Complex-Order Fractional Proportional–Resonant Controller for High-Frequency Applications

This article presents the design and implementation of a complex-order fractional proportional–resonant (COFPR) controller. The proposed COFPR controller is an evolution of the fractional proportional–resonant (FPR) controller suitable for high-frequency tracking. The best performance of the COFPR controller is obtained by reducing the excitation region promoted by FPR controllers and proportional–resonant (PR) controllers. The COFPR controller is analyzed in the frequency domain. For comparison purposes, proportional–resonant with harmonic compensator, FPR, and COFPR controllers are designed for the current regulation of a voltage-source converter. They are compared considering the same controller gain tuning criteria and the same phase margin. A set of simulations and experimental results on a 3.6-kVA gallium nitride inverter is discussed. The proposed COFPR controller performs superiorly at high frequencies when the same gains for the controllers are used. The COFPR controller can reduce excitation regions in PR controllers tuned with a similar phase margin without losing close tracking capability. This advantage promotes the COFPR controller as a proper alternative regarding program memory and execution time required, as it can be properly implemented within a specific frequency range by an approximation of third or fourth order.