The problem of satellite attitude stabilization in the geomagnetic field

V. I. Kalenova   ; V. M. Morozov   ; A. A. Tikhonov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 4, pp. 499-517

Résumé

A satellite moving along a circular Keplerian orbit in near-Earth space was explored, focusing on its attitude stabilization in the orbital coordinate system using the intrinsic magnetic and Lorentz force moments. Fluctuations in geomagnetic induction that occur as the satellite orbits cause the coefficients in the dynamical equations governing the satellite’s attitude motion to vary over time. The results show that, although the linearized system of differential equations of the satellite’s motion is non-stationary, it can be reduced to a stationary system of higher order, which holds even for high-precision multipole models of the geomagnetic field. Thus, a control law design was proposed to stabilize the satellite. The controllability of the system was analyzed, and an optimal stabilization algorithm based on the LQR method was developed. The effectiveness of the proposed approach was validated by computer modeling.

Détail

Mots-clés : satellite
Keywords: satellite attitude stabilization, geomagnetic field, controllability, optimal control.

Bibliographie

[1] Antipov K.A., Tikhonov A.A., “Multipole models of the geomagnetic field: Construction of the N-th approximation”, Geomagn. Aeron., 53:2 (2013), 257–267 | DOI | DOI

[2] Morozov V.M., Kalenova V.I., Rak M.G., “Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field”, Itogi Nauki Tekh. Ser. Sovrem. Mat. Ee Prilozh. Tematich. Obz., 220, 2023, 71–85 (In Russian) | DOI

[3] Morozov V.M., Kalenova V.I., Rak M.G., “Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field”, Itogi Nauki Tekh. Ser. Sovrem. Mat. Ee Prilozh. Tematich. Obz., 221, 2023, 71–92 (In Russian) | DOI

[4] Morozov V.M., Rak M.G., Kalenova V.I., “Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field”, Itogi Nauki Tekh. Ser. Sovrem. Mat. Ee Prilozh. Tematich. Obz., 222, 2023, 42–63 (In Russian) | DOI

[5] Morozov V.M., Kalenova V.I., Rak M.G., “Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field”, Itogi Nauki Tekh. Ser. Sovrem. Mat. Ee Prilozh. Tematich. Obz., 223, 2023, 84–106 (In Russian) | DOI

[6] Morozov V.M., Kalenova V.I., Rak M.G., “Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field”, Itogi Nauki Tekh. Ser. Sovrem. Mat. Ee Prilozh. Tematich. Obz., 224, 2023, 115–124 (In Russian) | DOI

[7] Ovchinnikov M.Yu., Roldugin D.S., “Current algorithms for active magnetic attitude control of satellites”, Kosm. Appar. Tekhnol., 3:2 (2019), 73–86 (In Russian) | DOI

[8] Tikhonov A.A., “Refinement of the oblique dipole model in the evolution of rotary motion of a charged body in the geomagnetic field”, Cosmic Res., 40:2 (2002), 157–162 | DOI

[9] Morozov V.M., Kalenova V.I., “Satellite control using magnetic moments: Controllability and stabilization algorithms”, Cosmic Res., 58:3, 158–166 | DOI | DOI

[10] Kalenova V.I., Morozov V.M., “Novel approach to attitude stabilization of satellite using geomagnetic Lorentz forces”, Aerosp. Sci. Technol., 106 (2020), 106105 | DOI

[11] Kalenova V.I., Morozov V.M., “Stabilization of satellite relative equilibrium using magnetic and Lorentzian moments”, Cosmic Res., 59:5 (2021), 343–356 | DOI | DOI

[12] Morozov V.M., Kalenova V.I., Rak M.G., “On the stabilization of the regular precessions of satellites by means of magnetic moments”, Mech. Solids, 56:8 (2021), 1486–1499 | DOI | DOI

[13] Morozov V.M., Kalenova V.I., “Stabilization of satellite relative equilibrium using magnetic moments and aerodynamic forces”, Cosmic Res., 60:3 (2022), 213–219 | DOI | DOI

[14] Kalenova V.I., Morozov V.M., Linear Time-Varying Systems and Their Application to the Problems of Mechanics, Fizmatlit, M., 2010, 207 pp. (In Russian)

[15] Kalenova V.I., Morozov V.M., Rak M.G., “On methodology for solving control problems of one class of time-varying systems”, Lobachevskii J. Math., 44:11 (2023), 4994–5000 | DOI

[16] Aleksandrov A.Yu., Aleksandrova E.B., Tikhonov A.A., “Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system”, Adv. Space Res., 62:1 (2018), 142–151 | DOI

[17] Antipov K.A., Tikhonov A.A., “On satellite electrodynamic attitude stabilization”, Aerosp. Sci. Technol., 33:1 (2014), 92–99 | DOI

[18] Beletskii V.V., Motion of an Artificial Satellite about its Center of Mass in the Gravitational Field, Izd. Mosk. Univ., M., 1975, 308 pp. (In Russian)

[19] Wertz J. (ed.), Spacecraft Attitude Determination and Control, Astrophysics and Space Science Library, 73, D. Reidel Publ. Co., Dordrecht, 1978, xviii+858 pp. | DOI

[20] Tikhonov A.A., “A method of semipassive attitude stabilization of a spacecraft in the geomagnetic field”, Cosmic Res., 41:1 (2003), 63–73 | DOI

[21] Petrov K.G., Tikhonov A.A., “The moment of Lorentz forces acting on a charged satellite in the Earth's magnetic field. Part 2. the determination of the moment and estimations of its components”, Vestn. S.-Peterb. Univ. Ser. 1, 3:15 (1999), 81–91 (In Russian)

[22] Aleksandrov A.Yu., Tikhonov A.A., “Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite”, Aerosp. Sci. Technol., 104 (2020), 105963 | DOI

[23] Nababi M., Barati M., “Mathematical modeling and simulation of the Earth's magnetic field: A comparative study of the models on the spacecraft of attitude control application”, Appl. Math. Modell., 46 (2017), 365–381 | DOI

[24] Alken P., Thébault E., Beggan C.D., Amit H., Aubert J., Baerenzung J., Bondar T.N., Brown W.J., Califf S., Chambodut A., Chulliat A., Cox G.A., Finlay C.C., Fournier A., Gillet N., Grayver A., Hammer M.D., Holschneider M., Huder L., Hulot G., Jager T., Kloss C., Korte M., Kuang W., Kuvshinov A., Langlais B., Léger J.-M., Lesur V., Livermore P.W., Lowes F.J., Macmillan S., Magnes W., Mandea M., Marsal S., Matzka J., Metman M.C., Minami T., Morschhauser A., Mound J.E., Nair M., Nakano S., Olsen N., Pavón-Carrasco F.J., Petrov V.G., Ropp G., Rother M., Sabaka T.J., Sanchez S., Saturnino D., Schnepf N.R., Shen X., Stolle C., Tangborn A., Tøffner-Clausen L., Toh H., Torta J.M., Varner J., Vervelidou F., Vigneron P., Wardinski I., Wicht J., Woods A., Yang Y., Zeren Z., Zhou B., “International Geomagnetic Reference Field: The thirteenth generation”, Earth, Planets Space, 73 (2021), 49 | DOI

[25] Morozov V.M., Kalenova V.I., Linear Time-Varying Systems and Stabilization of a Satellite near the Center of Mass in the Geomagnetic Field, Izd. Mosk. Univ., M., 2023, 174 pp. (In Russian)

[26] Brewer J.W., “Kronecker products and matrix calculus in system theory”, IEEE Trans. Circuits Syst., 25:9 (1978), 772–781 | DOI

[27] Alexandrov A.Y., Tikhonov A.A., “Electrodynamic control with distributed delay for AES stabilization in an equatorial orbit”, Cosmic Res., 60:5 (2022), 366–374 | DOI | DOI

[28] Ovchinnikov M.Yu., Roldugin D.S., Penkov V.I., “Three-axis active magnetic attitude control asymptotical study”, Acta Astronaut., 110 (2015), 279–286 | DOI