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Stabilization methods for nonlinear second-order systems

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Języki publikacji
EN
Abstrakty
EN
The goal of this paper is to study stabilization techniques for a system described by nonlinear second-order differential equations. The problem is to determine the feedback control as a function of the state variables. It is shown that the following controllers can asymptotically stabilize the system: linear position feedback, linear velocity feedback and a group of nonlinear feedbacks. The asymptotic stability of the closed-loop system has been proved by LaSalle's invariance principle. The results of numerical computations are included to verify theoretical analysis and mathematical formulation.
Rocznik
Strony
205--216
Opis fizyczny
Bibliogr. 17 poz., rys.
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Bibliografia
  • [1] J. M. GUCKENHEIMER and P. HOLMS: Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Berlin, Germany, Springer, 1983.
  • [2] C. HAYASHI: Nonlinear oscillations in physical systems. New York, McGraw-Hill, 1964.
  • [3] T. KOBAYASHi: Low gain adaptive stabilization of undamped second order systems. Arch. Control ScL, 11(1-2), (2001), 63-75.
  • [4] J. LASALLE and S. LEFSCHETZ: Stability by Liapunov's direct method with ap-plications. New York and London, Academic Press, 1961.
  • [5] A. H. NAYFEH and D.T. MOOK: Nonlinear oscillations. New York, John Wiley & Sons, 1979.
  • [6] N. MINORSKY: Theory of nonlinear control systems. New York, McGraw-Hill, 1969.
  • [7] W. MITKOWSKI: Stabilization of dynamie systems. Warsaw, Poland, WNT, 1991.
  • [8] W. MITKOWSKI: Dynamie feedback in LC ladder network. Buli. Pol. Acad. ScL Tech. ScL, 51(2), (2003), 173-180.
  • [9] W. MITKOWSKI: Stabilization of LC ladder network. Buli. Pol. Acad. ScL Tech. ScL, 52(2), (2004), 109-114.
  • [10] W. MITKOWSKI: Analysis of undamped second order systems with dynamie feed-back. Control Cybern., 33(4), 2004.
  • [11] W. MITKOWSKI and P. SKRUCH: Stabilization of second-order systems by linear position feedback. Proc. of the Wth IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2004), 273-278.
  • [12] W. MITKOWSKI and P. SKRUCH: Stabilization methods of a non-linear oscilla-tor. Proc. of the Ilth IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2005), 215-220.
  • [13] F. C. MOON: Chaotic vibrations: An introduction for applied scientists and engi-neers. New York, John Wiley & Sons, 2004.
  • [14] AJ. PRITCHARD: Stability and stabilization of second-order systems. IMA J. Appl. Math., 7 (1971), 348-360.
  • [15] P. SKRUCH: Stabilization of second-order systems by non-linear feedback. Int. J. Appl. Math. Comput. ScL, 14(4), (2004), 455-460.
  • [16] P. SKRUCH: Stabilization of linear infinite dimensional oscillatory systems. PhD dissertation, AGH University of Science and Technology, Institute of Automatics, Kraków, Poland, 2006.
  • [17] M. W. SPONG and M. VIDYASAGAR: Robot dynamics and control. New York, Willey, 1989.
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Bibliografia
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bwmeta1.element.baztech-article-BSW3-0061-0011
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