Optimal control of the process of alphylation of benzene by propylene in the liquid phase
DOI:
https://doi.org/10.18372/2310-5461.48.15091Keywords:
benzene alkylation process, mathematical model, optimality criterion, optimal feedback control, Ricatti's matrix differential equationAbstract
In this work, the process of alkylation of benzene with propylene in the liquid phase was investigated. In the production of alkylation of benzene, the most important apparatus is the alkylator, which is intended directly for alkylation with the participation of aluminum chloride. That is why this reactor is being studied as a technological control object. The pressure in the apparatus is maintained by the flow rate of the reaction gases at the outlet of the alkylator and the dynamic characteristics of this parameter are not considered in the future. Also, no environmental losses are considered above, as the alkylator housing has been provided for this and there is thermal insulation. Temperatures and concentrations of input streams and absence of impurity-inhibitors are constant. Based on the above, the defining parameters of this process are the concentration of alkylate at the outlet of the alkylator, as well as the temperature in the reactor. To achieve the set concentration it is necessary to regulate the flow rate of the propane-propylene fraction, and to achieve a constant temperature in the reactor with a variable water flow rate, because it is with it that a significant amount of heat is removed. The main disturbance that acts in the device is the temperature of the cooling water at the inlet to the alkylator, because this parameter can vary to some extent. In this paper, a mathematical model of the dynamics of temperature and concentration at the outlet of the alkylator is developed. Static and dynamic characteristics of the control and perturbation channels are determined on the basis of the created mathematical model of the alkylator. The influence of assumptions on the type and nature of dynamic properties is investigated. The system was maintained in the state space. The criterion of optimality is offered. The optimal control of the process of alkylation of benzene with propylene in the liquid phase is found. The optimal linear regulator is synthesized. This approach allowed to synthesize the optimal linear law based on the application of the matrix Ricati differential equation. The optimal control of the process of alkylation of benzene by propylene in the liquid phase is found. The graphic results of the research are given.
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