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Non-linear sliding mode surfaces for a class of underactuated mechanical systems [Brief Paper]

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3 Author(s)
López-Mart́́nez, M. ; Dept. de Ing. de Sist. y Autom., Univ. de Sevilla, Sevilla, Spain ; Acosta, J.A. ; Cano, J.M.

This study presents a new non-linear sliding surface to control a class of non-minimum phase underactuated mechanical systems, taking into account uncertainties in their physical parameters. The non-linear surface is designed through a fictitious output, which provides the minimum-phase property and allows to prove stability using Lyapunov theory. The non-linear surface is based on the fictitious output and augmented with a non-linear external controller designed using the Lyapunov theory. The present approach assures exponential stability of the equilibrium point and robust stability to parametric uncertainties, avoiding the appearance of non-desired phenomena, as limit cycles. Two pendulum-like examples inside the class are thoroughly analysed and solved, that is, the pendulum on a cart and the inertia wheel pendulum. Performance, time response and parametric robustness are shown through simulations.

Published in:

Control Theory & Applications, IET  (Volume:4 ,  Issue: 10 )