Data-Driven Design of Fractional-Order PID Controllers: Optimization of Robust Servo-Regulator Performance

This study proposes a data-driven optimal robust design methodology for a fractional-order proportional-integral-derivative (FOPID) controller. This methodology concurrently determines the parameters of the FOPID controller and reference model under a stability-margin constraint by utilizing only one-shot input-output data. The stability margin, which is quantitatively defined as the maximum value of the sensitivity function, is specified by the designer. This approach ensures a balanced design based on the trade-off between robust stability and servo or regulator performance at a given robust-stability level. Numerical examples substantiate the superiority of the FOPID controller over the conventional integer-order proportional-integral-derivative controller.