Dynamic Real–Time Optimization with Closed-Loop Prediction for Nonlinear MPC–Controlled Plants

Current trends toward globalization and electricity market deregulation are requiring increasingly dynamic operation of chemical processes. In this paper, we develop a dynamic real-time optimization (DRTO) formulation for plants controlled by NMPC. It utilizes a prediction of the plant under the action of constrained NMPC. At every prediction time-step, an NMPC problem determines the control inputs that are applied to the dynamic process model. We show that the unconstrained NMPC problem for SISO systems affine in the inputs has a single stationary point that corresponds to the global optimum, and numerical experiments suggest that a similar property holds for the constrained problem. This allows the embedded NMPC subproblems in the DRTO formulation to be replaced by their first-order Karush-Kuhn-Tucker (KKT) conditions, yielding a single-level optimization problem. We show that the DRTO with embedded NMPC subproblems can lead to significant improvement in plant performance, and also compare the performance of NMPC to that of linear MPC.