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.

本文介绍了具有主动抗扰控制 (ADRC) 算法和降阶扩展状态观测器 (RESO) 的闭环系统的稳定性分析。该控制器设计用于一阶加延迟时间过程，并且对 RESO 的一个输入信号进行延迟以补偿系统延迟的影响。如果过程延迟已知，则可以实现观察器输入信号之间的完美同步。在更现实的情况下，过程延迟并不精确，由此产生的不完美同步可能导致闭环系统不稳定。完美的同步案例表明闭环系统可以在任何延迟下保持稳定。对于不完美同步的情况，为简单的调谐方法推导出延迟相关的稳定性条件。