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Automation and Remote Control

, Volume 73, Issue 6, pp 1085–1115 | Cite as

The invariance property of control systems with imperfect relay elements

  • S. A. Kochetkov
  • V. A. Utkin
Large Scale Systems Control

Abstract

We consider the problem of ensuring the invariance property for a linear stationary system with relay controls. In the case of perfect relays, wide-class exogenous disturbances are compensated theoretically on the basis of sliding mode theory. Existing imperfections of relay elements make it impossible to implement a perfect sliding mode; thus, the closed-loop system has dynamics in a zero neighborhood of the given variety. This causes undesirable oscillations in a steady-state mode (“chattering”), leading to missed invariance with respect to exogenous and parametric disturbances. This paper solves the problem of ensuring invariance under imperfect relay elements and involves two approaches. The first one allows for making the relay characteristic close to that of the perfect counterpart (by means of increasing the feedback amplification coefficient); consequently, the chattering problem is eliminated. The second approach proceeds from the high-frequency modulation principle and performs regularization of relay switchings; using the linearization effect for the relay characteristics, the second approach guarantees the invariance property.

Keywords

Remote Control Operation Unit Invariance Property Switching Frequency Combine Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Controlling Finite-dimensional Linear Objects), Moscow: Nauka, 1976.Google Scholar
  2. 2.
    Nguen Huang Hyng and Utkin, V.A., Control of DC Electric Motor, Autom. Remote Control, 2006, no. 5, pp. 767–782.Google Scholar
  3. 3.
    Sistemy avtomaticheskogo upravleniya s peremennoi strukturoi (Automated Control Systems with Variable Structure), Emel’yanov, S.V., Ed., Moscow: Nauka, 1967.Google Scholar
  4. 4.
    Utkin, V.A. and Utkin, V.I., Design of Invariant-Systems by the Method of Separation of Motions, Autom. Remote Control, 1983, vol. 44, no. 12, pp. 1559–1567.zbMATHGoogle Scholar
  5. 5.
    Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya (Sliding Modes in Optimization and Control Problems), Moscow: Nauka, 1982.Google Scholar
  6. 6.
    Utkin, V.I. and Yang, K.D., Methods for Constructing Discontinuity Planes inMultidimensional Variable Structure Systems, Autom. Remote Control, 1978, vol. 39, no. 10, part 1, pp. 1466–1470.zbMATHGoogle Scholar
  7. 7.
    Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer-Verlag, 1979. Translated under the title Lineinye mnogomernye sistemy upravleniya. Geometricheskii podkhod, Moscow: Nauka, 1980.zbMATHGoogle Scholar
  8. 8.
    Fel’dbaum, A.A., Elektricheskie sistemy avtomaticheskogo regulirovaniya (Electric Systems of Automatic Control), Moscow: Oborongiz, 1957.Google Scholar
  9. 9.
    Tsypkin, Ya.Z., Releinye avtomaticheskie sistemy (Automatic Relay Systems), Moscow: Nauka, 1974.Google Scholar
  10. 10.
    Bartolini, G., Ferrara, A., and Usai, E., Chattering Avoidance by Second-order Sliding Mode Control, IEEE Trans. Automat. Control, 1998, vol. 43, no. 2, pp. 241–246.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Bondarev, A.G., Bondarev, S.A., Kostyleva, N.Ye., and Utkin, V.I., Sliding Modes in Systems with Asymptotic State Observers, Autom. Remote Control, 1985, vol. 46, no. 6, pp. 679–684.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Drazenovic, B., The Invariance Condition in Variable-Structure Systems, Automatica, 1969, vol. 5, no. 3, pp. 287–295.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Utkin, V.A., The Method of Dynamic Compensation in a Problem of Estimation of External Disturbances, Proc. SICPRO’06, Moscow, 2006, pp. 754–771.Google Scholar
  14. 14.
    Utkin, V.I., Guldner, J., and Shi, J., Sliding Mode Control in Electromechanical Systems, London: Tailor and Francis, 1999.Google Scholar
  15. 15.
    Young, K.K., Kokotovic, P.V., and Utkin, V.I., A Singular Perturbation Analysis of High-gain Feedback Systems, IEEE Trans., 1977, vol. AC-22, pp. 931–939.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • S. A. Kochetkov
    • 1
  • V. A. Utkin
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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