A Simple Frequency-domain Tuning Method of Fractional-order PID Controllers for Fractional-order Delay Systems

The fractional-order proportional-integral-derivative (FOPID) controller is an improvement over the traditional PID controller. However, most existing methods of FOPID controller design are complex and not suitable for practical application. This paper presents a simple and efficient design method of FOPID controllers for fractional-order controlled plants with time delays. The method is based on four frequency-domain specifications—namely, gain crossover frequency, phase margin, phase crossover frequency and gain margin. The implicit nonlinear equations related to the controller parameters are formulated using these specifications. To simplify the mathematical calculation, the explicit equations of the controller parameters are analytically derived. Then, the FOPID controller parameters can be adjusted in a graphical manner. Two fractional-order plus time-delay plants are considered as simulation examples. The results show that the design requirements are successfully met and superior control performance is obtained via the proposed tuning method.