Processes 2023 , 11 , 809
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200
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150
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Degree of polymerization
14,000
DP Set point
12,000
10,000
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Figure 9. Trajectories of the Kappa number and degree of polymerization as obtained from the closed-loop simulation. 5. Conclusions In conclusion, in this article, we presented the development of a layered multiscale model that integrates mass and energy balance equations from the extended Purdue model with a kMC algorithm to predict the temporal evolution of crucial paper properties, such as the Kappa number and cellulose DP . The model describes the degradation of wood chips associated with the dissolution of wood chip components and the depolymerization of cellulose due to alkaline hydrolysis, peeling-off, and stopping reactions. The multiscale model, which acts as a virtual experiment, was validated and then used offline with different sets of operating conditions to obtain a rich set of data for training the LSTM-ANN model with an R 2 value of over 0.98. Finally, a closed-loop controller was designed using the LSTM-ANN-based neural network to obtain optimal profiles of operating conditions that are a combination of time- invariant inputs (such as the cooking time and NaOH concentration) and time-varying inputs (such as the free liquor temperature). The controller achieved target set-point values for the Kappa number and cellulose DP with minimal offset while considering process constraints. This trained LSTM-ANN model can, thus, be utilized in place of the complex first-principles model to significantly reduce the computation time while using an online controller. Author Contributions: Conceptualization, P.S., H.-K.C. and J.S.-I.K.; methodology, P.S., H.-K.C. and J.S.-I.K.; software, P.S. and H.-K.C.; validation, P.S.; formal analysis, P.S., H.-K.C. and J.S.-I.K.; investigation, P.S. and J.S.-I.K.; resources, P.S., H.-K.C. and J.S.-I.K.; data curation, P.S. and H.-K.C.; writing—original draft preparation, P.S.; writing—review and editing, P.S. and J.S.-I.K.; visualization, P.S., H.-K.C. and J.S.-I.K.; supervision, J.S.-I.K.; project administration, J.S.-I.K.; funding acquisition, J.S.-I.K. All authors have read and agreed to the published version of the manuscript.
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