Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control

被引:9
作者
Simpson, D. J. W. [1 ]
Kuske, R. [1 ]
Li, Y. -X. [1 ]
机构
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
关键词
Inverted pendulum; Delay differential equation; Nonsmooth system; Discontinuity-induced bifurcation; PIECEWISE-LINEAR SYSTEMS; INVERTED PENDULUM; ANKLE STIFFNESS; STABILITY; INSTABILITY; VISION; NOISE; SWAY;
D O I
10.1007/s00332-011-9111-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the state of the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits originate in various discontinuity-induced bifurcations. We also show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.
引用
收藏
页码:135 / 167
页数:33
相关论文
共 48 条
  • [1] [Anonymous], 2009, Surveys and Tutorials in the Applied Mathematical Sciences
  • [2] [Anonymous], DELAY DIFFERENTIAL E
  • [3] [Anonymous], 1988, Differential Equations with Discontinuous Righthand Sides
  • [4] [Anonymous], 1993, INTRO FUNCTIONAL DIF, DOI 10.1007/978-1-4612-4342-7
  • [5] A Model of Postural Control in Quiet Standing: Robust Compensation of Delay-Induced Instability Using Intermittent Activation of Feedback Control
    Asai, Yoshiyuki
    Tasaka, Yuichi
    Nomura, Kunihiko
    Nomura, Taishin
    Casadio, Maura
    Morasso, Pietro
    [J]. PLOS ONE, 2009, 4 (07):
  • [6] Bajd T., 2010, ROBOTICS INTELLIGENT
  • [7] Braunl T., 2008, Embedded Robotics: Mobile Robot Design and Applications With Embedded Systems
  • [8] Bullo F., 2005, TEXT APPL M, V49, DOI 10.1007/978-1-4899-7276-7
  • [9] Controlling instability with delayed antagonistic stochastic dynamics
    Cabrera, JL
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 356 (01) : 25 - 30
  • [10] On-off intermittency in a human balancing task
    Cabrera, JL
    Milton, JG
    [J]. PHYSICAL REVIEW LETTERS, 2002, 89 (15) : 158702/1 - 158702/4