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Physical Dissipation and the Method of Controlled Lagrangians

Woolsey, C. A. and Bloch, A. M. and Leonard, N. E. and Marsden, J. E. (2001) Physical Dissipation and the Method of Controlled Lagrangians. In: ECC '01 : proceedings. European Union Control Association , Porto, Portugal, pp. 2570-2575.

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We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including “balance” systems such as the pendulum on a cart. Since the method involves modifying a system’s kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be “reversed” through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems.

Item Type:Book Section
Additional Information:The authors thank Dong Eui Chang for his helpful comments.
Subject Keywords:Stabilization of Non-linear Systems, Dissipative and Energy-based Design
Record Number:CaltechAUTHORS:20101005-151547749
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20311
Deposited By: Tony Diaz
Deposited On:17 Nov 2010 00:42
Last Modified:03 Oct 2019 02:08

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