Design of Kinetic Parameter Estimators for Reaction Systems: A Dynamic Regressor Extension and Mixing Procedure Approach
DOI:
https://doi.org/10.22146/ajche.27340Keywords:
Chemical Reactor, Gradient-descent Estimator, Interval Excitation, Linear Regression Model, System Identification, Vessel ExtentAbstract
This paper aims to design a globally convergent estimator for estimating kinetic parameters of reaction rates, namely activation energies and kinetic constants, using a dynamic regressor extension and mixing (DREM) procedure approach. It is important to note that the appearance of activation energies in exponential terms, from the modeling perspective of the Arrhenius law, leads to non-separable nonlinearities, thereby limiting the applicability of the standard gradient-descent (SGD) estimator. To address this challenging issue, we first propose an overparameterized linear regression equation, where reaction rates are computed using the extent-based reactor model. The DREM procedure with a second-order differential operator is then applied to this equation for designing a modified gradient-descent (MGD) estimator. Interestingly, all kinetic parameters can be estimated simultaneously under an interval excitation condition, which is weaker than the persistently exciting condition. Simulations of the reaction system that synthesizes glycerol (C3H8O3) via the hydration of 2-3-epoxy-1-propanol (C3H6O2) in a non-isothermal continuous stirred tank reactor illustrate the proposed MGD estimator.
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