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Volume 2017, Article ID 1972921, 8 pages
Research Article

Design of Robust Supertwisting Algorithm Based Second-Order Sliding Mode Controller for Nonlinear Systems with Both Matched and Unmatched Uncertainty

Laboratory of Engineering of Industrial System and Renewable Energy (LISIER), Higher National Engineering School of Tunis (ENSIT), 5 Avenue Taha Hussein, BP 56, Bab Menara, 1008 Tunis, Tunisia

Correspondence should be addressed to Marwa Jouini; moc.liamg@7iniuojawram

Received 4 August 2017; Revised 8 November 2017; Accepted 22 November 2017; Published 13 December 2017

Academic Editor: Olfa Boubaker

Copyright © 2017 Marwa Jouini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a robust supertwisting algorithm (STA) design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.