NDLI: On the stability of sliding mode control for a class of underactuated nonlinear systems

Content Provider	IEEE Xplore Digital Library
Author	Nersesov, S.G. Ashrafiuon, H. Ghorbanian, P.
Copyright Year	2010
Description	Author affiliation: Dept. of Mech. Eng., Villanova Univ., Villanova, PA, USA (Nersesov, S.G.; Ashrafiuon, H.; Ghorbanian, P.)
Abstract	A system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed-loop system trajectory reaches the surface it moves along the surface while converging to the origin. In this paper, we present a general framework that provides sufficient conditions for asymptotic stabilization by a sliding mode controller for a class of underactuated nonlinear systems with two degrees of freedom. We show that, with the sliding mode controller presented, the closed-loop system trajectories reach the sliding surface in finite time. Furthermore, we develop a constructive methodology to determine exponential stability of the reduced-order closed-loop system while on the sliding surface thus ensuring asymptotic stability of the overall closed-loop system and provide a way to determine an estimate of the domain of attraction. Finally, we implement this framework on the example of an inverted pendulum.
Starting Page	3446
Ending Page	3451
File Size	469335
Page Count	6
File Format	PDF
ISBN	9781424474264
ISSN	07431619
e-ISBN	9781424474271
DOI	10.1109/ACC.2010.5531082
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-30
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Sliding mode control Nonlinear systems Control systems Nonlinear control systems Lyapunov method Actuators Asymptotic stability Nonlinear dynamical systems Lagrangian functions Convergence
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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