PID Controller Tuning for Heat Exchanger Systems: A Comparative Study of Classical, Model-Based, Optimization, and Reinforcement Learning Approaches

Öz

Heat exchangers are among the fundamental components of industrial processes, and effective temperature control is critical for process efficiency and product quality. This study presents a comparative analysis of PID controller tuning methods for a heat exchanger system from four different paradigms. As the classical approach, Ziegler–Nichols (ZN); as the model-based approach, Internal Model Control (IMC); as the metaheuristic optimization approach, Particle Swarm Optimization (PSO); and as the reinforcement learning approach, Soft Actor-Critic (SAC) are investigated. For the ZN and IMC methods, a single run is executed using fixed hyperparameters, whereas a two-stage methodology is followed for the PSO and SAC methods. Hyperparameter selection is performed via random search, evaluating 20 configurations and selecting the parameters that yield the lowest ITAE. Using the chosen hyperparameters, 20 independent runs are conducted, and statistical analysis is performed. For all tuning methods, the controller's tracking performance for step, sinusoidal, triangular, and square-wave reference signals is computed using RMSE, IAE, ISE, and ITAE metrics. The results show that the PSO-PID method achieves the lowest error metrics for all reference signals. In the step response, PSO provides 90.8% improvement in ITAE and 25.2% improvement in RMSE compared to ZN. The Wilcoxon rank-sum test indicates that the differences between PSO and SAC are statistically significant for most metrics (P<0.05). The controller obtained via the IMC method exhibits a slow response due to the system's large time constant and substantial phase lag for periodic signals. The SAC method shows higher variance than PSO but delivers better performance than classical methods. Overall, the study reveals the strengths and weaknesses of various approaches and provides guidance on method selection for industrial heat exchanger control. The outputs also demonstrate that the PSO algorithm is an effective and reliable method for PID parameter tuning in slow, time-delay systems such as heat exchangers.

Anahtar Kelimeler

• PID controller tuning
• Heat exchanger
• Ziegler–Nichols (ZN)
• Internal Model Control (IMC)
• Particle Swarm Optimization (PSO)
• Soft Actor-Critic (SAC)

Kaynakça

1. Al-Dhaifallah, M. (2023). Fuzzy fractional-order PID control for heat exchanger. Alexandria Engineering Journal, 63, 11–16. https://doi.org/10.1016/j.aej.2022.07.066
2. Bobič, M., Gjerek, B., Golobič, I., & Bajsić, I. (2020). Dynamic behaviour of a plate heat exchanger: Influence of temperature disturbances and flow configurations. International Journal of Heat and Mass Transfer, 163, 120439. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120439
3. Franklin, G. F., Powell, J. D., & Emami-Naeini, A. (2021). Feedback control of dynamic systems (8th ed., Global ed.). Pearson.
4. Haarnoja, T., Zhou, A., Abbeel, P., & Levine, S. (2018). Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor. arXiv:1801.01290. https://arxiv.org/abs/1801.01290
5. Jamil, A. A., Tu, W. F., Ali, S. W., Terriche, Y., & Guerrero, J. M. (2022). Fractional-Order PID Controllers for Temperature Control: A Review. Energies, 15(10), 3800. https://doi.org/10.3390/en15103800
6. Kennedy, J. & Eberhart, R. (1995). Particle swarm optimization. Proceedings of ICNN'95-International Conference on Neural Networks. (pp. 1942-1948), 4, Perth, WA, Australia. https://doi.org/10.1109/ICNN.1995.488968
7. Maya-Rodriguez, M. C., Carvajal-Mariscal, I., López-Muñoz, R., Lopez-Pacheco, M. A., & Tolentino-Eslava, R. (2023). Temperature Control of a Chemical Reactor Based on Neuro-Fuzzy Tuned with a Metaheuristic Technique to Improve Biodiesel Production. Energies, 16(17), 6187. https://doi.org/10.3390/en16176187
8. Olana, F. D., Abose, T. A. (2021). PID Temperature Controller Design for Shell and Tube Heat Exchanger. International Journal of Engineering and Manufacturing (IJEM), 11(1), 37-46. https://doi.org/10.5815/ijem.2021.01.05

9. Oravec, J., Bakošová, M., Trafczynski, M., Vasičkaninová, A., Mészáros, A., & Markowski, M. (2018). Robust model predictive control and PID control of shell-and-tube heat exchangers. Energy, 159, 1–10. https://doi.org/10.1016/j.energy.2018.06.106
10. Ouyang, M., Wang, Y., Wu, F., & Lin, Y. (2023). Continuous Reactor Temperature Control with Optimized PID Parameters Based on Improved Sparrow Algorithm. Processes, 11(5), 1302. https://doi.org/10.3390/pr11051302
11. Pai, S. S., & Weibel, J. A. (2022). Machine-learning-aided design optimization of internal flow channel cross-sections. International Journal of Heat and Mass Transfer, 195, 123118. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123118
12. Rivera, D. E., Morari, M., & Skogestad, S. (1986). Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development, 25(1), 252–265. https://doi.org/10.1021/i200032a041
13. Sallam, O. K., Azar, A. T., Guaily, A., Ammar, H. H. (2020). Tuning of PID Controller Using Particle Swarm Optimization for Cross Flow Heat Exchanger Based on CFD System Identification. In: Hassanien, A., Shaalan, K., Tolba, M. (eds) Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2019. AISI 2019. Advances in Intelligent Systems and Computing, 1058. Springer, Cham. https://doi.org/10.1007/978-3-030-31129-2_28
14. Sun, L., Ren, C., & Luo, X.-L. (2022). Online control system reconfiguration towards long period energy-saving optimization of heat exchanger networks. Journal of Cleaner Production, 367, 132940. https://doi.org/10.1016/j.jclepro.2022.132940
15. Tomar, B., Kumar, N. & Sreejeth, M. (2024). PLC and SCADA based temperature control of heat exchanger system through fractional order PID controller using metaheuristic optimization techniques. Heat Mass Transfer, 60, 1585–1602. https://doi.org/10.1007/s00231-024-03509-5
16. Zhang, C., & Tan, Z. (2025). Entropy-driven deep reinforcement learning for HVAC system optimization. J. Renewable Sustainable Energy, 17(1), 015101. https://doi.org/10.1063/5.0238799
17. Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controllers. Transactions of the ASME, 64(8), 759-768. http://doi.org/10.1115/1.4019264
18. Zou, J., Hirokawa, T., An, J., Huang, L., & Camm, J. (2023). Recent advances in the applications of machine learning methods for heat exchanger modeling—a review. Frontiers in Energy Research, 11, 1294531. https://doi.org/10.3389/fenrg.2023.1294531