Optimal stabilization of small spacecraft angular motion in the process of deployment of an orbital tether system


The problem of stabilizing the motion of small spacecraft relative to the center of mass in the process of deploying an orbital tether system is presented in the paper. Stabilization is carried out with respect to the direction of the tether and is characterized by the classical Euler angles (precession, nutation and proper rotation). The proposed method of suboptimal control is based on the joint application of the principle of Bellman's dynamic programming and the averaging method. The integral quadratic optimality criterion that depends on operating deviations and low control inputs is used. Control synthesis is accomplished using the model of angular motion recorded for small angles of nutation. An example of calculating optimal control of an orbital tether system deployed for the purpose of de-orbiting small satellites to the Earth is given. The efficiency of the optimal control arrived at is confirmed by numerical calculations for the basic nonlinear model of motion of an orbital tether system.

About the authors

Yu. M. Zabolotnov

Samara State Aerospace University

Author for correspondence.
Email: yumz@yandex.ru

Russian Federation

Doctor of Science (Engineering), Professor
Professor of the Department of Software Systems

A. A. Lobankov

Samara State Aerospace University

Email: mart1989@mail.ru

Russian Federation

Post-graduate student of the Department of Software Systems


  1. Beletskiy V.V., Levin E.M. Dinamika kosmicheskikh trosovykh sistem [Dynamics of space tether systems]. Moscow: Nauka Publ., 1990. 336 p.
  2. Ishkov S.A., Naumov S.A. Control over orbital tether system unfolding. Vestnik of the Samara State Aerospace University. 2006. No. 1(9). P. 77-85. (In Russ.)
  3. Zabolotnov Y.M. Control of the deployment of a tethered orbital system with a small load into a vertical position. Journal of Applied Mathematics and Mechanics. 2015. V. 79, Iss. 1. P. 28-34. doi: 10.1016/j.jappmathmech.2015.04.015
  4. Zabolotnova O.Y. Synthesis of Control Algorithms for Deployment of Space Tether System. Polet. Obshcherossiyskiy nauchno-tekhnicheskiy zhurnal. 2010. No. 11. P. 36-42. (In Russ.)
  5. Naumov O.N. Damping Oscillations of Landing Capsule During Controlled Deployment of Tether System. Polet. Obshcherossiyskiy nauchno-tekhnicheskiy zhurnal. 2012. No. 2. P. 45-50. (In Russ.)
  6. Razygraev A.P. Osnovy upravleniya poletom kosmicheskikh apparatov i korabley [Fundamentals of spacecraft flight control]. Moscow: Mashinostroenie Publ., 1977. 472 p.
  7. Moiseev N.N. Asimptoticheskie metody nelineynoy mekhaniki [Asymptotic methods of nonlinear mechanics]. Moscow: Nauka Publ., 1981. 380 p.
  8. Moiseev N.N. Matematicheskie zadachi sistemnogo analiza [Mathematical problems of system analysis]. Moscow: Nauka Publ., 1981. 488 p.
  9. Chernous'ko F.L., Akulenko L.D., Sokolov B.N. Upravlenie kolebaniyami [Vibration control]. Moscow: Nauka Publ., 1980. 384 p.
  10. Lebedev V.N. Raschet dvizheniya kosmicheskogo apparata s maloy tyagoy [Calculation of low-thrust spacecraft motion]. Moscow: VTs AN SSSR Publ., 1968. 106 p.
  11. Ishkov S.A., Khramov A.A. Correction maneuvers calculation of quasi elliptical and circular orbits by engine with low and limit thrust. Izvestiya Samarskogo nauchnogo tsentra RAN. 2002. V. 4, no. 1. P. 144-152. (In Russ.)
  12. Bellman R. Dinamicheskoe programmirovanie [Dynamic programming]. Moscow: IL Publ., 1969. 457 p.
  13. Letov A.M. Dinamika poleta i upravlenie [Flight dynamics and control]. Moscow: Nauka Publ., 1969. 360 p.
  14. Zabolotnov Y.M., Naumov O.N. Motion of a descent capsule relative to its center of mass when deploying the orbital tether system. Cosmic Research. 2012. V. 50, no. 2. P. 177-187. doi: 10.1134/s0010952512020098
  15. Hapaev M.M. Usrednenie v teorii ustoychivosti [Averaging in the theory of stability]. Moscow: Nauka Publ., 1986. 191 p.



Abstract - 62

PDF (Russian) - 32

Article Metrics

Metrics Loading ...




  • There are currently no refbacks.

Copyright (c) 2016 VESTNIK of the Samara State Aerospace University

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies