Effects on the chaotic system of fractional order PI ? controller

Abstract

When a Lur'e-type system which cannot exhibit chaotic behavior and whose linear part is of a second order, is tried to be controlled by an integer order controller, chaotic behaviors can occur depending on the controller parameters. In this article, in the case when a fractional order PI (alpha) is chosen, provided that the controller parameters remain unchanged, the effect of the integral order alpha for the interval 0 < 1 has been investigated. It has been shown through two examples that depending on the integral order alpha, the fractional order PI (alpha) controller prevents the chaotic behavior by releasing the extra dynamics that was loaded onto the system by the integer order PI controller. To determine at which alpha parameter the system exhibits chaotic behavior, the frequency domain approach based chaos prediction method-Genesio-Tesi conjecture-has been used.