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Paper machine cross-directional control near spatial domain boundaries

This work is concerned with the modification of an existing industrial paper machine crossdirectional (CD) control law near spatial domain boundaries (paper sheet edges), taking into account relevant control engineering criteria: closed-loop stability, performance, and robustness. Paper machine C D control systems belong to a set of large, multivariable, spatiallydistributed control systems, having 30-300 control inputs and 200-2000 process outputs. The objective of C D control is to reduce the variations of a particular paper sheet property (basis weight weight per unit area, moisture content, or thickness) in the cross-direction (the direction perpendicular to the sheet travel direction) as much as possible. C D control systems can properly be described as two-dimensional systems, with one time dimension and one spatial dimension (cross-direction). The state-of-the-art industrial C D controllers of interest in this work are designed assuming spatially-invariant C D processes. Indeed, a lot of recently developed techniques for the design of spatially-distributed control laws make use of the spatial-invariance assumption. However, very many of the real-life systems (including paper machine C D processes) are not spatially-invariant. Paper machine edges represent a clear disruption of the assumed spatial-invariance. As a result, initially designed spatially-invariant control laws must be modified before implementation on the real (spatially-variant) paper machines. The current industrial techniques for modifying C D control laws near spatial domain boundaries are based on techniques for extending finite-width signals, borrowed from the field of signal processing. As these techniques do not take into account relevant control engineering criteria, they can lead to very poor control near the edges, and potentially even destabilize the overall C D control system. The main contributions of this work are the three novel approaches to modifying the existing industrial C D control law that directly take into account important control engineering criteria. In addition, the newly developed closed-loop approach has also been successfully tested on a paper machine in a working paper mill . A developed closed-loop stability transfer approach is a straightforward perturbation technique for the spatially-invariant C D controller, that is guaranteed to stabilize a closedloop system with the actual (spatially-variant) C D plant. Next, the similarities between effects observed near spatial domain boundaries of the industrial C D control systems and the well-known Gibbs effect are illustrated. Subsequently, based on the techniques for mitigating the Gibbs effect, the so-called open-loop approach to modifying the existing C D control law is developed and illustrated with a closed-loop simulation example.