Skip to main content
SpringerLink
Log in

Optimal limited-rate slewing of a flexible spacecraft

  • Published:
International Applied Mechanics Aims and scope

The paper presents an efficient method of finding the optimal program control for the reorientation of a spacecraft with flexible appendages at a limited slewing rate. The appendages are incorporated into the mathematical model based on the quasistatic approximation. The problem is solved analytically by parametrizing the functional of a multipoint boundary-value problem. The optimal solution is illustrated graphically for different parts of the attainability domains

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. E. Bryson and Yu-Chi Ho, Applied Optimal Control, Hemisphere, Washington, DC (1975).

  2. A. E. Zakrzhevskii, “Optimal control of elastic systems as active vibroprotection,” in: Problems of Reliability and Vibration Protection of Instruments [in Russian], Irkutsk. Politekhn. Inst., Irkutsk (1972), pp. 134–139.

  3. A. E. Zakrzhevskii, “Optimal control of slewing of a free rigid body with flexible elements,” in: Controlled Mechanical Systems [in Russian], Irkutsk. Politekhn. Inst., Irkutsk (1977), pp. 4–14.

  4. A. E. Zakrzhevskii, “Optimal slewing of a flexible spacecraft,” Int. Appl. Mech., 39, No. 10, 1208–1214 (2003).

    Article  Google Scholar 

  5. P. M. Bainum and F. Li, Optimal Large Angle Maneuvers of a Flexible Spacecraft, from Dynamics of Flexible Structures in Space, Computational Mechanics Publications, Southampton; Springer Verlag, Berlin (1990).

  6. A. K. Banerjee, N. Pedreiro, and W. E. Singhose, “Vibration reduction for flexible spacecraft following momentum dumping with/without slewing,” J. Guidance, Control, and Dynamics, 24, No. 3, 417–427 (2001).

    Article  Google Scholar 

  7. E. Bayo, M. A. Serna, P. Papadopulos, and J. Stube, “Inverse dynamics and kinematics of multi-link elastic robots. An iterative frequency domain approach,” Int. J. Robotics Research, 8, No. 6, 49–92 (1989).

    Article  Google Scholar 

  8. J. Ben-Asher, J. A. Burns, and E. M. Cliff, “Time-optimal slewing of flexible spacecraft,” J. Guidance, Control, and Dynamics, 15, No. 2, 360–367 (1992).

    Article  MATH  Google Scholar 

  9. A. Di Meglio and A. Ercoli Finz, “Minimum time control of flexible spacecraft by Hamilton’s principle,” Meccanica, 32, 555–565 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  10. R. L. Farrenkopf, “Optimal open loop maneuver profiles for flexible spacecraft,” J. Guidance and Control, 2, No. 6, 491–498 (1979).

    Article  MATH  Google Scholar 

  11. D. Gorinevsky and G. Vukovich, “Control of flexible spacecraft using nonlinear approximation of input shape dependence on reorientation maneuver parameters,” Control Eng. Practice, 5, No. 12, 1661–1671 (1997).

    Article  Google Scholar 

  12. T. V. Karnaukhova and E. V. Pyatetskaya, “Damping the flexural vibration of a clamped viscoelastic rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 45, No. 5, 546–557 (2009).

    Article  Google Scholar 

  13. V. G. Karnaukhov and Ya. V. Tkachenko, “Damping the vibrations of a rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 44, No. 2, 182–187 (2008).

    Article  Google Scholar 

  14. V. B. Larin, “Control problems for wheeled robotic vehicles,” Int. Appl. Mech., 45, No. 4, 363–388 (2009).

    Article  Google Scholar 

  15. V. B. Larin, “Solutions of matrix equations in problems of mechanics and control,” Int. Appl. Mech., 45, No. 8, 847–872 (2009).

    Article  Google Scholar 

  16. Q. Liu and B. Wie, “Robust time-optimal control of uncertain flexible spacecraft,” J. Guidance, Control, and Dynamics, 15, No. 3, 597–604 (1992).

    Article  MATH  Google Scholar 

  17. J. L. Meyer and L. Silverberg, “Fuel optimal propulsive maneuver of an experimental structure exhibiting spacelike dynamics,” J. Guidance, Control, and Dynamics, 19, No. 1, 141–149 (1996).

    Article  MATH  Google Scholar 

  18. L. Y. Pao, “Minimum-time control characteristics of flexible structures,” J. Guidance, Control, and Dynamics, 19, No. 1, 123–129 (1996).

    Article  MATH  Google Scholar 

  19. G. Singh, P. T. Kabamba, and N. H. McClamroch, “Planar, time-optimal, rest-to-rest slewing maneuvers of flexible spacecraft,” J. Guidance, Control, and Dynamics, 12, No. 1, 71–81 (1989).

    Article  MathSciNet  Google Scholar 

  20. T. Singh, “Fuel/time optimal control of the benchmark problem,” J. Guidance, Control, and Dynamics, 18, No. 6, 1225–1231 (1995).

    Article  MATH  Google Scholar 

  21. T. Singh and S. R. Vadali, “Robust time-optimal control: A frequency domain approach,” J. Guidance, Control, and Dynamics, 17, No. 2, 346–353 (1994).

    Article  MATH  Google Scholar 

  22. T. Singh and S. R. Vadali, “Input-shaped control of three-dimensional maneuvers of flexible spacecraft,” J. Guidance, Control, and Dynamics, 16, No. 6, 1061–1068 (1993).

    Article  ADS  Google Scholar 

  23. W. Singhose, S. Derezinski, and N. Singer, “Extra-insensitive input shapers for controlling flexible spacecraft,” J. Guidance, Control, and Dynamics, 19, No. 2, 385–391 (1996).

    Article  Google Scholar 

  24. W. Singhose, A. Banerjee, and W. Seering, “Slewing flexible spacecraft with deflection-limiting input shaping,” J. Guidance, Control, and Dynamics, 20, No. 2, 291–298 (1997).

    Article  MATH  Google Scholar 

  25. W. VanderVelde and J. He, “Design of space structure control systems using on-off thrusters,” J. Guidance, Control, and Dynamics, 6, No. 1, 53–60 (1983).

    Article  Google Scholar 

  26. B. Wie, R. Sinha, J. Sunkel, and K. Cox, “Robust fuel- and time-optimal control of uncertain flexible space structures,” in: AIAA Guidance, Navigation, and Control Conf. (Monterey, CA), AIAA Paper 93-3804, AIAA, Washington, DC (1993), pp. 939–948.

  27. A. E. Zakrzhevskii, “Slewing of flexible spacecrafts with minimal relative flexible acceleration,” J. Guidance, Control, and Dynamics, 31, No. 3, 563–570 (2008).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    A. E. Zakrzhevskii

Authors
  1. A. E. Zakrzhevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Zakrzhevskii.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 46, No. 3, pp. 124–135, March 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakrzhevskii, A.E. Optimal limited-rate slewing of a flexible spacecraft. Int Appl Mech 46, 348–358 (2010). https://doi.org/10.1007/s10778-010-0316-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-010-0316-2

Keywords

Search

Navigation