Optimal white water and broke recirculation policies in paper mills via jump linear quadratic control

With the increasing closure of white water circuits in paper mills, breaks in the sheet of paper have become a system-wide disturbance. Upon recognizing that such breaks can be modeled as a Markov chain type of process which, when interacting with the continuous mill dynamics, yields a jump Markov model, jump linear theory is proposed as a means of constructing white water and broke recirculation strategies which minimize process variability. Reduced process variability comes at the expense of relatively large swings in white water and broke tank levels. Since the linear design does not specifically account for constraints on the state space, under the resulting control law, damaging events of tank overflows or emptiness can occur. A methodology, mainly founded on the first passage-time theory of stochastic processes, is proposed to choose the performance measure design parameters to limit process variability while maintaining sufficiently long mean times between incidents of fluid in broke and white water tanks either overflowing or reaching dangerously low levels. The heart of the tuning approach is an approximation technique for evaluating mean first passage-times of the controlled tank height processes. This technique appears to have an applicability which largely exceeds the problem area it was designed for.