(617d) Dynamic Risk-Based Batch Reactor Quality Control through Hierarchical Multi-Parametric Optimization

Batch reaction processes are a cornerstone in the chemical manufacturing industry widely applied to produce pharmaceuticals, high-value added chemicals, etc. However, their inherently dynamic operations have been a central question to control engineers as the product quality remains unknown until the end of a batch [1]. Extensive research works have been developed for batch quality control, such as the integration of principal component analysis with statistical process control or model predictive control (MPC) [2-4]. Several recent works also explored the use of nonlinear MPC through Gaussian process techniques and robust constraints with application in semi-batch processes [5-7]. As the decision making of regulatory process control and end-batch quality control span multiple time scales, it typically results in a large-scale dynamic optimization problem which poses challenges in the online computational efficiency and algorithmic tractability. In addition, the paradigm shift toward Industry 4.0 has emphasized the importance of proactive process safety management through advanced control [8-10]. A multi-time-scale operational optimization approach is thus essential, while currently lacking, to systematically identify the safe and optimal operating trajectories by accounting for the interactions and trade-offs between process control, prescriptive risk management, and end-batch quality control.

To address this gap, we present a methodology framework for dynamic risk-based model predictive quality control, as an extension of our recent work on risk-based control in continuous processes [11]. A statistical dynamic risk model is utilized as the indicator of real-time process safety performance which is a function of safety-critical process variables (e.g., temperature, pressure) [12]. The batch reactor model can adapt a first-principle model, data-driven model using measured data, or hybrid physics-informed model updating [13]. On this basis, the proposed framework features three hierarchical decision-making algorithms: (i) Short-term risk-aware controller – An MPC problem is formulated based on the integrated dynamic process and risk model to operate the batch systems with desired process safety performance. The MPC moving horizon estimation allows to forecast the process risk into the near future, thereby raising alarms ahead of fault occurrence when necessary. (ii) Long-term quality and safety optimizer – A batch quality model is developed utilizing information from the closed-loop risk-aware control. In this way, the batch quality of the system can be mathematically mapped as a function of process state variables and the setpoints of the risk-aware controller. The batch quality model must be on a larger time scale to be able to predict the end-point quality of the reactor. (iii) Intermediate surrogate model – For substantially different time scales, the batch quality model can omit crucial intermediate dynamics of the system or suggest overly aggressive changes in set points. In such cases, a surrogate model is necessitated to interpret the input and output setpoints from the optimizer for the risk-aware controller over an intermediate time scale to ensure smooth operational transitions. In this way, the decisions from upper-level decision making (in longer term) can be seamlessly conveyed to the lower-level decision making (in shorter term), while the lower-level dynamics are explicitly incorporated into the long-term representation. Notably, all of these three decision making problems are formulated as multi-parametric (mixed-integer) quadratic programming problems, thereby maximally replacing online optimization with explicit solutions and optimal look-up maps generated a priori via offline optimization. The efficacy of this framework is demonstrated through a case study on a safety-critical batch reactor that is conceptualized from the T2 Laboratories incident.

References

1. [1] Mhaskar, P., Garg, A., & Corbett, B. (2019). Modeling and Control of Batch Processes: Theory and Applications. Springer International Publishing.
2. [2] Nomikos, P., & MacGregor, J. F. (1994). Monitoring batch processes using multiway principal component analysis. AIChE Journal, 40(8), 1361–1375.
3. [3] Nomikos, P., & MacGregor, J. F. (1995). Multi-way partial least squares in monitoring batch processes. Chemometrics and Intelligent Laboratory Systems, 30(1), 97–108.
4. [4] Aumi, S., Corbett, B., & Mhaskar, P. (2012). Model predictive quality control of batch processes. 2012 American Control Conference (ACC), 5646–5651.
5. [5] Jang, H., Lee, J. H., & Biegler, L. T. (2016). A robust NMPC scheme for semi-batch polymerization reactors. IFAC-PapersOnLine, 49(7), 37–42.
6. [6] Chang, L., Liu, X., & Henson, M. A. (2016). Nonlinear model predictive control of fed-batch fermentations using dynamic flux balance models. Journal of Process Control, 42, 137–149.
7. [7] Thombre, M., (Joyce) Yu, Z., Jäschke, J., & Biegler, L. T. (2021). Sensitivity-Assisted multistage nonlinear model predictive control: Robustness, stability and computational efficiency. Computers & Chemical Engineering, 148, 107269.
8. [8] Khan, F., Amyotte, P., & Adedigba, S. (2021). Process safety concerns in process system digitalization. Education for Chemical Engineers, 34, 33–46.
9. [9] Bhadriraju, B., Kwon, J. S. I., & Khan, F. (2021). Risk-based fault prediction of chemical processes using operable adaptive sparse identification of systems (OASIS). Computers & Chemical Engineering, 152, 107378.
10. [10] Khan, F., Hashemi, S. J., Paltrinieri, N., Amyotte, P., Cozzani, V., & Reniers, G. (2016). Dynamic risk management: A contemporary approach to process safety management. Current Opinion in Chemical Engineering, 14, 9–17.
11. [11] Ali, M., Cai, X., Khan, F. I., Pistikopoulos, E. N., & Tian, Y. (2023). Dynamic risk-based process design and operational optimization via multi-parametric programming. Digital Chemical Engineering, 7, 100096
12. [12] Bao, H., Khan, F., Iqbal, T., Chang, Y. (2011). Risk‐based fault diagnosis and safety management for process systems. Process Saf. Prog., 30(1), 6-17.
13. [13] Wang, W., Wang, Y., Tian, Y., & Wu, Z. Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes via Multi-Parametric Programming.