Skip to main content
SpringerLink
Log in

Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters

  • Published:
International Applied Mechanics Aims and scope

Abstract

Stability conditions for a nonstationary automatic-control system of variable structure in sliding mode are established. The controller of the system has feedback-switched filters functioning together with the shaper and actuator. The nonstationary parameters of the system vary within given ranges, at a finite rate, under appropriate control laws, with adjustment for the error signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach to stability analysis is based on the existence conditions for the sliding mode at the switching boundary in the phase space. The general stability and instability criteria are applied to nonstationary automatic filtered-control systems of variable structure of the third order

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. L. T. Ashchepkov, Optimal Control of Discontinuous Systems [in Russian], Nauka, Novosibirsk (1987).

    MATH  Google Scholar 

  2. N. N. Bogolyubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).

    Google Scholar 

  3. B. N. Bublik, F. G. Garashchenko, and N. F. Kirichenko, Structurally Parametric Optimization and Stability of Beam Dynamics [in Russian], Naukova Dumka, Kyiv (1985).

    Google Scholar 

  4. V. I. Zubov, Lectures on Control Theory [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  5. S. V. Emel’yanov, V. I. Utkin, V. A. Taran, et al., Theory of Systems with Variable Structure [in Russian], Nauka, Moscow (1970).

    MATH  Google Scholar 

  6. V. M. Kuntsevich and M. M. Lychak, Synthesis of Automatic-Control Systems Using Lyapunov Functions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. A. A. Martynyuk and K. S. Matviichuk, “On the comparison principle for a system of differential equations with rapidly rotating phase,” Ukr. Mat. Zh., 31, No. 5, 498–503 (1979).

    MATH  MathSciNet  Google Scholar 

  8. K. S. Matviichuk, “Technical stability in measure of the solutions of nonlinear differential equations describing the controlled vertical motion of an elastic body,” Avtomat. Telemekh., No. 1, 13–28 (2005).

  9. K. S. Matviichuk, “Technical-stability conditions for autonomous control systems of variable structure,” Probl. Upravl. Inform., No. 6, 5–22 (1999).

  10. G. N. Nikol’skii, “A note on the automatic stability of a ship on the course,” Tr. Tsentr. Laborat. Provod. Svyazi, Issue 1, 36–45 (1934).

  11. B. N. Petrov, N. I. Sokolov, A. V. Lipatov, et al., Automatic-Control Systems for Objects with Variable Parameters [in Russian], Mashinostroenie, Moscow (1986).

    Google Scholar 

  12. V. V. Stepanov, A Course of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  13. V. I. Utkin, Sliding Modes and Their Applications in Variable-Structure Systems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  14. A. F. Filippov, Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

  15. V. B. Larin, “Motion planning for a mobile robot with two steerable wheels,” Int. Appl. Mech., 41, No. 5, 552–559 (2005).

    Article  MathSciNet  Google Scholar 

  16. V. B. Larin, “On the inverse optimization problem for periodic systems,” Int. Appl. Mech., 41, No. 12, 1413–1417 (2005).

    Article  Google Scholar 

  17. K. S. Matviichuk, “Stability of nonstationary automatic-control systems of variable structure in forced motion,” Int. Appl. Mech., 39, No. 10, 1221–1230 (2003).

    Article  MathSciNet  Google Scholar 

  18. K. S. Matviichuk, “Technical stability of forced motion in nonstationary automatic-control systems of variable structure,” Int. Appl. Mech., 40, No. 1, 103–114 (2004).

    Article  MathSciNet  Google Scholar 

  19. K. S. Matviichuk, “Asymptotic technical stability in measure of the nonlinear controllable motion of an elastic flight vehicle,” Int. Appl. Mech., 40, No. 4, 471–479 (2004).

    Article  MathSciNet  Google Scholar 

  20. K. S. Matviychuk, “Technical stability of an automatic-control system with a changing structure in the neutral case,” J. Math. Sci., 107, No. 2, 3776–3786 (2001).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv

    K. S. Matviichuk

Authors
  1. K. S. Matviichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 116–134, October 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matviichuk, K.S. Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters. Int Appl Mech 42, 1179–1194 (2006). https://doi.org/10.1007/s10778-006-0190-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-006-0190-0

Keywords

Search

Navigation