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. http://resolver.caltech.edu/CaltechAUTHORS:20101005-151547749
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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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||17 Nov 2010 00:42|
|Last Modified:||26 Dec 2012 12:30|
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