What question did this study set out to answer?

This study aims to compare different PID controller tuning methods for heat exchangers to determine the most effective approach for temperature control.

March 17, 2026Open Access

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

Key Points

This study aims to compare different PID controller tuning methods for heat exchangers to determine the most effective approach for temperature control.
Comparative analysis of PID tuning methods: Ziegler–Nichols, Internal Model Control, Particle Swarm Optimization, Soft Actor-Critic.
Single run executed for ZN and IMC using fixed hyperparameters.
Two-stage methodology for PSO and SAC with hyperparameter selection via random search.
Statistical analysis conducted on performance metrics: RMSE, IAE, ISE, ITAE.
PSO-PID 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.
Statistical analysis shows significant differences between PSO and SAC for most metrics.

Abstract

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

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