Laszlo E. Kollar, Gabor Stepan, & Janos Turi
Abstract:
In this paper the dynamics of the
controlled pendulum is investigated assuming backlash and time
delays. The upper equilibrium of the pendulum is stabilized by a
piecewise constant control force which is the linear combination
of the sampled values of the angle and the angular velocity of the
pendulum. The control force is provided by a motor which drives
one of the wheels of the cart through an elastic teeth belt. The
contact between the teeth of the gear (rigid) and the belt
(elastic) introduces a nonlinearity known as "backlash" and causes
the oscillation of the controlled pendulum around its upper
equilibrium. The processing and sampling delays in the
determination of the control force tend to destabilize the
controlled system as well. We obtain conditions guaranteeing that
the pendulum remains in the neighborhood of the upper equilibrium.
Experimental findings obtained on a computer controlled inverted
pendulum cart structure are also presented showing good agreement
with the simulation results.
Published February 28, 2003.
Subject classifications: 34K35, 37C75.
Key words: Stability analysis, backlash, digitally controlled pendulum..
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Laszlo E. Kollar Department of Applied Sciences University of Qu\'ebec at Chicoutimi 555, Boul. de l'Universite, Chicoutimi G7H 2B1 Quebec, Canada E-mail address: laszlo_kollar@uqac.ca |
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Gabor Stepan Department of Applied Mechanics Budapest University of Technology and Economics H-1521 Budapest, Hungary E-mail address: stepan@mm.bme.hu |
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Janos Turi Department of Mathematical Sciences The University of Texas at Dallas P.O. Box 830688, MS EC 35, Richardson, Texas 75083-0688, USA E-mail address: turi@utdallas.edu |
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