Fractional-order hybrid 2-DOF PID control with a complex basis: A novel framework for MIMO systems

This study presents a new hybrid fractional two-degree-of-freedom (2DOF) proportional–integral–derivative (PID) controller designed for nonlinear multiple-input multiple-output (MIMO) systems. This innovative control strategy merges fractional calculus with a 2DOF PID controller, resulting in a hybrid approach that improves transient response, tracking accuracy, and disturbance rejection, while keeping low control effort. A notable feature of this approach is the use of complex basis functions, offering a robust and adaptable framework for optimizing controller performance across multiple interacting subsystems. Furthermore, the suitability of the proposed controller for nonlinear MIMO processes increases its applicability in real-world industrial settings. The findings of this research demonstrate the effectiveness of the proposed method in tackling challenges related to coupled nonlinear MIMO systems.