DOI: https://doi.org/10.9767/jcerp.20731

Study on the Model Prediction Control and MRAS in Electrodeposited Process Control System for Vehicle Painting

Faculty of Control Science, University of Sciences, Unjong District, Pyongyang 999093, North Korea

Received: 11 May 2026; Revised: 10 Jun 2026; Accepted: 22 Jun 2026; Available online: 3 Jul 2026; Published: 26 Dec 2026.
Editor(s): Istadi Istadi
Open Access Copyright (c) 2026 by Authors, Published by Universitas Diponegoro and BCREC Publishing Group
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Fulltext View|Download

Citation Format:
Cover Image
Abstract

Electrodeposition is widely used in automotive painting due to its high adhesion and uniform coating. Temperature control is critical for coating quality, but stirred tanks exhibit nonlinear dynamics with large inertia and time-varying parameters. This study aims to develop an integrated control strategy combining model predictive control (MPC) with a model reference adaptive system (MRAS) to improve temperature control accuracy and robustness in a stirred electrodeposition tank. A robust MPC with N-step-free control action was designed based on an ARX-identified state-space model, and an MRAS estimator with PI adaptation was integrated to online-update the dominant time constant perturbed by stirring. Simulation and experimental results demonstrated that the proposed MPC-MRAS method achieved temperature control accuracy within ±0.2 °C, superior set-point tracking, and robust disturbance rejection compared to conventional MPC without parameter adaptation. The integrated strategy effectively compensates for model uncertainties caused by fluid agitation and operational variations, showing significant potential for industrial electrodeposition applications. Copyright © 2026 by Authors, Published by Universitas Diponegoro and BCREC Publishing Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).

Keywords: Painting; Stirring; Temperature; Model predictive control; MRAS; Electrochemical reactor

Article Metrics:

Article Info
Section: Original Research Articles
Language : EN
Recent articles
The Application of Transition Metal Nitride Catalyst in the HDO Reaction of Lignin and Its Model Compounds Br-LMG/PVB Film: A Novel UVC Dosimeter for Process Monitoring in Chemical and Environmental Engineering Energy Optimization of Methanol Production using CO₂ from Natural Gas Sweetening via Reactor Heat Recovery, Compressor Integration, and Cooling Water Reuse Effect of Temperature and Pressure Variation on CO₂ Methanation Performance in a PFR Reactor Using Ni/Al₂O₃ Catalyst More recent articles
  1. Luo, J., Çıtmacı, B., Jang, J.B., Abdullah, F., Morales-Guio, C.G., Christofides, P.D. (2023). Machine learning-based predictive control using on-line model linearization: Application to an experimental electrochemical reactor. Chemical Engineering Research and Design, 197, 721-737. DOI: 10.1016/j.cherd.2023.08.017
  2. Besra, L., Liu, M. (2007). A review on fundamentals and applications of electrophoretic deposition (EPD). Progress in Materials Science, 52(1), 1-61. DOI: 10.1016/j.pmatsci.2006.07.001
  3. Wang, Y., Ahmadkhaniha, D., Sieber, N., Zanella, C. (2024). Controlling coating thickness distribution for a complex geometry using pulse reverse current: A simulation study. The International Journal of Advanced Manufacturing Technology, 128, 2409-2423. DOI: 10.1007/s00170-024-12635-4
  4. Li, M., Shi, D., Christofides, P.D. (2004). Diamond Jet Hybrid HVOF thermal spray: gas-phase and particle behavior modeling and feedback control design. Industrial & Engineering Chemistry Research, 43(14), 3632-3652. DOI: 10.1021/ie030559i
  5. Çıtmacı, B., Luo, J., Jang, J.B. (2022). Machine learning-based ethylene concentration estimation, real-time optimization and feedback control of an experimental electrochemical reactor. Chemical Engineering Research and Design, 185, 87-107. DOI: 10.1016/j.cherd.2022.06.044
  6. Çıtmacı, B., Luo, J., Jang, J.B., Morales-Guio, C.G., Christofides, P.D. (2023). Machine learning-based ethylene and carbon monoxide estimation, real-time optimization, and multivariable feedback control of an experimental electrochemical reactor. Chemical Engineering Research and Design, 191, 658-681. DOI: 10.1016/j.cherd.2023.02.003
  7. Qin, S.J., Badgwell, T.A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11(7), 733-764. DOI: 10.1016/S0967-0661(02)00186-7
  8. Lee, J.H. (2011). Model predictive control: Review of the three decades of development. International Journal of Control, Automation and Systems, 9(3), 415-424. DOI: 10.1007/s12555-011-0300-6
  9. [9]Landau, I.D. (1979). Adaptive Control: The Model Reference Approach. Marcel Dekker. ISBN: 978-0824769468
  10. Del Rio Chanona, M.E., Wu, Z., Christofides, P.D., Wu, W. (2024). A tutorial review of machine learning-based model predictive control methods. Reviews in Chemical Engineering. DOI: 10.1515/revce-2024-0055
  11. Alhajeri, M.S., Abdullah, F., Wu, Z., Christofides, P.D. (2022). Physics-informed machine learning modeling for predictive control using noisy data. Chemical Engineering Research and Design, 186, 34-49. DOI: 10.1016/j.cherd.2022.07.035
  12. Zou, C., Pramanik, S., Anwar, S. (2020). Electrochemical model based charge optimization for lithium-ion batteries. IEEE Transactions on Control Systems Technology, 28(3), 1029-1042. DOI: 10.1109/TCST.2019.2923704
  13. Abdullah, F., Wu, Z., Christofides, P.D. (2021). Sparse-identification-based model predictive control of nonlinear two-time-scale processes. Computers & Chemical Engineering, 153, 107411. DOI: 10.1016/j.compchemeng.2021.107411
  14. Guduri, B., Batra, R.C. (2022). Adaptive Control of the Atmospheric Plasma Spray Process for Functionally Graded Thermal Barrier Coatings. Advances in Materials Science and Engineering, 2022, Article ID 5432541. DOI: 10.1155/2022/5432541
  15. Guduri, B., Batra, R.C. (2022). Robust model reference adaptive controller for atmospheric plasma spray process. SN Applied Sciences, 4, 128. DOI: 10.1007/s42452-022-05012-0
  16. Åström, K.J., Wittenmark, B. (1995). Adaptive Control (2nd ed.). Addison-Wesley. ISBN: 978-0201558668
  17. Ioannou, P.A., Sun, J. (1996). Robust Adaptive Control. Prentice Hall. ISBN: 978-0134391007
  18. Alhajeri, M.S., Wu, Z., Christofides, P.D. (2021). Machine-learning-based state estimation and predictive control of nonlinear processes. Chemical Engineering Research and Design, 167, 158-179. DOI: 10.1016/j.cherd.2021.01.009
  19. Abdullah, F., Christofides, P.D. (2023). Data-based modeling and control of nonlinear process systems using sparse identification: An overview. Computers & Chemical Engineering, 174, 108247. DOI: 10.1016/j.compchemeng.2023.108247
  20. Chen, S., Wu, Z., Christofides, P.D. (2020). Decentralized machine-learning-based predictive control of nonlinear processes. Chemical Engineering Research and Design, 160, 80-93. DOI: 10.1016/j.cherd.2020.09.014
  21. Marusak, P.M. (2020). Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction---Application to a Chemical Reactor. Algorithms, 13(6), 143. DOI: 10.3390/a13060143
  22. Hong, S., ?ıtmacı, B., Cui, X., Abdullah, F. (2024). Model predictive control of an electrically-heated steam methane reformer. Digital Chemical Engineering, 9, 100120. DOI: 10.1016/j.dche.2024.100120
  23. Dubljevic, S., Christofides, P.D. (2006). Predictive control of parabolic PDEs with boundary control actuation. Chemical Engineering Science, 61(18), 6239-6247. DOI: 10.1016/j.ces.2006.05.041
  24. Li, M., Christofides, P.D. (2004). Feedback control of HVOF thermal spray process accounting for powder size distribution. Journal of Thermal Spray Technology, 13(1), 108-120. DOI: 10.1361/10599630418086
  25. Li, M., Christofides, P.D. (2005). Multi-scale modeling and analysis of an industrial HVOF thermal spray process. Chemical Engineering Science, 60(12), 3649-3669. DOI: 10.1016/j.ces.2005.02.043

Last update:

No citation recorded.

Last update:

No citation recorded.