A Weighted Fractional Order PID Controller for Nonlinear Systems with Variable Delay

This paper presents a Weighted Fractional Order PID (WFO-PID) controller that enhances the conventional Fractional Order PID (FOPID) structure by introducing explicit weighting factors for the tuning terms. These weights, combined with fractional orders and gain parameters, provide greater flexibility in tuning, enabling for more precise control over system dynamics. The proposed controller is applied to a mixing tank process with variable time delay, a representative case of industrial processes with challenging dynamics. Its performance is benchmarked against both PID and FOPID controllers, demonstrating improved reference tracking and disturbance rejection, particularly under varying delay conditions and noise in the transmitter. The findings highlight the WFO-PID method’s efficiency in managing intricate control situations.