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Machines 2014, 2(3), 176-201; doi:10.3390/machines2030176

Limit Cycles in Nonlinear Systems with Fractional Order Plants

1
School of Engineering and Informatics, Department of Engineering and Design, Sussex University, Brighton, BN1 9QT, UK
2
Department of Electrical and Electronics Engineering, İnönü University, Malatya 44280, Turkey
3
Department of Computer Engineering, İnönü University, Malatya 44280, Turkey
4
Department of Mechatronics Engineering, Fırat University, Elazığ 23100, Turkey
*
Author to whom correspondence should be addressed.
Received: 31 March 2014 / Revised: 9 June 2014 / Accepted: 1 July 2014 / Published: 17 July 2014
(This article belongs to the Special Issue Advances in Control Engineering)

Abstract

In recent years, there has been considerable interest in the study of feedback systems containing processes whose dynamics are best described by fractional order derivatives. Various situations have been cited for describing heat flow and aspects of bioengineering, where such models are believed to be superior. In many situations these feedback systems are not linear and information on their stability and the possibility of the existence of limit cycles is required. This paper presents new results for determining limit cycles using the approximate describing function method and an exact method when the nonlinearity is a relay characteristic. View Full-Text
Keywords: Tsypkin locus; A function; fractional order systems; nonlinear systems with fractional order plants; describing function; limit cycles Tsypkin locus; A function; fractional order systems; nonlinear systems with fractional order plants; describing function; limit cycles
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Atherton, D.P.; Tan, N.; Yeroglu, C.; Kavuran, G.; Yüce, A. Limit Cycles in Nonlinear Systems with Fractional Order Plants. Machines 2014, 2, 176-201.

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