Extended state observer for uncertain lower triangular nonlinear systems

The extended state observer (ESO) is a key part of the active disturbance rejection control approach, a new control strategy in dealing with large uncertainty. In this paper, a nonlinear ESO is designed for a kind of lower triangular nonlinear systems with large uncertainty. The uncertainty may come from unmodeled system dynamics and external disturbance. We first investigate a nonlinear ESO with high constant gain and present a practical convergence. Two types of ESO are constructed with explicit error estimations. Secondly, a time varying gain ESO is proposed for reducing peaking value near the initial time caused by constant high gain approach. The numerical simulations are presented to show visually the peaking value reduction. The mechanism of peaking value reduction by time varying gain approach is analyzed.