Station-keeping in the vicinity of the collinear Lagrange points

Abstract

In this thesis, the performance of three different station-keeping methods applied to Sun-Earth L2 halo orbits is investigated. In order to evaluate these methods, first a framework for accurate satellite dynamics was developed. This was done by starting off at the Circular Restricted Three Body Problem, and extending that to a more accurate model in the Roto-Pulsating Reference Frame (RPF). The dynamics in the RPF were implemented in a propagator, written in C, which forms the basis for any analysis that has been done for this thesis. The propagator includes real planetary ephemerides from JPL, perturbations from all solar-system bodies and Solar Radiation Pressure and has functionalities for orbit generation, STM propagation, reference frame transformations and manoeuvre calculations. The three station-keeping methods that have been investigated in this thesis are: Optimal Continuation Strategy (OCS), Discrete-time Sliding Mode Control (DSMC) and Fuzzy-logic Sliding Mode Control (FLSMC). All of these methods were implemented in C, within the developed propagator and were tuned using an optimization library for C. After the implementation of the three methods, a performance analysis was done, applying the methods to a Sun-Earth L2 halo orbit in a Monte-Carlo simulation, taking into account uncertainties in the orbit determination process, the perturbations and the manoeuvre execution. The total ΔV, as well as the number of manoeuvres, for the three methods were calculated, and subsequently compared against eachother. This was done for a time span of 500 days with a minimum manoeuvre interval of 12 days. The resulting comparison and the result of this analysis clearly shows that the DSMC and FLSMC perform much better both in terms of total ΔV as well as in the variance that arises from the Monte-Carlo simulations. The FLSMC provides another significant, yet smaller, improvement when compared to the DSMC, which was theorized by Lian et al. The fuzzy-logic layer that is implemented makes for smoother behaviour when the actual orbit of the satellite is close to the desired reference orbit, where the normal DSMC exhibits more chattering around the reference orbit. It is clear from this analysis that the proposal of Lian et al. to add this fuzzy logic layer does contribute significantly to the performance of the method and that FLSMC is a potent and efficient method for halo orbit station-keeping, provided a good reference orbit is chosen for the method to follow. The analysis performed in this thesis was restricted to Sun-Earth L2 halo orbits but all techniques mentioned and developed within this research can easily be applied to halo orbits around any of the collinear lagrange points in any three-body system, with only minor changes.