On Modelling and Estimation of Curl and Twist in Multi-Ply Paperboard

Abstract: This thesis describes a grey-box model for the dimensionalstability properties (i.e. curl and twist) of the carton boardproduced at AssiDomän Frövi paper mill in Sweden.AssiDomän Frövi AB is one of Sweden major cartonboard manufacturer, and produces some 350000 ton of board peryear.Curl is defined as the departure from a at form, and it mayseriously affect the processing of the paper. For this reason,customers impose quite restrictive limits on the allowedcurvatures of the board. So, it is becoming more and moreimportant to be able to produce a carton board with a curlwithin certain limits. Due to the economic significance of thecurl problem, much research has been performed to find sheetdesign and processing strategies to eliminate or reducecurl.The approach we used to tackle this problem is based ongrey-box modelling. The reasons for such an approach is thatthe physical process is very complex and nonlinear. The inuenceof some inputs is not entirely understood, and besides itdepends on a number of unknown parameters andunmodelled/unmesurable disturbances.One of the main part of the model is based on classicallaminate theory which is used to model the dimensionalstability of multi-ply board. The main assumption is that eachlayer is considered as an homogeneous elastic medium.The model is then complemented with a sub-model forunmodelled/umeasurable disturbances which are described asstates of a dynamical system, and estimated by means of anextended Kalman filter.The simulated curvatures show a general agreement with themeasurements. However, the prediction errors are too large forthe model to be used in an effective way, and a bigger efforthas to be carried out in order to improve the physicalsub-models.A chapter of this thesis discusses the modelling of thewet-end part of the paper machine with Dymola, a modelling toolfor simulation of large systems based on Modelica language.