Integrating the RTO in the MPC: An adaptive gradient-based approach

Model Predictive Control (MPC) is the most used advanced control technique in process industries, since it ensures stability, constraints satisfaction and convergence to the setpoint. The optimal setpoint is calculated by the Real Time Optimizer (RTO), minimizing the economic objective taking into account the operational limits of the plant. Since RTO employs complex stationary nonlinear models to perform the optimization and a larger sampling time than the controller, the economic setpoints calculated by the RTO may be inconsistent for the MPC layer and the economic performance of the overall controller may be worse than expected. The aim of this work is to propose an MPC controller that explicitly integrates the RTO into the MPC control layer. The proposed strategy is based on the MPC for tracking; the optimization problem to be solved only requires one evaluation of the gradient of the economic cost function at each sampling time. Based on this gradient, a second order approximation of the economic function is obtained and used in the MPC optimization problem resulting in a convex optimization problem. Recursive feasibility and convergence to the optimal equilibrium point is ensured.