Optimal nonsingular control of fed‐batch fermentation

Presented is a new simple method for multidimensional optimization of fed‐batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau–Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.

[1]  H C Lim,et al.  General characteristics of optimal feed rate profiles for various fed‐batch fermentation processes , 1986, Biotechnology and bioengineering.

[2]  H C Lim,et al.  Simple nonsingular control approach to fed‐batch fermentation optimization , 1989, Biotechnology and bioengineering.

[3]  J Hong,et al.  Optimal substrate feeding policy for a fed batch fermentation with substrate and product inhibition kinetics , 1986, Biotechnology and bioengineering.

[4]  H. Lim,et al.  Optimization of biphasic growth of Saccharomyces carlsbergensis in fed‐batch culture , 1989, Biotechnology and bioengineering.

[5]  Tsuneo Yamane,et al.  Start‐up of chemostat: Application of fed‐batch culture , 1979 .

[6]  A Constantinides,et al.  Optimization of batch fermentation processes. I. Development of mathematical models for batch penicillin fermentations. , 1970, Biotechnology and bioengineering.

[7]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[8]  T. Takamatsu,et al.  Optimal control of a semibatch fermentation , 1976, Biotechnology and bioengineering.

[9]  M. Reuss,et al.  Evaluation of feeding strategies in carbon‐regulated secondary metabolite production through mathematical modeling , 1981 .

[10]  Tsuneo Yamane,et al.  Fed-batch techniques in microbial processes , 1984 .

[11]  G Stephanopoulos,et al.  Optimization of fed‐batch penicillin fermentation: A case of singular optimal control with state constraints , 1989, Biotechnology and bioengineering.

[12]  Satish J. Parulekar,et al.  Modeling, optimization and control of semi-batch bioreactors , 1985 .

[13]  L Cazzador,et al.  On the optimal control of fed‐batch reactors with substrate‐inhibited kinetics , 1988, Biotechnology and bioengineering.

[14]  A. Johnson,et al.  The control of fed-batch fermentation processes - A survey , 1987, Autom..

[15]  Costas J. Spanos,et al.  Advanced process control , 1989 .

[16]  H. Lim,et al.  Computational algorithms for optimal feed rates for a class of fed‐batch fermentation: Numerical results for penicillin and cell mass production , 1986, Biotechnology and bioengineering.

[17]  W. A. Knorre,et al.  Optimal substrate profile for antibiotic fermentations , 1981 .