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The Stoker Problem for Multidimensional Discrete Phase Control Systems

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Abstract

Upper and lower estimates for the number of cycle slippings in the transition processes in multidimensional discrete phase control systems under external action are derived by the Lyapunov function method with the frequency theorem and a modified method of nonlocal reduction of discrete systems. The effectiveness of analytical results is illustrated with an example on the transition processes in a pulse phase-locked system with proportionally integrating filter and standard phase detector characteristics.

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REFERENCES

  1. Sistemy fazovoi avtopodstroiki chastoty s elementami diskretizatsii (Frequency-Locking Systems with Discretization Elements), Shakhgil'dyan, V.V., Ed., Moscow: Svyaz', 1979.

    Google Scholar 

  2. Stoker, J.J. Nonlinear Vibrations in Mechanical and Electrical Systems, New York: Interscience, 1950.

    Google Scholar 

  3. Leonov, G.A. and Ershova, O.B., Frequency Estimates for the Number of Cycle Slippings in Phase-locked Automatic Control Systems, Avtom. Telemekh., 1983, no. 5, pp. 65–72.

  4. Ali-Habib, S., Morozov, A.V., and Shepelyavyi, A.I., Estimates for the Number of Cycle Slippings in Synchronization Systems, Proc. Int. Conf. devoted to the 175-Birthday of P.L. Chebyshev, Moscow, 1996, vol. 1, pp. 16–19.

    Google Scholar 

  5. Ali-Habib, S., Morozov, A.V., and Shepelyavyi, A.I., Frequency Estimates for the Number of Cycle Slippings in Phase-locked Systems: Stability and Oscillations of Nonlinear Control Systems, Proc. IV Int. Seminar, Moscow, 1996, p. 85.

  6. Utina, N.V., A Lower Estimate for the Number of Cycle Slippings in Multidimensional Discrete Systems, Vest. S.-Peterburg. Gos. Univ., 2003, ser. 1, vol. 1, no.1, pp. 46–56.

    MATH  MathSciNet  Google Scholar 

  7. Smirnova, V.B., Utima, N.V., and Shepelyavyi, A.I., An Upper Estimate for the Number of Cycle Slippings in Discrete Systems with Periodic Nonlinearity, Vest. S.-Peterburg. Gos. Univ., 2003, ser. 1, vol. 2, no.9, pp. 48–57.

    Google Scholar 

  8. Utina, N.V., Estimates for the Transition Processes in Discontinuous Phase-locked Systems, Electronic Journal www.neva.ru/jornal, Diff. Uravn. Protsessy Upravlen., 2003, no. 3, pp. 88–115.

  9. Leonov, G.A. and Shepelyavyi, A.I., Chastotnyi kriterii neustoichivosti diskretnykh fazovykh sistem (Frequency Stability Criteria for Discrete Phase-locked Systems), Moscow, 1984, Dep. VINITI, no. 4502-84.

  10. Leonov, G.A. and Shepelyavyi, A.I., Neustoichivost' diskretnykh sistem upravleniya s periodicheskoi nelineinost'yu (Instability of Discrete Control Systems with Periodic Nonlinearity), Available from VINITI, 1984, Moscow, no. 5758-84.

  11. Karpychev, A.N., Koryakin, Yu.A., Leonov, G.A., and Shepelyavyi, A.I., Frequency Stability Criteria and Instability of Multidimensional Discontinuous Phase-locked Systems, Voprosy Kibern. Vychisl. Tekh., Diskretn. Sist., 1990, no. 87, pp. 20–23.

  12. Leonov, G.A., Reitman, V., and Smirnova V.B., Nonlocal Methods for Pendulum-like Feedback Systems, Stuttgard: Teubner, 1992.

    Google Scholar 

  13. Andreev, V.A. and Shepelyavyi, A.I., Design of Optimal Controls for Discrete Systems in Minimization of a Quadratic Functional, Elektron. Inf. Kybernetik, 1972, no. 8/9, pp. 549–567.

  14. Andreev, V.A. and Shepelyavyi, A.I., Design of Optimal Controls for Pulse-Amplitude Systems in Minimization of the Mean of a Quadratic Functional, Sib. Mat. Zh., 1973, vol. 14, no.2, pp. 250–276.

    Google Scholar 

  15. Belyustina, L.N., Bykov, V.V., Kiveleva, K.G., and Shalfeev, V.D., Capture Range for Phase-locked Systems with Proportionally Integrating Filters, Izv. Vuzov, Radiofizika, 1970, vol. 13, no.4, pp. 561–567.

    Google Scholar 

  16. Shepelyavyi, A.I., Absolute Instability of Pulse-Amplitude Control Systems. Frequency Criteria, Avtom. Telemekh., 1972, no. 6, pp. 49–56.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    N. V. Utina & A. I. Shepelyavyi

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  1. N. V. Utina
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  2. A. I. Shepelyavyi
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__________

Translated from Avtomatika i Telemekhanika, No. 11, 2005, pp. 65–73.

Original Russian Text Copyright © 2005 by Utina, Shepelyavyi.

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Utina, N.V., Shepelyavyi, A.I. The Stoker Problem for Multidimensional Discrete Phase Control Systems. Autom Remote Control 66, 1761–1767 (2005). https://doi.org/10.1007/s10513-005-0210-2

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  • DOI: https://doi.org/10.1007/s10513-005-0210-2

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