Design of Novel Complex Fractional Order Controller Using Genetic Algorithm for Fractional Order System

Abstract

In this paper, a Novel Complex Fractional Order Proportional Integral Derivative (CFOPID) controller structure is developed of the form ${\text{P}}{\text{I}}^{\text{x+iy}}{\text{D}}^{\text{a+ib}}$ for fractional order systems. This novel type of controller has more (seven) parameters to tune than the conventional PID and fractional order PID controllers, resulting in a higher degree of control freedom. However, the complexity of CFOPID is due to many tuning parameters, making design and tuning cumbersome. Therefore, this work uses a Genetic algorithm optimization technique with cost function as Integral Absolute Error (IAE). The performance of the proposed CFOPID controller is compared to that of PID and fractional order PID controllers, and then validated on an identified real heat exchanger system. In terms of performance measures such as rise time, settling time, and IAE, the results reveal that the CFOPID controller outperforms integer and fractional order PID controllers for set point and disturbance rejection. Also, the stability is investigated through frequency response using Bode plot.