Data-Driven Robust Servo-Regulator Trade-Off Design of Fractional-Order PID Controllers in the Frequency Domain

Abstract

PID controllers are widely used in industrial applications; however, achieving a balance between robustness and control performance, particularly between servo and regulator functions, remains challenging. This paper presents a data-driven PID controller design methodology that addresses these tradeoffs in the frequency domain. Robustness is quantified and constrained via the sensitivity function, allowing direct specification of a desired stability margin. Within this constraint, controller parameters are optimized to improve tracking performance while explicitly considering the trade-off between reference tracking (servo) and disturbance rejection (regulator). The framework applies to conventional integer-order PID controllers and is further extended to the proposed fractional-order PID controllers, thereby providing additional degrees of freedom for dynamic shaping. Numerical simulations show that the method systematically balances robustness, tracking, and disturbance rejection, achieving superior performance compared with conventional PID designs.