Effects of fractional order structures on the nonlinear behaviors

In this thesis, the effects on a nonlinear system dynamics in the case of employing fractional order PI? type controllers, instead of integer order PID type controllers which are frequently used in industry, are investigated. For this purpose, firstly, when the controller parameters Kp and Ki which create the effect of instability on nonlinear system dynamics of integer order PI controller are chosen as the parameters of fractional order PI? controller, oscillations known as Limit Cycle (LC) with respect to the value of fractional ? integral order are shown and thus, the system is prevented from instability. In addition, when the controller parameters, Kp and Ki, creating the behavior of instable LC on nonlinear system dynamics of integer order PI controller are chosen as the parameters of fractional order PI?, it is observed that the initial values determining LC depend on ? integral value. It is shown that as ? integral value decreases, the initial values determining the system response increase. In order to diagnose the fractional ? range, Describing Function is used. Similarly, in a chaotic system with PI controller, in case the controller parameters remain unchanged and instead of integer order PI controller, a fractional order PI? controller is chosen, the effect of ? integral order is investigated and it is shown that the fractional order PI? controller, saves the system from chaotic behavior depending on ? integral order. In order to diagnose for which ? integral order the system exhibits a chaotic behavior, the frequency domain approach based chaos prediction method Genesio-Tesi conjecture is used.In this study, also, the fractional order models of single and two-cell autonomous Delayed Cellular Neural Network (DCNN) exhibiting chaotic behavior are given. For the system order ??0.1 in both DCNN with fractional order, a chaos is seen with numerical simulations. In addition, the fractional order model of a nonlinear autonomous continuous-time difference-differential equation and with only one variable is given. In this model, numerical simulation results of the fractional order model demonstrate the existence of chaos when system order ??0.2.Keywords: Fractional order nonlinear systems, Describing function, Genesio-Tesi conjecture, Fractional order control, Fractional order chaotic systems.