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  • 标题:Bifurcation Theory In Mechanical Systems.
  • 本地全文:下载
  • 作者:Diego M. Alonso ; Eduardo E. Paolini ; Jorge L. Moiola
  • 期刊名称:Mecánica Computacional
  • 印刷版ISSN:2591-3522
  • 出版年度:2002
  • 卷号:XXI
  • 期号:13
  • 页码:1232-1247
  • 出版社:CIMEC-INTEC-CONICET-UNL
  • 摘要:In this paper, bifurcation theory is used to classify di􀀞erent dynamical behaviors occurring
    in a mechanical system under bounded control actions. The example is a pendulum
    with an inertia disc mounted in its free extreme. By design, the control action can only be
    introduced by means of an external torque applied by a DC motor to the inertia disc. Imposing
    a bounded control action places an important obstacle to the design of a controller
    capable to drive the pendulum from rest to the inverted position and to stabilize it there.
    The only way in which the pendulum can reach the inverted position is by oscillations
    of increasing amplitudes. Due to the saturation of the control law the trivial equilibrium
    points -the rest and the inverted position- experiment a pitchfork bifurcation when one
    key parameter is varied. Therefore, two additional equilibrium points associated to each
    equilibrium of the non-forced system do appear. If another control parameter is varied,
    homoclinic and heteroclinic bifurcations, saddle-node bifurcations of periodic orbits, and
    Hopf bifurcations of equilibria do appear. Some of these codimension one bifurcations
    are organized in a codimension two Bogdanov-Takens bifurcation, when varying two parameters
    simultaneously. The application of both numerical and analytical tools from
    bifurcation theory to understand and classify the dynamical behavior of the closed-loop
    system facilitates the control law design, as shown in the paper.
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