Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (6): 1563-1573.doi: 10.23919/JSEE.2024.000077

• CONTROL THEORY AND APPLICATION • Previous Articles    

On stability analysis of nonlinear ADRC-based control system with application to inverted pendulum problems

Jie LI1,2(), Yuanqing XIA1,2,*()   

  1. 1 School of Automation, Beijing Institute of Technology, Beijing 100081, China
    2 Intelligent Multi-source Sensing and Fusion Innovation Research Center, Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314019, China
  • Received:2023-05-30 Accepted:2023-05-30 Online:2024-12-18 Published:2025-01-14
  • Contact: Yuanqing XIA E-mail:lijienewlife@bit.edu.cn;xia_yuanqing@bit.edu.cn
  • About author:
    LI Jie was born in 1988. He received his B.E., M.E. and Ph.D. degrees from the Department of Unmanned Aerial Vehicle Engineering, Mechanical Engineering College, Shijiazhuang, China, in 2010, 2012, 2016, respectively. Currently he is a associate research fellow at Yangtze Delta Region Academy of Beijing Institute of Technology. His research interests cover process control, flight control of UAV, cooperative control and intelligent decision making of UAVs swarm, theory and application of active disturbance rejection control. E-mail: lijienewlife@bit.edu.cn

    XIA Yuanqing was born in 1971. He received his M.S. degree in fundamental mathematics from Anhui University, Hefei, China, in 1998 and Ph.D. degree in control theory and control engineering from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2001. Currently he is a professor in Beijing Institute of Technology. His research interests are in the fields of networked control systems, robust control and signal processing, active disturbance rejection control. E-mail: xia_yuanqing@bit.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (61836001).

Abstract:

This paper mainly focuses on stability analysis of the nonlinear active disturbance rejection control (ADRC)-based control system and its applicability to real world engineering problems. Firstly, the nonlinear ADRC(NLADRC)-based control system is transformed into a multi-input multi-output (MIMO) Lurie-like system, then sufficient condition for absolute stability based on linear matrix inequality (LMI) is proposed. Since the absolute stability is a kind of global stability, Lyapunov stability is further considered. The local asymptotical stability can be determined by whether a matrix is Hurwitz or not. Using the inverted pendulum as an example, the proposed methods are verified by simulation and experiment, which show the valuable guidance for engineers to design and analyze the NL ADRC-based control system.

Key words: active disturbance rejection control (ADRC), stability analysis, linear matrix inequality (LMI), inverted pendulum system