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On the optimal control of fed‐batch reactors with substrate‐inhibited kinetics
Author(s) -
Cazzador Lorenzo
Publication year - 1988
Publication title -
biotechnology and bioengineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.136
H-Index - 189
eISSN - 1097-0290
pISSN - 0006-3592
DOI - 10.1002/bit.260310707
Subject(s) - substrate (aquarium) , biomass (ecology) , optimal control , arc (geometry) , constant (computer programming) , sequence (biology) , index (typography) , mathematics , control (management) , control theory (sociology) , chemistry , process engineering , computer science , mathematical optimization , engineering , biology , biochemistry , ecology , geometry , artificial intelligence , world wide web , agronomy , programming language
The optimal feed rate profiles, for fed‐batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the “turnpike property” of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.