Chapter

Computer Applications in Fermentation Technology: Modelling and Control of Biotechnological Processes

pp 367-371

Sensitivity Analysis in Static Optimization of Fermentation Plants

  • C. PostenAffiliated withArbeitsbereich Regelungstechnik und Systemdynamik, TU Hamburg-Harburg

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Abstract

For static optimization of plants a set of optimal inputs u * has to be found minimizing a cost criterion J(x,u,p) under the constraints of model equations f(x,u,p) = 0. These inputs may be design values like volume ratios or easy to control values like feeding rates. But in biotechnology several difficulties may occur [1]. Firstly, the model parameters p are uncertain. For example, during scaling-up a pilot plant has to be designed on the basis of physiological parameters that have been identified only by a few experiments on the laboratory scale. Secondly, some inputs are not as precisely realizable as they should be, like feeding rates that are controlled by up-stream processes. Thirdly, the cost function contains terms that are not exactly known at the time of planning, such as the costs of raw materials or proceeds from products. Nevertheless, it is desirable to make statements about optimal working conditions. This can be achieved by calculating the minimum of the cost criterion
$${{\rm{J}}^*}( \in ) = \mathop {\min }\limits_u {\rm{J}}(x,u,p, \in )$$
as a function of disturbances . For each an optimal u * () has to be computed. Here three different ways to find these functions are discussed.