Periodic H2 synthesis for spacecraft in elliptical orbits with atmospheric drag and J2 perturbations

Alain Théron (1) , Christophe Farges (1, 2) , Dimitri Peaucelle (1) , Denis Arzelier (1)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 IMS - Laboratoire de l'intégration, du matériau au système

The problem of the stationkeeping for a small spacecraft is studied and a solution based on periodic feedback control laws is considered. Linearized equations of the relative motion of the satellite near an eccentric reference orbit are derived in the presence of the second zonal gravitational harmonic J2 and atmospheric drag perturbations. The obtained linear continuous-time model of the relative motion is T-periodic where T is the orbital period. After a discretization of the model, a state-feedback control law with performance requirement defined by the generalized H2 operator norm may be computed by a linear matrix inequality-based algorithm. Illustrative non linear simulations show the efficiency of the approach based on the use of linearized spacecraft relative motion dynamics associated to systematic H2 synthesis of stabilizing memoryless N-periodic state-feedback control laws.

Mots clés: Linear periodic discrete-time systems; H2 performance; spacecraft; relative station-keeping

Domaines: Automatique

Alain Théron, Christophe Farges, Dimitri Peaucelle, Denis Arzelier. Periodic H2 synthesis for spacecraft in elliptical orbits with atmospheric drag and J2 perturbations. American Control Conference. ACC'07., Jul 2007, New York, United States. pp.2473-2478, ⟨10.1109/ACC.2007.4282879⟩. ⟨hal-00331210⟩