Stabilization of oscillations through backstepping in high-dimensional systems

Author

Aracil, Javier ; Gordillo, Francisco ; Ponce, Enrique

Author_Institution

Departamento de Ingenieria de Sistemas y Automatica, Escuela Superior de Ingenicros, Seville, Spain

Volume

50

Issue

5

fYear

2005

fDate

5/1/2005 12:00:00 AM

Firstpage

705

Lastpage

710

Abstract

This note introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n≥2. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Then, the controller is extended to the full system by a backstepping procedure. It is shown that the closed-loop system turns out to be generalized Hamiltonian and that the limit cycle can be thought as born in a Hopf bifurcation after moving a parameter.

Keywords

bifurcation; closed loop systems; feedback; limit cycles; nonlinear control systems; oscillations; stability; Hopf bifurcation; backstepping control; closed-loop system; feedback law; generalized Hamiltonian system; limit cycle stability; second-order subsystem; self-sustained oscillation; single input nonlinear system; Backstepping; Bifurcation; Control systems; Displays; Equations; Feedback; Limit-cycles; Nonlinear control systems; Nonlinear systems; Robustness; Backstepping control; Hopf bifurcation; generalized Hamiltonian systems; limit cycle stabilization; nonlinear oscillations;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.847038

Filename

1431055