On the absolute stability of nonlinear ADRC for SISO systems

This paper concerns with the condition for absolute stability of nonlinear active disturbance rejection control (ADRC) for SISO systems. Firstly, a nonlinear ADRC system for a linear plant is transformed into the form of a Lurie system, for which the off-axis circle criterion is applied and a sufficient condition is obtained. Furthermore, for comparison, the circle criterion and Popov criterion are also applied, leading to the conclusion that the off-axis circle criterion method is more convenient and practical in some case, because it is based on frequency domain, graphical interpretation and it is less conservative. The proposed methods can also be extended to the stability analysis of a control system which applies linear ADRC to a plant with one nonlinear term.