In this paper, a control scheme is elaborated in order to perform the station keeping of a geostationary satellite equipped with electric propulsion while minimizing the fuel consumption. The use of electric thrusters imposes to take into account some additional non linear and operational constraints that make the overall station keeping optimal control problem difficult to solve directly. That is why the station keeping problem is decomposed in three successive control problems. The first one consists in solving a classical optimal control problem with an indirect method initialized by a direct method without enforcing the thrusters operational constraints. Starting from this non feasible solution for the genuine problem, the thrusters operating constraints are incorporated in the second problem, whose solution produces a feasible but non optimal control profile via two different ways. Finally, the third optimizes the commutation times thanks to a method borrowed to the switched systems theory. Simulation results on a realistic example validate the benefit of this particular control scheme in the reduction of the fuel consumption for the geostationary station keeping problem.
Abstract:A control scheme is elaborated to perform the station keeping of a geostationary satellite equipped with electric propulsion. The use of electric thrusters imposes to take into account some additional mutually exclusive constraints on the control function that can be reformulated as logical constraints. The resulting fuel optimal station keeping problem is thus not solved with classical methods, either direct or indirect, but is transformed into a linear integer programming problem. The linearised relative velocity of the satellite is computed and some linear constraints on this velocity are added to the original station keeping problem in order to perform the station kepping over one week after another. Simulation results validate the efficiency of the optimal control thrusts obtained by the solution of the overall linear integer programming problem.
In this paper, a fuel optimal rendezvous problem is tackled in the Hill-Clohessy-Wiltshire framework with several operational constraints as bounds on the thrust, non linear non convex and disjunctive operational constraints (on-off profile of the thrusters, minimum elapsed time between two consecutive firings...). An indirect method and a decomposition technique have already been combined in order to solve this kind of optimal control problem with such constraints. Due to a great number of parameters to tune, satisfactory results are hard to obtain and are sensitive to the initial condition. Assuming that no singular arc exists, it can be shown that the optimal control exhibits a bang-bang structure whose optimal switching times are to be found. Noticing that a system with a bang-bang control profile can be considered as two subsystems switching from one with control on to with control off, and vice-versa, a technique coming from the switching systems theory is used in order to optimise the switching times.
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