Abstract
For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process.
Highlights
Theoretical aspects for the practical application of adaptive control systems that operate in unknown, nonlinear, and time-varying biotechnological environments are still to be developed, investigated and implemented
The Food and Drug Administration (FDA) have stated that “the goal of ProcessAnalytical Technology (PAT) is to understand and control the manufacturing processes, which is consistent with our current drug quality system: quality cannot be tested into products, it should be built-in or should be by design” [1]
The maximum substrate consumption profile is found by performing fed-batch cultivation with feeding carried out in portions; the subsection describes the motivation for gray box model selection and its probabilistic assumptions; the third subsection contains the derivation of the optimization criterion for model fitting; the fourth subsection exposes the relationship of this study’s numerical routines to the convex pathway, which is inherited from physical applications; and the fifth subsection describes the implementation of the numerical algorithm to identify the gray box model parameters
Summary
Theoretical aspects for the practical application of adaptive control systems that operate in unknown, nonlinear, and time-varying biotechnological environments are still to be developed, investigated and implemented. This work is an example of how ME helps to develop high-speed numerical semi-global optimization routines for a multivariate problem of gray box model fitting. The maximum substrate consumption profile is found by performing fed-batch cultivation with feeding carried out in portions; the subsection describes the motivation for gray box model selection and its probabilistic assumptions; the third subsection contains the derivation of the optimization criterion for model fitting; the fourth subsection exposes the relationship of this study’s numerical routines to the convex pathway, which is inherited from physical applications; and the fifth subsection describes the implementation of the numerical algorithm to identify the gray box model parameters. The fourth section consists of experimental analysis: a practical illustration of bioprocess reproducibility and controllability achievement; an assessment of goodness of fit to dataset, acquired from a third party; and sensitivity analysis of the numerical routines to the seed values of initial parameters, which shows the practically beneficial outcome of the convex outlook in this work
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