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Second‐order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum
Author(s) -
Riachy Samer,
Orlov Yuri,
Floquet Thierry,
Santiesteban Raul,
Richard JeanPierre
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1200
Subject(s) - control theory (sociology) , underactuation , inverted pendulum , sliding mode control , robustness (evolution) , stability theory , controller (irrigation) , manifold (fluid mechanics) , dimension (graph theory) , computer science , mathematics , nonlinear system , engineering , physics , control (management) , mechanical engineering , biochemistry , chemistry , quantum mechanics , artificial intelligence , biology , pure mathematics , agronomy , gene
Second‐order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed‐loop system is provided by applying a quasihomogeneous second‐order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first‐order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second‐order sliding mode appears on the zero dynamics manifold which is of co‐dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart–pendulum system. Copyright © 2007 John Wiley & Sons, Ltd.