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

Huixia Zhang; Yan Liang; Haiyan Cheng

doi:10.1016/j.isatra.2023.07.005

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

ISA Trans. 2023 Oct:141:392-400. doi: 10.1016/j.isatra.2023.07.005. Epub 2023 Jul 10.

Authors

Huixia Zhang¹, Yan Liang², Haiyan Cheng³

Affiliations

¹ School of Automation, Northwestern Polytechnical University, Xi'an, 710072 China. Electronic address: zhanghuixia@mail.nwpu.edu.cn.
² School of Automation, Northwestern Polytechnical University, Xi'an, 710072 China. Electronic address: liangyan@nwpu.edu.cn.
³ School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China. Electronic address: chenghaiyan@stu.xjtu.edu.cn.

PMID: 37481440
DOI: 10.1016/j.isatra.2023.07.005

Abstract

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.

Keywords: Active disturbance rejection control; Convergence; Lyapunov approach; Tracking differentiator.