Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller designs for first order plus time delay (FOPTD) systems

In this paper, systematic design schemes of fractional order proportional integral (FOPI) controller and fractional order [proportional integral] (FO[PI]) controller for the first order plus time delay (FOPTD) system are presented, respectively. For comparison between the fractional order and the integer order controllers, the integer order proportional integral derivative (IOPID) controller is also designed following the same proposed tuning specifications to achieve the robustness requirement. It is found that the three controllers designed by the proposed tuning methods not only make the system stable, but also improve the performance and robustness for the first order plus time delay (FOPTD) systems. Simulation results are presented to validate the proposed tuning schemes. Furthermore, from the simulation results, it can be seen that the FOPI controller outperforms the other two controllers.