The prediction of chaotic behaviors in feedback control systems

ABSTRACT Master Thesis THE PREDICTION OF CHAOTIC BEHAVIORS IN FEEDBACK CONTROL SYSTEMS Vedat ÇELİK Fırat University Graduate School of Natural and Applied Sciences Department of Electrical and Electronics Engineering 2004, Page: 87 In this thesis, a method to predict a nonlinear behavior namely chaotic behavior, which is observed in nonlinear feedback systems, is given. In the literature, this method is called the Genesio-Tesi conjecture. In the thesis, the characteristic of the limit cycle, which can occur in closed loop systems, is obtained by employing Describing Function (DF). In addition, the relationship between the Genesio-Tesi conjecture and DF is given and chaotic behavior is observed and studied by both. Analytical,. Graphical methods in which demolished limit cycle behavior obtained by adjusting linear part of the system dynamics. In the end of the thesis, an attention is given to a nonlinear feedback control system that chaotic behavior cannot be observed, but it observed when the system controlled by a PI controller with unsuitable controller design parameters. Keywords: Nonlinear feedback system, Limit cycle, Describing function, Chaos, PI controlled nonlinear feedback system VII