Design of Optimal PID[FOPID] Controller for Linear System

This article propose a hybrid fractional order PIDcontroller which is optimized with classical proportional integralderivative controller (PID) gives an exquisite response. Here thetwo tuning method are used to evaluate the parameters of PIDcontroller, first one is Ziegler-Nichols and other one is Astrom-Hagglund method. The parameters of FO-PID controller in useas the proportional constant, integral constant are by Ziegler-Nichols and derivative constant by Astrom-Hagglund method. In order to obtain required solutions, two non-linear equationsare derived to find the fractional order of the integral term andderivative term The step response shows the benefits of abovediscussed hybrid fractional order PID controller when comparingwith existing controller. Simulated results are carried by matlab2012(a).