Dynamics and control of a chain pendulum on a cart

Author

Taeyoung Lee ; Leok, Melvin ; McClamroch, N.H.

Author_Institution

Mech. & Aerosp. Eng., George Washington Univ., Washington, DC, USA

fYear

2012

fDate

10-13 Dec. 2012

Firstpage

2502

Lastpage

2508

Abstract

A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of n rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by a horizontal control force while the chain pendulum can undergo complex motion in 3D due to gravity. The configuration of the system is in (S²)ⁿ×ℝ². We examine the rich structure of the uncontrolled system dynamics: the equilibria of the system correspond to any one of 2ⁿ different chain pendulum configurations and any cart location. A linearization about each equilibrium, and the corresponding controllability criterion is provided. We also show that any equilibrium can be asymptotically stabilized by using a proportional-derivative type controller, and we provide a few numerical examples.

Keywords

PD control; asymptotic stability; controllability; nonlinear control systems; nonlinear dynamical systems; numerical analysis; pendulums; Euler-Lagrange equations; PD type controller; asymptotic stability; cart location; chain pendulum configurations; controllability criterion; geometric form; horizontal control force; horizontal plane; linearization; nonlinear control; nonlinear dynamics; proportional-derivative type controller; rigid links; serial connection; uncontrolled system dynamics; Dynamics; Equations; Gravity; Kinetic energy; Mathematical model; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2012 IEEE 51st Annual Conference on

Conference_Location

Maui, HI

ISSN

0743-1546

Print_ISBN

978-1-4673-2065-8

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2012.6427059

Filename

6427059