Tensor-based blind alignment of MIMO CD processes

A key issue in paper–machine cross-directional (CD) control is alignment, i.e., accurate spatial mapping of the actuators to the scanning points. Typically, this mapping problem is a non-linear and slowly time-varying phenomenon. Most current methods require bump tests, in which a few actuators are excited, and the peaks in the observed scan data are assigned to the excited actuators. A major drawback of these methods is that they need to be manually initiated and thus require the CD control system to be in manual mode. This paper presents a novel, deterministic, tensor-based modeling of the CD process and an alignment method that works while the closed-loop CD controlled system is running. First, we link the CD data to the parallel factor (PARAFAC) model. Exploiting this link, we derive a deterministic blind PARAFAC decomposition as an alignment method with performance close to non-blind minimum mean-square error (MMSE). We show that blind alignment follows from simultaneous matrix decomposition. The proposed PARAFAC capitalizes on the physical location of the actuators, scanning databoxes and their temporal diversities. Its performance is verified in several simulations for different actuator models. The discussed algorithm is then tested on industrial paper–machine data and evaluated as an identification tool.