Second order sliding mode control of underactuacted mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up / balancing control

Raul Santiesteban 1 Thierry Floquet 2, 3 Yuri Orlov 1 Samer Riachy 4, 2 Jean-Pierre Richard 2, 3
1 CICESE - Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico]
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
3 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : Orbital stabilization of an underactuated cart-pendulum system is under study. The quasihomogeneous control synthesis is utilized to design a second order sliding mode controller that drives the actuated cart to a periodic reference orbit in finite time, while the non-actuated pendulum produces bounded oscillations. A modified Van der Pol oscillator is introduced into the synthesis as an asymptotic generator of the periodic motion. The resulting closed-loop system is capable of moving from one orbit to another by simply changing the parameters of the Van der Pol modification. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of the swing up/balancing control problem of moving a pendulum, located on an actuated cart, from its stable downward position to the unstable inverted position and stabilizing it about the vertical.
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International Journal of Robust and Nonlinear Control, Wiley, 2008, 18 (4-5), pp.544-556
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Raul Santiesteban, Thierry Floquet, Yuri Orlov, Samer Riachy, Jean-Pierre Richard. Second order sliding mode control of underactuacted mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up / balancing control. International Journal of Robust and Nonlinear Control, Wiley, 2008, 18 (4-5), pp.544-556. 〈inria-00179858〉

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