Quasihomogeneity Approach to the Pendubot Stabilization around Periodic Orbits

Abstract Orbital stabilization of a simple underactuted manipulator, namely, two-link PENDUlum roBOT is under study. Since underactuated systems can not be locally stabilized by means of smooth feedback, the solution to the stabilization problem is sought within switched control methods. The quasihomogeneity-based synthesis is applied to design a switched controller that drives the PENDUBOT to its zero dynamics in finite time and maintains it there in sliding mode. The constructed controller is such that the pendubot zero dynamics is generated by a modified Van der Pol oscillator, being viewed as the reference model. The proposed Van der Pol modification aims to enlarge the region of attraction of the zero dynamics while also exhibiting a desired stable periodic behavior. Performance issues of the controller constructed are illustrated in a simulation study.

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