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

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

Proc. of the International Conference on Robotics and Automation 1999, IEEE, 500-505

Abstract:

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.