Limit Cycles in Nonlinear Systems with Fractional Order Plants

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.