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Asymptotic harmonic generator design via modification of Van der Pol oscillator
Periodic Control Systems, Volume # 3 | Part# 1
Authors
Y. Orlov; L. T. Aguilar; L. Acho; A. Ortiz
Digital Object Identifier (DOI)
10.3182/20070829-3-RU-4912.00015
Page Numbers:
90-94
Index Terms
variable structure control,orbital stabilization,Van der Pol equation
Abstract
A well-known Van der Pol oscillator is modified to be introduced into the synthesis as an asymptotic harmonic generator of the periodic motion. The proposed modification possesses a limit cycle, producing a single harmonic as opposed to multi-harmonics of a standard harmonic oscillator. The parameters of the asymptotic harmonic generator are shown to specify damping, amplitude, and frequency of the limit cycle production. A model orbit stabilization approach to swing up control of a two-link pendulum robot (Pendubot) is used as a case of study. The quasihomogeneous control synthesis is utilized to design a variable structure controller that drives the actuated link of the Pendubot to a periodic reference orbit in finite time. Performance issues of the controller constructed are illustrated in an experimental study.
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