Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems

In this paper, two fractional order proportional integral controllers are designed to improve the performance and robustness for a class of fractional order systems which can better model many real systems such as bioengineering systems. For comparison between the fractional order proportional integral controllers and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. Unfortunately, the designed IOPID controller can not meet the required specification. However, the designed fractional order proportional integral (FOPI) and fractional order [proportional integral] (FO[PI]) controllers both can satisfy all the three specifications proposed. From the simulation results presented, it can be seen that both the FOP] and FO[PI] controllers designed work efficiently. Furthermore, we can observe that the FO[PI] controller outperforms the FOPI controller following the proposed design schemes for the fractional order systems considered.