Modellbildung und Modellreduktion für Prozesse der Chemischen Verfahrenstechnik
Modeling and Model Reduction for Chemical Engineering Processes
Chemical engineering processes usually are strongly nonlinear; they are modeled either by high order systems of ordinary differential equations or by partial differential equations. Modern state space control methods on the other hand can reasonably be applied only to linear systems of low to medium order. Hence techniques are required which allow to approximate the behaviour of high order non-linear models within a certain range of operating conditions by low order linear models.
Two different methods of model reduction are discussed. The model of a three component distillation column with side stream products is reduced by means of a least squares approximation to its transient temperature response. The model for a catalytic fixed bed reactor is reduced by non-equidistant discretization of the spatial derivatives and linearization of the resulting system of ordinary differential equations. In both cases the resulting linear models contain only a few temperatures as the "reduced states" of the system. Cases, where this kind of model reduction fails are briefly discussed.
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