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

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 theo...

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Bibliographic Details
Published in:Journal of systems science and complexity 2018-12, Vol.31 (6), p.1449-1468
Main Authors: Zhang, Dongyang, Wu, Qinghe, Yao, Xiaolan
Format: Article
Language:English
Subjects:
Active control
Complex Systems
Control
Control stability
Liapunov functions
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear control
Nonlinear systems
Operations Research/Decision Theory
Perturbation theory
Rejection
Root locus
Stability analysis
State observers
Statistics
Step response
Systems Theory
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Summary: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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-018-7073-4