Robust control of the Hill's problem with drag

• Published in: International journal of robust and nonlinear control Vol. 31; no. 1; pp. 268 - 286
• Main Authors: Limebeer, David J. N., Sabatta, Deon
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10-01-2021
• Subjects: Control stability; Drag; Halo orbit; Halo orbit symmetries; Hill's problem; Lagrangian equilibrium points; Libration; Orbital stability; Orbits; periodic Riccati equation; periodic robust control; Robust control; State feedback; Trajectory analysis; Trajectory control; two‐degree‐of‐freedom controller
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5290

Summary
There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three‐body problem (CRTBP) equations, the Hill's equations support three‐dimensional “halo” orbits that require station‐keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two‐degree‐of‐freedom ℋ∞ control strategy is used to maintain a pre‐selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time‐periodic ℋ∞ state feedback law, and a time‐periodic feed‐forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.