Optimal fractional order PID controllers design based on genetic algorithm for time delay systems

In this paper a new method to design optimal fractional order proportional-integral-derivative (PI^λD^μ) controllers for time delay systems is presented. In PI^λD^μ controllers' parameters are composed of proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer-order proportional-integral-derivative (PID) controller. In this study, Genetic Algorithm (GA) is employed to determine the optimum set of parameters of a 2-DOF fractional PI^λD^μ controller. The structure of the controller consists of a conventional PD and a fractional PI^λD^μ controller. The objective is to design a controller so that the process output follows, in some desired way, the corresponding reference signal, and the influence of the disturbance is minimal. The problem of finding appropriate parameters for this 2-DOF controller is transferred into an optimization problem that could be solved by GA. Simulation results demonstrate the excellence of the proposed fractional order PI^λD^μ controller to conventional integer order PID controllers.