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Asymptotic harmonic generator design via modification of van der Pol oscillator

Y. Orlov, Luis T. Aguilar, Leonardo Acho, Adan Ortiz
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. While being used as a reference model, the proposed Van der Pol modification proves to be well-suited for a model orbit stabilization of a two-link pendulum robot (Pendubot). 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 of the laboratory Pendubot.
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