On the stability of active disturbance rejection control for first-order plus delay time processes

Abstract The paper presents a stability analysis of a closed-loop system with an active disturbance rejection control (ADRC) algorithm and a reduced-order extended state observer (RESO). The controller is designed for first-order plus delay time processes, and one of the input signals to the RESO is delayed to compensate for the effect of the system delay. If the process delay is known, perfect synchronization between the observer input signals can be achieved. In a more realistic case, the process delay is not precisely known, and the resulting imperfect synchronization may lead to instability of the closed-loop system. The perfect synchronization case shows that the closed-loop system can be stabilized for any delay. For the imperfect synchronization case, delay-dependent stability conditions are derived for a simple tuning method.