Open AccessAbsolute stability analysis of non‐linear active disturbance rejection control for single‐input–single‐output systems via the circle criterion method
Author(s) -
Li Jie,
Xia Yuanqing,
Qi Xiaohui,
Gao Zhiqiang,
Chang Kai,
Pu Fan
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0320
Subject(s) - control theory (sociology) , stability (learning theory) , linear system , circle criterion , mathematics , taylor series , active disturbance rejection control , exponential stability , computer science , nonlinear system , control (management) , mathematical analysis , artificial intelligence , quantum mechanics , machine learning , physics , state observer
This study focuses on the stability analysis of non‐linear active disturbance rejection control (ADRC) for single‐input–single‐output systems. Firstly, a non‐linear ADRC system for a linear plant is transformed into a Lurie system. Secondly, two extended circle criteria are obtained, and two numerical examples are presented to illustrate the absolute stability analysis, including both stable and unstable linear plants. Thirdly, local asymptotic stability of a non‐linear ADRC system for a non‐linear plant is also performed through linearisation by Taylor expansion. Finally, a comparison with the existed processing methods is further made, including the describing function method and time domain stability analysis method. It can be concluded that the circle criterion method is more convenient and practical for its frequency domain and graphical interpretation. The circle criterion method can also be extended to the stability analysis of a control system which applies linear ADRC to a plant with one non‐linear term.