A Normal Form for Energy Shaping: Application to the Furuta Pendulum
Sujit Nair and Naomi Ehrich Leonard
41st IEEE Conference on Decision and Control,
2002
In this paper we derive a nonlinear control law for stabilization
of the Furuta pendulum system with the pendulum in the upright
position and the rotating rigid link at rest at the origin. The
control law is derived by first applying feedback that makes the
Furuta pendulum look like a planar pendulum on a cart plus a
gyroscopic force. The planar pendulum on a cart is an example of a
class of mechanical systems which can be stabilized in full state
space using the method of controlled Lagrangians. We consider this
class of systems as our normal form and for the case of the Furuta
pendulum, we add to the first transforming feedback law, the
energy-shaping control law for the planar pendulum system. The
resulting system looks like a mechanical system plus
feedback-controlled dissipation and an external force that is
quadratic in velocity. Using energy as the Lyapunov function we
prove local exponential stability and demonstrate a large region
of attraction.