Comparison of variable fractional order PID controller for different types of variable order derivatives

In this paper tuning algorithm of variable fractional PID controller for switching objective function is presented. The time constant parameters of PID controller are obtained by well-known, traditional Ziegler-Nichols methods. Then, the orders of integral and derivative actions are obtained based on minimization for different objective functions separately. This objective function can be switched during control process by changing orders of fractional PID controller. It leads to variable fractional order PID controller which can be implemented differently, according to above definitions. The paper presents also numerical results of applying proposed method to the control system. Then, obtained results for different type of variable order differences are compared and analysed.