Refinement of periodic solution obtained via describing function method

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Abstract

A solution of the periodic problem in a nonlinear system comprising a static symmetric n on linearity and linear dynamics is presented. The solution is designed as an iterative algorithm of refinement of the approximate solution obtained via application of the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. It is also based upon the concept of the periodic signal mapping applied to the open-loop equivalent nonlinear system. The solution is sought for as a fixed point of the periodic signal mapping. The proposed approach is illustrated by examples of analysis of periodic motions in nonlinear systems. A good convergence and accuracy is demonstrated.

Original languageBritish English
Title of host publicationProceedings of the 2006 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1517-1522
Number of pages6
ISBN (Print)1424402107, 9781424402106
DOIs
StatePublished - 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: 14 Jun 200616 Jun 2006

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Conference

Conference2006 American Control Conference
Country/TerritoryUnited States
CityMinneapolis, MN
Period14/06/0616/06/06

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