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

• Autor(a) principal: Brito,Alexandro Garro
• Data de Publicação: 2011
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Journal of Aerospace Technology and Management (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2175-91462011000100021
• topic: Limit cycle; Multimodal optimization; Describing functions

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.