Two on-line adaptive optimization algorithms based on input-output model identification were in simulation study applied to a high-cell-density culture of yeast for ethanol production. The model system consisted of a continuous bioreactor and a membrane filter unit for cell recycle. The objective of optimization was to maximize the ethanol productivity by manipulating dilution rate at a fixed bleeding ratio.
In one of the two algorithms tested the bilevel forgetting factor (BFF) method was used for model parameter estimation(or model identification) and in the other the regularized constant-trace method. Both parameter estimation methods are modified versions of the recursive least squares method. During the course of optimization new values of the dilution rate were recurrently determined based on results of the model parameter estimation by using the steepest ascent method.
Two cases were investigated: the bleeding ratio is 0.03 and 0.10. The BFF algorithm showed a good optimization speed and accuracy when the ratio is 0.10. However, when the bleeding ratio is 0.03, which is unrealistically low, and the operation was started with a dilution rate higher than the optimum the algorithm could not effectively drive the process to the optimum steady state probably due to a increased capacity of the system. The regularized constant-trace algorithm showed a very poor parameter estimation capability and failed to optimize the process.
The long-term stability of the BFF method was tested. The process was stably maintained at the optimum point for an extended period of time up to 3000 hours, although the tendency of "estimator wind-up" was monotonically increasing with time. This estimator instability phenomenon is one of the major problems to be solved in the future study.