Electric Station Keeping of Geostationary Satellites: a Differential Inclusion Approach

Abstract

International audienceThe aim of this paper is to consider the modelling and control issues arising in the design of a station keeping system for geostationary satellites based on electric propulsion. In particular, a linear time-varying model for the dynamics of a geostationary satellite affected by perturbations is derived and the longitude and latitude station keeping problem is then formulated as a constrained linear quadratic optimal control problem. A direct method based on the so-called differential inclusion approach is then proposed. Simulation results showing the feasibility of the control task on a spacecraft equipped with electric thrusters are also presented and discussed

A three-step decomposition method for solving the minimum-fuel geostationary station keeping of satellites equipped with electric propulsion

“…This reference also describes the advantages (complete control of the three orbit vectors, remaining diagonal pair of thruster for a complete control in case of failure of one thruster) of this specific propulsion system based on HS 702 satellite with a xenon ion propulsion system. It has been widely used as a typical configuration for electric propulsion in the literature [17], [18], [19] and more recently [20]. Nowadays the electric propulsion is a viable alternative to the chemical one, in particular in the case of SK of GEO satellite ( [21]), despite limiting thrust operations constraints (large on board power needs, mission requirements restricting the duration of use of the electric power system, impossibility to perform SK maneuvers at eclipse epochs, minimum elapsed time between two consecutive firing, on-off profile of the thrusters, thrust allocation).…”

“…To deal with on-off models of thrusts, the references [31,32] use the Pulse Width Modulation technique to generate rectangular profiles from a continuous one. [18] has formulated a method based on differential inclusion, and a first avenue for the use of decomposition methods to solve the problem is given in [19].…”

Low-Thrust Control of a Lunar Mapping Orbit

“…Much recent work related to low-thrust stationkeeping [13][14][15] considers the stationkeeping of satellites in geostationary orbit about Earth. In each of these works, it is desired to stationkeep the orbit by minimizing the variations in latitude and longitude, therefore maintaining the satellite over a certain position on Earth.…”

Integer Programming for Optimal Control of Geostationary Station Keeping of Low-Thrust Satellites

“…To deal with onoff models of the thrusts, rectangular profiles may be generated from a continuous one with the Pulse Width Modulation technique (see Vazquez et al (2015) and the references therein). Losa et al (2005) has formulated a method based on differential inclusion and Losa et al (2006) and Gazzino et al (2016) have implemented a decomposition technique. In this last reference, an equivalent problem has been tackled by means of a two-step methodology combining the application of the maximum principle on a simplified version of the SK problem and a transcription method initialized with the solution of the first step.…”