Extension of harmonic balance principle and its application to analysis of convergence rate of second-order sliding mode control algorithms

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Abstract

The harmonic balance condition is revisited. The existing methodology of analysis of periodic motions is extended to analysis of vanishing oscillations of variable frequency. Transient processes in the systems controlled by second-order sliding mode (SOSM) algorithms are analyzed. A simple criterion of the existence of finite-time convergence is proposed. It is shown that the convergence rate depends on the angle between the high-frequency asymptote of the Nyquist plot of the plant and the low-amplitude asymptote of the negative reciprocal of the describing function of the controller, which is named the phase deficit.

Original languageBritish English
Title of host publication2008 American Control Conference, ACC
Pages4691-4696
Number of pages6
DOIs
StatePublished - 2008
Event2008 American Control Conference, ACC - Seattle, WA, United States
Duration: 11 Jun 200813 Jun 2008

Publication series

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

Conference

Conference2008 American Control Conference, ACC
Country/TerritoryUnited States
CitySeattle, WA
Period11/06/0813/06/08

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