Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский

Controlling the orientation of a polar-orbiting satellite by means of magnetic moments

Published: 12.09.2018

Authors: Morozov V.M., Kalenova V.I.

Published in issue: #9(81)/2018

DOI: 10.18698/2308-6033-2018-9-1798

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

The article considers the problem of controlling the orientation of a polar-orbiting satellite in a circular orbit by means of magnetic moments. A direct magnetic dipole has been adopted as a model of the geomagnetic field. The system of equations of motion is linearized in a neighborhood of the relative equilibrium position. A system of equations of controlled motion belonging to a special class of linear nonstationary systems, for which there exists a transformation leading these systems to stationary systems of higher dimension, is explicitly indicated. On the basis of the given stationary system, controllability is investigated; efficient algorithms for optimal stabilization of the satellite relative equilibrium position are constructed. For these algorithms the control action is a function of the stationary system variables of a higher order than the initial nonstationary system. To synthesize control directly in the initial system, auxiliary variables are introduced, so as to make the transition from the state vector of the reduced stationary system to the state vector of the initial system, supplemented by auxiliary variables. The results of mathematical simulation of the constructed algorithms confirming the effectiveness of the proposed methodology are presented

[1] Psiaki M.L. Magnetic torque attitude control via asymptotic periodic linear quadratic regulation. Journal of Guidance, Control, and Dynamics, 2001, vol. 24, no. 2, pp. 386–304.
[2] Lovera M., Astolfi A. Global magnetic attitude control of spacecraft in the presence of gravity gradient. IEEE Transactions on Aerospace and Electronic Systems, 2006, vol. 42, no. 3, pp. 796–805.
[3] Lovera M., Astolfi A. Spacecraft attitude control using magnetic actuators. ELSEVIER, Automatica, 2004, vol. 40, iss. 8, pp. 1405–1414.
[4] Silani E., Lovera M. Magnetic spacecraft attitude control: a survey and some new results. Control Engineering Practice, 2005, vol. 13, no. 3, pp. 357–371.
[5] Giulietti F., Quarta A.A., Tortora P. Optimal control laws for momentum-wheel desaturaton using magnetorquers. Journal of Guidance Control and Dynamics, 2006, vol. 29, no. 6, pp. 1464–1468.
[6] Cubas J., Farrahi A., Pindado S. Magnetic attitude control for satellites in polar or sun-synchronous orbits. Journal of Guidance Control and Dynamics, 2015, vol. 38, no. 10, pp. 1947–1958.
[7] De Angelis E., Giulietti F., de Ruiter A.H.J., Avanzini G. Spacecraft attitude control using magnetic and mechanical actuation. Journal of Guidance Control and Dynamics, 2016, vol. 39, no. 3, pp. 564–573.
[8] Yaguang Yang. Controllability of spacecraft using only magnetic torques. IEEE Transactions on Aerospace and Electronic Systems, 2016, vol. 52, no. 2, pp. 955–962.
[9] Ovchinnikov M.Y., Roldugin D.S., Ivanov D.S., Penkov V.I. Choosing control parameters for three axis magnetic stabilization in orbital frame. Acta Astronautica, 2015, vol. 116, pp. 74–77.
[10] Ovchinnikov M.Y., Penkov V.I., Roldugin D.S., Ivanov D.S. Magnitnye sistemy orientatsii malykh sputnikov [Magnetic systems for small satellite orientation]. Moscow, Keldysh Institute of Applied Mathematics Publ., 2016, 366 p.
[11] Ivanov D.S., Ovchinnikov M.Yu., Penkov V.I., Ovchinnikov A.V. Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties. Acta Astronautica, 2016, vol. 132, pp. 103–110.
[12] Beletsky V.V. Dvizhenie sputnika otnositelno tsentra mass v gravitatsionnom pole [The satellite motion relative to the center of mass in the gravitational field]. Moscow, MSU Publ., 1975, 308 p.
[13] Kalenova V.I., Morozov V.M. Lineynye nestatsionarnye sistemy i ikh prilozheniya k zadacham mekhaniki [Linear nonstationary systems and their applications to problems of mechanics]. Moscow, Fizmatlit Publ., 2010, 208 p.
[14] Kalenova V.I., Morozov V.M. Prikladnaya matematika i mekhanika — Journal of Applied Mathematics and Mechanics, 2012, vol. 76, no. 4, pp. 576–588.
[15] Kalenova V.I., Morozov V.M. Izvestiya RAN. Teoriya i sistemy upravleniya — Journal of Computer and Systems Sciences International, 2013, no 3, pp. 6–15.
[16] Morozov V.M., Kalenova V.I. Linear time-varying systems and their applications to cosmic problems. AIP Conference Proceedings, 2018, vol. 1959, pp. 020–003.
[17] Bellman R. Introduction to matrix analysis. NY, Toronto, London, McGraw-Hill Book Company, Inc. Publ., 1960, 348 p. [In Russ.: Bellman R. Vvedenie v teoriyu matrits. Moscow, Nauka Publ., 1969, 368 p.].
[18] Laub A.J., Arnold W.F. Controllability and observability criteria for multivariable linear second order models. IEEE Transaction on Automatic Control, 1984, vol. AC-29, no. 2, pp. 163–165.