Skip to main content
Log in

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

  • Robust and Adaptive Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

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.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

  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.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

  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.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. Xia, X., Global Frequency Estimation Using Adaptive Identifiers, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1188–1193.

    Article  MathSciNet  Google Scholar 

  19. Hsu, L., Ortega, R., and Damm, G., A Globally Convergent Frequency Estimator, IEEE Trans. Automat. Control, 1999, vol. 46, pp. 967–972.

    MathSciNet  Google Scholar 

  20. Marino, R. and Tomei, R., Global Estimation of Unknown Frequencies, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1324–1328.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

  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.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.A. Bobtsov, S.A. Kolyubin, A.S. Kremlev, A.A. Pyrkin, 2012, published in Avtomatika i Telemekhanika, 2012, No. 8, pp. 64–75.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobtsov, A.A., Kolyubin, S.A., Kremlev, A.S. et al. An iterative algorithm of adaptive output control with complete compensation for unknown sinusoidal disturbance. Autom Remote Control 73, 1327–1336 (2012). https://doi.org/10.1134/S0005117912080061

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912080061

Keywords

Navigation