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Compensating unremovable imperfections in operation units

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Abstract

We consider the problem of stabilizing a linear stationary system with disconnected control laws, where imperfections of operation units lead to autooscillations (“chattering”) in a stabilized mode. If constructive possibilities have been exhausted, and unremovable imperfections still lead to an unsatisfactory control process, one has to use additional possibilities connected with feedback control algorithms. This work presents algorithms in which increasing the feedback amplification coefficients and using an additional high-frequency signal leads to reduced “chattering.” We obtain numerical estimates of the parameters that characterize the quality of stabilized modes for a finite frequency of switching the relay elements.

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References

  1. Filippov, A.F., Differential Equations with Disconnected Right-Hand Side, Mat. Sb., 1960, vol. 51, no. 93:1, pp. 99–128.

    MathSciNet  Google Scholar 

  2. Aizerman, M.A. and Pyatnitskii, E.S., Foundations of a Theory of Discontinuous Systems. I, Autom. Remote Control, 1974, vol. 35, no. 7, part 1, pp. 1066–1079.

    MathSciNet  Google Scholar 

  3. Sistemy avtomaticheskogo upravleniya s peremennoi strukturoi (Automated Control Systems with Variable Structure), Emel’yanov, S.V., Ed., Moscow: Nauka, 1967.

    Google Scholar 

  4. Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya (Sliding Modes in Optimization and Control Problems), Moscow: Nauka, 1982.

    Google Scholar 

  5. Modern Sliding Mode Control Theory, in Series Lecture Notes in Control and Information Sciences, Bartolini, G., Fridman, L., Pisano, A., and Usai, E., Eds., Berlin: Springer, 2008, vol. 375.

  6. Fel’dbaum, A.A., Elektricheskie sistemy avtomaticheskogo regulirovaniya (Electric Systems of Automatic Control), Moscow: Oborongiz, 1957.

    Google Scholar 

  7. 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.

    MATH  MathSciNet  Google Scholar 

  8. Utkin, V.I. and Yang, K.D., Methods for Constructing Discontinuity Planes in Multidimensional Variable Structure Systems, Autom. Remote Control, 1978, vol. 39, no. 10, part 1, pp. 1466–1470.

    MATH  MathSciNet  Google Scholar 

  9. Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with a Non-Unique Equilibrium State), Moscow: Nauka, 1978.

    Google Scholar 

  10. Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with Disconnected Right-Hand Side), Moscow: Nauka, 1985.

    Google Scholar 

  11. Bogolyubov, N.N. and Mitropol’skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in Nonlinear Oscillations Theory), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  12. Tsypkin, Ya.Z., Releinye avtomaticheskie sistemy (Automatic Relay Systems), Moscow: Nauka, 1974.

    Google Scholar 

  13. Nguen Huang Hyng and Utkin, V.A., Control of DC Electric Motor, Autom. Remote Control, 2006, no. 5, pp. 767–782.

  14. Krasovskii, A.A., On a Vibrational Approach to Linearizing Certain Nonlinearities), Avtom. Telemekh., 1948, no. 1, pp. 34–42.

  15. Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Controlling Finite-dimensional Linear Objects), Moscow: Nauka, 1976.

    Google Scholar 

  16. 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.

    MATH  Google Scholar 

  17. Utkin, V.A., The Method of Dynamic Compensation in a Problem of Estimation of External Disturbances, Proc. SICPRO’06, Moscow, 2006, pp. 754–771.

  18. Iannelli, L. and Vasca, F., Dither for Chattering Reduction in Sliding Mode Control Systems, Proc. IEEE Int. Sympos. Circuits Syst., Vancouver, 2004, vol. 4, pp. 709–712.

    Google Scholar 

  19. Iannelli, L., Johansson, K.H., Jönsson, U.T., and Vasca, F., Averaging of Nonsmooth Systems Using Dither Automatica, 2006, vol. 42, no. 4, pp. 669–676.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    S. A. Kochetkov & V. A. Utkin

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  1. S. A. Kochetkov
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  2. V. A. Utkin
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Original Russian Text © S.A. Kochetkov, V.A. Utkin, 2010, published in Avtomatika i Telemekhanika, 2010, No. 5, pp. 21–47.

This work was supported in part by the Russian Foundation for Basic Research, project no. 09-08-00429-a, the President of the Russian Federation, project no. MK-2548.2009.8, the Branch of Power Engineering, Machine Building, Mechanics, and Control Processes, Russian Academy of Sciences (Program 15).

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Kochetkov, S.A., Utkin, V.A. Compensating unremovable imperfections in operation units. Autom Remote Control 71, 747–771 (2010). https://doi.org/10.1134/S0005117910050036

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