Limit Cycles in Nonlinear Systems with Fractional Order Plants

Machines

Derek P. Atherton¹  Nusret Tan⁴  Celaleddin Yeroglu³  Gürkan Kavuran² 

[1] School of Engineering and Informatics, Department of Engineering and Design, Sussex University, Brighton, BN1 9QT, UK; E-Mail:;Department of Mechatronics Engineering, Fırat University, Elazığ 23100, Turkey; E-Mail:;Department of Computer Engineering, İnönü University, Malatya 44280, Turkey; E-Mail:;Department of Electrical and Electronics Engineering, İnönü University, Malatya 44280, Turkey; E-Mail:

关键词: Tsypkin locus;    A function;    fractional order systems;    nonlinear systems with fractional order plants;    describing function;    limit cycles;   

DOI  :  10.3390/machines2030176

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.