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Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum

Samer Riachy 1, 2 Yuri Orlov 3 Thierry Floquet 2, 4 Raul Santiesteban 3 Jean-Pierre Richard 2, 4
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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.
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Submitted on : Tuesday, October 16, 2007 - 6:32:20 PM
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Samer Riachy, Yuri Orlov, Thierry Floquet, Raul Santiesteban, Jean-Pierre Richard. Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum. International Journal of Robust and Nonlinear Control, Wiley, 2008, 18 (4-5), pp.529-543. ⟨10.1002/rnc.1200⟩. ⟨inria-00179854⟩

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