The talk describes a grey-box model for the dimensional stability properties (i.e. curl and twist) of the carton board produced at AssiDomän Frövi paper mill in Sweden. AssiDomän Frövi AB is one of Sweden major carton board manufacturer, and produces some 350000 ton of board per year.
Curl is defined as the departure from a flat form, and it may seriously affect the processing of the paper. For this reason, customers impose quite restrictive limits on the allowed curvatures of the board. So, it is becoming more and more important to be able to produce a carton board with a curl within certain limits. Due to the economic significance of the curl problem, much research has been performed to find sheet design and processing strategies to eliminate or reduce curl.
The approach we used to tackle this problem is based on grey-box modelling. The reasons for such an approach is that the physical process is very complex and nonlinear. The influence of some inputs is not entirely understood, and besides it depends on a number of unknown parameters and unmodelled/unmesurable disturbances.
One of the main part of the model is based on classical laminate theory which is used to model the dimensional stability of multi-ply board. The main assumption is that each layer is considered as an homogeneous elastic medium.
The model is then complemented with a sub-model for unmodelled/umeasurable disturbances which are described as states of a dynamical system, and estimated by means of an extended Kalman filter.
The simulated curvatures show a general agreement with the measurements. However, the prediction errors are too large for the model to be used in an effective way, and a bigger effort has to be carried out in order to improve the physical sub-models.