Modeling of Biological Systems with Time Delays.
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Unlike chemical reactor dynamics, microbial behavior depends not only on the present state of the environment surrounding a microorganism but, more importantly, on its past history, as well. Herein lies a major obstacle in the modeling of a biological process with a simple set of equations. By incorporating a culture's past history in the form of a time- delay kernel, a novel approach to bioprocess identification and modeling is formulated. A time delay kernel is included in the state equations, and a generalized method the mathematical simplification via the transformation of an integro-differential equation to a set of first order ODE's is developed. The resulting model possesses the combined advantages of the simplicity of an unstructured, lumped-parameter model and the power of a complex structured model. The experimental determination of the kernel will be discussed, with an emphasis on the on-line parameter estimation, control, and optimization of a biochemical reactor.