Multivariable model predictive control (4x4) of methanol-water separation in dimethyl ether production

The use of the Model Predictive Control (MPC) controller in DME production from synthesis gas has shown better results than the Proportional-Integral (PI) controller. However, this SISO MPC controller makes the DME production process uneconomical due to the cost of expensive MPC controllers. In this study, a Multivariable Model Predictive Control (MMPC 4x4) controller was designed with four manipulated variables (MV) and four controlled variables (CV). MMPC controllers are proposed to reduce the number of controllers used and overcome inter-variable interactions that affect control performance. The design of the controller includes the identification of inter-variable interactions through first-order plus dead time (FOPDT) empirical modeling and controller adjustments. The four CV's include condenser temperature, output cooler temperature, condenser liquid level, and column liquid level, while the four MV's include condenser duty, cooler duty, distillate product flow rate, and bottom product flow rate. The results show that the interactions between the variables identified include all variables involved, so that a 4x4 matrix containing 16 FOPDT models is obtained. The control parameter values in the form of sampling time (T), prediction horizon (P), and control horizon (M) with optimum control performance are 2, 24, and 10. MMPC control performance is better than MPC, which is shown by IAE decline was 19.92% to 72.86% and ISE reduction was 19.16% to 83.58%.