Dynamics of relay relaxation oscillators

Author

Varigonda, Subbarao ; Georgiou, Tryphon T.

Author_Institution

Dept. of Chem. Eng. & Mater. Sci., Minnesota Univ., Minneapolis, MN, USA

Volume

46

Issue

1

fYear

2001

fDate

1/1/2001 12:00:00 AM

Firstpage

65

Lastpage

77

Abstract

Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring

Keywords

bifurcation; control nonlinearities; controllability; dynamics; feedback; hysteresis; linear systems; observability; relaxation oscillators; state-space methods; asymmetric orbits; complex orbits; coupled relay oscillators; degenerate orbits; entrainment; external forcing; feedback system; integrator; linear system; periodic orbits; phase locking; relay hysteresis; relay relaxation oscillators; unimodal periodic orbits; Biological system modeling; Chemical elements; Circuits; Feedback; Hysteresis; Linear systems; Orbits; Relays; Ring oscillators; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.898696

Filename

898696