Orthogonal functions for cross-directional control of web forming processes

The cross-directional behaviour of web forming processes can be represented in terms of orthogonal basis functions. By choosing a suitable basis set, it is possible to separate controllable and uncontrollable components of the profile into low- and high-order spectral components and hence obtain a parsimonious representation. In most cases if there are sufficient actuators to control all low-order spectral components then the interaction matrix is likely to be ill-conditioned, which necessitates the incorporation of input constraints into the control design. The representation in terms of orthogonal functions allows the design of finite-horizon predictive controllers with hard inequality constraints on the input that are computationally feasible for commercial machines. It is also possible to exploit such a representation to construct efficient estimators for the process.