Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control |
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Authors: | D J W Simpson R Kuske Y-X Li |
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Institution: | (1) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;(2) Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA;(3) Department of Physics, Federal University, of Technology, Akure, PMB 704, Nigeria;(4) The Neuroscience Institute, Georgia State University, Atlanta, GA 30303, USA;; |
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Abstract: | 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. |
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