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.
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.
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