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Computing a transverse linearization for mechanical systems with two and more passive degrees of freedom
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
St. Petersburg University.
2010 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 4, 893-906 p.Article in journal (Refereed) Published
Abstract [en]

This study examines the mechanical systems with an arbitrary number of passive (non-actuated) degrees of freedom and proposes an analytical method for computing coefficients of a linear controlled system, solutions of which approximate dynamics transverse to a feasible motion. This constructive procedure is based on a particular choice of coordinates and allows explicit introduction of a moving Poincaré section associated with a nontrivial finite-time or periodic motion. In these coordinates, transverse dynamics admits analytical linearization before any control design. If the forced motion of an underactuated mechanical system is periodic, then this linearization is an indispensable and constructive tool for stabilizing the cycle and for analyzing its orbital (in)stability. The technique is illustrated with two challenging examples. The first one is stabilization of a circular motion of a spherical pendulum on a puck around its upright equilibrium. The other one is creating stable synchronous oscillations of an arbitrary number of planar pendulums on carts around their unstable equilibria.

Place, publisher, year, edition, pages
2010. Vol. 55, no 4, 893-906 p.
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:umu:diva-30765DOI: 10.1109/TAC.2010.2042000OAI: oai:DiVA.org:umu-30765DiVA: diva2:286688
Available from: 2010-01-15 Created: 2010-01-15 Last updated: 2012-08-08Bibliographically approved

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Shiriaev, AntonFreidovich, Leonid

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