In this work, the comparison of a control system based on coupled PIDs and a GPC for MIMO systems applied to a Wood and Berry model distillation column has been carried out. The control law has been obtained based on the free and forced responses. Then, the design of independent TITO controls was carried out, using the Simulink/Matlab environment. Likewise, the evaluation of the interactions has been developed by using the relative gain matrix (RGA), to later perform the coupling of the loops with PIDs. Within the study, the behavior in the face of changes in the prediction horizon, changes in the control horizon, and the behavior in the face of changes in lambda and delta weights in the objective function have been analyzed, and additionally, the behavior in the face of disturbances was observed, this to make a comparison between the performance of a PID control (coupled system) and a GPC control. It has been found that the GPC control strategy presents a much better performance concerning the rise time, to the establishment time for the strategy with coupled PIDs. However, the PID still has the advantage of faster tuning due to the tuning tools.