Gain-analytical equations generalized for FOPID controllers — An application with DC–DC power converters

Abstract

This study presents algebraic formulations for determining the gains of a fractional-order PID (FOPID) regulator, with attention to gain crossover frequency, phase margin, and robustness against gain variations (iso-damping). The differential evolution (DE) algorithm is employed for optimal tuning of fractional-order values, aligned with FOPID gain parameters. FPGA-in-the-loop simulations for Buck and DC–DC Boost converters are conducted to validate the DE-tuned FOPID controllers, optimized using the $L^2$ norm and compared to MATLAB-Simulink simulations. The approach introduces a key innovation: disaggregating the FOPID equation for memory efficiency. Simulations and experiments demonstrate the controller’s precision in setpoint tracking and resilience to load and input voltage variations in Buck and DC–DC Boost converters, with effective damping of load disturbances. A test bench validated the proposed method, which was also compared to conventional PID, Type 3, and PIDD2-IMC controllers. While the proposed FOPID controller performed better in the presented results, a conclusive comparison could not be drawn due to unequal tuning efforts. Future work will focus on a more thorough comparison of controllers.