Indirect estimation of state variables of industrial reaction-regeneration systems based on computer simulation

Abstract

A reaction-regeneration system is described, which is a hardware part of industrial production and is characterized by an exceptional feature – pronounced nonlinearity in the form of a plurality of stationary solutions of model differential equations. This feature forces one to resort to engineering solutions that are alternative to direct measurements. The problem of indirect estimation of the components of the state vector of the reaction-regeneration system is considered. The incorrectness of the indirect assessment of the state of such objects on the basis of the theory of Kalman filters is shown. The incorrectness is due to the ambiguity of the mapping of the state space into the space of vectors tangent to the trajectories. An approach based on synchronous simulation in dynamics is proposed, which consists in comparing two evolutions “object – model” with minimization of the mismatch. A technique based on the inclusion of the second derivatives of the state variables into the mismatch function is presented. The methodology of the sensitivity of indirect estimation systems based on maximizing the similarity of the compared evolutions “object – model” in the regime of strict synchronization with respect to external disturbances and control levers is considered. It is shown that the accuracy of the indirect estimation of physically unmeasurable coordinates is largely determined by the mathematical aspects of minimizing the mismatch function, which, due to the multiplicity of solutions to model equations, has a complex structure of the response surface.