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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 789156, 21 pages
http://dx.doi.org/10.1155/2012/789156
Research Article

Distribution-Based Identification of Yield Coefficients in a Baker’s Yeast Bioprocess

Department of Automatic Control, University of Craiova, A.I. Cuza 13, 200585 Craiova, Romania

Received 24 August 2011; Revised 16 November 2011; Accepted 30 November 2011

Academic Editor: Alexander Pogromsky

Copyright © 2012 Dorin Sendrescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A distribution-based identification procedure for estimation of yield coefficients in a baker’s yeast bioprocess is proposed. This procedure transforms a system of differential equations to a system of algebraic equations with respect to unknown parameters. The relation between the state variables is represented by functionals using techniques from distribution theory. A hierarchical structure of identification is used, which allows obtaining a linear algebraic system of equations in the unknown parameters. The coefficients of this algebraic system are functionals depending on the input and state variables evaluated through some test functions from distribution theory. First, only some state equations are evaluated throughout test functions to obtain a set of linear equations in parameters. The results of this first stage of identification are used to express other parameters by linear equations. The process is repeated until all parameters are identified. The performances of the method are analyzed by numerical simulations.