Closed-loop Formulation for Nonlinear Dynamic Real-time Optimization*

Dynamic real-time optimization (DRTO) is a higher level online strategy that exploits plant economic potential by making appropriate adjustments to the lower level controller set-point trajectories. In this work, we propose a closed-loop formulation for a nonlinear DRTO calculation in the form of a bilevel programming problem. A nonlinear differential algebraic equation (DAE) system that describes the process dynamic behavior is utilized with an embedded constrained predictive control (MPC) optimization subproblem to generate the approximate closed-loop response dynamics at the primary economic optimization layer. The bilevel DRTO problem is reformulated as a single-level mathematical program with complementarity constraints (MPCC) by replacing the MPC optimization subproblem by its Karush-Kuhn-Tucker (KKT) optimality conditions. We investigate the economics and control performance of the proposed strategy based on a polymer grade transition case study in the presence of plant-model mismatch and a disturbance, and a comparison is made with the application of a linear DRTO prediction model.