Written Paper

Optimal control of biomass selection from the apparatus  [2017]

Kozhevnikov, Yu.E. Sukhanova, N.V., Voronezh State Univ. of Engineering Technologies (Russian Federation)

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Variant of solving problem of biomass selection optimal control from apparatus using Pontryagin maximum principle is presented. Device's maximum productivity was chosen as optimality criterion. On a finite-dimensional space the Pontryagin function, the Hamiltonian function, and the end function were defined. To describe the dynamics of the development of the yeast population, the Ferhulst-Gause equation was used. It is proved that optimal control (in the chosen criterion) is possible with the found ratios of the coefficient of natural growth epsilon and the coefficient beta taking into account the intraspecies competition of microorganisms. To determine the optimal concentration of microorganisms and the biomass selection value, it is necessary to determine the numerical values of the coefficients of the model epsilon and beta during the cultivation process. The method for determining the model coefficients and the optimal biomass selection from the apparatus was presented. The algorithm and the system for optimal control of the selection of biomass from the apparatus were developed. They differ in that here found theoretical relationships of the named coefficients are used. To study the optimal control system, a computer experiment was carried out using experimental data on the hourly accumulation of microorganisms taken at the Voronezh yeast plant. The data were obtained for a 13-hour culturing process with selection of the culture medium after 6 h. The
selection is conducted in such a way that the accumulation (yeast concentration) of X during sampling remains unchanged with a constant culture medium selection. I.e. the volume of biomass equal to the volume of the medium supplied with the feeding is taken. The graphs of the hourly change in yeast concentration and the dynamics of selection were obtained. The results of analysis show that the use of such a system in the process of controlling yeast production makes it possible to shorten the cultivation duration by 1 h.