Shaping the energy of mechanical systems without solving partial differential equations

A. Donaire R. Mehra Roméo Ortega 1 S. Satpute J. Romero F. Kazi N. Singh
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this paper a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.
Type de document :
Communication dans un congrès
2015 American Control Conference (ACC), Jul 2015, Chicago, United States. Proceedings of the American Control Conference. 〈10.1109/acc.2015.7170921 〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01262147
Contributeur : Myriam Baverel <>
Soumis le : mardi 26 janvier 2016 - 12:21:03
Dernière modification le : jeudi 27 septembre 2018 - 14:30:03

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L2S | SUP_LSS | SUP_SYSTEMES | CENTRALESUPELEC | TDS-MACS | UNIV-PARIS-SACLAY

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A. Donaire, R. Mehra, Roméo Ortega, S. Satpute, J. Romero, et al.. Shaping the energy of mechanical systems without solving partial differential equations. 2015 American Control Conference (ACC), Jul 2015, Chicago, United States. Proceedings of the American Control Conference. 〈10.1109/acc.2015.7170921 〉. 〈hal-01262147〉

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