The utilization of closed‐loop prediction for dynamic real‐time optimization

Real‐time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set‐points are computed for the underlying plant control system. RTO calculations are traditionally based on steady‐state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open‐loop response dynamics of the process, with controller set‐point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed‐loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed‐loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed‐loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush‐Kuhn‐Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single‐level mathematical program with complementarity constraints (MPCC). Closed‐loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed‐loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.