A comment on thermodynamically consistent feasibility condition of asymptotic observers. (18th May 2019) - Hoang, N. Ha; Dochain, Denis
Highlights: An overview of thermodynamic concepts including reaction invariants is outlined. Asymptotic observers are adapted to thermodynamically consistent chemical reactors. A sufficient condition related to the process estimation selection is proposed. The convergence proof is shown using the port-Hamiltonian framework. Illustration of theoretical developments by simulations is included. Abstract: In this note, an extension of the design of asymptotic observers is proposed for the thermodynamically consistent non-isothermal continuous stirred tank reactor (involving n c active chemical species with n r independent reactions) that has incomplete state information. The two well-known constraints for the implementations of the asymptotic observer are the process operating conditions and the availability of temperature measurement together with ( n r - 1 ) concentration measurements. However, even though the process operating conditions are justified, the requirement of having good estimation performances and high accuracy of ( n c - n r + 1 ) state estimates may only be guaranteed if a so-called feasibility condition of the observer is fulfilled. This feasibility condition is formulated via the full rank constraint of a structural matrix, which is related to the stoichiometric coefficient matrix. A sufficient condition for the fulfilment of the full rank constraint shows that the process estimation selection is not made arbitrarily. Interestingly, as the designed observer is based on thermodynamic information only and does not require knowledge of reaction kinetics, the solution proposed to the feasibility condition has a clear physical meaning. Numerical simulations considered for Van de Vusse reaction system illustrate the application of the theoretical results.