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UBC Theses and Dissertations

Paper machine cross-directional control near spatial domain boundaries Mijanovic, Stevo


This work is concerned with the modification of an existing industrial paper machine cross-directional (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 CD control systems belong to a set of large, multivariable, spatially-distributed control systems, having 30-300 control inputs and 200-2000 process outputs. The objective of CD 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. CD 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 CD controllers of interest in this work are designed assuming spatially-invariant CD 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 CD 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 CD 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 CD control system. The main contributions of this work are the three novel approaches to modifying the existing industrial CD 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 CD controller, that is guaranteed to stabilize a closed-loop system with the actual (spatially-variant) CD plant. Next, the similarities between effects observed near spatial domain boundaries of the industrial CD 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 CD control law is developed and illustrated with a closed-loop simulation example. Finally, in a closed-loop approach to modifying the existing industrial CD controller, the objective is restated in terms of a block-decentralized static output feedback design problem. Static modifications of the existing controller's two constant matrix components are then sequentially computed by the use of a novel low-bandwidth static output feedback controller design algorithm. The relevant control engineering criteria (closed-loop stability, performance, and robustness) are all systematically taken into account with this approach. Since the resulting closed-loop system robustness margins near the sheet edges are directly considered, the possibility of CD control instability originating from the edges and 'creeping' into the rest of the system is eliminated with the new approach. The new approach has a clear economic benefit for the papermakers, since with a stable, robust, and performance improving control law near the sheet edges, the quality of the paper sheet near the edges can be significantly improved, thus resulting in less paper being trimmed off and more on-spec paper being produced from which the papermaker can extract his orders. The newly developed closed-loop approach to modifying the existing industrial CD control law near spatial domain boundaries is tested and verified on a paper machine in a working paper mill. The obtained closed-loop control results are presented.

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