Model predictive orbit control of a Low Earth Orbit satellite using Gauss’s variational equations

Abstract

In this paper, an autonomous orbit control of a satellite in Low Earth Orbit is investigated using model predictive control. The absolute orbit control problem is transformed to a relative orbit control problem in which the desired states of the reference orbit are the orbital elements of a virtual satellite which is not affected by undesirable perturbations. The relative motion is modeled by Gauss’s variational equations including J2 and drag perturbations which are the dominant perturbations in Low Earth Orbit. The advantage of using Gauss’s variational equations over the Cartesian formulations is that not only the linearization errors are much smaller, but also each orbital element can be controlled independently. Model predictive control finds the finite horizon optimal firing times of the satellite thrusters. The problem of orbit control has been cast as a linear programming which is a subset of convex optimization problems. As a result, model predictive control can maintain and control orbits of Low Earth Orbit satellites in optimal way, and this modern control technique can be an alternative for traditional analytical-based orbit control methods. Also, a comparison between model predictive control and linear quadratic regulator orbit control showed the superiority of MPC in fuel consumption.