Linear Active Disturbance Rejection Control with a Fractional-Order Integral Action

Linear active disturbance rejection control (LADRC) is a powerful control structure thanks to its performance in uncertainties, internal and external disturbances estimation and cancelation. An extended state observer (ESO) based controller is the key to the LADRC method. In this article, the LADRC scheme combined with a fractional-order integral action (FOI-LADRC) is proposed to improve the robustness of the standard LADRC. Using the robust closed-loop Bode’s ideal transfer function (BITF), an appropriate pole placement method is proposed to design the set-point tracking controller of the FOI-LADRC scheme. Numerical simulations and experimental results on a cart-pendulum system will illustrate the effectiveness of the proposed FOI-LADRC scheme for the disturbance rejection, the set-point tracking and the improved robustness. To illustrate the LADRC control schemes and to verify the performance of the proposed FOI-LADRC, compared to the standard LADRC and IOI-LADRC structures, two tests will be carried out. First, simulation tests on an academic example will be presented to show the effect of the different parameters of the control law on the performance of the closed-loop system. Then, these three control structures are implemented on an experimental test bench, the cart-pendulum system, to show their efficiency and to show the superiority of the proposed method compared to the two other structures.