Aracil, Javier; Gordillo, Francisco; Åström, Karl J. 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]. Cited in 3 Documents 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 Keywords:enlarged energy function; stability criterion; inverted pendulum PDFBibTeX XMLCite \textit{J. Aracil} et al., Lect. Notes Control Inf. Sci. 366, 341--352 (2007; Zbl 1141.70014) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.