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Optimization of Spatial Rotations of the Spacecraft Controlled by Inertial Actuators

American Journal of Mathematical and Computational Sciences
Vol.3 , No. 1, Publication Date: Jan. 16, 2018, Page: 22-30

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Authors

[1]	Mikhail Valer'evich Levskii, Research Institute of Space Systems, Khrunichev State Space Research-and-Production Center Korolev, Moscow Region, Russia.

Abstract

The problem of correct choosing the time of optimal rotation from an arbitrary initial position into prescribed final angular position is investigated. The case, when slew maneuver is carried out with minimal magnitude of spacecraft angular momentum, is considered. Calculated dependences for constructing optimal program of reorientation (in sense of minimum angular momentum) are written as the law of variation of the angular velocity vector. Optimal control is in the class of regular motions. Dynamics of spacecraft rotation during the slew maneuver is similar to the known method of control, designed earlier, which includes as much as possible fast acceleration of a spacecraft, rotation with constant modulus of angular momentum and as much as possible fast cancellation of angular momentum. The formalized equations are presented, and computational expressions for determination of optimal duration of reorientation maneuver are obtained for known mass-inertial characteristics of a spacecraft, if attitude control is made by inertial actuators (system of control moment gyroscopes, gyrodynes). The knowledge of fit range of preferable duration of a slew maneuver helps to plan correctly the flight program of spacecraft controlled by the powered gyroscopes. The condition for determining the moment of the beginning of deceleration which uses current parameters of motion (information on angular position of a spacecraft and measurements of angular velocity) was given, what considerably increases accuracy of spacecraft move into a required position. Example of optimal spacecraft rotation and results of mathematical simulation adds the made theoretical descriptions, and illustrates reorientation process in visual form.

Keywords

Optimal Control, Spatial Orientation, Spacecraft Attitude, Optimized Functions, Control Moment Gyroscopes

Reference

[01]	Levskii M. V. Some issues of time-optimal control over a spacecraft programmed turn. Cosmic Research, 2011, Vol. 49, No. 6.
[02]	Levskii M. V. A special case of spacecraft optimal attitude control. Journal of Computer and Systems Sciences International, 2012, Vol. 51, No. 4.
[03]	Branets V. N., Shmyglevskii I. P. Use of quaternions in problems of orientation of solid bodies. Moscow: Nauka, 1973. [in Russian].
[04]	Alekseev K. B., Bebenin G. G. Space vehicles control. Moscow: Mashinostroenie, 1974. [in Russian].
[05]	Zubov N. E. Optimal control over terminal reorientation of a spacecraft based on algorithm with a prognostic model. Cosmic Research, 1991, Vol. 29, No. 3.
[06]	Ermoshina O. V., Krishchenko A. P., Synthesis of programmed controls of spacecraft orientation by the method of inverse problem of dynamics. Journal of Computer and Systems Sciences International, 2000, Vol. 39, No. 2.
[07]	Alekseev K. B., Malyavin, A. A., Shadyan A. V. Extensive control of spacecraft orientation based on fuzzy logic. Flight, 2009, No. 1. [in Russiian].
[08]	Van’kov A. I. Adaptive robust control of attitude motion of a spacecraft using prognostic models. Cosmic Research, 1994, Vol. 32, No. 4–5.
[09]	Raushenbakh B. V., Tokar’ E. N. Spacecraft orientation control. Moscow: Nauka, 1974. [in Russian].
[10]	Levskii M. V. On optimal spacecraft damping. Journal of Computer and Systems Sciences International, 2011, Vol. 50, No. 1.
[11]	Levskii M. V. Control of a spacecraft’s spatial turn with minimum value of the path functional. Cosmic Research, 2007. Vol. 45, No. 3.
[12]	Levskii M. V. A solving the problem of optimal control over turn of a spacecraft within the class of regular motions. Cosmonautics and rocketry-constructing, 1999, No. 16. [in Russian].
[13]	Levskii M. V. Method of Controlling a Spacecraft Turn. Russian Federation Patent (Invention's Certificate) No. 2093433. Bulletin “Inventions. Applications and Patents”, No. 29 (1997) Published 20 October, 1997. [in Russian].
[14]	Kovtun V. S., Mitrikas V. V., Platonov V. N., Revnivykh S. G., Sukhanov N. A. Mathematical Support for Conducting Experiments with Attitude Control of Space Astrophysical Module Gamma. News from Academy of Sciences USSR. Technical Cybernetics, 1990, No. 3. [in Russian].
[15]	Castruccio P. A., Irby J. E., All-Digital Attitude Control System for Skylab, in Proc. of the 5th IFAC Symposium on Automatic Control in Space, New York: Pergamon, 1973.
[16]	Sarychev V. A., Belyaev M. Yu., Zykov S. G., Sazonov V. V., Teslenko V. P., Mathematical Models of Processes for Supporting Orientation of the Mir Orbital Station with the Use of Gyrodynes, Preprint of Keldysh Institute of Applied Mathematics (Russian of Academy of Sciences), Moscow, 1989, No. 10. [in Russian].
[17]	Sarychev V. A., Belyaev M. Yu., Zykov S. G., Zueva E. Yu., Sazonov V. V., Saigiraev Kh. U., Some Problems of Attitude Control of the Orbital Complex Mir – Kvant-1 – Kvant-2 (in Proceedings of the 25th Readings Devoted to Elaboration and Development of K. E. Tsyolkovsky’s Scientific Heritage. Section “Issues of Rocket and Space Engineering”), Moscow: IIET name of Vavilov S. I. (Russian of Academy of Sciences), 1991. [in Russian].