Physical Dissipation and the Method of Controlled Lagrangians
Woolsey, C., A. M. Bloch, N. E. Leonard and J. E. Marsden
Proceedings of the European Control Conference
Porto, Portugal, September 2001, 2570-2575.
Abstract:
We describe the effect of physical dissipation on
stability of equilibria which have been stabilized, in the
absence of damping, using the method of controlled Lagrangians.
This method applies to a class of underactuated mechanical
systems including "balance" systems such as the pendulum on a
cart. Since the method involves modifying a system's kinetic
energy metric through feedback, the effect of dissipation is
obscured. In particular, it is not generally true that damping
makes a feedback-stabilized equilibrium asymptotically stable.
Damping in the unactuated directions does tend to enhance
stability, however damping in the controlled directions must be
"reversed" through feedback. In this paper, we suggest a choice
of feedback dissipation to locally exponentially stabilize a
class of controlled Lagrangian systems.