Stabilization of the Pendulum on a Rotor Arm by the Method of Controlled Lagrangians

A.M. Bloch, N.E. Leonard and J.E. Marsden

In Proceedings of the IEEE Int. Conf. on Robotics and Automation, May 1999, to appear.


This paper 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.

Postscript Version (6 pages postcript)

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