Physical Dissipation and the Method of Controlled Lagrangians
Abstract
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.
Additional Information
The authors thank Dong Eui Chang for his helpful comments.Attached Files
Published - WoBlLeMa2001.pdf
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Additional details
- Eprint ID
- 20311
- Resolver ID
- CaltechAUTHORS:20101005-151547749
- Created
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2010-11-17Created from EPrint's datestamp field
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2019-10-03Created from EPrint's last_modified field