COMPUTATION OF MULTIPLE LIMIT CYCLES IN NONLINEAR CONTROL SYSTEMS – A DESCRIBING FUNCTION APPROACH. doi: 10.5028/jatm.2011.03017010
Keywords:Limit cycle, Multimodal optimization, Describing functions.
AbstractLimit 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.
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