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UBC Theses and Dissertations

Cross directional control of basis weight on paper machines using Gram polynomials Kristinsson, Kristinn


In this thesis a control algorithm for cross-directional basis weight control based on orthogonal polynomials is presented. Instead of controlling the cross-directional values at each point, the parameters of the orthogonal polynomials are controlled, taking into account the maximum bending moment of the slice lip and the relative stiffness of the slice with respect to the actuators. Problems with slice lip bending are dealt with in two ways. Implicitly, by modelling it as a polynomial such that the slice is not bent more than the highest degree of the polynomial, which is chosen beforehand. Explicitly, by calculating the bending moment and then use quadratic programming to limit the bending moment. By modeling the measurements and the actuators positions by polynomials the mapping between the actuators and the sensors, which is the key element of the current control systems, is effectively eliminated. Computational requirements are greatly reduced by avoiding inverses of big matrices.

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