An Application of First Passage-Time Theory in the Design of Optimal Broke Recirculation Strategies in Paper Mills
Linear quadratic jump regulation theory can be used to derive 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 tanks levels. Since the linear design does not specifically account for constraints on the state-space, under the control law damaging events of tanks overflow 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 mean time between incidents of fluid in broke and white water tanks either overflowing, or reaching dangerously low levels, sufficiently long. The corresponding approximation technique involved in evaluating mean first passage-times of the controlled stochastic processes appears to have an applicability which largely exceeds the problem area it was designed for.
Khanbaghi, M., Malhame, R., & Perrier, M. (1998). An application of first passage-time theory in the design of optimal broke recirculation strategies in paper mills. Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 3, 2704–2709 vol.3. https://doi.org/10.1109/CDC.1998.757862