White water and broke recirculation policies in paper mills via Markovian jump linear quadratic control

Khanbaghi, Maryam; Malhamé, Roland P.; Perrier, Michel

doi:10.1109/acc.1998.703505

Cited by 4 publications

(4 citation statements)

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“…Given the desirability of achieving nearly constant broke recirculation flow rate and limited white water flow rates so as to limit process variability, we show in [4] how to use the resulting mathematical model of the paper break process as a basis for the design of adequate white water and broke recirculation control policies. A simplified two tanks model of white water and broke recirculation dynamics with random paper break disturbances has been developed.…”

Section: I1 -Background and Problem Definitionmentioning

confidence: 99%

“…Thus, undesirable incidents of tank overflow or tank emptiness are likely to occur. This is why an iterative design strategy is proposed in [4], whereby set points are shifted in Eq. (4), and variability penalty coefficients in matrix R are gradually decreased to allow for more swings in the flow rates in exchange for longer mean times between incidents.…”

Section: I1 -Background and Problem Definitionmentioning

confidence: 99%

“…We wish to use the algorithm to evaluate the performance of the optimal controls as developed in [4], from the point of view of susceptibility to leading the tanks overflows or emptiness. Unfortunately, under the applied control policies the rate of change of tank height corresponds to the integral over time of the expression in Eq.…”

Section: Iii1 -Mathematical Approximation and Hedging Controlmentioning

confidence: 99%

“…In [4] a method to optimally control the broke and white water tank levels and the variation of their inputs and outputs is proposed. It is founded on jump linear regulator theory.…”

Section: -Introductionmentioning

confidence: 99%

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An application of first passage-time theory in the design of optimal broke recirculation strategies in paper mills

Khanbaghi

Malhamé²,

Perrier³

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)

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With the increasing closure of white water circuits in paper mills, breaks in the sheet of paper have become a systemwide disturbance. Upon recognizing that such breaks can be modelled as a Markov chain type of process which when interacting with the continuous mill dynamics yields a jump Markov model, 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. I -INTRODUCTIONA paper machine is a very complex unit operation. It has several types of tanks that allow the recuperation, the storage and the recirculation of white water (water coming from the pulp and containing small fibres which are responsible for its white colouration) and broke (pulp coming from the paper breaks). Paper breaks could occur in different parts of a paper machine and are recuperated in generally distinct broke tanks. White water coming from the paper machine is also recuperated in a white water tank. Whenever necessary, the brokes are diluted with white water until the mix reaches an appropriate level of fluidity to be sent back to the paper machine. Also the thermomechanical pulp mill (TMP) which provides the pulp to the paper machine, allows the recuperation of a significant amount of white water.In [4] a method to optimally control the broke and white water tank levels and the variation of their inputs and outputs is proposed. It is founded on jump linear regulator theory. The solution to the problem emerges as a piecewise constant gain feedback law, for a given choice of the performance measure. However, this solution does not account for the fact that tanks can overflow or become empty. Therefore an iterative method is suggested to adjust parameters of the performance measure so as to achieve minimal recirculation flows variability while keeping mean times to overflow or emptiness of tanks at sufficiently high levels. The implementation of the tuning methodology for performance measure parameters requires in general repeated, both lengthy and computationaly expensive Monte-Carlo types of simulations. The aim of this paper is to use the theory of stochastic processes and their first passagetimes to develop approximat...

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Section: I1 -Background and Problem Definitionmentioning

confidence: 99%

Section: I1 -Background and Problem Definitionmentioning

confidence: 99%

Section: Iii1 -Mathematical Approximation and Hedging Controlmentioning

confidence: 99%

“…In [4] a method to optimally control the broke and white water tank levels and the variation of their inputs and outputs is proposed. It is founded on jump linear regulator theory.…”

Section: -Introductionmentioning

confidence: 99%

See 2 more Smart Citations