Automation and Remote Control

, Volume 73, Issue 8, pp 1327–1336 | Cite as

An iterative algorithm of adaptive output control with complete compensation for unknown sinusoidal disturbance

  • A. A. Bobtsov
  • S. A. Kolyubin
  • A. S. Kremlev
  • A. A. Pyrkin
Robust and Adaptive Systems

Abstract

The problem is considered for the output control of a linear, parametrically indeterminate object subjected to the effect of an external unknown, sinusoidal disturbing influence. The solution of this problem is found in the class of iterative adaptive algorithms involving the channels of stabilization and identification of the frequency of a disturbing influence.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bodson, M. and Douglas, S.C., Adaptive Algorithms for the Rejection of Periodic Disturbances with Unknown Frequencies, Automatica, 1997, vol. 33, pp. 2213–2221.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Marino, R., Santosuosso, G.L., and Tomei, P., Robust Adaptive Compensation for Biased Sinusoidal Disturbances with Unknown Frequency, Automatica, 2003, vol. 9, pp. 1755–1761.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Marino, R. and Tomei, R., Output Regulation for Linear Minimum Phase Systems with Unknown Order Exosystem, IEEE Trans. Automat. Control, 2007, vol. 52, pp. 2000–2005.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bobtsov, A.A. and Kremlev, A.S., Synthesis of an Observer in the Problem of Compensation for Finite-Dimensional Quasiharmonic Disturbance, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 3, pp. 5–11.Google Scholar
  5. 5.
    Bobtsov, A.A. and Kremlev, A.S., The Algorithm of Compensation for Unknown Sinusoidal Disturbance for a Linear Nonminimum-Phase Object, Mekhatronika, Avtomatiz., Upravl., 2008, no. 10, pp. 14–17.Google Scholar
  6. 6.
    Bobtsov, A.A., Output Control Algorithm with the Compensation for Biased Harmonic Disturbances, Autom. Remote Control, 2008, vol. 69, no. 8, pp. 1289–1296.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Bobtsov, A.A., Adaptive Output Control with Compensation of Biased Harmonic Disturbance, J. Comput. Syst. Sci. Int., 2009, vol. 48, no. 1, pp. 41–44.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Bobtsov, A.A. and Pyrkin, A.A., Compensation of Unknown Sinusoidal Disturbances in Linear Plants of Arbitrary Relative Degree, Autom. Remote Control, 2009, vol. 70, no. 3, pp. 449–456.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bobtsov, A.A., Kolyubin, S.A., and Pyrkin, A.A., Compensation of Unknown Multi-harmonic Disturbances in Nonlinear Plants with Delay Control, Autom. Remote Control, 2010, vol. 71, no. 11, pp. 2383–2394.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Pyrkin, A., Smyshlyaev, A., Bekiaris-Liberis, N., and Krstic, M., Rejection of Sinusoidal Disturbance of Unknown Frequency for Linear Systems with Input Delay, Am. Control Conf., Baltimore, 2010.Google Scholar
  11. 11.
    Bobtsov, A.A., Kremlev, A.S., and Pyrkin, A.A., Compensation of Harmonic Disturbances in Nonlinear Plants with Parametric and Functional Uncertainty, Autom. Remote Control, 2011, vol. 72, no. 1, pp. 111–118.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.Google Scholar
  13. 13.
    Bobtsov, A.A. and Nikolaev, N.A., Fradkov Theorem-Based Design of the Control of Nonlinear Systems with Functional and Parametric Uncertainties, Autom. Remote Control, 2005, vol. 66, no. 1, pp. 108–118.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Bobtsov, A.A., The Algorithm of Compensation for Uncontrollable Disturbance in the Problem of Output Variable Stabilization of a Linear Object with Unknown Parameters, Izv. Vyssh. Uchebn. Zaved., Priborostr., 2003, no. 1, pp. 22–27.Google Scholar
  15. 15.
    Bobtsov, A.A. and Nikolaev, N.A., Control Law Design for Stabilization of a Nonlinear System in Output Measurements with Compensation for Unknown Disturbance, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 5, pp. 5–11.Google Scholar
  16. 16.
    Bobtsov, A.A., A Robust Control Algorithm for Tracking the Command Signal with Compensation for the Parasitic Effect of External Unbounded Disturbances, Autom. Remote Control, 2005, vol. 66, no. 8, pp. 1287–1295.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Babakov, N.A., Voronov, A.A., Voronova, A.A., et al., Teoriya avtomaticheskogo upravleniya: uchebnik dlya vuzov po spetsial’nosti “Avtomatika i telemekhanika.” I. Teoriya lineinykh sistem avtomaticheskogo upravleniya (Theory of Automatic Control: Manual for Institution of Higher Educat. in specialty “Automation and Remote Control.” Part 1. Theory of Linear Automatic Control Systems), Voronov, A.A., Ed., Moscow: Vysshaya Shkola, 1986.Google Scholar
  18. 18.
    Xia, X., Global Frequency Estimation Using Adaptive Identifiers, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1188–1193.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Hsu, L., Ortega, R., and Damm, G., A Globally Convergent Frequency Estimator, IEEE Trans. Automat. Control, 1999, vol. 46, pp. 967–972.MathSciNetGoogle Scholar
  20. 20.
    Marino, R. and Tomei, R., Global Estimation of Unknown Frequencies, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1324–1328.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Mojiri, M. and Bakhshai, A.R., An Adaptive Notch Filter for Frequency Estimation of a Periodic Signal, IEEE Trans. Automat. Control, 2004, vol. 49, pp. 314–318.MathSciNetCrossRefGoogle Scholar
  22. 22.
    Aranovskii, S.V., Bobtsov, A.A., Kremlev, A.S., and Luk’yanova, G.V., A Robust Algorithm for Identification of the Frequency of a Sinusoidal Signal, J. Comput. Syst. Sci. Int., 2007, vol. 46, no. 3, pp. 371–376.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Aranovskiy, S., Bobtsov, A., Kremlev, A., Nikolaev, N., et al., Identification of Frequency of Biased Harmonic Signal, Eur. J. Control, 2010, no. 2, pp. 129–139.Google Scholar
  24. 24.
    Bobtsov, A., New Approach to the Problem of Globally Convergent Frequency Estimator, Int. J. Adapt. Control Signal Proc., 2008, no. 3, pp. 306–317.Google Scholar
  25. 25.
    Aranovskii, S.V., Bobtsov, A.A., and Pyrkin, A.A., Adaptive Observer of an Unknown Sinusoidal Output Disturbance for Linear Objects, Autom. Remote Control, 2009, vol. 70, no. 11, pp. 1862–1870.MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Pyrkin, A.A., Adaptive Algorithm to Compensate Parametrically Uncertain Biased Disturbance of a Linear Plant with Delay in the Control Channel, Autom. Remote Control, 2010, vol. 71, no. 8, pp. 1562–1577.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. A. Bobtsov
    • 1
    • 2
  • S. A. Kolyubin
    • 1
  • A. S. Kremlev
    • 1
  • A. A. Pyrkin
    • 1
  1. 1.State Institute of Information TechnologiesMechanics and OpticsSt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations