New fractional-order LADRC scheme based on a novel filtered-Bode’s ideal transfer function for integer-order systems

Abstract

In this paper, a new Fractional-Order Linear Active Disturbance Rejection Control scheme (FO-LADRC) is proposed to enhance the robustness against loop gain variations of the standard Active Disturbance Rejection Control (ADRC) in the case of uncertain integer-order systems. A new filtered Bode’s ideal transfer function (F-BITF) is proposed to be used as a reference model in the design approach of the proposed control scheme to ensure the dynamic behavior of the closed-loop BITF to the controlled system. A Fractional-order Extended State Observer (F-ESO) is used in the proposed FO-LADRC structure to approximate the system to be controlled by a filtered fractional-order integrator. The fractional order of the F-ESO is a design parameter to tune to achieve the desired overshoot of the closed-loop step response. For the tuning of FO-LADRC structure, an analytical method is proposed. The performance of the proposed FO-LADRC and the Chen’s et al. FO-ADRC structures are evaluated thorough numerical simulation, and then validated in practice in the case of a Cart-Pendulum. Both the simulation and the experimental results show that the proposed FO-LADRC is able to achieve the desired dynamics of the F-BITF and guarantee the robustness with respect to the controller gain variation and the system parameter uncertainties. The comparative study conducted also reveals that the proposed control scheme is more robust than that of Chen.