CROSS-DIRECTIONAL CONTROL ON PAPER MACHINES USING GRAM POLYNOMIALS

A control algorithm for cross-directional basis weight control based o n orthogonal polynomials is presented. Instead of controlling the cros s-directional values at each point, the parameters of the orthogonal p olynomials are controlled, taking into account the maximum bending mom ent of the slice lip and the relative stiffness of the slice with resp ect to the actuators. The Gram polynomials have inherent ability to li mit bending of the slice lip in a way that conventional control does n ot. The slice lip will have smooth deflection, governed by the maximum order of the polynomial, which can be lowered if the bending limits a re exceeded. By modelling the measurements and the actuator positions by polynomials, the mapping between the actuators and the sensors, whi ch is the key element of the current control systems, is effectively e liminated. Computational requirements are greatly reduced by avoiding inverses of large matrices, or the inverses are found for a diagonal m atrix. The performance of the Gram polynomial control method is shown to be superior to conventional control methods, especially for badly c onditioned matrices.