Longitudinal interactions in multipass processes

The authors´ previous work on the stability of repetitive processes exhibiting strong interaction between successive passes (transverse interaction) is extended to cover cases of longitudinal interaction occurring along each pass. It is shown that such interaction can be represented by transfer functions whose associated impulse responses are delayed even functions and therefore not encountered in normal process modelling. The beneficial effects of such transfer functions on system stability are demonstrated, but other types of longitudinal interaction, arising from geometrical offset, are shown to affect stability adversely. Consideration is also given to multipass processes having more than one control loop and it is shown that, where the sensor for one loop can be sited in advance of that for another, easily implemented feedforward techniques can be applied to stabilise a multipass process which would otherwise be inherently unstable.