Subspace identification for batch processes

We propose a general methodology for converting available batch plant data into prediction models by using the subspace identification method, which has been reserved almost exclusively for continuous systems, to develop an interand intra-batch correlation model. In this context, the state of the model is a holder of relevant information contained in the past batch data for predicting the behavior of current and future batches. Hence, the modeling framework allows the user to capture any inter- as well as intra-batch correlations between the variables reflected in the modeling data and take advantage of them in the prediction and control. We show that the correlation model can be converted into a regular time transition model that can be used to predict the future behavior of the relevant variables, including the end-quality variables, in real time based on incoming measurements. We address various practical issues such as the reduction of dimensionality and incorporation of delayed laboratory measurements of quality variables.