Metaheuristic-Based PID Controller Design with MOOD Decision Support Applied to Benchmark Industrial Systems

This paper presents a comprehensive methodology for the multiobjective tuning of MIMO proportional integral derivative (PID) controllers using advanced metaheuristic strategies. The proposed approach formulates a cost function based on two conflicting performance criteria—the integral of absolute error (IAE) and the integral of absolute derivative of control (IADU)—to explore the trade-off between tracking performance and control effort systematically. Three metaheuristic techniques are employed: stochastic hill climbing, a Voronoi-based heuristic, and the Nondominated Sorting Genetic Algorithm (NSGA-II). A novel Multiobjective Optimization Design (MOOD)-based classification framework is incorporated to facilitate decision making across the Pareto front. The methodology is validated on three benchmark MIMO plants, demonstrating its robustness and generalizability. The results highlight that the NSGA-II controller achieves the lowest IADU value of 0.3694 in the mass damper system while maintaining acceptable performance metrics. The inclusion of a PID-split strategy further enhances system flexibility. This study emphasizes the value of metaheuristics in navigating complex design spaces and delivering tailored control solutions for multiobjective scenarios.