Identification of paper machines cross-directional models in closed-loop

Paper machines cross-directional (CD) processes are a class of spatially distributed systems. Due to economic constraints, identification experiments are usually severely limited making the identification of this large dimension multi-variable model challenging. The industrial identification technique uses bump test data where a few actuators are stepped while the CD process is running in open-loop. This paper presents a technique for the identification of paper machines CD models in closed-loop. The spatial interaction matrix is replaced by a noncausal spatial finite impulse response (FIR) model to account for the actuator response in the cross-direction (CD). The non-causal FIR model is identified in a prediction error frame using least squares. Least squares identification delivers parameter uncertainty bounds that translate to bounds on the uncertainties in the spatial interaction matrix which are less than the values assumed in industrial practice. Identifying the spatial model from a rich spatial input signal provides accurate CD response models from limited scans in a low signal-to-noise ratio (SNR). The proposed techniques are illustrated by identification experiments conducted on an industrial paper machine simulator.