Abstract
The problem of searching for and holding the International Space Station in a position of dynamic equilibrium is considered. The equilibrium orientation of the International Space Station (ISS) is determined by the superposition of gravitational, gyroscopic, and aerodynamic moments acting on it. The system of powered gyroscopes installed on the space station plays the role of effectors in this task. Using this example as an example, we consider the possibility of applying the method of the sequential closure of the modes of motion to synthesize the multi-input multi-output (MIMO) control law, a multidimensional multiply connected dynamic system. It is proposed to use the generalized Butterworth polynomial as the reference polynomial determining the location of the poles of the closed system. Using the mathematical modeling of the control system in the search mode and maintaining the dynamic equilibrium, the advantage of using the generalized Butterworth polynomials in comparison with the classical Butterworth polynomials is demonstrated.
Similar content being viewed by others
REFERENCES
A. V. Sumarokov, “The onboard algorithm for averaging the orbital motion parameters of the International Space Station in the ICARUS experiment,” J. Comput. Syst. Sci. Int. 57, 273 (2018).
F. A. Voronin, D. S. Nazarov, P. A. Pakhmutov, et al., “On principles behind developing software for the information and control system of the Russian orbital segment of the International Space Station,” Vestn. MGTU im. N. E. Baumana, Ser. Priborostr., No. 2, 69–86 (2018).
M. Yu. Belyaev, L. V. Desinov, D. Yu. Karavaev, et al., “Features of imaging the Earth surface and using the results of the imaging made by the ISS Russian segment crews,” Kosm. Tekh. Tekhnol., No. 1, 17–30 (2015).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, V. N. Ryabchenko, S. N. Timakov, and E. A. Cheremnykh, “Identification of the position of an equilibrium attitude of the International Space Station as a problem of stable matrix completion,” J. Comput. Syst. Sci. Int. 51, 291 (2012).
V. N. Platonov and A. V. Sumarokov, “Studying the possibility of ensuring the stabilization accuracy characteristics of an advanced spacecraft for remote sensing of the Earth,” J. Comput. Syst. Sci. Int. 57, 655 (2018).
S. N. Timakov, K. A. Bogdanov, and S. E. Nefedov, “Sequential closing method for modes of movement for multidimensional, multilinked dynamical systems,” Vestn. MGTU im. N. E. Baumana, Ser. Priborostr., No. 5, 40–59 (2014).
N. Yu. Borisenko and A. V. Sumarokov, “On the rapid orbital attitude control of manned and cargo spacecraft Soyuz MS and Progress MS,” J. Comput. Syst. Sci. Int. 56, 886 (2017).
A. V. Sumarokov and S. N. Timakov, “On an adaptive control system for angular motion of a communication satellite,” J. Comput. Syst. Sci. Int. 47, 795 (2008).
V. N. Branets, V. N. Platonov, A. V. Sumarokov, and S. N. Timakov, “Stabilization of a wheels carrying communication satellite without angle and angular velocity sensors,” J. Comput. Syst. Sci. Int. 47, 118 (2008).
D. A. Efimov, A. V. Sumarokov, and S. N. Timakov, “On the stabilization of a communication satellite without measuring its angular velocity,” J. Comput. Syst. Sci. Int. 51, 732 (2012).
J. T. Harduvel, “Continuous momentum management of Earth-oriented spacecraft,” J. Guidance, Control Dyn. 15, 1417–1426 (1992).
B. Wie et al., “A new momentum management controller for the space station,” J. Guidance, Control Dyn. 12, 714–722 (1989).
W. Warren, B. Wie, and D. Geller, “Periodic-disturbance accommodating control of the space station for asymptotic momentum management,” J. Guidance, Control Dyn. 13, 984–992 (1990).
A. A. Voronov, Theory of Automatic Control, Part 1 (Vyssh. Shkola, Moscow, 1986) [in Russian].
H. Kwakernaak and R. Sivan, Linear Optimal Control Systems (Wiley-Interscience, New York, 1977).
A. B. Filimonov and N. B. Filimonov, “Concerning the problem of nonrobust of spectrum in tasks of modal control,” Mekhatron., Avtomatiz. Upravl., No. 10, 8–13 (2011).
B. P. Demidovich, Lectures on the Mathematical Theory of Stability (Nauka, Moscow, 1967) [in Russian].
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Synthesis of decoupling laws for attitude stabilization of a spacecraft,” J. Comput. Syst. Sci. Int. 51, 80 (2012).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Modification of the exact pole placement method and its application for the control of spacecraft motion,” J. Comput. Syst. Sci. Int. 52, 279 (2013).
N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Stabilization of coupled motions of an aircraft in the pitch–yaw channels in the absence of information about the sliding angle: Analytical synthesis,” J. Comput. Syst. Sci. Int. 54, 93 (2015).
M. Sh. Misrikhanov and V. N. Ryabchenko, “Pole placement in large dynamical systems with many inputs and outputs,” Dokl. Math. 84, 1 (2011).
N. E. Zubov, E. Yu. Zybin, E. A. Mikrin, M. Sh. Misrikhanov, A. V. Proletarskii, and V. N. Ryabchenko, “Output control of a spacecraft motion spectrum,” J. Comput. Syst. Sci. Int. 53, 576 (2014).
Funding
The work was supported by the Russian Foundation for Basic Research, project nos. 17-08-01635, 18-08-01379.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bogdanov, K.A., Zykov, A.V., Subbotin, A.V. et al. Application of Generalized Butterworth Polynomials for Stabilization of the Equilibrium Position of a Space Station. J. Comput. Syst. Sci. Int. 59, 451–465 (2020). https://doi.org/10.1134/S106423072003003X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106423072003003X