Abstract
The problem of spacecraft damping (damping of initial angular velocity to zero) for a minimal time is studied. Two variants of formulation of the optimization problem are considered; these variants differ in the form of constraints on the control torque. Analytical solution to the formulated problem is obtained in the closed form and numerical expressions for synthesis of optimal angular velocity control program are given. Similar problem of time-optimal angular acceleration of the spacecraft to the given value is also solved. Procedure for determination of the control torque at the initial time instant for the problem of acceleration of the spacecraft to the required angular velocity is presented. Numerical example of solution of the problems of buildup and damping of spacecraft rotation velocity for a minimal time is given.
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References
K. B. Alekseev and G. G. Bebenin, Spacecraft Control (Mashinostroenie, Moscow, 1974).
N. E. Zubov, “Optimal Control of Terminal Re-Orientation of a Spacecraft Based on the Algorithm with a Predictive Model”, Kosm. Issled., 29(3) (1991).
A. A. Krasovskii, Automatic Flight Control Systems and Their Analytical Design (Nauka, Moscow, 1973).
A. I. Van’kov, “Adaptive Robust Control of Angular Motion of a Spacecraft Using Predictive Models”, Kosm. Issled., 32(4–5) (1994).
B. V. Raushenbakh and E. N. Tokar’, Attitude Control of Orientation of Spacecraft (Nauka, Moscow, 1974).
V. N. Branets and I. P. Shmuglevskii, Application of Quaternions in Problems of Orientation of a Solid Body (Nauka, Moscow, 1973).
M. V. Levskii, “Pontryagin’s Maximum Principle in Optimal Control Problems of Orientation of a Spacecraft”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 6 (2008) [Comp. Syst. Sci. 47 (6), 974–986 (2008)].
Yu. V. Golubev and V. N. Demidov, “Optimal Control Law in Rotation Damping,” Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, No. 2 (1986).
A. P. Markeev, Theoretical Mechanics (Nauka, Moscow, 1990).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkelidze, et al., The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983).
N. N. Moiseev, Numerical Methods in Optimal Systems Theory (Nauka, Moscow, 1971) [in Russian].
M. Yu. Belyaev, Scientific Experiments on Spacecraft and Orbital Stations (Mashinostroenie, Moscow, 1984) [in Russian].
V. I. Vetlov, S. M. Novichkova, V. V. Sazonov, et al., “Regime of Biaxial Satellite Rotation in Orbit Plane,” Kosm. Issl. 38(6) (2000).
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Original Russian Text © M.V. Levskii, 2011, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2011, No. 1, pp. 147–161.
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Levskii, M.V. On optimal spacecraft damping. J. Comput. Syst. Sci. Int. 50, 144–157 (2011). https://doi.org/10.1134/S1064230711010138
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DOI: https://doi.org/10.1134/S1064230711010138