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Transverse linearization for mechanical systems with passive links, impulse effects, and friction forces
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.ORCID iD: 0000-0003-0730-9441
2009 (English)In: Proceedings of the 48th IEEE conference on decision and control, 2009, held jointly with the 2009 28th Chinese control conference (CDC/CCC 2009), IEEE conference proceedings, 2009, 6490-6495 p.Conference paper (Refereed)Text
Abstract [en]

We consider a class of mechanical systems with an arbitrary number of passive (non-actuated) degrees of freedom. In addition to control forces, we take into account viscous and Coulomb friction forces and impacts with the environment modeled as impulsive updates of the states. We assume that a motion planning task is solved and a feasible forced periodic motion is described in terms of piece-wise smooth virtual holonomic constraints. The main contribution is an analytical method for computing coefficients of an impulsive linear control system, solutions of which approximate dynamics transversal to the preplanned trajectory. This linear system is shown to be useful for stability analysis and for design of feedback controllers orbitally stabilizing forced periodic motions in the hybrid mechanical system. As an illustration, we apply the obtained theoretical results providing a rigorous proof of orbital exponential stability of the periodic tumbling motion for a model of a descending strip of paper in a still air.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2009. 6490-6495 p.
, IEEE Conference on Decision and Control, ISSN 0191-2216
Keyword [en]
Moving Poincare section, Periodic solutions, Orbital stability, Transverse linearization, Underactuated mechanical systems, Virtual holonomic constraints, Impulsive Mechanical Systems
National Category
Engineering and Technology
URN: urn:nbn:se:umu:diva-116060DOI: 10.1109/CDC.2009.5399859ISI: 000336893606164ISBN: 978-1-4244-3872-3ISBN: 978-1-4244-3871-6OAI: diva2:901492
Joint 48th IEEE Conference on Decision and Control (CDC) / 28th Chinese Control Conference (CCC), DEC 15-18, 2009, Shanghai, PEOPLES R CHINA
Available from: 2016-02-08 Created: 2016-02-08 Last updated: 2016-02-15Bibliographically approved

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Freidovich, Leonid BShiriaev, Anton S
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ReferencesLink to record
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