Mini-max control of cross-directional variations on a paper machine

The control strategy is based on minimising the expected range of variations observed within a single scan across the width of the sheet. This can be considered as an l_∞ minimisation problem and implemented using efficient algorithms based on the simplex method of linear programming. The BIBO stability of the controlled system is analysed and it is shown that the stability of the full multivariable system is determined by the stability of a scalar dynamic term. In general, the controller is suboptimal in the sense that it minimises an upper bound on the expected range of variations across the sheet, but for a certain class of disturbance models the expected value of the range can be minimised optimally by using the minimum variance solution