Skip to main content
Log in

High-accuracy control systems with singular perturbations

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

Abstract

In this paper, a linear quadratic problem for a continuous scalar control plant with stationary perturbations is considered. A class of perturbations is selected, in which arbitrary high accuracy of control by the criterion of steady-state response variance is ensured. An algorithm for synthesizing a stabilizing controller providing the desired control performance is proposed.

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. Bunich, A.L., Degenerate Problems of Designing the Control System of a Linear Discrete Plant, Avtom. Telemekh., 2005, No. 11, pp. 35–45.

  2. Rozanov, Yu.A., Statsionarnye sluchainye protsessy, Moscow: Nauka, 1990. Translated into English under the title Stationary Random Processes, San Francisco: Holden-Day, 1967.

    Google Scholar 

  3. Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnykh svyazei, Moscow: Nauka, 1997. Translated into English under the title Control of Complex and Uncertain Systems: New Types of Feedback, London: Springer, 2000.

    Google Scholar 

  4. Yurkevich, V.D., Singular Perturbations and Nonlinear Control Systems with the Highest Derivative in Feedback, Tr. VI Mezhd. konf. “Identifikatsiya sistem i zadachi upravleniya” SICPRO’07 (Pr. VI Int. Conf. “Systems Identification and Control Problems” SICPRO’07), Moscow: Inst. Probl. Uptavlen., 2007, pp. 899–927.

    Google Scholar 

  5. Meerov, M.V., Sintez struktur sistem avtomaticheskogo regulirovaniya vysokoi tochnosti (Synthesis of High-Accuracy Automatic Control Systems), Moscow; Nauka, 1967.

    Google Scholar 

  6. Byrnes, C.I., Isidory, A., and Willems, J.C., Passivity, Feedback Equivalence and the Global Stabilization of Minimum Phase Nonlinear Systems, IEEE Trans. Automat. Control, 1991, vol. AC-36, pp. 1228–1240.

    Article  Google Scholar 

  7. Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob″ektami (Adaptive Control of Dynamical Plants), Moscow: Nauka, 1981.

    MATH  Google Scholar 

  8. Aström, K.J., Introduction to Stochastic Control Theory, New York: Academic, 1970. Translated under the title Vvedenie v stokhasticheskuyu teoriyu upravleniya, Moscow: Mir, 1973.

    MATH  Google Scholar 

  9. Korolyuk, V.S., Portenko, N.I., Skorokhod, A.V., and Turbin, A.F., Spravochnik po teorii veroyatnostei i matematicheskoi statistike (Handbook on the Probability Theory and Mathematical Statistics), Moscow: Nauka, 1985.

    Google Scholar 

  10. Cramer, H. and Leadbetter, M., Stationary and Related Stochastic Processes, New York: Wiley, 1967. Translated under the title Statsionarnye sluchainye protsessy, Moscow: Mir, 1969.

    MATH  Google Scholar 

  11. Abdullaev, N.D. and Petrov, Yu.P., Teoriya i metody proektirovaniya optimal’nykh regulyatorov (Theory and Methods for Optimal Controllers Design), Leningrad: Energoatomizdat, 1985.

    Google Scholar 

  12. Keel, L. and Bhattacharyya, S.P., Robust, Fragile, or Optimal?, IEEE Trans. Automat. Control, 1997, vol. 42, no. 6, pp. 1098–1105.

    Article  MATH  Google Scholar 

  13. Bulinskii, A.V. and Shiryaev, A.N., Teoriya sluchainykh protsessov (Theory of Random Processes), Moscow: Fizmatlit, 2005.

    Google Scholar 

  14. Yakubovich, V.A., Linear-Quadratic Problem of Forced Oscillations Damping in the Presence of an Unknown Harmonic External Perturbation, Dokl. Akad. Nauk., 1993, vol. 333, no. 2, pp. 170–172.

    Google Scholar 

  15. Daugavet, I.K., Vvedenie v teoriyu priblizheniya funktsii (Introduction to the Theory of Function Approximation), Leningrad: Leningr. Univ., 1977.

    Google Scholar 

  16. Aizerman, M.A., A Letter to O. Yu. Shmidt, Academician and Vice-President of the Academy of Sciences of the USSR, in G. V. Shchipanov i teoriya invariantnosti (G.V. Shchipanov and Invariance Theory), Moscow: Fizmatlit, 2004, pp. 261–269.

    Google Scholar 

  17. Kulebakin, V.S., Invariance Theory of Automtically Controlled Systems, Tr 1 kongr. IFAK po avtomaticheskomu upravleniyu (Proc. I IFAC Congr. on Automatic Control), Moscow: Akad. Nauk SSSR, 1960, vol. 1.

    Google Scholar 

  18. Aizerman, M.A., G.V. Shchipanov i teoriya invariantnosti (G.V. Shchipanov and Invariance Theory), Moscow: Fizmatlit, 2004.

    Google Scholar 

  19. Yakubovich, V.A., Universal Controllers in Stochastic Problems of Optimal Control of Linear Stationary Plants, Avtom. Telemekh., 1997, no. 6, pp. 170–182.

  20. Bradbury, R., A Sound of Thunder, in Bradbury Stories: 100 of His Most Celebrated Tales, New York: HarperCollins, 2003. Translated under the title I gryanul grom. “O skitaniyakh vechnykh i o Zemle,” Moscow: EKSMO, 2003.

    Google Scholar 

  21. Balandin, D.V., Limiting Possibilities of Linear Systems Control and Estimation of the Minimal H -norm, Izv. Ross. Akad. Nauk. Teor. Sist. Upravlen., 2001, no. 6, pp. 50–56.

  22. Kolmogorov, A.N., Teoriya informatsii i teoriya algoritmov, Moscow: Nauka, 1987. Translated into English under the title Selected Works of A.N. Kolmogorov, 3 vol.: Information Theory and the Theory of Algorithms (Mathematics and Its Applications), Tikhomirov, V.M., Ed., Dordrecht: Kluwer, 1993.

    MATH  Google Scholar 

  23. Bogatyrev, A.A., Ekstremal’nye mnogochleny i rimanovy poverkhnosti (Extremal Polynomials and Riemann Surfaces), Moscow: MTsNMO, 2005.

    Google Scholar 

  24. Qui, L. and Davison, E.J., Performance Limitations of Non-minimum Phase Systems in the Servomechanism Problem, Automatica, 1993, vol. 29, no. 2, pp. 337–349.

    Article  Google Scholar 

  25. Nikol’skii, N.K., Lektsii ob operatore sdviga, Moscow: Nauka, 1980. Translated into English under the title Treatise on the Shift Operator. Spectral Function Theory, Berlin: Springer, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.L. Burnich, 2007, published in Avtomatika i Telemekhanika, 2007, No. 7, pp. 3–17.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bunich, A.L. High-accuracy control systems with singular perturbations. Autom Remote Control 68, 1119–1133 (2007). https://doi.org/10.1134/S0005117907070016

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907070016

PACS number

Navigation