Identification of the temperature product quality relationship in a multi-component distillation column

In this paper, we show that in finding a mathematical expression to predict the relationship between temperatures measured inside a multi-component distillation column and the quality of the produced product at the top of the column, the application of a recently developed systematic procedure to identify Wiener nonlinear systems [20], supports the user in retrieving from the data accurate information about both the structure and initial parameter estimates of the model to be identified with iterative parameter optimization methods. This property enables the user to improve his prior knowledge instead of being dependent on it for getting parameter estimates as is the case in most existing parametric identification methods. A consequence of this dependency is that wrong prior information leads to models with poor prediction capability on one hand, and very little information on the other hand on how to modify the model structure in order to get improved results. The latter often results in very time consuming "trial-and-error" approaches that furthermore may yield poor results because of the possibility of getting stuck in local minima. The outlined approach has the potential to overcome these drawbacks. One common source of the use of wrong prior knowledge in the identification of multicomponent distillation columns is the presence of a static nonlinearity of exponential type that can be removed by taking the logarithm of the measured product quality. It is shown that this "trick" to linearize the system decreases the accuracy of the predicted producted quality. The outlined approach is also compared to a simple NARX neural network black-box identification method that have the potential to approximate general nonlinear input-output behaviours. This comparison shows that the neural network approach easily requires twice as much observations compared to the Wiener identification approach applied in this paper when the variance of the predicted product quality needs to be the same. The real-life measurement used in this paper were collected at a refinery of the Dutch State Mines (DSM). Finally, in order to use the model obtained with one (training) data set under other operational conditions, that is to extrapolate the model a simple observer design is discussed and validated with real-life measurements.