Novel GA-Based Complex Fractional Order PID Controller Design for First-Order Integer and Non-integer Systems

In this paper, a Complex Fractional Order Proportional Integral Derivative (CFOPID) controller is designed for a stable first-order system and complex order system. The increased complexity in tuning of the CFOPID controller with seven parameters needs to be addressed compared to PID with three parameters and Fractional Order PID (FOPID) controller with five parameters. The CFOPID tuning becomes tedious with conventional tuning methods. Hence, Genetic Algorithm (GA) is used for tuning the CFOPID controller with cost function as integral absolute error (IAE). The closed-loop response of the chosen systems with the CFOPID controller is compared against PID and FOPID controllers tuned using GA method. The indicators used to assess the performance are settling time and IAE for servo and regulation. A Bode plot is provided to check the stability.