Model predictive control of low Earth-orbiting satellites using magnetic actuation

This paper presents a model predictive control approach for regulating the attitude of magnetically actuated satellites. Unlike other contributions in this area, a predictive control approach is developed which guarantees closed-loop stability of satellite configurations with unstable open-loop pitch dynamics. With the pitch axis being unstable, two magnetic dipoles are used exclusively for regulation of this axis. This allows the dynamics to be treated as a linear time-invariant system, and a simple proportional-derivative (PD) scheme is implemented. A model predictive controller is designed to regulate the lateral dynamics, with a Lyapunov function derived to guarantee asymptotic stability of the closed-loop system. The regulation of the lateral dynamics is achieved with a singe dipole moment, with a novel reformulation of the lateral dynamics also providing an explicit link between the two controllers. Simulations demonstrate the effectiveness and stability of the proposed algorithm when applied to the European Space Agency's GOCE satellite.