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.
Highlights
A process carried out in a bioreactor can be defined as a set of m biochemical reactions involving n components with n ≥ m
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
The paper presents a distribution-based identification procedure for offline estimation of yield coefficients in a baker’s yeast bioprocess. This procedure is a functional type method, which transforms a differential system of equations to an algebraic system in unknown parameters
Summary
A process carried out in a bioreactor can be defined as a set of m biochemical reactions involving n components with n ≥ m. The parameter identification of deterministic nonlinear continuous-time systems NCTSs , modelled by polynomial-type differential equations has been considered by numerous authors 13, 14. They use the modulating functions as a sum of sinusoids, whose fundamental period has a fixed length, to convert differential equations into an algebraic form in the frequency domain. These methods can be applied only if the NCTS is exactly integrable.
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