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Controlled Lagrangian systems with gyroscopic forcing and dissipation

Woolsey, Craig and Reddy, Chevva Konda and Bloch, Anthony M. and Chang, Dong Eui and Leonard, Naomi Ehrich and Marsden, Jerrold E. (2004) Controlled Lagrangian systems with gyroscopic forcing and dissipation. European Journal of Control, 10 (5). pp. 478-496. ISSN 0947-3580. http://resolver.caltech.edu/CaltechAUTHORS:WOOejc04

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Abstract

This paper describes a procedure for incorporating artificial gyroscopic forces and physical dissipation in the method of controlled Lagrangians. Energy-conserving gyroscopic forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural damping. We apply the technique to the inverted pendulum on a cart,a case study from previous papers. We develop a controller that asymptotically stabilizes the inverted equilibrium at a specific cart position for the conservative dynamic model. The region of attraction contains all states for which the pendulum is elevated above the horizontal plane. We also develop conditions for asymptotic stability in the presence of linear damping.


Item Type:Article
Additional Information:Author preprint. Publisher version includes figures. Article appears in a special issue, "Lagrangian and Hamiltonian Methods for Nonlinear control; Guest editors: ASTOLFI Alessandro, VAN DER SCHAFT Arjan J." Research partially supported by NSF grant CMS-0133210 and ONR grant N00014-01-1-0588. Research partially supported by NSF grants DMS 0103895 and 0305837 and AFOSR. Research partially supported by NSF grant CCR-9980058, ONR grants N00014–02–1–0826 and N00014–02–1–0861 and AFOSR grant F49620-01-1-0382. Research partially supported by the California Institute of Technology and ONR Contract N00014-02-1-0826.
Subject Keywords:Energy shaping, Gyroscopic forces, Nonlinear stabilization, Underactuated mechanical systems
Record Number:CaltechAUTHORS:WOOejc04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:WOOejc04
Alternative URL:http://ejc.revuesonline.com/login.jsp?articleId=5932
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:532
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:13 Jul 2005
Last Modified:26 Dec 2012 08:40

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