Fractional-order PID Controller Design using PSO and GA

Over the past few years, fractional-order PID controllers (FOPID) have been introduced in control system theory to enhance the stability and performance of mainly real complex systems. The fractional-order PID controller (FOPID) is considered as a special type of the classical PID controller, in which both integral and derivative orders are fractional instead of an integer. FOPID has five parameters to be tuned instead of three, which gives two extra degrees of freedom to achieve the control objectives. This article deals with the design process of FOPID controllers using metaheuristic optimization methods. In this paper, both particle swarm optimization (PSO) and genetic algorithm (GA) are implemented in order to design appropriate FOPID controllers. The tuning of the five unknown parameters of the FOPID controller is based on minimizing an objective function defined as the integral of time-weighted absolute error (ITAE). To evaluate the performance of the FOPID controller, a simulation example to control DC motors is given, where both PSO and GA algorithms are implemented to obtain suitable values of the FOPID parameters. To show the superiority of FOPID controller over the traditional PID, a performance comparison and robustness tests are carried out. Overall, the simulation results show that Genetic Algorithm (GA) is the most applicable tuning method among the other tested algorithms.