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Transverse linearization for mechanical systems with several passive degrees of freedom with applications to orbital stabilization
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.
2009 (English)In: American Control Conference, 2009. ACC '09, 2009, 3039-3044 p.Conference paper (Refereed)
Abstract [en]

A class of mechanical systems with many unactuated degrees of freedom is studied. An analytical method for computing coefficients of a linear controlled system, solutions of which approximate dynamics of transverse part of coordinates of an underactuated mechanical system along a feasible motion, is proposed. The procedure is constructive and is based on a particular choice of coordinates in a vicinity of the motion. It allows explicit introduction of the so-called moving Poincare section associated with a finite-time or periodic motion. It is shown that the coordinates admit analytical linearization of transverse part of the system dynamics prior to any controller design. If the motion is periodic, then these coordinates are used for developing feedback controllers. Necessary and sufficient conditions for exponential orbital stabilization of a cycle for underactuated mechanical systems are derived. Two illustrative examples are elaborated in details.

Place, publisher, year, edition, pages
2009. 3039-3044 p.
, Proceedings / American Control Conference ; sponsored by the American Automatic Control Council, ISSN 0743-1619
Keyword [en]
Moving Poincare section, periodic solutions, orbital stability, transverse linearization, underactuated mechanical systems, virtual holonomic constraints, spherical pendulum, synchronization of mechanical systems
URN: urn:nbn:se:umu:diva-37695DOI: 10.1109/ACC.2009.5159989ISBN: 978-1-4244-4523-3OAI: diva2:369753
2009 American Control Conference -- ACC2009, St. Louis, Missouri, USA, June 10 - 12, 2009
Available from: 2010-11-11 Created: 2010-11-11 Last updated: 2010-12-13Bibliographically approved

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Shiriaev, Anton S.Freidovich, Leonid B.
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ReferencesLink to record
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