Exact periodic solution for control system containing static nonlinear function

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Abstract

A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity 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 (DF) method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system and the concept of the periodic signal mapping applied to the latter. The solution is sought for as a fixed point of the periodic signal mapping. It is shown that the DF method can be viewed as a method of approximate calculation of the periodic signal mapping. It is proved via the exact approach that for the considered type of nonlinear systems, the necessary conditions of sliding mode existence, previously obtained via the DF method, are valid. The proposed approach is illustrated by examples of analysis of periodic motions in nonlinear systems.

Original languageBritish English
Title of host publicationProceedings of the 2006 International Workshop on Variable Structure Systems, VSS'06
Pages149-154
Number of pages6
DOIs
StatePublished - 2006
Event2006 International Workshop on Variable Structure Systems, VSS'06 - Alghero, Italy
Duration: 5 Jun 20067 Jun 2006

Publication series

NameProceedings of the 2006 International Workshop on Variable Structure Systems, VSS'06
Volume2006

Conference

Conference2006 International Workshop on Variable Structure Systems, VSS'06
Country/TerritoryItaly
CityAlghero
Period5/06/067/06/06

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