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Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1449–1468 | Cite as

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

  • Dongyang Zhang
  • Qinghe Wu
  • Xiaolan Yao
Article
  • 11 Downloads

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.

Keywords

Active disturbance rejection control (ADRC) bandwidth converse Lyapunov theorem disturbance theory nonlinear uncertain systems stability 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina

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