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.