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Automation and Remote Control

, Volume 79, Issue 9, pp 1673–1686 | Cite as

Controllers Design via Given Oscillation Index: Parametric Uncertainty and Power-Bounded External Disturbances

  • V. N. Chestnov
  • N. I. Samshorin
Control Sciences
  • 12 Downloads

Abstract

The problem is considered of output controllers design for linear multivariable systems with deviating in prescribed bounds physical parameters of the plant, and subjected to the influence of unknown polyharmonic external disturbances, limited only in power. The controller is built so that to provide the prescribed bounds of mean-square values of controlled variables in addition to the robust stability of the closed-loop system. The problem solution is reduced to the H-optimization procedure produced in some specific way. The solution of the well-known “benchmark” problem is considered.

Keywords

robust stability oscillation index external disturbances bounded in power H-control 

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References

  1. 1.
    Ackermann, J., Robust Control: System with Uncertain Physical Parameters, London: Springer, 1993.CrossRefzbMATHGoogle Scholar
  2. 2.
    Barmich, B.R., New Tools for Robustness of Linear Systems, New York: Macmillan, 1994.Google Scholar
  3. 3.
    Bhattacharyya, S.P., Keel, L.A., and Chapellat, H., Robust Control: The Parametric Approach, Hertfordshire: Prentice Hall, 1995.zbMATHGoogle Scholar
  4. 4.
    Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.Google Scholar
  5. 5.
    Chestnov, V.N., Synthesis of Robust Controllers of Multivariable Systems Using Circular Frequency Inequalities: The Case of Parametric Uncertainty, Autom. Remote Control, 1999, vol. 60, no. 3, part 2, pp. 484–491.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Chestnov, V.N., Design of Controllers of Multidimensional Systems with a Given Radius of Stability Margins Based on the H∞-Optimization Procedure, Autom. Remote Control, 1999, vol. 60, no. 7, pp. 986–993.MathSciNetzbMATHGoogle Scholar
  7. 7.
    Agafonov, P.A. and Chestnov, V.N., Controllers of a Given Radius of Stability Margin: Their Design by the H∞-Approach with Regard for External Disturbances, Autom. Remote Control, 2004, vol. 65, no. 10, pp. 1611–1617.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chestnov, V.N., Synthesizing H∞-Controllers for Multidimensional Systems with Given Accuracy and Degree of Stability, Autom. Remote Control, 2011, no. 10, pp. 2161–2175.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chestnov, V.N., An Approach to the Margin Synthesis Problem for the Parameters of Linear Multivariable Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1995, no. 2, pp. 72–79.Google Scholar
  10. 10.
    Chestnov, V.N., H∞-approach to Controller Synthesis under Parametric Uncertainty and Polyharmonic External Disturbances, Autom. Remote Control, 2015, vol. 76, no. 6, pp. 1036–1048.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chestnov, V.N., Design of H∞ Controllers under Parametric Uncertainty and Power-Bounded External Disturbances, Proc. 8th IFAC Symp. on Robust Control Design (ROCOND-2015), Bratislava: IFAC Publication, 2015, pp. 56–61.Google Scholar
  12. 12.
    Samshorin, N.I. and Chestnov, V.N., Synthesis of Robust Controllers in Case of Parametric Uncertainty and External Disturbances, Tr. XII Vseross. soveshchan. po problemam upravleniya (Proc. XII All- Russian Meeting on Control Problems), Moscow: Inst. Probl. Upravlen., 2014, pp. 1033–1045.Google Scholar
  13. 13.
    Samshorin, N.I. and Chestnov, V.N., Synthesis of Controllers in Case of Parametric Uncertainty and Bounded in Power External Disturbances, Tr. 7-oi vseross. nauch. konf. “Sistemnyi sintez i prikladnaya sinergetika” (SSPS-2015) (Proc. 7th All-Russian Sci. Conf. “System Synthesis and Applied Synergetics”), Taganrog: Taganrog. Tekhn. Inst. Yuzhn. Fed. Univ., 2015, pp. 271–282.Google Scholar
  14. 14.
    Voronov, A.A., Ustoichivost’, upravlyaemost’, nablyudaemost’ (Stability, Controllability, Observability), Moscow: Nauka, 1979.zbMATHGoogle Scholar
  15. 15.
    Chestnov, V.N., Synthesis of Multivariable Systems of Given Accuracy by the Mean-Square Criterion, Autom. Remote Control, 1998, vol. 59, no. 12, part 2, pp. 1786–1793.MathSciNetzbMATHGoogle Scholar
  16. 16.
    Doyle, J.C. and Stein, G., Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis, IEEE Trans. Automat. Control, 1981, vol. 26, no. 1, pp. 4–16.CrossRefzbMATHGoogle Scholar
  17. 17.
    Voronov, A.A., Osnovy teorii avtomaticheskogo upravleniya: avtomaticheskoe regulirovanie nepreryvnykh lineinykh sistem (Fundamentals of Automatic Control: Automatic Regulation of Continuous Linear Systems), Moscow: Energiya, 1980.Google Scholar
  18. 18.
    The Control Handbook, Levine, W.S., Ed., Boca Raton: CRC/IEEE Press, 1996.zbMATHGoogle Scholar
  19. 19.
    Balas, G.J., Chiang, R.Y., Packard, A., et al., Robust Control Toolbox 3. User’s Guide, Natick: Math-Works, 2010.Google Scholar
  20. 20.
    Gahinet, P. and Apkarian, P., A Linear Matrix Inequality Approach to H∞ Control, Int. J. Control, 1994, vol. 4, pp. 421–448.MathSciNetzbMATHGoogle Scholar
  21. 21.
    Farag, A. and Werner, H., Robust H2 Controller Design and Tuning for the ACC Benchmark Problem and a Real-time Application, Proc. 15th IFAC World Congress, Barcelona, Spain, 2002.Google Scholar
  22. 22.
    Haddad, W.M., Collins, E.G., and Bernstein, D.S., Robust Stability Analysis Using the Small Gain, Circle, Positivity and Popov Theorems. A Comparative Study, IEEE Trans. Control Syst. Technol., 1993, vol. 1, no. 4, pp. 290–293.CrossRefGoogle Scholar
  23. 23.
    Chilali, M. and Gahinet, P., H∞ Design with Pole Placement Constraints: An LMI Approach, IEEE Trans. Automat. Control, 1996, vol. AC-41, no. 3, pp. 358–367.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.JSC Electrostal Heavy Engineering Works (EZTM)ElectrostalRussia

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