently generated using a Taylor series expansion to approximate solutions of the Hamilton–Jacobi equations. These controllers are applied to the problem of Earth-pointing spacecraft in circular orbits. The controllers are compared using both input–output and initial condition simulations, in an effort to gauge the improvements made possible by nonlinear feedback.