Dissipation and controlled Euler-Poincare systems

Author

Woolsey, C.A. ; Bloch, A.M. ; Leonard, N.E. ; Marsden, J.E.

Author_Institution

Dept. of Aerosp. & Ocean Eng., Virginia Polytech. Inst. & State Univ., Blacksburg, VA, USA

Volume

4

fYear

2001

fDate

2001

Firstpage

3378

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. We consider the effect of damping on Euler-Poincare (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-Poincare systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor

Keywords

Lie groups; Lyapunov methods; asymptotic stability; closed loop systems; damping; feedback; Euler-Poincare systems; asymptotic stability; closed-loop stable equilibrium; conservative system model; controlled Lagrangians; damped rigid body; feedback dissipation; generic damping; intermediate axis rotation; physical damping; single internal rotor; underactuated mechanical systems; Aerodynamics; Aerospace control; Aerospace engineering; Control systems; Damping; Feedback; Kinetic energy; Lagrangian functions; Lyapunov method; Vehicle dynamics;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980356

Filename

980356