Asymptotic Harmonic Generator Design Via Modification of Van Der Pol Oscillator

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. Copyright© 2007, IFAC.