An Approach to Preserve Optimality in Implementation of Fractional Order PID Controllers Considering Approximation Methods

Preservation of optimal values for a fractional order PID (FOPID) controller design can be a problem in the real-world implementation. This is because a FOPID controller, which has theoretically ideal design in the frequency domain, needs to be implemented by using an approximation method in the real-world. Incorporating the approximation method into the design process can overcome this problem so that optimal design parameters can be preserved in the controller implementation. In this study, an optimal FOPID was designed by incorporating the approximation method into the design process. In addition, for comparison purposes, FOPID controllers were designed without including the approximation method in the design process. The frequency responses obtained for these FOPIDs were compared with those obtained with the ideal FOPIDs. It has been shown that optimal values can be preserved in an implementation with the proposed approach. FOPID controller parameters were obtained using a genetic algorithm for an inverse controller design based on the Bode's ideal transfer function.