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A discrete‐time nonlinear state observer for the anaerobic digestion process
Author(s) -
Chaib Draa K.,
Zemouche A.,
Alma M.,
Voos H.,
Darouach M.
Publication year - 2018
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.4434
Subject(s) - linear matrix inequality , control theory (sociology) , nonlinear system , observer (physics) , bilinear interpolation , mathematics , state (computer science) , state observer , computer science , mathematical optimization , control (management) , algorithm , statistics , artificial intelligence , physics , quantum mechanics
Summary This paper is concerned with the design of an LMI‐based H ∞ discrete‐time nonlinear state observer for an anaerobic digestion model. In presence of disturbances in both the dynamics of the model and the output measurement signals, the proposed observer robustly estimates all state variables including bacteria concentrations, which are costly and difficult to measure. In the goal to increase applicability of the proposed observer for other systems, we present the theoretical results in a general way. First, due to the use of Young's inequality in a convenient way, we get new sufficient conditions, expressed in terms of bilinear matrix inequalities (BMIs), ensuring the H ∞ criterion. Then, to render the BMIs convex, two alternative solutions are proposed, where both lead to linear matrix inequality (LMI) conditions. It is shown analytically and numerically that these two solutions provide less conservative LMI conditions compared to the existing methods in the literature. To validate the proposed methodology on a real‐world model, an application to an anaerobic digestion model is given.