Exhaustive grid search for multivariable model predictive control parameter optimization in dimethyl ether synthesis

• First complete structural interaction map of T–P–M in industrial MMPC • Moves MPC tuning beyond heuristics toward deterministic design • Demonstrates sampling time as a first-order structural parameter • Defines a robust tuning envelope, not a single empirical optimum • Integrates nonlinear UniSim dynamics with validated FOPDT surrogate • Confirms statistical significance via multi-scenario Friedman testing • Establishes a reproducible benchmark for future MPC tuning research The performance of Multivariable Model Predictive Control (MMPC) in strongly coupled distillation systems is highly sensitive to the structural selection of sampling time (T), prediction horizon (P), and control horizon (M). Despite their critical role, systematic interaction mapping among these parameters remains limited in the literature, where tuning is often based on heuristics or stochastic optimization strategies. This study addresses this gap by proposing a deterministic exhaustive grid-search framework for structural MMPC tuning in a 4 × 4 methanol–water purification unit within dimethyl ether (DME) synthesis. A total of 888 structured T–P–M combinations were evaluated using a disturbance-augmented FOPDT (first order plus dead time) multivariable model under six closed-loop scenarios comprising setpoint tracking and measurable disturbance rejection. Performance was assessed through cumulative integral error metrics, followed by multi-scenario ranking consistency analysis. The results reveal that sampling time is the dominant structural parameter, with moderate intervals (0.5–1.0 s) consistently outperforming excessively coarse (2.0 s) and overly fine (0.25 s) discretization schemes. Prediction horizon improvements saturate beyond 50–75 steps, while smaller control horizons (≈10% of P) enhance multivariable robustness by limiting aggressive actuation. Statistical validation using the Friedman non-parametric test confirms significant performance differentiation among configurations, and α–β weighting sensitivity analysis demonstrates that the identified optimal region is structurally stable and not dependent on a specific objective weighting choice. Although T = 0.50 s yields the lowest cumulative simulation error, T = 1.00 s provides a practically implementable alternative while preserving comparable robustness. By providing full structural interaction visibility and stability boundary characterization, the proposed deterministic framework advances MMPC (multivariable model predictive control) tuning from heuristic parameter selection toward a transparent and reproducible structural design methodology for strongly coupled industrial distillation systems.