Processes 2023 , 11 , 809
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A cooking time of 80 min and a NaOH concentration of 62 wt% were obtained. The optimal free-liquor temperature profile also varied between 390 and 430 K with control actions being taken every 10 min. Figure 9 shows the output under MPC operation. It is seen that the cellulose DP drops quickly in value at the start and then stabilizes near the desired set-point value. The Kappa number steadily decreases over the course of the process, and attains a value close to the set-point value of 90. Thus, our framework demonstrated its capability to obtain optimal constant values for the cooking time and NaOH concentration in addition to a time-varying profile for the free-liquor temperature. Remark5. All the kMC simulations, MPC calculations, and neural network training were per- formed on a computer with an Intel Core i7–4770 CPU with 3.40 GHz and 16.0 GB RAM running on a Windows 10, 64-bit operating system using MATLAB 2022a. The multiscale model took around 10–15 min to run, while the LSTM-ANN model within the MPC could be executed within seconds. As control actions are taken every 10 min, this provides enough time for the user to adjust the operating conditions and rerun the MPC for the next iteration.
Figure 8. Optimal input profiles and bounds for the cooking time, NaOH concentration, and free- liquor temperature as obtained from the closed-loop simulation.
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