By Denis Dochain
Giving an outline of the demanding situations within the keep watch over of bioprocesses, this accomplished booklet provides key leads to quite a few fields, together with: dynamic modeling; dynamic homes of bioprocess versions; software program sensors designed for the online estimation of parameters and nation variables; keep an eye on and supervision of bioprocesses.
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Additional resources for Automatic Control of Bioprocesses (Control Systems, Robotics and Manufacturing)
When N is very large, the increase in the value of the denominator will be proportional to the increase in the value of the objective function Jopt which is typically a sum N of errors, raised to the power of two. 21). We will now concentrate on the methods, which enable the reduction of V . Different approaches have been developed for planning experiments on the basis of covariance matrix V , or equivalently, on the basis of Fisher information matrix F , via the optimization of certain scalar measurements of these matrices [MUN 91]: – A – optimal design criterion: min[tr(F −1 )] – Modified A – optimal design criterion: max[tr(F )] – D – optimal design criterion: max[det(F )] – E – optimal design criterion: max[λmin (F )] – Modified E – optimal design criterion: min λmax (F ) λmin (F ) where λmin (F ) and λmax (F ) are the lowest and the highest eigenvalues of the Fisher information matrix, respectively.
20, pp. 427–434, 1986. [MON 42] J. M ONOD, Recherches sur la Croissance des Cultures Bactériennes, Hermann, Paris, 1942. E. M OSEY, “Mathematical modelling of the anaerobic digestion process: regulatory mechanisms for the formation of short-chain volatile acids from glucose”, Water Science and Technology, vol. 15, pp. 209–232, 1983. [PAV 94] A. PAVÉ, Modélisation en Biologie et en Ecologie, Aléas, Lyon, 1994. [QUE 99] I. Q UEINNEC, D. L ÉONARD and C. B EN YOUSSEF, “State observation for fedbatch control of phenol degradation by R alstonia eutropha”, in Proc.
In theory, validation of a model consists of verifying statistical assumptions: differences between predictions and measurements must follow a normal law of zero average [WAL 97]. Practically, and considering the difficulty of validating in the strictest sense the biotechnological models, we are satisfied with a good visual adequacy. We can possibly reinforce this subjective criterion by an analysis of correlation between predictions and measurements. 7. 1. 2 that the models must be constructed, in such a manner as to respect constraints as positivity of state variables.