Premium
Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective
Author(s) -
AguilarIbañez Carlos,
SiraRamirez Hebertt,
Acosta José Ángel
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3812
Subject(s) - control theory (sociology) , tracking error , perturbation (astronomy) , lyapunov stability , lyapunov function , exponential stability , stability (learning theory) , convergence (economics) , mathematics , computer science , control (management) , nonlinear system , physics , quantum mechanics , artificial intelligence , machine learning , economics , economic growth
Summary In this work, we introduce a simple stability analysis to justify, under some suitable assumptions, the active disturbance rejection control method, used in the feedback regulation of a substantially uncertain plant. A criterion is obtained that allows us to define under what conditions closed‐loop stability can be assured. When the plant is mostly unknown, the criterion allows us to guarantee exponential convergence for the output‐feedback regulation problem, in the presence of a constant external perturbation, and practical stability when the external perturbation and the tracking reference signal are both time‐varying. In the latter case, the confinement error can be made as small as desired. To carry out the corresponding stability analysis, we derive the tracking error equation, and the observation error equation. To decouple these error equations, we use the Sylvester equation. Finally, we applied the direct Lyapunov method to analyze the corresponding convergence of the observation error and of the tracking error. Copyright © 2017 John Wiley & Sons, Ltd.