Losa, Damiana (2007) High vs Low Thrust Station Keeping Maneuver Planning for Geostationary Satellites. PhD thesis Automatique, Robotique et Informatique temps réel, ENSMP - CMA Centre de Mathmatiques Appliques, ENSMP.

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Abstract

Our thesis work focuses on the problem of station keeping maneuver planning for geostationary satellites equipped with thrusters at low thrust level. We evaluate the opportunity of substituting such a planning to the more traditional one used for geostationary satellites equipped with thrusters at high thrust.

Since the birth of low thrust technology, its use has always met with the spacecraft companies approval. The well-known advantage of low fuel consumption due to the high specific impulse achieved by the high values of specific impulsion makes this technology highly competitive with respect to the high trust level one, especially during transfer and rendez vous phases of space missions.

The trajectory optimization problems which have to be solved during the mission design in order to analyze the feasibility of transfer and rendez vous mission phases have begun to be solved with alternative optimization solutions, since the low thrust propulsion systems have to be activated for longer periods of the transfer time. High thrust trajectory optimization problems, typically formulated as discrete, have been replaced with low thrust trajectory optimization problems formulated as continuous and solved by continuous control techniques.

The goal of this thesis is to understand what is the impact of the low thrust propulsion technology on the station keeping phase feasibility analysis performed during the design of a geostationary mission. In particular we study the impact that the low thrust propulsion systems have on the station keeping maneuver planning and on the realization of the whole station keeping control loop. The goal is to deduce whether the maneuver planning related with this technology is competitive with respect to the more classical one based on high thrust level.

Usually the well known long term strategies for the SK maneuver are deduced from simplified propagation orbit models

(in function of mean orbital elements) mainly because the following three conditions are met: high thrust level propulsions, SK dead band box sizes not very stringent and the possibility to execute low frequency maneuvers.

In the framework of this dissertation, given the low thrust level propulsion and increasingly stringent dead band requirements, we think it is more appropriate to make the hypothesis of a much higher maneuver execution frequency in order to achieve a finer control of the GEO satellite position and to use an orbit propagation model described by the motion equations in terms of osculating elements.

For the maneuver planning we propose a solution based on a direct approach considered as the transcription in terms of parameter optimization problem of the constrained optimal control problem associated to the planning task. Two optimization techniques have been considered: the fixed horizon optimization under constraints and the receding horizon one.

This second is also used with the linearized motion equations appropriately transformed via a Lyapunov variable change on the state space of the osculating equinoctial element deviations. This Lyapunov transformation leads to the definition of a new set of orbital parameters. It makes the planning process more immediately understandable from a control viewpoint and easier to implement from a numerical viewpoint, thanks to the differential flatness and inclusion concepts.

All the low thrust maneuver planning results are obtained in a first time in terms of thrust velocity increments and in a second time directly in terms of thrust, considering typical propulsion system configurations with the goal of determining the more efficient one in nominal conditions and in the condition of failure of one of the thrusters.

The problem of collocation of more geostationary satellites in a same big box has not been explicitly addressed but is implicitly solved once the fine control technique with a relative stringent dead band requirement is proposed for each satellite.

Table of content

Contents. Résumé. Introduction (en français). Abstract. Acknowledgements. Contents. List of Figures. List of Tables. Dictionary of Symbols, Constants, Acronyms and Mathematical Notations. 1 Introduction. 1.1 Motivations and Objectives. 1.2 Approache Proposed . 1.3 Thesis Dissertation Outline. 2 Background. 2.1 Time Systems. 2.1.1 Local Sidereal Time (LST) and Coordinated Universal Time (UTC). 2.1.2 Epoch and Calendar Date. 2.2 Reference Frames and Coordinate Systems (RFCSs). 2.2.1 Earth Centered Inertial RFCS. 2.2.2 Earth Centered Earth Fixed RFCS . 2.2.3 Geostationary Clohessy-Wiltshire RFCS. 2.2.4 Gaussian and Equinoctial RFCSs. 2.2.5 Spacecraft Body Fixed RFCS. 2.3 Satellite State Representations. 2.3.1 Position and Velocity Coordinates. 2.3.2 Classical Orbital Elements. 2.3.3 Equinoctial Orbital Elements. 2.3.4 Conversion Formulas. 2.4 Osculating and Mean Orbital Elements. 2.5 Perturbation Techniques. 3 Environmental and Thrust Perturbing Accelerations. 3.1 Environmental Disturbing Potentials and Accelerations. 3.1.1 Gravity Attraction of the Earth. 3.1.2 Gravity Attraction of the Sun and the Moon. 3.1.3 Solar Radiation Pressure. 3.2 Thrust Accelerations. 3.2.1 Performance Parameters of Space Propulsion Systems. 3.2.2 Chemical and Electric Propulsion. 3.2.3 Propulsion System Acceleration Model. 3.2.3.1 Chemical, Hybrid, Full Electrical Propulsion Systems. 4 Translational Dynamics of GEO Satellites. 4.1 Nonlinear Models in Unperturbed Keplerian Conditions. 4.2 Nonlinear Models in Perturbed Keplerian Conditions. 4.2.1 Gauss’ Variation of Parameter (VOP) Equations. 4.2.2 Lagrange’s VOP Equations. 4.3 Geographical Position Vector. 4.4 A Linearized Geostationary Orbit Model. 5 GEO Satellite Station Keeping: Problem Statement and State of the Art. 5.1 GEO Satellite Orbital Requirements. 5.2 High and Low Thrust Station Keeping Maneuvers. 5.3 GEO Satellite Station Keeping (SK) Problem Statement. 5.4 GEO Satellite Station Keeping Control Loop. 5.5 GEO Satellite SK Maneuver Planning: a Survey of Related Work. 5.5.1 High Thrust SK Manoeuvre Planning. 5.5.1.1 Strategic Planning of North-South High Thrust SK Maneuvers . 5.5.1.2 Strategic Planning of East-West High Thrust SK Maneuvers. 5.5.2 Low Thrust SK Manoeuvre Planning. 5.5.3 A Different Approach to Plan SK Maneuvers. 5.5.3.1 An Example 6 Fixed and Receding Horizon Optimal SK Maneuver Planning. 6.1 Problem Formulation with State Constraints Only . 6.1.1 Direct Methods to Find Optimal Trajectories: State of the Art. 6.1.2 Linear Translational Dynamics of GEO Spacecraft. 6.1.3 GEO Station Keeping Parameter Optimization Problem. 6.2 Fixed and Receding Horizon Optimization Approaches. 6.2.1 Fixed Horizon Optimization (FHO) Approach. 6.2.2 Receding Horizon Optimization (RHO) Approach. 6.2.3 Some Remarks About the Receding Horizon Approach. 6.2.4 FHO Simulation Results. 6.2.5 RHO Simulation Results. 6.3 Technological Specifications. 6.3.1 Thrust Acceleration Effects. 6.3.1.1 Semi-Major Axis and Longitude Total Changes 6.3.1.2 Eccentricity Components Total Changes. 6.3.1.3 Inclination Components Total Changes. 6.3.2 On Off Maneuvers as Solutions of a Nonlinear POP. 7 Differential Flatness in the GEO Satellite SK Problem. 7.1 Differential Flatness. 7.2 Lyapunov Transformation in the EOE Deviation Space. 7.3 A New Set of Orbital Parameters. 7.4 Flat Outputs of the GEO Satellite Dynamics. 7.5 Summary. 8 Conclusion. 8.1 Thesis Contributions. 8.2 Areas of Future Works. 8.3 Final Comments. Conclusion (en français). Bibliography

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