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

Abstract

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.

Closed‐loop dynamic real‐time optimization with stabilizing model predictive control

“…Due to possible non‐uniqueness in solution with use of an economic objective function, the DRTO could potentially exhibit high variation in the output reference trajectory. One judicious way to mitigate this issue is to have set‐point hold (SPH) constraints 18 . This constraint ensures that the reference trajectory is held constant over a specific number of discretized intervals.…”

Preface of the 66th Canadian Chemical Engineering Conference: “Sustainability and Prosperity”

“…This special issue section would have not materialized without the efforts of the contributing authors and the reviewers to ensure, despite their busy schedules, that all accepted papers meet the quality standards of The Canadian Journal of Chemical Engineering . The guest editors are also sincerely thankful to the Editor‐in‐Chief of The Canadian Journal of Chemical Engineering , Prof. João Soares, for his support and guidance, and to his editorial staff for their efforts, in welcoming this series of papers on timely topics.…”

Issue Highlights

“…Techniques for approximating the closed‐loop response are presented, as well as strategies to reduce excessive set‐point variation. The method is illustrated through case studies, with its performance evaluated and discussed …”