مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

کنترل دمای رساناهای مختلف با استفاده از کنترل‌کننده مدل داخلی طراحی شده مبتنی بر یک مدل کاهش مرتبه یافته

نوع مقاله : مقاله پژوهشی

نویسندگان
مهدی احمدی
محمدامین کریمی
دانشکده مهندسی برق و کامپیوتر، مجتمع آموزش عالی فنی و مهندسی اسفراین، اسفراین، خراسان شمالی، ایران
10.48311/mme.2026.118761.82932
چکیده
این مقاله بر طراحی کنترل‌کننده برای کنترل دمای یک میله فلزی افقی با رسانایی‌های متفاوت و با استفاده از تغییر شار حرارتی متمرکز است. برای این منظور ابتدا معادلات با مشتقات جزئی حاکم بر میله با استفاده از روش تفاضل محدود به دسته‌ای از معادلات دیفرانسیل عادی تبدیل می‌شود که نمایش فضای حالت را برای سیستم تحت مطالعه نتیجه می‌دهد. با توجه به بالا بودن مرتبه سیستم تحت مطالعه در فرم فضای حالت، پارامترهای تابع تبدیل کاهش مرتبه یافته برای رسانایی‌های متفاوت و با استفاده از یک روش بهینه‌سازی استخراج می‌شوند که نتایج حاصل از شبیه‌سازی حلقه باز نشان می‌دهند مدل‌های مرتبه پایین بدست آمده برای رسانایی‌های مختلف دارای دقتی بیش از 99% می‌باشند. سپس با استفاده از مدل‌های مرتبه پایین بدست آمده، کنترل‌کننده‌های مدل داخلی برای حالات مختلف رسانایی طراحی شده و به سیستم اصلی اعمال می‌شوند. نتایج حاصل از شبیه‌سازی نشان می‌دهند که کنترل‌کننده مدل داخلی طراحی شده توانسته است در مقایسه با دیگر مراجع عملکرد مطلوبی را در ردیابی ورودی مرجع و دفع اثر اغتشاش از خود به نمایش بگذارد به نحوی که خروجی سیستم توانسته است دمای مطلوب را با سرعتی مناسب، با فراجهشی کوچک و بدون خطای حالت ماندگار دنبال کند.
کلیدواژه‌ها
سیستم انتقال حرارت هدایتی
میله فلزی افقی
روش تفاضل محدود
کاهش مرتبه مدل
کنترل دما
کنترل‌کننده مدل داخلی

موضوعات

عنوان مقاله English

Temperature Control of Different Conductors using a Reduced-Order Model-Based Internal Model Controller

نویسندگان English

Mahdi Ahmadi
Mohammad Amin Karimi
Faculty of Electrical and Computer Engineering, Esfarayen University of Technology, Esfarayen, North-Khorasan, Iran
چکیده English

This paper focuses on designing a controller to regulate the temperature of a horizontal metal bar with varying thermal conductivities by manipulating the heat flux. To this end, the governing partial differential equations of the bar are first discretized using the finite difference method, resulting in a set of ordinary differential equations that establish a state-space representation for the system. The high order of the resulting state-space model leads to a complex final controller, so reduced-order transfer function parameters are determined for different conductivity values using an optimization-based approach. Open-loop simulation results show that the obtained low-order models achieve over 99% accuracy for various conductivity cases. Internal model controllers are then designed for different conductivity scenarios using these reduced-order models and applied to the original system. Simulation results indicate that the designed internal model controller exhibits enhanced performance in tracking the desired reference input and rejecting disturbances compared to other methods. The system output effectively follows the desired temperature profile with appropriate speed, minimal overshoot, and zero steady-state error.

کلیدواژه‌ها English

Conductive Heat Transfer System
Horizontal Metal Bar
Finite Difference Method
Model Order Reduction
Temperature Control
Internal Model Controller
[1]           G. V. K. H. Aschemann, A. Rauh, and V. V. Saurin, “Approaches to control design and optimization in heat transfer problems,” Journal of Computer and Systems Sciences International, vol. 49, no. 3, pp. 380–391, 2010. doi:10.1134/S106423071003007X.
[2]           Z. C. C. Pan, Q. Tang, Z. He, L. Wang, H. Li, and W. Zhou, “Heat Dissipation Improvement of Lithium Battery Pack with Liquid Cooling System Based on Response-Surface Optimization,” Journal of Energy Engineering, vol. 148, no. 4, May 2022, Art no. 04022028. doi:10.1061/(ASCE)EY.1943-7897.0000845.
[3]           J. S. Z. Lyu, Z. Li, X. Li, H. Yan, and L. Chen, “A compact hybrid battery thermal management system for enhanced cooling,” Dec 2024. doi:10.48550/arXiv.2412.00999.
[4]           T. O. I. Winfield, J. Madril, M. Matthews, and G. Romero, “High-performance cooling for power electronics via electrochemical additive manufacturing,” IEEE Micro, vol. 44, no. 3, pp. 48–54, May–Jun 2024. doi:10.1109/MM.2024.3360255.
[5]           M. K. Kisomi, “Thermal Management of Lithium-Ion Batteries: A Comparative Study of Phase Change Materials and Air-Cooling Systems Equipped with Fins,” Mar 2025. doi:10.48550/arXiv.2503.10244.
[6]           Y. Y. R. Li, F. Liang, J. Liu, and X. Chen, “Investigation on Battery Thermal Management Based on Enhanced Heat Transfer Disturbance Structure within Mini-Channel Liquid Cooling Plate,” Electronics, vol. 12, no. 4, p. 832, Feb 2023. doi:10.3390/electronics12040832.
[7]           T. C. A. Mahmood, G. de Boer, J. Voss, and H. Thompson, “Heat Transfer Modeling and Optimal Thermal Management of Electric Vehicle Battery Systems,” Energies, vol. 17, no. 18, p. 4575, 2024. doi:10.3390/en17184575.
[8]           F. P. Incropera, D. P. DeWitt, T. L. Bergman, and A. S. Lavine, Fundamentals of Heat and Mass Transfer. Hoboken, NJ, USA: John Wiley & Sons, 2013, pp. 1-432.
[9]           R. B. W. a. D. G. Cahill, “Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments,” Nature Communications, vol. 5, Oct 2014. doi:10.1038/ncomms6075.
[10]         W. G. Faris, Lectures on Partial Differential Equations. Providence,RI, USA: American Mathematical Society, 2004, pp. 49-69.
[11]         D. L. Powers, Boundary Value Problems and Partial Differential Equations, 5th ed ed. Boston, MA, USA: Elsevier Academic Press, 2006.
[12]         A. Y. C. G. V. Grenkin, A. E. Kovtanyuk, N. D. Botkin, and K.-H. Hoffmann, “Boundary optimal control problem of complex heat transfer model,” Journal of Mathematical Analysis and Applications, vol. 433, no. 2, pp. 1243–1260, Jan 2016. doi:10.1016/j.jmaa.2015.08.049.
[13]         D. W. Hahn and M. N. Özisik, Heat Conduction, 3rd ed. Hoboken, NJ, USA: John Wiley & Sons, 2012.
[14]         R. A. Meric, “Finite element analysis of optimal heating of a slab with temperature dependent thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 22, no. 10, pp. 1347–1353, Oct 1979. doi:10.1016/0017-9310(79)90197-2.
[15]         R. A. Meric, “Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem,” International Journal for Numerical Methods in Engineering, vol. 14, no. 12, pp. 1851–1863, 1979. doi:10.1002/nme.1620141207.
[16]         Z. W. K. Li, T. Q. Dinh, and J. Yoon, “Reinforcement learning-based hyperparameter tuning for adaptive model predictive controllers in battery thermal management,” IEEE Transactions on Vehicular Technology, vol. 74, no. 8, pp. 10459–10470, Aug 2025. doi:10.1109/TVT.2025.3552968.
[17]         A. M. a. J.-P. Corriou, “Distributed control of nonlinear diffusion systems by input–output linearization,” International Journal of Robust and Nonlinear Control, vol. 24, no. 3, pp. 389–405, Aug 2012. doi:10.1002/rnc.2892.
[18]         S. F. F. Wang, F. Ju, K. Rowe, and N. Hofmann, “Print Surface Thermal Modeling and Layer Time Control for Large-Scale Additive Manufacturing,” IEEE Transactions on Automation Science and Engineering, vol. 18, no. 1, pp. 244–254, Jan 2021. doi:10.1109/TASE.2020.3001047.
[19]         P. X. S. Wan, K. Wang, J. Yang, and S. Li, “Real-time estimation of thermal boundary of unsteady heat conduction system using PID algorithm,” International Journal of Thermal Sciences, vol. 153, Jul 2020. doi:10.1016/j.ijthermalsci.2020.106395.
[20]         R. L. P. Castro, M. Manana, M. J. Martin, and D. del Campo, “Infrared Temperature Measurement Sensors of Overhead Power Conductors,” Sensors, vol. 20, no. 24, Dec 2020. doi:10.3390/s20247126.
[21]         J. P. H. Mu, Y. Li, F. He, C. Xia, and Z. Pan, “Layer-by-layer model-based adaptive control for wire arc additive manufacturing of thin-wall structures,” Journal of Intelligent Manufacturing, vol. 33, no. 33, pp. 1165–1180, Apr 2022. doi:10.1007/s10845-022-01920-5.
[22]         I. B. Q. A. W. L. Torres, J. B. Menezes Filho, and A. G. Costa Junior, “Mathematical modeling and PID controller parameter tuning in a didactic thermal plant,” IEEE Latin America Transactions, vol. 15, no. 7, pp. 1250–1256, Jul 2017. doi:10.1109/TLA.2017.7959343.
[23]         N. B. a. S. Kuntanapreeda, “Backstepping boundary control: An application to rod temperature control with Neumann boundary condition,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 228, no. 5, pp. 295–302, Feb 2014. doi:10.1177/0959651813520146.
[24]         M. V. M. Luzi, and M. Lemma, “A tuning methodology of Model Predictive Control design for energy efficient building thermal control,” Journal of Building Engineering, vol. 21, pp. 28–36, Jan 2019. doi:10.1016/j.jobe.2018.09.022.
[25]         J. L. Z. Zhang, N. Zhang, X. Cao, Y. Yuan, M. Sultan, and S. Attia, “Dynamic discharging performance of a latent heat thermal energy storage system based on a PID controller,” Journal of Energy Storage, vol. 71, Nov 2023. doi:10.1016/j.est.2023.107911.
[26]         S. F. A. Oudi, M. Hosseini, and Y. Davoodbeygi, “Adjustment of optimal parameters to control the temperature in different conductors,” Journal of Modeling in Engineering, vol. 22, no. 77, pp. 107–116, Aug 2024. doi:10.22075/jme.2023.28427.2336.
[27]         T. G. A. a. C. Pupaza, “The development of PID temperature controllers based on FEM thermal analysis,” MATEC Web of Conferences, vol. 342, Jul 2021. doi:10.1051/matecconf/202134206008.
[28]         J. Kacprzyk, Optimal Control in Thermal Engineering: Studies in Systems, Decision and Control. Warsaw, Poland: Springer Polish Academy of Sciences, 2021, pp. 89-160.
[29]         T. S. K. Klinar, M. Muñoz Rojo, and A. Kitanovski, “Fluidic and mechanical thermal control devices,” Advanced Electronic Materials, vol. 7, no. 3, Dec 2020. doi:10.1002/aelm.202000623.
[30]         Y. Z. P. Chen, J. Wang, A. T. Azar, I. A. Hameed, I. K. Ibraheem, N. A. Kamal, and F. A. Abdulmajeed, “Adaptive internal model control based on parameter adaptation,” Electronics, vol. 11, no. 23, Nov 2022. doi:10.3390/electronics11233842.
[31]         P. R. M. Ahmadi, and M. Haeri, “A multi-model control of nonlinear systems: A cascade decoupled design procedure based on stability and performance,” Transactions of the Institute of Measurement and Control, vol. 42, no. 7, pp. 1271–1280, Jul 2020. doi:10.1177/0142331219888368.
[32]         M. A. a. M. Haeri, “A systematic decomposition approach of nonlinear systems by combining gap metric and stability margin,” vol. 43, no. 9, pp. 2006–2017, Sep 2021. doi:10.1177/0142331221989009.
[33]         M. Ahmadi, “Nonlinearity measure for nonlinear dynamic systems using a multimodel framework,” J. Computational and. Nonlinear Dynamics, vol. 20, no. 4, Apr 2025. doi:10.1115/1.4067913.
[34]         N. Burger, A. Laachachi, M. Ferriol, M. Lutz, V. Toniazzo, and D. Ruch, “Review of thermal conductivity in composites: Mechanisms, parameters and theory,” Progress in Polymer Science, vol. 61, pp. 1-28, 2016/10/01/ 2016. doi:10.1016/j.progpolymsci.2016.05.001.
[35]         Kendall Atkinson, Weimin Han, and David E. Stewart, Numerical Solution of Ordinary Differential Equations. Hoboken, New Jersey, USA: John Wiley & Sons, 2009.
[36]         R. Kumar and A. Sikander, “Review and analysis of model order reduction techniques for high-dimensional complex systems,” Microsystem Technologies, vol. 30, no. 9, pp. 1177-1190, 2024. doi:10.1007/s00542-023-05605-8.
[37]         M. Morari and E. Zafiriou, Robust process control. Morari, 1989.
مهندسی مکانیک مدرس
دوره 26، شماره 7
تیر 1405
صفحه 571-581