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Model Predictive Orbit Control of a LEO Satellite Using Gauss’s Variational Equations

Tavakkoli, Mohammad Mahdi | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43850 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Asadian, Nima
  7. Abstract:
  8. In comparison to attitude control of a satellite which is widely used in practical missions, orbit control (espescialy autonomous orbit control) has been only recently paid attention. Autonomous, on-board orbit control, also called autonomous stationkeeping, means the automatic maintenance of all of orbital elements by the satellite itself. In this thesis, an autonomous absolute orbit control strategy for a single Low Earth Orbit (LEO) satellite is presented. When the satellite violates the control trigger error limits, then the controller is activated and calculates a sequence of orbital maneuvers that move the satellite towards its desired states. The absolute orbit control of the satellite is transformed to a relative orbit control problem in which the desired states of the absolute reference orbit treated as a virtual satellite which not affected by undesirable perturbations and therefore the differences between the states of the main satellite and the states of the virtual satellite must vanish. Relative motion equations like Clohessy-Wiltshire lose their accuracy when the distance between the satellites is large. Therefore Gauss’s Variational Equations (GVEs) which are linearized about orbital elements and therefore have smaller linearization error are used for modeling the relative motion of the satellite with respect to the reference orbit. GVEs in this thesis include J_2 and drag perturbations which are the dominant perturbations in LEO. The Model Predictive Control (MPC) is utilized to control the orbit which solves the infinite horizon optimal control problem on-line to compute the acceleration inputs. Then the inputs converted from accelerations to impulses and then to the ON-time of ON-OFF thruster. The problem of orbit control was cast as a Linear Programming (LP) which is a subset of convex optimization. The convexity of the LP problem essentially means that if local minimum is found for this problem, this point is also global minimum for the problem. Some different cases of MPC absolute orbit control and effects of variation of some control parameters are presented. Therefore MPC can maintain and control orbits of LEO satellites (e.g. Sun-synchronous and repeating ground-track) in optimal way and this modern control technique can be an alternative for traditional analytical-based orbit control methods
  9. Keywords:
  10. Model Predictive Control ; Convex Optimization ; Linear Programming ; Autonomous Orbit Control ; Gaussian Variational Equations

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