State and Parameter Estimation in Dynamic Real-Time Optimization with Embedded MPC

The goal of dynamic real-time optimization (DRTO) applications is to compute an optimal operational trajectory for a plant by generating set-points for the lower-level control algorithm to track. This approach can be further improved by directly incorporating the control algorithm (such as Model Predictive Control, MPC) into a closed-loop DRTO (CL-DRTO). By doing so, CL-DRTO can predict both the plant and controller responses to set-point adjustments, enhancing the performance of the entire system. However, CL-DRTO schemes require a mechanism to utilize plant measurements to adapt the model to the current plant conditions. Otherwise, the decisions will be based on a nominal model and are likely to be suboptimal. This study proposes a plant feedback scheme using an extended Kalman filter within a CL-DRTO framework that embeds an MPC model. In this novel model adaptation approach in the context of CL-DRTO, not only the states and parameters of the plant model are updated but also the embedded linear MPC model, which is adapted via an output disturbance scheme. Moreover, by adding input constraints to the CL-DRTO problem, this formulation allows a simplified representation of the MPC solution at the CL-DRTO level without directly accounting for input constraints at the MPC level, which reduces computation time. The efficacy of the proposed CL-DRTO approach is demonstrated through application to a multi-input multi-output CSTR where a critical parameter is not measurable.