Advertisement

Calculation of Program Control Not Generating Singularities in Gyrosystems

  • E. I. DruzhininEmail author
CONTROL SYSTEMS OF MOVING OBJECTS

Abstract

A new approach to calculating the program controls of the spacecraft (SC) attitude by single-gimbal control moment gyros (gyroscopes in English terminology or gyrodynes in Russian terminology) is described in details. The novelty of the proposed method of calculating program controls is the virtual kinematic configuration of the actuator gyrosystem and the use of the angular momentum of the SC as a state variable when describing its dynamics. The formulation of the problem of calculating the control laws, based on these innovations, made it possible to directly use the total angular momentum of all the rotors of the gyrosystem in their motion relative to the main body of the SC, rather than its derivative, as a working tool for controlling the SC, and to accept the laws of the precessions of the gyro units, rather than the velocities of these precessions. A new approach to solving the problem of reorientation enables us to obtain control laws without such special (singular) positions of the gyro units in which the execution of the calculated laws is interrupted. This feature solves the well-known singularity problem of an actuator gyrosystem consisting of gyrodynes, and suggests that the presence of a singularity problem in the process of executing the calculated laws should be due only to their calculation method rather than due to certain specific features of the gyrosystem itself. The new method of calculating the control presented in this paper uses the structure of the space trajectory given a priori and the law of the motion along this trajectory is calculated in the process of forming the control. All the calculations are carried out on the standard onboard digital computer.

REFERENCES

  1. 1.
    E. I. Druzhinin, “Computation of program control implemented nonstop by means of power gyros,” Dokl. Akad. Nauk 476, 22–25 (2017).Google Scholar
  2. 2.
    M. N. Amster, R. P. Anderson, and H. M. Williams, “Analysis of twin-gyro attitude controller,” Final Summary Report EL-EOR-13005 (Chance Vought Aircraft, Dallas, TX, Inc., 1960).Google Scholar
  3. 3.
    A. E. Lopez, J. W. Ratcliff, and J. R. Havill, “Results of studies on a twin-gyro attitude-control system for space vehicles,” J. Spacecr. 1, 399–402 (1964).CrossRefGoogle Scholar
  4. 4.
    J. W. Crenshaw, “2-SPEED, a single-gimbal control moment gyro attitude control system,” AIAA Paper, No. 895, 1–10 (1973).Google Scholar
  5. 5.
    B. V. Raushenbakh and E. N. Tokar’, Orientation Control of Spacecraft (Nauka, Moscow, 1974) [in Russian].Google Scholar
  6. 6.
    R. V. van Riper and S. P. Liden, “A new fail operational control moment gyro configuration,” in Proceedings of the AIAA Guidance, Control and Flight Mechanics Conference, New York, 1971.Google Scholar
  7. 7.
    I. V. Bychkov, E. I. Druzhinin, Yu. I. Ogorodnikov, B. B. Belyaev, and A. I. Ul’yashin, “On the kinematic configuration of power gyrosystems,” in Proceedings of the 22nd SPb. International Conference on Integrated Navigation Systems (TsNII Elektropribor, St. Petersburg, 2015), pp. 234–239.Google Scholar
  8. 8.
    G. K. Suslov, Theoretical Mechanics (OGIZ, Moscow, 1946) [in Russian].Google Scholar
  9. 9.
    L. G. Loitsyanskii and A. I. Lur’e, The Course of Theoretical Mechanics (OGIZ, Moscow, Leningrad, 1948), Vol. 2 [in Russian].Google Scholar
  10. 10.
    E. N. Tokar’, V. P. Legostaev, M. V. Mikhailov, and V. P. Platonov, “Control of redundant gyro power systems,” Kosm. Issled. 18, 152–157 (1980).Google Scholar
  11. 11.
    H. Kurokawa, “Survey of theory and steering laws of single-gimbal control moment gyros,” J. Guidance, Control, Dyn. 30, 1331–1340 (2007).CrossRefGoogle Scholar
  12. 12.
    E. I. Druzhinin and A. V. Dmitriev, “Newton-Kantorovich method in the problem of controlling the final state of a nonlinear object,” in Method of Lyapunov Functions and its Applications (Nauka, Novosibirsk, 1984), pp. 251–254 [in Russian].Google Scholar
  13. 13.
    E. I. Druzhinin and A. V. Dmitriev, “On the theory of nonlinear boundary value problems of controlled systems,” in Differential Equations and Numerical Methods (Nauka, Novosibirsk, 1986), pp. 179–187 [in Russian].Google Scholar
  14. 14.
    S. N. Vasil’ev, V. A. Voronov, and E. I. Druzhinin, “New computational technology of software control formation in nonlinear systems,” in Proceedings of the 13th SPb. International Conference on Integrated Navigation Systems (TsNII Elektropribor, St. Petersburg, 2006), pp. 48–56.Google Scholar
  15. 15.
    V. A. Voronov and E. I. Druzhinin, “Precision programmed scanning of a planet surface by a nonrigid orbital telescope,” J. Comput. Syst. Sci. Int. 50, 654 (2011).CrossRefzbMATHGoogle Scholar
  16. 16.
    E. I. Druzhinin, “Conditionality of direct algorithms for calculating software controls of nonlinear systems,” in Proceedings of the International Seminar on Control Theory and Theory of Generalized Solutions of the Hamilton-Jacobi Equations (Ural. Univ., Ekaterinburg, 2006), vol. 2, pp. 136–142.Google Scholar
  17. 17.
    E. I. Druzhinin, “On the stability of direct algorithms for computing programmed controls in nonlinear systems,” J. Comput. Syst. Sci. Int. 46, 514 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    I. V. Bychkov, V. A. Voronov, E. I. Druzhinin, R. I. Kozlov, S. A. Ul’yanov, B. B. Belyaev, P. P. Telepnev, and A. I. Ul’yashin, “Synthesis of a combined system for precise stabilization of the Spektr UF observatory. I,” Cosmic Res. 51, 189 (2013).CrossRefGoogle Scholar
  19. 19.
    A. M. Malyshenko, V. I. Eyrikh, B. M. Yamanovsky, and M. A. Sutormin, “Force gyroscopic device for controlling the orientation of spacecraft,” RF Patent No. 183979792.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences (IDSTU SB RAS)IrkutskRussia

Personalised recommendations