(346l) Application of Latent Variable Model Predictive Control to Uneven Batch Process

When multivariate statistical process control(MSPC) methods are applied to batch processes, uneven duration of batch process is an important issue. Though most MSPC methods assume that all the batches have an equal duration, the batch durations vary with operations due to disturbances in practice [1,2]. To deal with the problem, synchronization methods such as the indicator variable technique(IVT), dynamic time warping(DTW), and extrapolative time warping(XTW) have been applied to batch process monitoring [1,3,4].

Latent variable model predictive control(LV-MPC) has an advantage over the conventional model predictive control(MPC) when constructing a first-principles model is difficult and time-consuming [5]. However, as it applies latent variable models for prediction, the same problem with the uneven batch monitoring occurs in the batch process. Many studies have applied LV-MPC to batch processes, but uneven duration of the batch process is rarely considered [6]. Although all the batch lengths are equal to the reference batch duration in the trajectory tracking, phase durations can be different from batch to batch, and the synchronization is necessary [7]. Furthermore, batch duration needed to achieve its goal is often different from batch to batch, but few studies deal with determining batch end time [2].

This work provides a modification of LV-MPC to deal with uneven batch problem by using online synchronization of ongoing batch and the reference trajectory. The proposed approach consists of two major steps. First, current data of the ongoing batch is aligned by comparing the squared prediction error of models that are only valid for a small region. When the current phase is determined by the alignment, the prediction model of LV-MPC is replaced by the local model corresponding to the phase. Second, future reference trajectory is also modified according to the current target value. The time index of the reference trajectory can be replaced with the synchronized index, because the goal of batch processes is to achieve the target value at the end of the operation, not to get a consistent duration in all batches. The synchronized index is obtained by minimizing the deviation between the reference and the current value within some constraints, so the ongoing batch can track the reference more easily. One of the original and the synchronized reference which proceeds faster is determined to be the future reference and the region between them are applied to state constraints with slack variables. As the length of the reference trajectory is adjusted batch-to-batch, batch duration is also varied with the progress of batch. The proposed method is applied to industrial-scale penicillin production process as a case study and result shows it successfully improved control performance by reducing mean squared error of the target variable.

References

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[2] Wan, Jian, Ognjen Marjanovic, Barry Lennox, Uneven batch data alignment with application to the control of batch end-product quality, ISA transactions 53.2 (2014) 584-590.

[3] P. Nomikos, J. F. MacGregor, Multivariate spc charts for monitoring batch processes, Technometrics 37 (1) (1995) 41-59.

[4] R. Srinivasan, M. Qian, Online temporal signal comparison using singular points augmented time warping, Industrial & engineering chemistry research 46 (13) (2007) 4531-4548.

[5] Jeong, Dong Hwi, Jong Min Lee, Ensemble learning based latent variable model predictive control for batch trajectory tracking under concept drift, Computers & Chemical Engineering 139 (2020) 106875.

[6] Golshan, Masoud, et al, Latent Variable Model Predictive Control (LV-MPC) for trajectory tracking in batch processes, Journal of Process Control 20.4 (2010) 538-550.

[7] H. J. Ramaker, E. N. van Sprang, J. A. Westerhuis, A. K. Smilde, Dynamic time warping of spectroscopic batch data, Analytica Chimica Acta 498 (1-2) (2003) 133-153.