Shape–Constrained Moving Horizon Estimators for Reaction Systems

In reaction systems, state estimators are used to improve the quality of estimates using measurements and process models with the number of moles or concentrations as states. The model of reaction systems can be reformulated in the extent domain with the reaction and flow extents as states. This work exploits the properties of the extents, such as nonnegativity and monotonicity, and formulates nonlinear and linear Shape-Constrained Moving Horizon Estimators (SCMHE) for reaction systems. It is shown that the linear SCMHE is a quadratic programming problem, and hence, it is computationally less expensive. The performance of the SCMHE schemes is compared with the Extended Kalman filters (EKF) and MHE in the concentration domain via simulation studies using two examples, namely, gas-phase isothermal batch reactor and lactic acid production in a fed-batch reactor. It is shown that the linear SCMHE provides better performance than EKF with a similar average computational time, while nonlinear SCMHE is computationally cheaper and performs better than the MHE in the concentration or mole domain.