A Graphical Design Method of Fractional-Order Proportional-Integral Controllers Based on Frequency-Domain Specifications

This study presents a graphical method for tuning fractional-order proportional-integral (FOPI) controllers for fractional-order plus time-delay systems. The gain crossover frequency, phase crossover frequency, and phase margin are selected as frequency-domain specifications to formulate the constraint equations of FOPI controller parameters. To avoid complicated mathematical calculations, these equations are converted into explicit equations using two theorems. Then, the graphical solution for the FOPI controller can be easily found. A practical fractional-order process is taken as an example. The simulation results show that this approach is simpler and more flexible than existing methods.