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Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians

Bloch, Anthony M. and Leonard, Naomi Ehrich and Marsden, Jerrold E. (1999) Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians. In: Proceedings of the 1999 IEEE International Conference on Robotics and Automation. Vol.1. Institute of Electrical and Electronics Engineers , Piscataway, NJ, pp. 500-505. ISBN 9780780351806.

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Obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy “matching” conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.

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Additional Information:“© 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Research partially supported by the National Science Foundation grants DMS-9496221 and DMS-9803181, AFOSR grant F49620-96-1-0100 and a Guggenheim Fellowship. Research partially supported by the National Science Foundation under grant BES-9502477 and by the Office of Nwal Research under grants N00014-96-1-0052 and N00014-98-1-0649. Research partially supported by AFOSR Grant F49620-95-1-0419.
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Deposited On:14 Jul 2005
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