Convergence analysis on a tracking differentiator used in active disturbance rejection control

This paper presents convergence analysis for a tracking differentiator of an active disturbance rejection control method which is widely applied but lacks theoretical analysis. Since a nonlinear piecewise function is used in the tracking differentiator, the convergence analysis is difficult for tracking errors. Convergence proof processes of the tracking differentiator are divided into three situations based on the nonlinear piecewise function. Tracking errors of the tracking differentiator are proved to be uniformly ultimately bounded considering three situations, and relationships between upper bounds of tracking errors and adjustment parameters are founded by a Lyapunov approach, which provides a basis for parameters adjustment. Finally, simulation and experiment results verify the effectiveness of the proposed convergence analysis.