Finite time model orbit stabilization of friction pendulum

A novel approach to orbital stabilization is presented and tested on a friction pendulum, operating under uncertain conditions. The quasihomogeneous control synthesis is utilized to design a variable structure controller that drives the pendulum to a model orbit in finite time in spite of the presence of external disturbances with an a priori known magnitude bound. 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. The resulting closed-loop system is capable of moving from one orbit to another by changing these parameters dynamically. Performance issues of the controller constructed are illustrated in an experimental study