(136c) Development of Fuzzy Dynamic Models: Application to Polymerization Systems
AIChE Spring Meeting and Global Congress on Process Safety
Tuesday, April 25, 2006 - 2:25pm to 2:50pm
The process of polymerization possess a sufficiently complex behavior, characterized for nonlinear dynamic and many times impracticable a reliable model to be shaped. Thus, precise dynamics models of the process become increasingly difficult to be derived and solved as process complexity increases and need to be considered to achieve predictive models for a broad range of conditions. This may lead to limitations and difficulties in the development and implementation of control strategies in chemical plants, especially when polymerization reactor are considered. However, nowadays the requirements for high and safe operational performance together with the need to achieve the product with desired quality demand for the plant to be operated under control. In order to develop a suitable control strategy, is necessary to have a model which should be at same time easy to solve and robust enough to capture the process dynamics. Full detailed deterministic models are not taillored to be used as internal control model, so that an alternative approach is welcome. In this work a cognitive approach based on fuzzy concepts is proposed, considering both linguistic and mathematical functional representation. The approach allows to take into account both quantitative and qualitative informations which lead the mathematical representation to accomodate the main process features. It has to be beared in muid that the proposed approach has advantage compared to artificial neural network since beyond the nonlinear behavior qualitative data are also considered in the model building. Fuzzy modelling methods plough an alternative to solve these problems, since for the attainment of the models an internal dynamic knowledge of the process is not necessary but only given of input/output. The solution copolymerization of methyl methacrylate and vinyl acetate in a continuous stirred tank reactor is used to illustrate the cognitive model development. The kinetic parameters and reactor operating conditions are obtained from the literature. A mathematical model is considered as plant for data generation. Cognitive Model Development: The system consists of seven entrances and four exits. Factorial design was used to discriminate the process variables with higher impact on the process performance (effects) and they are used to built up a dynamic model based on the functional fuzzy relationship of Takagi-Sugeno type. Consequence functions are obtained through an optimization problem solved by a least square based algorithm. Gaussian membership functions are used for the cognitive sets and subtractive clustering method supplied the parameters of the premises of the model. It is also important to show that the proposed cognitive model beyond good representative requires less computer time to be solved which is important for process control implementation. Conclusions: Dynamic cognitive models had been developed for a copolymerization process resulted satisfactory, what in it supplies a new alternative to them in the solution of problems of modeling in chemical processes.
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