Abstract
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.
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs11705-021-2058-6/MediaObjects/11705_2021_2058_Fig1_HTML.jpg)
Similar content being viewed by others
References
Kaiser E, Kutz J N, Brunton S L. 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
Sommeregger W, Sissolak B, Kandra K, von Stosch M, Mayer M, Striedner G. Quality by control: towards model predictive control of mammalian cell culture bioprocesses. Biotechnology Journal, 2017, 12(7): 1600546
Qin S J, Badgwell T A. A survey of industrial model predictive control technology. Control Engineering Practice, 2003, 11(7): 733–764
Öner M, Montes F C C, Ståhlberg T, Stocks S M, Bajtnerb J E, Sin G. Comprehensive evaluation of a data driven control strategy: experimental application to a pharmaceutical crystallization process. Chemical Engineering Research & Design, 2020, 163: 248–261
Al Seyab R K, Cao Y. Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. Journal of Process Control, 2008, 18(6): 568–581
Ljung L. Perspectives on system identification. Annual Reviews in Control, 2010, 34(1): 1–12
Mokhatab S, Poe W A. Handbook of Natural Gas Transmission and Processing. 2nd ed. Boston: Gulf Professional Publishing, 2012, 473–509
Venkateswarlu C, Venkat Rao K. Dynamic recurrent radial basis function network model predictive control of unstable nonlinear processes. Chemical Engineering Science, 2005, 60(23): 6718–6732
Štampar S, Sokolič S, Karer G, Žnidaršič A, Škrjanc I. Theoretical and fuzzy modelling of a pharmaceutical batch reactor. Mathematical and Computer Modelling, 2011, 53(5–6): 637–645
Alanis A Y, Arana-Daniel N, López-Franco C. Artificial Neural Networks for Engineering Applications. Washington: Academic Press, 2019, 55–63
Pan Y, Wang J. Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Transactions on Industrial Electronics, 2012, 59(8): 3089–3101
Schoukens J, Ljung L. Nonlinear system identification: a user-oriented road map. IEEE Control Systems, 2019, 39: 28–99
Arefi M, Montazeri A, Poshtan J, Jahed-Motlagh M. 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
Wu Z, Tran A, Rincon D, Christofides P D. Machine learning-based predictive control of nonlinear processes. Part I: theory. AIChE, 2019, 65(11): e16729
Wu Z, Tran A, Rincon D, Christofides P D. Machine-learning-based predictive control of nonlinear processes. Part II: computational implementation. AIChE, 2019, 65(11): e16734
Garnier H. Direct continuous-time approaches to system identification. Overview and benefits for practical applications. European Journal of Control, 2015, 24: 50–62
Frazier P I. A tutorial on Bayesian optimization. ar**v:1807.02811 [stat.ML], 2018
Bergstra J, Bengio Y. Random search for hyper-parameter optimization. Journal of Machine Learning Research, 2012, 13: 281–305
Berk J, Nguyen V, Gupta S, Rana S, Venkatesh S. 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
Seborg D E, Mellichamp D A, Edgar T F, Doyle F J III. Process dynamics and control. 3rd ed. New York: John Wiley & Sons, 2010
Binder B J T, Johansen T A, Imsland L. Improved predictions from measured disturbances in linear model predictive control. Journal of Process Control, 2019, 75: 86–106
Wong W C, Chee E, Li J, Wang X. Recurrent neural network-based model predictive control for continuous pharmaceutical manufacturing. Mathematics, 2018, 6(11): 242
Koppel L B. Input multiplicities in nonlinear, multivariable control systems. AIChE, 1982, 28(6): 935–945
Virtanen P, Gommers R, Oliphant T E, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 2020, 17(3): 261–272
Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, et al. Scikitlearn: machine learning in Python. Journal of Machine Learning Research, 2011, 12: 2825–2830
Akiba T, Sano S, Yanase T, Ohta T, Koyama M. 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
Shi Y, Li J, Li Z. Gradient boosting with piece-wise linear regression trees. ar**v:1802.05640 [cs.LG], 2019
Acknowledgements
The authors thank the MOE AcRF Grant in Singapore for financial support of the projects on Precision Healthcare Development, Manufacturing and Supply Chain Optimization (Grant No. R-279-000-513-133) and Advanced Process Control and Machine Learning Methods for Enhanced Continuous Manufacturing of Pharmaceutical Products (Grant No. R-279-000-541-114).
Author information
Authors and Affiliations
Corresponding author
Additional information
Code Availability Statement
Access to the GitHub repository containing the source code for this project is available upon request.
Electronic Supplementary Material
11705_2021_2058_MOESM1_ESM.pdf
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
Rights and permissions
About this article
Cite this article
Chee, E., Wong, W.C. & Wang, X. 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. 16, 237–250 (2022). https://doi.org/10.1007/s11705-021-2058-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11705-021-2058-6