On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis

Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively f...

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Bibliographic Details
Published inInternational journal of control Vol. 90; no. 10; pp. 2085 - 2097
Main Authors Shao, S., Gao, Z.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.10.2017
Taylor & Francis Ltd
Subjects
Active control
Active disturbance rejection control
Control stability
Control theory
Errors
extended state observer
Feedback loops
Perturbation methods
Rejection
Singular perturbation
singular perturbation theory
Stability analysis
State observers
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Summary:Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1236217