State and parameter estimation in closed-loop dynamic real-time optimization — A comparative study

Dynamic real-time optimization (DRTO) schemes have risen in popularity as plant environments have become increasingly dynamic due to globalization and deregulated energy markets. Inclusion of the impact of the plant control system on the predicted response gives rise to closed-loop DRTO (CL-DRTO). To avoid using a potentially inaccurate nominal model in CL-DRTO, this work explores incorporating plant measurements through various model updating strategies: bias update, state estimation, and combined parameter and state estimation, the latter two utilizing moving horizon estimation. The strategies are applied to two case studies, a distillation column and a continuous stirred tank reactor. Our findings suggest that the combined state and parameter estimation approach provides improvement in economic performance and fewer constraint violations when parametric uncertainty affects system dynamics nonlinearly. Conversely, the bias update strategy achieves satisfactory economic performance when the propagation of parameter uncertainty in the dynamic model is linear or mildly nonlinear.