Computation of multiple limit cycles in nonlinear control systems – a describing function approach

Abstract Limit cycles play an important role in nonlinear systems, provided that many control loops with common nonlinearities like relay, hysteresis, and saturation can present them. Thus, a proper description of this nonlinear phenomenon is highly desirable. A strategy for the linearized analysis...

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Bibliographic Details
Published inJournal of aerospace technology and management Vol. 3; no. 1; pp. 21 - 28
Main Author Brito, Alexandre Garro
Format Journal Article
LanguageEnglish
Published Departamento de Ciência e Tecnologia Aeroespacial 01.01.2011
Instituto de Aeronáutica e Espaço (IAE)
Subjects
Describing functions
ENGINEERING, AEROSPACE
Limit cycle
Multimodal optimization
Multimodal optimization
Limit cycle
Describing functions
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Summary:Abstract Limit cycles play an important role in nonlinear systems, provided that many control loops with common nonlinearities like relay, hysteresis, and saturation can present them. Thus, a proper description of this nonlinear phenomenon is highly desirable. A strategy for the linearized analysis is the describing function method, which is a frequency domain approach that allows the limit cycle prediction and stability analysis. Some papers had discussed the method for the simplified analysis; however, they are concentrated in the prediction of only one limit cycle even for systems with multiple conditions. This paper proposes a systematic way of multiple limit cycle determination, as well as the stability analysis of each one. All theoretical/computational issues involved in the approach are also discussed.
ISSN:2175-9146
1984-9648
2175-9146
DOI:10.5028/jatm.2011.03017010