Multi-Objective Optimization of a Neuro-Fuzzy Controller Using Non-dominated Sorting Genetic Algorithm II for Robust Stabilization of the Van de Vusse Reactor

A multi-objective neuro-fuzzy control strategy is proposed for a Van de Vusse continuous stirred tank reactor (CSTR), a benchmark system characterized by nonlinear dynamics and non-minimum phase behavior. The controller is based on a multi-input multi-output adaptive neuro-fuzzy inference system (ANFIS) whose parameters are optimized using the NSGA-II algorithm. The proposed framework adjusts membership functions, rule consequents, and integral gains simultaneously within a Pareto-based formulation that considers tracking performance (ITAE) and control effort. The results of the closed-loop simulation indicate improved performance compared to a classically tuned parallel PID controller and a non-optimized ANFIS baseline. The optimized controller reduces the ITAE from 159.17 (PID) and 50.29 (baseline ANFIS) to 2.51, while operating within thermal safety constraints. The controller can compensate for the inverse response dynamics within the simulated conditions. Robustness analysis under ±10% parametric uncertainty demonstrates stable performance within the evaluated scenario, although broader uncertainties, such as measurement noise and actuator dynamics, were not considered. Targeted ANOVA provides limited insight into the influence of selected integral gains, identifying the flow-related gain as a relevant factor, but does not constitute a comprehensive statistical validation of the full controller structure. Overall, the proposed ANFIS–NSGA-II framework is presented as a simulation-based proof of concept that shows potential for nonlinear process control. However, further validation under more realistic conditions and experimental implementation is required to assess its practical applicability and generalizability.

Neuro-fuzzy control; Nonlinear systems; Non-minimum phase systems; NSGA-II; Van de Vusse reactor

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