State Feedback Control in Equinoctial Variables for Orbit Phasing Applications

Orbit phasing operations play an important role in many spac e missions, being commonly performed for station acquisition and station keeping of Low-E arth-Orbit and Geostationary satellites, and in the initial part of rendezvous maneuvers. The classic l phasing approach consists of twoimpulse Hohmann transfer which takes a satellite away from a nd then back into its original orbit, so as to steer the satellite to the correct orbital position, see e.g., [ 1]. This control method is flightproven, conceptually simple, and fuel-efficient in most app lications, but suffers from two major limitations: it is inherently open-loop, and requires an im pulsive thrust approximation. Due to the tight positioning accuracy requirements of next-generati on space missions and the availability of new continuous-thrust propulsion technologies [ 2,3], there is a growing interest in the development of feedback control systems able to overcome such limitatio ns. To this aim, the orbit phasing problem can be treated as a rend ezvous problem between two satellites located at different angular positions within a n orbit. As long as the satellite relative distance is small compared to the orbit radius, standard linear iz d models such as the Hill-ClohessyWiltshire (HCW) [4] and Tschauner-Hempel (TH) [ 5] equations can be adopted for control design. Along this line, references [ 6–8] developed optimal and robust regulators solving the circu lar rendezvous problem. Model Predictive Control has been investi gated in [ 9–11] to deal with state and * Research associate, Department of Information Engineerin g and Mathematics, leomanni@diism.unisi.it †Professor, Department of Information Engineering and Math ematics,giannibi@diism.unisi.it ‡Professor, Department of Information Engineering and Math ematics,garulli@diism.unisi.it §Professor, Department of Information Engineering and Math ematics,giannitrapani@diism.unisi.it

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