Tuning FOPID controllers for weighted performance degradation in servo/regulatory control operation

In process control, the trade-off between servo and regulatory control has been extensively studied in the context of Proportional-Integral-Derivative (PID) controllers. However, this issue has not been systematically addressed for Fractional-Order PID (FOPID) controllers. In this paper, we highlight the importance of filling this gap, as the servo/regulatory balance strongly affects both performance and robustness in fractional-order control systems. We extend the Weighted Performance Degradation (WPD) methodology, previously developed for PID controllers, to the domain of FOPID controllers. The extension is grounded in three extreme rules: one previously proposed for self-regulating processes and two newly introduced here for integrating and unstable dynamics. These rules serve as limiting cases within the extended WPD framework, enabling its systematic application to FOPID controllers across different process types. The approach enables robust and balanced performance trade-offs, making it broadly applicable to control problems where FOPID controllers are employed.