OPTIMAL CONTROL OF METHANE STEAM-OXYGEN CONVERSION PROCESS
DOI:
https://doi.org/10.32782/mathematical-modelling/2024-7-1-15Keywords:
methane conversion process, mathematical model, optimality criterion, optimal control with feedback, nonlinear Riccatti differential equation with distributed parametersAbstract
In this work, the process of methane conversion was investigated. In the production of hydrogen and its mixtures, the most important device is the converter, which is intended directly for converting methane with the participation of oxygen and water vapor. Therefore, it is this reactor that is being studied as a technological control object. The pressure in the apparatus is maintained by the flow of reaction gases at the outlet of the converter, and the dynamic characteristics of this parameter are not considered further. Also, losses to the environment are not considered, since the converter housing was designed for this and has thermal insulation. The temperatures and concentrations of the incoming streams are constant. Based on the above, the determining parameter of this process is the concentration of methane at the outlet of the converter. In order to reach the given concentration, it is necessary to adjust the oxygen consumption. At the same time, the ratio of the steam-gas mixture and oxygen flows is ensured. Oxygen consumption is included in the boundary conditions of the mathematical model of the converter as an object with distributed parameters. In this work, a mathematical model of the dynamics of methane concentration at the outlet of the converter is developed. The static and dynamic characteristics of the control and disturbance channels are determined based on the created mathematical model of the converter. The influence of assumptions on the type and character of dynamic properties is studied. The system in the state space was studied. The proposed optimality criterion. The optimal control of the methane conversion process was found. An optimal linear regulator has been synthesized. This approach made it possible to synthesize an optimal linear law based on the application of the non-linear Riccatti differential equation with distributed parameters. The optimal control of the methane conversion process and the optimal state transition trajectory were found. The graphical results of the research are given.
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