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.
Keywords:
Limit cycle; Multimodal optimization; Describing functions
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Publication Dates
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Publication in this collection
Jan-Apr 2011
History
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Received
21 May 2010 -
Accepted
16 Aug 2010