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Optimal Control of Spacecraft on the Earth-Moon Lagrange Point Orbits considering Sun and other Planets and Elliptic Orbit Perturbations

Ghorbani, Mehrdad | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42883 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Assadian, Nima
  7. Abstract:
  8. In this thesis, optimal station keeping of spacecraft on the closed-orbits near the Earth-Moon Lagrange points has been investigated. Lagrange points L1 and L2 are unstable equilibrium points of the circular restricted three-body problem (CRTBP), and periodic orbits near them are the destination of modern missions. However, perturbations resulting from the gravitational forces of the Sun and the planets and the eccentricity of the orbit of the Moon around the Earth make the Lagrange point unstable, even L4 and L5, which are stable in CRTBP. The most suitable choice for spacecraft mission near the collinear Lagrange points is the Halo and other closed-orbits around them, which need station-keeping for rejecting the perturbation effects. In this study, some methods for optimal station-keeping of spacecrafts around these orbits have been presented. At first, a restricted four-body model is used to model the Sun perturbation. Afterward, this model has been extended to the generalized five-body problem to take the planets perturbations into account. The effect of the eccentricity of the Moon orbit around the Earth has been modeled utilizing the two-body model of the Moon-Earth orbit. Finally, the bi-elliptic model has been introduced and extended to the multi-elliptic generalized five-body model. This model has been validated comparing the numerical simulation results with propagation model of JPL Horizon System. The governing equations have been linearized in order to use the optimal linear quadratic regulator (LQR) controller. The LQR controller is then applied on the system. The nonlinear optimization technique has been also utilized to find nonlinear continuous control to keep the spacecraft on the desired reference orbit. The fuel consumption and deviation from the reference trajectory has been considered in the cost function. In discrete control approach, the impulsive maneuvers have been optimized using the shooting method and nonlinear programming. The difference of the trajectory from the reference orbit and the summation of the impulses have been included in the cost function. The results have been presented for the orbits near L1 and L2 Lagrange points with different control schemes.

  9. Keywords:
  10. Numerical Optimization ; Shooting Method ; impulsive Maneuver ; Optimal Station Keeping ; Lagrangian Points ; Perturbations in Circular Restricted Three-body Problem (CRTBP) ; Continuous Thrust

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