Potential shaping and the method of controlled Lagrangians

Author

Bloch, Anthony M. ; Leonard, Naomi Ehrich ; Marsden, Jerrold E.

Author_Institution

Dept. of Math., Michigan Univ., Ann Arbor, MI, USA

Volume

2

fYear

1999

fDate

6/21/1905 12:00:00 AM

Firstpage

1652

Abstract

We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

Keywords

control system analysis; stability; state-space methods; complete state-space stabilization; controlled Lagrangians; feedback-controlled dissipation; inverted pendulum; mechanical systems; potential shaping; state variables; state-space stabilization; symmetry variables; symmetry-preserving kinetic shaping; Aerospace engineering; Control systems; Equations; Lagrangian functions; Mathematics; Mechanical systems; Mechanical variables control; Potential energy; Shape control; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on

Conference_Location

Phoenix, AZ

ISSN

0191-2216

Print_ISBN

0-7803-5250-5

Type

conf

DOI

10.1109/CDC.1999.830261

Filename

830261