Fractional order PI-PD controller design for time delayed processes

In this study, a method for modifying the settings of fractional order PI-PD (FOPI-PD) controllers to handle time-delayed stable, unstable, and integrating processes is presented. The goal is to reduce the computational complexity associated with fractional controller design using analytical techniques. The approach involves updating the analytical weighted geometrical center (AWGC) method for tuning FOPI-PD controllers. The fractional integral and derivative orders are computed by minimizing the Integral of Squared Time Error (ISTE) using straightforward formulas. Additionally, there are analytical formulas provided for robustness characteristics such as maximum sensitivity (Ms), phase margin (PM), and gain margin (GM). The effectiveness of the technique is illustrated through unit-step responses under nominal, disturbed, and measurement situations. The method was evaluated using various metrics and an inverted pendulum mechanical system to demonstrate its industrial applicability. The results showed satisfactory outcomes in both performance and robustness.