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Title: EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT

Year

2024

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210

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Title

EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT

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Authors

L. K. Babadzanjanz; I. Yu. Pototskaya; Yu. Yu. Pupysheva; V. S. Korolev

DOI

10.5593/sgem2024/6.1/s28.64

DOI Issue

10.5593/sgem2024/6.1

ISSN

1314-2704

ISBN

978-619-7603-74-3

Language

English

Volume

Issue

6.1

Editor

• Prof. DSc. Oleksandr Trofymchuk, UKRAINE
• Prof. Dr. hab. oec. Baiba Rivza, LATVIA

Scientific Area

Space Technologies and Planetary Science

Abstract/ Foreword

Satellite motion control in the vicinity of the libration point with expenditure criteria is considered. Expenditure optimization is natural in the case, where it is necessary to keep mechanical system in the neighborhood of the equilibrium point for a long time. Disturbing factors from time to time distort this system unacceptably far from the equilibrium point, and we need to extinguish these deviations, using fuel or another resource, which reserves are limited.
Optimization of the satellite motion control according to this criterion is important not only from the economic and technical side, but also brings an environmental effect.
Features of the presented mathematical problem definition are following. While deviations from the equilibrium point are very small, its controlled motion can be by linear differential equations with constant coefficients. The admissible control is a piecewise polynomial function that blanks selected frequency components of the solution of linear equations at the terminated moment T. As the expenditure functional we use the integral of the sum of the control coordinates modules along the interval [0,T].
As the results of solving the problem, formulas and an algorithm for finding the control switching points satisfying the expenditure functional extremum necessary conditions are proposed.

References (click to open)

[1] Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Control with Expenditure Criteria in Rotational Motion of the Satellite Moving along a Circular Orbit, Greece, AIP Conference Proceeding Vol.1648, American Institute of Physics, 2015, pp.1-4.
[2] Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Expenditure Optimization in a Problem of Controlled Motion of Mechanical Systems, Greece, AIP Conference Proceeding Vol.1738, American Institute of Physics, 2016, pp.1-4.
[3] Alesova I.M., Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Saakyan A.T., Piecewise polynomial control in mechanical systems, Greece, AIP Conference Proceeding Vol. 1863, American Institute of Physics, 2017, pp.1-4.
[4] Alesova I.M., Babadzanjanz L.K., Bregman A.M., Bregman K.M., Pototskaya I.Yu., Pupysheva Yu.Yu., Saakyan A.T., Piecewise constant control of linear mechanical systems in the general case, Greece, AIP Conference Proceeding Vol. 1978, American Institute of Physics, 2018, pp.1-4.
[5] Farquhar, R.W., Dunham, D.W. Use of Libration-Point Orbits for Space Observatories. In: Kondo, Y. (eds) Observatories in Earth Orbit and Beyond. Astrophysics and Space Science Library, vol 166. Springer, Dordrecht, 1990. https://doi.org/10.1007/978-94-011-3454-5_52
[6] Szebehely Victor, Theory of Orbits, Academic Press, New York, 1967.
[7] Ardaens J.S., D’Amico S. Control of formation flying spacecraft at a Lagrange point. DLR, 2008.
[8] Markeev A.P. Tochki libratsii v nebesnoy mekhanike i kosmodinamike [Vibration points in celestial mechanics and cosmodynamics]. Moscow, Nauka Publ., 1978 (in Russ.).
[9] Korolev V., Polyakhova E., Pototskaya I., Prospects Of Photogravitational Celestial Mechanics For Space Systems, Bulgaria, SGEM Conference Proceeding, 2023, 23 (6.1) pp. 439–446.

Acknowledgements (click to open)

Type

conference

Url

https://doi.org/10.5593/sgem2024/6.1/s28.64

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Proceedings Тitle

Proceedings of 24th International Multidisciplinary Scientific GeoConference SGEM 2024

Note

24th International Multidisciplinary Scientific GeoConference SGEM 2024, 1 - 7 July, 2024

Type

Proceedings Paper

Publisher

STEF92 Technology

Series

International Multidisciplinary Scientific GeoConference Surveying Geology and Mining Ecology Management, SGEM

Organization

SWS Scholarly Society; Acad Sci Czech Republ; Latvian Acad Sci; Polish Acad Sci; Russian Acad Sci; Serbian Acad Sci and Arts; Natl Acad Sci Ukraine; Natl Acad Sci Armenia; Sci Council Japan; European Acad Sci, Arts and Letters; Acad Fine Arts Zagreb Croatia; Croatian Acad Sci and Arts; Acad Sci Moldova; Montenegrin Acad Sci and Arts; Georgian Acad Sci; Acad Fine Arts and Design Bratislava; Russian Acad Arts; Turkish Acad Sci.

Pages

451-458

Date

1 - 7 July, 2024

Online Source Type

website

Digital Source Type

9829

Keywords

expenditure criteria, libration point, piecewise polynomial control.

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Title: EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT

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