A Difference Equation Matrix Model Predictive Control Approach Applied to a Distillation Column

The Difference Equation Matrix Model (DEMM) is presented as an input–output Model Predictive Control (MPC) formulation derived from discrete difference equations. The proposed approach is compared with the widely used Dynamic Matrix Control (DMC) strategy from a structural perspective, highlighting differences in model parameterization, identification requirements, and matrix dimensions. The analysis indicates that DEMM provides a more compact model representation than the DMC formulation considered in this work while preserving the predictive-control framework. Furthermore, the DEMM strategy is applied to a binary distillation column, a multivariable nonlinear process, to illustrate its implementation and closed-loop behavior under disturbance, noise, and setpoint-change scenarios. Simulation results demonstrate satisfactory disturbance-rejection and tracking performance for the considered operating conditions.