Fractional Order Active Disturbance Rejection Controller for First Order Plus Time Delay Systems

This paper proposes a modified fractional order active disturbance rejection controller (MFOADRC) for the first order plus time delay systems. To improve the disturbance rejection ability, the model-based extended state observer with model informations is structured. The mathematical derivation and frequency-domain analysis verify that the proposed control system satisfies the separation principle. The foundational of separation principle and Bodes ideal transfer function plus time delay generate the fractional order feedback controller, which consists of a fractional order operator and a PI controller. A frequency-domain tuning method based on gain crossover frequency and phase margin is given to calculate the fractional order controller (FOC). A systematic and complete frequency-domain analysis method is introduced to reveal the disturbance rejection and noise suppression abilities of MESO, open-loop frequency characteristic, closed-loop frequency characteristic, disturbance rejection and noise suppression abilities of closed-loop system, and robustness to plant gain variations. Simulation illustrations for lag-dominant plant, lag-delay balanced plant and delay-dominant plant, using the proposed MFOADRC are presented to demonstrate the significant performance improvement, especially for ramp load disturbances rejection ability, over timedelay active disturbance rejection controller and fractional filter fractional order PID.