On the Bandwidth of the Extended State Observer

In this paper, a quantitative lower bound to the bandwidth of the extended state observer (ESO) used in the active disturbance rejection control (ADRC) is given for a class of second-order nonlinear uncertain systems with unknown gain b of control input. Then, it is proved that the closed-loop systems are stable and have satisfied dynamic tracking performance under the above quantitative lower bound condition of ESO bandwidth. Furthermore, based on the theoretical results, the relationship between the parameter $\hat b$ of ADRC, which is an estimation for unknown gain b, and the dynamic performance of the closed-loop systems is discussed. The simulation results are provided to show the significance of the theoretical results.