Design of Optimal Hybrid Fractional Order PID Controller

This article proposes a hybrid fractional order PID controller optimized with Tilted integral derivative controller (TID) which gives an exquisite response. The coefficients of PID controller are tuned with ziegler-Nichols and Astrom-Hagglund method. FO-PID controller parameters i.e. proportional constant(Kp), integral constant (Ki) are taken by Ziegler-Nichols, derivative constant (Kd) by Astrom-Hagglund method and Tilted integral derivative controller parameters are taken by Astrom-Hagglund. In order to calculate required solutions, two non-linear equations are derived to find the fractional order of the integral term (lambda) and derivative term (mu). The step response shows the benefits of above discussed hybrid fractional order PID controller when compared with existing controller. Simulated results are represented on matlab 2012(a)