An analytical design of Fractional Order Proportional Integral and [Proportional Integral] controllers for robust velocity servo

In this paper, two tuning methods of Fractional Order Proportional Integral (FOPI) controller and Fractional Order [Proportional Integral] (FO[PI]) controller for the typical first-order velocity servo system are discussed. Using the Integer Order Proportional, Integral and Derivative (IOPID) controller, the controller can not be designed to follow the proposed tuning idea to achieve the robustness requirement. However, the FOPI and FO[PI] controllers designed by the proposed tuning methods can improve the performance and robustness of the first order velocity servo system. Furthermore, following the proposed systematic and analytical design schemes, the FO[PI] controller outperforms the FOPI controller. Simulation results are presented to validate the proposed tuning methods.