Stabilization of autonomous oscillations and the Hopf bifurcation in the ball and beam

Author

Gordillo, Francisco ; Aracil, Javier ; Gómez-Estern, Fabio

Author_Institution

Dept. de Ingenieria de Sistemas y Autom., Escuela Superior de Ingenieros, Sevilla, Spain

Volume

4

fYear

2002

fDate

10-13 Dec. 2002

Firstpage

3924

Abstract

This paper presents a design method for the stabilization of oscillations in a class of nonlinear systems. The method consists of two steps. In the first one, a second-order generalized Hamiltonian subsystem, which presents stable oscillations, is matched. In the second step, the controller is extended to the full system using backstepping. It is shown that the oscillations emerge through a supercritical Hopf bifurcation. The method proposed was first applied to a second order system. In this paper the method is extended to higher order systems by backstepping. The method is introduced by its application to an underactuated mechanical system: the ball and beam.

Keywords

bifurcation; control system synthesis; feedback; limit cycles; nonlinear systems; oscillations; stability; Hamiltonian subsystem; Hopf bifurcation; autonomous oscillations; backstepping control; ball beam system; higher order systems; limit cycle; nonlinear systems; second order system; stabilization; stable oscillations; underactuated mechanical system; Backstepping; Bifurcation; Control systems; Design methodology; Equations; Feedback; Limit-cycles; Lyapunov method; Mechanical systems; Nonlinear control systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2002, Proceedings of the 41st IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7516-5

Type

conf

DOI

10.1109/CDC.2002.1184978

Filename

1184978