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A family of pumping-damping smooth strategies for swinging up a pendulum. (English) Zbl 1141.70014

Bullo, Francesco (ed.) et al., Lagrangian and Hamiltonian methods for nonlinear control 2006. Proceedings from the 3rd IFAC workshop, Nagoya, Japan, July 19–21, 2006. Berlin: Springer (ISBN 978-3-540-73889-3/pbk). Lecture Notes in Control and Information Sciences 366, 341-352 (2007).
Summary: We present some additional results regarding the pumping-damping strategy for swinging up a pendulum introduced in [the authors, in: 16th IFAC World Congress, Prague (2005)]. Here, the family of energy functions is enlarged and the corresponding pumping-damping functions are proposed giving rise to new smooth controllers that swing up and stabilize the pendulum. Furthermore, a generalization of the stability criterion is introduced for this larger class of controllers.
For the entire collection see [Zbl 1119.93006].

MSC:

70Q05 Control of mechanical systems
70K40 Forced motions for nonlinear problems in mechanics
70K20 Stability for nonlinear problems in mechanics
93B52 Feedback control
93C15 Control/observation systems governed by ordinary differential equations
93D20 Asymptotic stability in control theory
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References:

[1] José Ángel Acosta. Nonlinear control of underactuated systems. PhD thesis, University of Seville, 2004. In Spanish.
[2] Aracil, J.; Gordillo, F., The inverted pendulum: A challenge for nonlinear control, Revista Iberoamericana de Automätica e Informätica Industrial, 2, 2, 8-19 (2005)
[3] K. J. Åström, J. Aracil, and F. Gordillo. A new family of smooth strategies for swinging up a pendulum. In 16^thIFAC World Congress. Prague, 2005. · Zbl 1141.70014
[4] Åström, K. J.; Furuta, K., Swinging up a pendulum by energy control, Automatica, 36, 287-295 (2000) · Zbl 0941.93543 · doi:10.1016/S0005-1098(99)00140-5
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