Performance comparison on three parameter determination method of fractional PID controllers

The objective of this work is to define the fractional order PID and the approximation of the integral and derivation of fractional order to render the system from irrational to rational. The parameters of PID are determined by three methods. These fractional controllers have two parameters more than the conventional PID controller, two more specifications can be met, improving the performance of the system, the fractional orders, α and β are determined by minimized the ISE. For the tuning of the controller an iterative optimization method has been used, based on a nonlinear function minimization. Illustrative example is presented and simulation results show the effectiveness of this kind of controllers.