On Convergence of Nonlinear Active Disturbance Rejection Control for SISO Nonlinear Systems

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• 作者：Zhi-Liang Zhao ; Bao-Zhu Guo
• 关键词：Nonlinear system ; Lyapunov stability ; Feedback stabilization ; Robust design ; 93C15 ; 93B52 ; 34D20 ; 93D15 ; 93B51
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：22
• 期：2
• 页码：385-412
• 全文大小：1,034 KB
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• 作者单位：Zhi-Liang Zhao (1)
  Bao-Zhu Guo (2) (3)
  
  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, Shaanxi, People’s Republic of China
  2. Key Laboratory of System Control, Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190, People’s Republic of China
  3. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Wits, 2050, Johannesburg, South Africa
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

The active disturbance rejection control (ADRC) was proposed by Jingqing Han in the late 1990s, which offers a new and inherently robust controller building block that requires very little information of the plant. Originally, the proposal was based largely on experiments with numerous simulations on various systems of different nature. Later, the effectiveness of the control strategy has also been demonstrated in many engineering applications such as motion control, web tension regulation, and chemical processes. However, many theoretical issues, including its applicability in stabilization, output regulation remain unanswered. In this paper, we consider the nonlinear ADRC for general single input single output nonlinear systems subject to dynamical and external uncertainties. We establish conditions that guarantee the ADRC achieving closed-loop system practical stability, disturbance attenuation, and practical reference tracking. Rigorous proofs are given to show the convergence of the variables. The peaking value reduction and high-frequency noise filtering by combination of the time-varying gain in the initial stage and the constant high gain afterwards are explained by linear ADRC. Illustrative examples are also provided. Keywords Nonlinear system Lyapunov stability Feedback stabilization Robust design