Fractional order PI controller design for first order system with dead time

In this study, history of the fractional order mathematics and concept of fractional derivative – integral is firstly mentioned. Although flexibility of fractional order PI controller coefficient (kp, ki) is nearly similar to flexibility of the classical PI controller coefficient, the integral order (λ) flexibility is completely different from each other and the main difference between the controller structures results from integral order. The most important issue during designing the fractional order controller is not to make the closed loop system unstable. Thus, stability region of the controller coefficient is primarily found by using the boundary input-boundary output stable rule. When the system contains dead time, it is hard to find stability region of coefficient of fractional order controller. Therefore, different approaches of dead time are considered in order to solve the complexity. Most suitable approximation of dead time is "Pade Approximation". The extension of the achived dead time with this approach can be adjusted as desired. The higher dead time approximation order is, the more likely it is approaches to real dead time. With the use of this approach, system and approximated dead time can be handled as the two systems connected in series. In this case, it is easier to determine the stability region of fractional order controller coefficient for the system including the dead time. While the stability region of the fractional order controller coefficients is being determined, the integral order (λ) of the controller has very importance because the stability region is changeable according to the integral order value. Thus, the stability region is bounded with these three parameter (kp, ki, λ). The performance of the system is changeable according to different values of the controller parameters in the stability region. Simulation of the fractional order systems is not directly applied in MATLAB. Thus, the required MATLAB toolbox is introduced in order to simulate fractional order systems. Also, the functions in the toolbox can be easily used with the other MATLAB functions. The research until this stage is guideline for achieving the desired performance of the system. The required parameters to provide the desired performance of the system will be found with Big Bang- Big Crunch optimization algorithm and the results will be examined.