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A stabilization method of inhomogeneous ladder networks with nonlinear elements

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper, different structures of electric ladder networks are considered: RC, RL, and RLC. Such systems are composed of resistors, inductors and capacitors connected in series. The elements of the network are not identical and have nonlinear characteristics. The network's dynamic behavior can be mathematically described by nonlinear differential equations. A class of robust feedback controls is designed to stabilize the system. The asymptotic stability of the closed-loop system is analyzed and proved by the use of Lyapunov functionals and LaSalle's invariance principle. The results of computer simulations are included to verify theoretical analysis and mathematical formulation.
Rocznik
Strony
313--329
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
  • Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, Department of Automatics, AGH University of Science and Technology, Al. A. Mickiewicza 30/B1, 30-059 Krakow, Poland, pawel.skruch@agh.edu.pl
Bibliografia
  • [1] M. Dabrowski: Selected ideas of the theory of nonlinear electrical circuits. COMPEL: The Int. J. for Computation and Mathematics in Electrical and Electronic Engineering, 18(2), (1999), 204-214.
  • [2] J. Jeltsema, R. Ortega and J.M.A. Scherpen: On passivity and power-balance inequalities of nonlinear RLC circuits. IEEE Trans. on Circuits and Systems Part I: Fundamental Theory and Applications, 50(9), (2003), 1174-1179.
  • [3] J. Jeltsema, R. Ortega and J.M.A. Scherpen: Power shaping: a new paradigm for stabilization of nonlinear RLC circuits. IEEE Trans. on Automatic Control (Special Issue on New Directions in Nonlinear Control), 48(10), (2003), 1162-1167.
  • [4] T. Kobayashi: Low gain adaptive stabilization of undamped second order systems. Archives of Control Sciences, 11(1-2), (2001), 63-75.
  • [5] J. Lasalle and S. Lefschetz: Stability by Liapunov's direct method with applications. Academic Press, New York, London, 1961.
  • [6] A. M. Lyapunov: The general problem of the stability of motion. Int. J. of Control, 55(3), (1992), 531-773.
  • [7] S. Mitkowski: Nonlinear electric circuits. Wydawnictwa AGH, 1999.
  • [8] W. Mitkowski: Stabilization of dynamic systems. WNT, Warszawa, 1991.
  • [9] W. Mitkowski: Dynamic feedback in LC ladder network. Bulletin of the Polish Academy of Sciences, Technical Sciences, 51(2), (2003), 173-180.
  • [10] W. Mitkowski: Stabilisation of LC ladder network. Bulletin of the Polish Academy of Sciences, Technical Sciences, 52(2), (2004), 109-114.
  • [11] W. Mitkowski: Analysis of undamped second order systems with dynamic feedback. Control and Cybernetics, 33(4), (2004), 653-672.
  • [12] W. Mitkowski and P. Skruchw: Stabilization of second-order systems by linear position feedback. In: Proc. of the 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2004), 273-278.
  • [13] W. Mitkowski and P. Skruch: Stabilization methods of a non-linear oscillator. In: Proc. of the 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2005), 215-220.
  • [14] W. Mitkowski and P. Skruch: Stabilization results of second-order systems with delayed positive feedback. In: Modelling Dynamics in Processes and Systems, Series Studies in Computational Intelligence, W. Mitkowski, J. Kacprzyk (Eds.), 180 99-108, Springer, Berlin, Heidelberg, 2009.
  • [15] A. Oksasoglu and D. Vavriv: Interaction of low- and high-frequency oscillations in a nonlinear RLC circuit. IEEE Trans. on Circuits and Systems Part I: Fundamental Theory and Applications, 41(10), (1994), 669-672.
  • [16] P. Skruch and J. Baranowski: Linear feedback control of a nonlinear RLC circuit. In: Proc. of the 32th Int. Conf. on Fundamentals of Electrotechnics and Circuit Theory IC-SPETO 2009, Gliwice-Ustron, Poland, (2009), 75-76.
  • [17] P. Skruch and J. Baranowski: Nonlinear feedback control of a nonlinear RLC circuit. In: Proc. of the 32th Int. Conf. on Fundamentals of Electrotechnics and Circuit Theory IC-SPETO 2009, Gliwice-Ustron, Poland, (2009), 77-78.
  • [18] P. Skruch: Stabilization of second-order systems by non-linear feedback. Int. J. of Applied Mathematics and Computer Science, 14(4), (2004), 455-460.
  • [19] P. Skruch: Stabilization of linear infinite dimensional oscillatory systems. PhD dissertation, Akademia Gorniczo-Hutnicza, Department of Automatics, Krakow, Poland, 2005.
  • [20] P. Skruch: Stabilization methods for nonlinear second-order systems. Archives of Control Sciences, 19(2), (2009), 205-216.
  • [21] P. Skruch: Feedback stabilization of distributed parameter gyroscopic systems. In: Modelling Dynamics in Processes and Systems, Series Studies in Computational Intelligence, W. Mitkowski, J. Kacprzyk (Eds.), 180, 85-97, Springer, Berlin, Heidelberg, 2009.
  • [22] P. Skruch: Stabilization of nonlinear RLC ladder network. In: Proc. of the 7th Conf. on Computer Methods and Systems, Krakow, Poland, (2009), 259-264.
  • [23] P. Skruch: Feedback stabilization of a class of nonlinear second-order systems. Nonlinear Dynamics, 59(4), (2010), 681-692.
  • [24] P. Skruch: Stabilization of a class of SISO nonlinear systems by dynamic feed-back. Automatyka, 14(2), (2010), 197-209.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0097-0006
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