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Bandwidth Based Stability Analysis of Active Disturbance Rejection Control for Nonlinear Uncertain Systems

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Abstract

This paper focuses on the stability analysis of the active disturbance rejection control (ADRC) for a class of uncertain systems. To overcome the difficulty of defining a reasonable Lyapunov function and setting limitations of system parameters, the converse Lyapunov theorem and the disturbance theory are employed. This paper proves that the estimation error of the extended state observer (ESO) and the tracking error of the closed-loop system using ADRC are uniformly ultimately bounded and monotonously diminishing with the increase of their respective bandwidth, so that the stability of the ADRC system could be performed. In order to further illustrate the relationship between the stability range and bandwidths, it analyzes quantitatively the performance of ESO and ADRC based on the root locus and the step response. Finally, an example based on a typical control system is carried out, and simulation results verify the theoretical analysis proved in this paper.

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Authors and Affiliations

  1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Dongyang Zhang, Qinghe Wu & Xiaolan Yao

Authors
  1. Dongyang Zhang
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  2. Qinghe Wu
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  3. Xiaolan Yao
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Corresponding author

Correspondence to Xiaolan Yao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61304026.

This paper was recommended for publication by Editor LIU Yungang.

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Zhang, D., Wu, Q. & Yao, X. Bandwidth Based Stability Analysis of Active Disturbance Rejection Control for Nonlinear Uncertain Systems. J Syst Sci Complex 31, 1449–1468 (2018). https://doi.org/10.1007/s11424-018-7073-4

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  • DOI: https://doi.org/10.1007/s11424-018-7073-4

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