Indirect Estimation of State Variables of Reaction–Regeneration Systems Based on Computer Simulation

The article describes a reaction–regeneration system, which is a hardware part of industrial production, characterized by a pronounced nonlinearity in the form of multiple stationary solutions to the model differential equations. This aspect entails the use of engineering solutions that are alternative to direct measurements. The study also considers the problem of indirect estimation of the components of the state vector of the reaction–regeneration system and presents the incorrectness of the indirect assessment of the state of such objects based on the theory of Kalman filters. The incorrectness is due to the ambiguity of mapping of the state space into the space of vectors tangent to the trajectories. An approach based on synchronous simulation in dynamics is proposed, involving the comparison of two “object–model” evolutions 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 article also presents the methodology of the sensitivity of indirect estimation systems based on maximizing the similarity of the compared “object–model” evolutions in the strict synchronization mode with respect to external disturbances and control levers. The accuracy of the indirect estimation of physically unmeasurable coordinates is shown to be largely determined by the mathematical aspects of minimizing the mismatch function, which, due to the multiplicity of solutions to the model equations, yields a response surface with a complex structure.