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Abstract

A new two-dimensional (2D) variation modeling and control technique for a machine producing a web of material, such as paper, uses functional transformation with basis functions which are wavelets, preferably wavelets derived from and closely resembling the responses generated by actuation of cross direction (CD) actuators of the machine. By using the disclosed functional transformation together with carefully selected basis functions, memory and real-time processing requirements are substantially reduced so that practical controls can be readily implemented. In addition, the functional transformation technique of the present application expands conventional CD correction to also correct for a portion of the residual variations which, until now, have remained uncorrected. The new 2D profile is treated as the superposition of two main components: a pure machine direction (MD) variation component and a two-dimensional sheet variation component. The pure MD variation is identical to the conventional MD variation; however, the two-dimensional sheet variation represents the evolution of a sheet property being measured in both a temporal direction (TD) and a spatial direction (SD), i.e. it includes both the traditional pure CD profile and a portion of the residual variation. The TD is aligned with the MD and the SD is perpendicular to the TD or is aligned with the CD. The new 2D variation is controlled by a new 2D control arrangement which includes an optimal predictive SD controller and a model based TD controller to quickly achieve 2D web uniformity.

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