Nonlinear Station-Keeping Control in the Vicinity of the Sun-Earth Point Using Solar Radiation Pressure
Publication: Journal of Aerospace Engineering
Volume 29, Issue 3
Abstract
The use of solar radiation pressure for station-keeping at a sub- Sun-Earth/Moon collinear libration point is presented. Numerical halo and Lissajous reference trajectories are generated for the sub- libration point. Owing to the instability of these orbits, active station-keeping is required to prevent spacecraft escape after orbit insertion. The control inputs for solar sail control include area variation and solar sail pitch and roll angle variations. A nonlinear higher order control method is developed to utilize solar radiation pressure to minimize the trajectory tracking error. The stability of the proposed controllers is established using the Lyapunov theory. The performance of the proposed controllers is tested through numerical simulation of the governing nonlinear equations of motion and is applied for station-keeping in the elliptical restricted three-body problem. It is shown that underactuated control is able to keep the spacecraft motion bounded, but the tracking error remains high. The fully actuated control is able to provide accurate station-keeping for both halo and Lissajous trajectories. The numerical results demonstrate the effectiveness of the proposed control technique for precise station-keeping using solar radiation pressure at a sub- libration point.
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References
Bartolini, G., Ferrara, A., Usai, E., and Utkin, V. (2000). “On multi-input chattering free second order sliding mode control.” IEEE Trans. Autom. Control, 45(9), 1711–1717.
Biggs, J. D., and McInnes, C. R. (2009). “Control of solar sail periodic orbits in the elliptic three-body problem.” J. Guidance Control Dyn., 32(1), 318–320.
Bookless, J., and McInnes, C. (2008). “Control of Lagrange point orbits using solar sail propulsion.” Acta Astronaut., 62(2–3), 159–176.
Boskovic, J., Chen, L., and Mehra, R. (2004). “Adaptive control design for nonaffine models arising in flight control.” J. Guidance Control Dyn., 27(2), 209–217.
Brucker, E., and Gurfil, P. (2007). “Analysis of gravity-gradient-perturbed rotational dynamics at the collinear Lagrange points.” J. Astronaut. Sci., 55(3), 271–291.
Canalias, E., Gomez, G., Marcote, M., and Masdemont, J. (2004). “Assessment of mission design including utilization of libration points and weak stability boundaries.”, European Space Agency, Noordwijk, Netherlands.
Cielaszyk, D., and Wie, B. (1996). “New approach to halo orbit determination and control.” J. Guidance Control Dyn., 19(2), 266–273.
Demiryont, H., and Moorehead, D. (2009). “Electrochromic emissivity modulator for spacecraft thermal management.” Sol. Energy Mater. Sol. Cells, 93(12), 2075–2078.
Farquhar, R. (1968). “The control and use of libration point satellites.” Ph.D. thesis, Stanford Univ., CA.
Farres, A., and Jorba, A. (2008). “Station-keeping close to unstable equilibrium points with a solar sail.” Adv. Astronaut. Sci., 2(129), 1503–1522.
Gardner, J., et al. (2006). “The James Webb space telescope.” Space Sci. Rev., 123(4), 485–606.
Giamberardino, P. D., and Monaco, S. (1996). “On halo orbits spacecraft stabilization.” Acta Astronaut., 38(12), 903–925.
Gurfil, P., and Meltzer, D. (2006). “Station-keeping on unstable orbits: Generalization to the elliptic restricted three-body problem.” J. Astronaut. Sci., 54(1), 29–51.
Hexi, B., and McInnes, C. R. (2006). “Solar sail equilibria in the elliptical restricted three-body problem.” J. Guidance Control Dyn., 29(3), 538–543.
Hovakimyan, N., Lavretsky, E., and Sasne, A. (2007). “Dynamic inversion for nonaffine-in-control systems via time scale separtion. Part I.” J. Dyn. Control Syst., 13(4), 451–465.
Howell, K., and Pernicka, H. (1993). “Station-keeping method for libration point trajectories.” J. Guidance Control Dyn., 16(1), 151–159.
IMSL (International Mathematical and Statistical Library). (1997). Math library, version 3.0, Visual Numerics, Houston.
Kulkarni, J., and Campbell, M. (2006). “Stabilization of spacecraft flight in halo orbits: An infinity approach.” IEEE Trans. Control Syst. Technol., 14(3), 572–578.
Lawrence, D., and Piggott, S. (2004). “Solar sailing trajectory control for sub-l1 station-keeping.” AIAA Guidance Navigation and Control Conf., AIAA, Reston, VA.
Lawson, P., et al. (2008). “Terrestrial planet finder interferometer: 2007–2008 progress and plans.” Optical and Infrared Interferometry, SPIE, Bellingham, WA.
Levant, A. (1993). “Sliding order and sliding accuracy in sliding mode control.” Int. J. Control, 58(6), 1247–1263.
McInnes, A. I. S. (2000). “Strategies for solar sail mission design in the circular restricted three-body problem.” M.S. thesis, Purdue Univ., West Lafayette, IN.
McInnes, C., McDonald, A., Simmons, J., and MacDonals, E. (1994). “Solar sail parking in the restricted three body problem.” J. Guidance Control Dyn., 17(2), 399–406.
Mignard, F., et al. (2007). “The Gaia mission: Expected applications to asteroid science.” Earth Moon Planets, 101(3–4), 97–125.
Modi, V. J., and Kumar, K. (1972). “Attitude control of satellites using the solar radiation pressure.” J. Spacecraft Rockets, 9(9), 711–713.
Montenbruck, O. (1989). Practical ephemeris calculations, Springer, Germany, 29.
Pernicka, H., and Howell, K. (1987). “Numerical determination of lissajous trajectories in the restricted three body problem.” Celestial Mech., 41(1), 107–124.
Richardson, D. (1980). “Analytic construction of periodic orbits about the collinear points.” Celestial Mech., 22(3), 241–253.
RiosReyes, L. (2006). “Solar sails modeling estimation and trajectory control.” Ph.D. thesis, Univ. of Michigan, Ann Arbor, MI.
Shahid, K. (2010). “Spacecraft maneuvering at the sun/earth-moon l2 libration point.” Ph.D. thesis, Ryerson Univ., Toronto.
Simo, C., Gomez, G., Llibre, J., Martinez, R., and Rodriguez, J. (1987). “On the optimal station-keeping control of halo orbits.” Acta Astronaut., 15(6), 391–397.
Simo, J., and McInnes, C. (2010). “Displaced solar sail orbits: Dynamics and applications.” AIAA/AAS Space Flight Mechanics Meeting, American Astronautical Society, Springfield, VA, 1–11.
Slotine, J., and Li, W. (1991). Applied nonlinear control, Prentice-Hall, Upper Saddle River, NJ.
Waters, T., and McInnes, C. (2008a). “Invariant manifolds and orbit control in the solar sail three body problem.” J. Guidance Control Dyn., 31(3), 554–562.
Waters, T., and McInnes, C. R. (2008b). “Periodic orbits above the ecliptic plane in the solar sail restricted 3-body problem.” J. Guidance Control Dyn., 30(3), 687–693.
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© 2015 American Society of Civil Engineers.
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Received: Apr 23, 2014
Accepted: Jul 20, 2015
Published online: Oct 27, 2015
Discussion open until: Mar 27, 2016
Published in print: May 1, 2016
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