[논문]Fuel-Optimal Altitude Maintenance of Low-Earth-Orbit Spacecrafts by Combined Direct/Indirect Optimization

Kim, Kyung-Ha; Park, Chandeok; Park, Sang-Young

doi:10.5140/jass.2015.32.4.379

Fuel-Optimal Altitude Maintenance of Low-Earth-Orbit Spacecrafts by Combined Direct/Indirect Optimization 원문보기

Journal of astronomy and space sciences, v.32 no.4, 2015년, pp.379 - 386

Kim, Kyung-Ha (Astrodynamics and Control Laboratory, Department of Astronomy, Yonsei University) , Park, Chandeok (Astrodynamics and Control Laboratory, Department of Astronomy, Yonsei University) , Park, Sang-Young (Astrodynamics and Control Laboratory, Department of Astronomy, Yonsei University)

Abstract ▼ AI-Helper

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.

주제어

AI 본문요약
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가설 설정

In this study, the J2 perturbation, which has significant effect on LEO spacecrafts, is considered along with air drag. Also, both a pseudospectral (direct) and a shooting (indirect) method are used together to improve the accuracy of optimization results obtained from previous studies.

이론/모형

While the thrust profile was similar to bang-off, it was difficult to precisely determine the switching time by using only a pseudospectral method. As an attempt to precisely determine the switching time and its associated optimal thrust history, a shooting method was employed with its initial guess obtained from a solution using the pseudospectral method. By analyzing the results with solar activity, fuel consumption during the maximum solar activity was found to be three times more than that during the minimum solar activity.
The process of updating the initial guesses is iterated until the transversality conditions are satisfied, and this process of solving nonlinear algebraic equations is performed using the MATLAB built-in function, ‘fsolve’. The ‘fsolve’ finds a root (zero) of a system of nonlinear equations (MathWorks 2015b).

성능/효과

6), the spacecraft raises its altitude for about 2/3 of the operation time, and then drops rapidly for about 1/3 of the operation time owing to the high atmospheric density
8), a spacecraft reaches the peak altitude at about 1/4 of the operation time, and then descends slowly for the remaining operation time
Pseudospectral and shooting methods were combined to optimize the fuel consumption for altitude maintenance of spacecrafts at 300 km circular orbits where atmospheric drag is sufficiently strong to cause orbital decay. Based on the physical characteristics of KOMPSAT-2, simulations showed that a satellite ascended with full thrust at the early stage and then descended with null thrust. While the thrust profile was similar to bang-off, it was difficult to precisely determine the switching time by using only a pseudospectral method.
As an attempt to precisely determine the switching time and its associated optimal thrust history, a shooting method was employed with its initial guess obtained from a solution using the pseudospectral method. By analyzing the results with solar activity, fuel consumption during the maximum solar activity was found to be three times more than that during the minimum solar activity. This implies that the solar activity cycle is a critical factor while designing a LEO mission.
This is possible because with extended maneuver periods, satellites reach higher altitudes where the atmospheric drag is relatively weak. For the case considering J2 perturbation with drag, more fuel was used to maintain the altitude than for the case considering only drag; J2 perturbation has a remarkable effect on LEO spacecrafts, and should be taken into account for a more realistic mission design.
This implies that the solar activity cycle is a critical factor while designing a LEO mission. Furthermore, fuel consumption was reduced when the maneuver period of satellites was increased. This is possible because with extended maneuver periods, satellites reach higher altitudes where the atmospheric drag is relatively weak.
Pseudospectral and shooting methods were combined to optimize the fuel consumption for altitude maintenance of spacecrafts at 300 km circular orbits where atmospheric drag is sufficiently strong to cause orbital decay. Based on the physical characteristics of KOMPSAT-2, simulations showed that a satellite ascended with full thrust at the early stage and then descended with null thrust.
Furthermore, fuel consumption was reduced when the maneuver period of satellites was increased. This is possible because with extended maneuver periods, satellites reach higher altitudes where the atmospheric drag is relatively weak. For the case considering J2 perturbation with drag, more fuel was used to maintain the altitude than for the case considering only drag; J2 perturbation has a remarkable effect on LEO spacecrafts, and should be taken into account for a more realistic mission design.
Based on the physical characteristics of KOMPSAT-2, simulations showed that a satellite ascended with full thrust at the early stage and then descended with null thrust. While the thrust profile was similar to bang-off, it was difficult to precisely determine the switching time by using only a pseudospectral method. As an attempt to precisely determine the switching time and its associated optimal thrust history, a shooting method was employed with its initial guess obtained from a solution using the pseudospectral method.

참고문헌 (13)

Elnagar G, Kazemi MA, Razzaghi M, The Pseudospectral Legendre Method for Discretizing Optimal Control Problems, IEEE Trans. Autom. Control 40, 1793-1796 (1995). http://dx.doi.org/10.1109/9.467672

상세보기
Halbach LE, A Numerical Study of Fuel-Optimal Low-Earth-Orbit Maintenance, Master Dissertation, Naval Postgraduate School (2000).
Jo JH, Park IK, Choe NM, Choi MS, The Comparison of the Classical Keplerian Orbit Elements, Non-Singular Orbital Elements (Equinoctial Elements), and the Cartesian State Variables in Lagrange Planetary Equations with J2 Perturbation: Part I, J. Astron. Space Sci. 28, 37-54 (2011). http://dx.doi.org/10.5140/JASS.2011.28.1.037

원문보기 상세보기
Kennewell J, Satellite Orbital Decay Calculations, IPS Radio and Space Services, The Australian Space Weather Agency, Sydney, Australia (1999).
Kim K, Current Status and Future Plan of Development of High-Resolution Earth-Observing Optical Satellites, Study on Aeronautical Industry, 65-85 (2013).
Kim K, Fuel Optimization for Altitude Maintenance of Low-Earth-Orbit (LEO) Spacecraft by Combining Direct and Indirect Methods, Master Dissertation, Yonsei University (2014).
Kluever CA, Pierson BL, Optimal Low-Thrust Three-Dimensional Earth-Moon Trajectories, J. Guid. Control Dyn. 18, 830-837 (1995). http://dx.doi.org/10.2514/3.21466

상세보기
MathWorks, fmincon [Internet] cited 2015a, available from: http://kr.mathworks.com/help/optim/ug/fmincon.html
MathWorks, fsolve [Internet] cited 2015b, available from: http://kr.mathworks.com/help/optim/ug/fsolve.html
Park C, Necessary Conditions for the Optimality of Singular Arcs of Spacecraft Trajectories Subject to Multiple Gravitational Bodies, Adv. Space Res. 51, 2125-2135 (2013). http://dx.doi.org/10.1016/j.asr.2013.01.005

상세보기
Park J, Moon YJ, Kim KH, Cho KS, Kim HD, et el., Drag Effect of KOMPSAT-1 during Strong Solar and Geomagnetic Activity, J. Astron. Space Sci. 24, 125-134 (2007). http://dx.doi.org/10.5140/JASS.2007.24.2.125

원문보기 상세보기
Park YJ, Park SY, Kim YR, Choi KH, Fuel Optimization for Low Earth Orbit Maintenance, J. Astron. Space Sci. 25, 167-180 (2008). http://dx.doi.org/10.5140/JASS.2008.25.2.167

원문보기 상세보기
Pontryagin LS, Mathematical Theory of Optimal Processes (CRC Press, New York, 1987).

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