Dissipation and Controlled Euler-Poincaré Systems
Woolsey, C., A. M. Bloch, N. E. Leonard and J. E. Marsden
2001 Conference on Decision and Control
Orlando, FL, December 2001, 3378-3383
Abstract:
The method of controlled Lagrangians is a technique for stabilizing
underactuated mechanical systems which involves modifying a system's
energy and dynamic structure through feedback. These modifications
can obscure the effect of physical dissipation in the closed-loop.
For example, generic damping can destabilize an equilibrium which is
closed-loop stable for a conservative system model. In this paper, we
consider the effect of damping on Euler-Poincaré (special reduced
Lagrangian) systems which have been stabilized about an equilibrium using
the method of controlled Lagrangians. We describe a choice of feedback
dissipation which asymptotically stabilizes a sub-class of controlled
Euler-Poincaré systems subject to physical damping. As an example,
we consider intermediate axis rotation of a damped rigid body with a
single internal rotor.