A multi-way LPV modeling method for batch processes

By several simple local linear models a complex nonlinear process can be well approximated, so the linear parameter varying (LPV) method can largely simplify the complexity of model development and is widely used in the continuous process. Directly employing the regular LPV method in batch processes may develop a model for a single batch run; however, a whole batch process usually covers a number of batch runs. To develop a model for the whole batch process, this paper proposes a multi-way LPV (MLPV) approach for batch process modeling. In the proposed MLPV method, a sample is constructed by the measurements of all batch runs at each sampling instant. Comparing with the regular LPV model, the MLPV method extends the input, output and scheduling variables along the time dimension to along both the time dimension and the batch dimension. Then, the regular LPV method is performed on these “extended” samples according to the “extended” scheduling variable, by which both the variation among the batch runs and the dynamics within each batch run are summarized in the model development. The application of the MLPV method in three cases illustrates its advantages.