Is Complexity Always Better? A Comparative Evaluation of Classical PID and Data-Driven MPC

This work presents a structured comparison between classical and data-driven control strategies, focusing on the performance trade-offs associated with model complexity. A PID controller tuned using the Simple Internal Model Control methodology is evaluated against a Model Predictive Control (MPC) approach based on the Koopman operator. The study is conducted on two representative nonlinear multivariable systems: a thermal laboratory platform implemented in a real experimental setup and a simulated multi-tank system. Both control strategies are assessed under equivalent operating conditions using standardized performance indices. The results show that, in systems with relatively simple dynamics, the classical PID controller achieves superior performance across all evaluated metrics. In contrast, for systems with stronger coupling and more complex dynamics, the predictive controller demonstrates advantages in managing time-dependent error, although not consistently outperforming the classical approach in all criteria. These findings highlight that control performance is not solely determined by algorithmic complexity, but strongly depends on system characteristics and evaluation criteria. In this context, this study provides evidence that well-designed classical controllers remain competitive alternatives to advanced data-driven methods.