The active disturbance rejection control for nonlinear systems using time-varying-gain

The active disturbance rejection control, as a new control strategy in dealing with the large uncertainties, has been developed rapidly in the last two decades. Basically, the active disturbance rejection control is composed of three main parts: the differential tracking; the extended state observer; and the extended observer-based feedback control. In these three parts, the extended state observer plays a crucial role toward the active disturbance rejection control. The most of the extended state observers are based on the constant high gain parameter tuning which results inherently in the peaking problem near the initial time, and at most the attenuation effect for the uncertainty. In this paper, a time-varying-gain extended state observer is proposed for a class of nonlinear systems, which is shown to reject completely the disturbance and to avoid effectively the peaking phenomena by the proper choice of the gain function. The convergence of the extended state observer for the open-loop system is independently proved. The convergence for the closed-loop system which is based on the extended state observer feedback is also presented. Examples and numerical simulations are used to illustrate the convergence and the peaking diminution.