Absolute stability analysis of non-linear active disturbance rejection control for single-input-single-output systems via the circle criterion method

作者：Li Jie; Xia Yuanqing^*; Qi Xiaohui; Gao Zhiqiang; Chang Kai; Pu Fan

来源：IET Control Theory and Applications, 2015, 9(15): 2320-2329.

DOI：10.1049/iet-cta.2015.0320

• nonlinear control systems
• asymptotic stability
• absolute stability analysis
• nonlinear active disturbance rejection control
• single-input-single-output systems
• circle criterion method
• ADRC
• linear plant
• Lurie system
• local asymptotic stability
• nonlinear ADRC system
• nonlinear plant
• Taylor expansion
• time domain stability analysis method
• graphical interpretation
• frequency domain

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.

• 出版日期2015-10-8
• 单位北京理工大学