Evaluation of initialization strategies in fuzzy self-tuning PI control for a 4×4 methanol–water distillation system

Abstract

Effective control of methanol–water distillation is essential in dimethyl ether (DME) production due to strong nonlinearities and multivariable interactions. This study presents a comparative evaluation of fuzzy self-tuning proportional–integral (FSTPI) controllers with different initialization strategies in a 4×4 multivariable distillation system. Three variants—working-space (FSTPI-WS), working-range (FSTPI-WR), and PI-initialized FSTPI (FSTPI-PI Tuned)—are benchmarked against conventional PI controllers using a validated dynamic model implemented in MATLAB/Simulink with a C-based S-function for real-time adaptation. Controller performance is evaluated under ±5% setpoint changes and realistic disturbances in feed temperature and flow rate using integral absolute error (IAE), integral squared error (ISE), and interaction analysis. The results demonstrate that initialization strategy critically determines adaptive control performance. The FSTPI-PI Tuned consistently achieves the best performance, reducing IAE and ISE by more than 98% in the most interactive loop (condenser liquid level). For temperature-induced disturbances, IAE and ISE reductions exceed 98% and 99%, respectively. These findings indicate that fuzzy self-tuning is most effective when applied as an adaptive refinement layer atop a well-tuned PI controller, rather than as a standalone compensation mechanism, thereby providing a practical and computationally efficient solution for multivariable distillation control.