An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system
Ewan Chee1, Wee Chin Wong2, Xiaonan Wang1()
1. Department of Chemical & Biomolecular Engineering, Faculty of Engineering, National University of Singapore, Singapore 117585, Singapore 2. Chemical Engineering & Food Technology Cluster, Singapore Institute of Technology, Singapore 138683, Singapore
Advanced model-based control strategies, e.g., model predictive control, can offer superior control of key process variables for multiple-input multiple-output systems. The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization. This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control. To showcase this approach, five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system. This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges. These controllers also had reasonable per-iteration times of ca. 0.1 s. This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which, in the face of process uncertainties or modelling limitations, allow rapid and stable control over wider operating ranges.
. [J]. Frontiers of Chemical Science and Engineering, 2022, 16(2): 237-250.
Ewan Chee, Wee Chin Wong, Xiaonan Wang. An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system. Front. Chem. Sci. Eng., 2022, 16(2): 237-250.
E Kaiser, J N Kutz, S L Brunton. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proceedings—Royal Society. Mathematical, Physical and Engineering Sciences, 2018, 474(2219): 20180335 https://doi.org/10.1098/rspa.2018.0335
2
W Sommeregger, B Sissolak, K Kandra, M von Stosch, M Mayer, G Striedner. Quality by control: towards model predictive control of mammalian cell culture bioprocesses. Biotechnology Journal, 2017, 12(7): 1600546 https://doi.org/10.1002/biot.201600546
M Öner, F C C Montes, T Ståhlberg, S M Stocks, J E Bajtnerb, G Sin. Comprehensive evaluation of a data driven control strategy: experimental application to a pharmaceutical crystallization process. Chemical Engineering Research & Design, 2020, 163: 248–261 https://doi.org/10.1016/j.cherd.2020.08.032
5
R K Al Seyab, Y Cao. Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. Journal of Process Control, 2008, 18(6): 568–581 https://doi.org/10.1016/j.jprocont.2007.10.012
S Mokhatab, W A Poe. Handbook of Natural Gas Transmission and Processing. 2nd ed. Boston: Gulf Professional Publishing, 2012, 473–509
8
C Venkateswarlu, K Venkat Rao. Dynamic recurrent radial basis function network model predictive control of unstable nonlinear processes. Chemical Engineering Science, 2005, 60(23): 6718–6732 https://doi.org/10.1016/j.ces.2005.03.070
9
S Štampar, S Sokolič, G Karer, A Žnidaršič, I Škrjanc. Theoretical and fuzzy modelling of a pharmaceutical batch reactor. Mathematical and Computer Modelling, 2011, 53(5-6): 637–645 https://doi.org/10.1016/j.mcm.2010.09.016
10
A Y Alanis, N Arana-Daniel, C López-Franco. Artificial Neural Networks for Engineering Applications. Washington: Academic Press, 2019, 55–63
11
Y Pan, J Wang. Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Transactions on Industrial Electronics, 2012, 59(8): 3089–3101 https://doi.org/10.1109/TIE.2011.2169636
12
J Schoukens, L Ljung. Nonlinear system identification: a user-oriented road map. IEEE Control Systems, 2019, 39: 28–99
13
M Arefi, A Montazeri, J Poshtan, M Jahed-Motlagh. Nonlinear model predictive control of chemical processes with a wiener identification approach. In: 2006 IEEE International Conference on Industrial Technology. Mumbai: IEEE, 2006, 1735–1740
14
Z Wu, A Tran, D Rincon, P D Christofides. Machine learning-based predictive control of nonlinear processes. Part I: theory. AIChE, 2019, 65(11): e16729 https://doi.org/10.1002/aic.16729
15
Z Wu, A Tran, D Rincon, P D Christofides. Machine-learning-based predictive control of nonlinear processes. Part II: computational implementation. AIChE, 2019, 65(11): e16734 https://doi.org/10.1002/aic.16734
16
H Garnier. Direct continuous-time approaches to system identification. Overview and benefits for practical applications. European Journal of Control, 2015, 24: 50–62 https://doi.org/10.1016/j.ejcon.2015.04.003
17
P I Frazier. A tutorial on Bayesian optimization. arXiv:1807.02811 [stat.ML], 2018
18
J Bergstra, Y Bengio. Random search for hyper-parameter optimization. Journal of Machine Learning Research, 2012, 13: 281–305
19
J Berk, V Nguyen, S Gupta, S Rana, S Venkatesh. Exploration enhanced expected improvement for bayesian optimization. In: Berlingerio M, Bonchi F, Gärtner T, Hurley N, Ifrim G, eds. Machine Learning and Knowledge Discovery in Databases. Cham: Springer International Publishing, 2019, 621–637
20
D E Seborg, D A Mellichamp, T F Edgar, F J Doyle III. Process dynamics and control. 3rd ed. New York: John Wiley & Sons, 2010
21
B J T Binder, T A Johansen, L Imsland. Improved predictions from measured disturbances in linear model predictive control. Journal of Process Control, 2019, 75: 86–106 https://doi.org/10.1016/j.jprocont.2019.01.007
22
W C Wong, E Chee, J Li, X Wang. Recurrent neural network-based model predictive control for continuous pharmaceutical manufacturing. Mathematics, 2018, 6(11): 242 https://doi.org/10.3390/math6110242
P Virtanen, R Gommers, T E Oliphant, M Haberland, T Reddy, D Cournapeau, E Burovski, P Peterson, W Weckesser, J Bright, et al.. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 2020, 17(3): 261–272 https://doi.org/10.1038/s41592-019-0686-2
25
F Pedregosa, G Varoquaux, A Gramfort, V Michel, B Thirion, O Grisel, M Blondel, P Prettenhofer, R Weiss, V Dubourg, et al.. Scikit-learn: machine learning in Python. Journal of Machine Learning Research, 2011, 12: 2825–2830
26
T Akiba, S Sano, T Yanase, T Ohta, M Koyama. Optuna: a next-generation hyperparameter optimization framework. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. New York: Association for Computing Machinery, 2019, 2623–2631
27
Y Shi, J Li, Z Li. Gradient boosting with piece-wise linear regression trees. arXiv:1802.05640 [cs.LG], 2019