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Sufficient Global Stability Condition for a Model of the Synchronous Electric Motor under Nonlinear Load Moment

  • B. I. Konosevich
  • Yu. B. Konosevich
Mathematics
  • 11 Downloads

Abstract

We study a model of the synchronous electric motor, which is described by a system of ordinary differential equations, including equations for electric currents in the windings of the rotor. The load moment is assumed to be a nonlinear function of the angular velocity of the rotor, allowing a linear estimate. The system of differential equations under consideration has a countable number of stationary solutions corresponding to the operating mode of uniform rotation of the rotor with the angular velocity equal to the angular velocity of rotation of the magnetic field in the stator. An effective sufficient condition is derived under which any motion of the rotor of the synchronous electric motor tends with time to uniform rotation.

Keywords

synchronous electric motor global stability reduction method LaSalle invariance principle 

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References

  1. 1.
    A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities (Nauka, Moscow, 1978; World Sci. Singapore, 2004).zbMATHGoogle Scholar
  2. 2.
    G. A. Leonov, “Phase synchronization: Theory and applications,” Autom. Remote Control 67, 1573–1609 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    G. A. Leonov, “The second Liapunov method in the theory of phase synchronization,” J. Appl. Math. Mech. 40, 215–222 (1976) [in Russian].CrossRefzbMATHGoogle Scholar
  4. 4.
    F. Tricomi, “Integrazione di unequazione differenziale presentasi in electrotechnica,” Ann. Roma Schuola Norm. Super. Pisa 2 (2), 1–20 (1933).Google Scholar
  5. 5.
    G. A. Leonov and A. M. Zaretskiy, “Global stability and oscillations of dynamical systems describing synchronous electrical machines,” Vestn. St. Petersburg Univ. Math. 45, 157–163 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    B. I. Konosevich and Yu. B. Konosevich, “Sufficient condition of global stability of a model of the synchronous electric motor,” Mekh. Tverd. Tela, No. 46, 73–90 (2016).MathSciNetzbMATHGoogle Scholar
  7. 7.
    E. A. Barbashin, Introduction to the Theory of Stability (Nauka, Moscow, 1967; Wolters-Noordhoff, Groningen, 1970).zbMATHGoogle Scholar
  8. 8.
    J. LaSalle and S. Lefschetz, Stability by Liapunov’s Direct Method (Mir, Moscow, 1964; Academic, New York, 1961).Google Scholar
  9. 9.
    E. A. Barbashin and V. A. Tabueva, Dynamical Systems with Cylindrical Phase Space (Nauka, Moscow, 1969) [in Russian].zbMATHGoogle Scholar
  10. 10.
    B. I. Konosevich and Yu. B. Konosevich, “Approximation of the critical value of the damping parameter for the synchronous electric motor,” Tr. Inst. Prikl. Mat. Mekh. 29, 121–126 (2014).zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsDonetskUkraine

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