AN IMPROVED ALGORITHM FOR SINGULAR CONTROL PROBLEMS WITH APPLICATION TO THE OPTIMIZATION OF THE FED-BATCH PENICILLIN FERMENTATION
Abstract
An easy-to-use software package for the solution of optimal control problems with control variable and terminal state variable constraints was developed. A conjugate gradient method is used for non-singular problems and a modified conjugate gradient method was developed for singular problems. Penalty functions are used to force satisfaction of the terminal constraints. The modified method required up to 50% less computer time than the unmodified method to solve the singular problems being considered. This is apparently due to the modified algorithm forcing the switching function to stay nearer zero than the standard conjugate gradient method does. Studies were done of the optimal feeding policies for three fed-batch penicillin production models. One structured and two unstructured models were studied. Also studied were the effects of substrate feed concentration (S(,F)), initial volume (V(,0)), and batch time (t(,f)) on productivity and titer. The effect on the optimal profile of the form used to model penicillin production and the use of optimal feeding policies for model discrimination and evaluation were also examined. Penicillin titers were found to be directly proportional to S(,F). Optimal batch times, on either a maximum titer or maximum productivity basis, increased with decreasing V(,0), and the optimal batch times based on productivity were generally shorter than those based on titer. Results obtained at small V(,0) (relative to fermentor volume) are questionable as the models predict achievement of higher cell concentrations (> 100 g/l) than typically seen in practice. Structured model results for optimal productivity indicate an overproduction of penicillin producing cell mass, a result of an overproduction of hyphae tips. This gives an overly high estimate of penicillin productivity. Differences seen in the optimal control and state variable profiles for the various models indicate the suitability of optimal control studies for model discrimination.
Degree
Ph.D.
Subject Area
Chemical engineering
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