Woolsey, C. A. and Bloch, A. M. and Leonard, N. E. and Marsden, J. E. (2001) Dissipation and Controlled Euler-Poincaré Systems. In: Proceedings of the 40th IEEE Conference on Decision and Control, 2001. IEEE , Piscataway, NJ, pp. 3378-3383. ISBN 0780370619 http://resolver.caltech.edu/CaltechAUTHORS:20101025-103909189
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The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor.
|Item Type:||Book Section|
|Additional Information:||© 2001 IEEE. The authors thank Dong Eui Chang for helpful comments. We acknowledge partial support from the NSF, ONR and AFOSR.|
|Subject Keywords:||Lie groups , Lyapunov methods , asymptotic stability , closed loop systems , damping , feedback|
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|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||30 Nov 2010 18:45|
|Last Modified:||26 Dec 2012 12:33|
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