Synthesis of a control system for the process of diesel fuel hydropuring with the Adar method

. Currently, one of the main important tasks at oil refineries is to increase their productivity and product quality. Hydrotreating of diesel fuel is important in the oil refining process. The main purpose of hydrotreating is to improve the quality of fuel and remove sulfur, nitrogen and oxygen compounds from it. The diesel fuel hydrotreating process has a significant impact on product quality. As an object of study, a chemical reactor has a nonlinear characteristic and has the property of a reverse chemical reaction during the hydrotreating of diesel fuel. Also, the diesel fuel hydrotreating process is considered a nonlinear and multidimensional control object, and all its parameters cannot be measured online. Therefore, a mathematical model was developed that takes into account the features of the technological process that arises when creating a highly efficient control system. The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a synergistic controller for a class of indefinite nonlinear dynamic systems. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ADAR)


Introduction
Modern complex systems of diverse nature constitute a complex of various subsystems that perform certain technological functions and are interconnected by processes of intense dynamic interaction and energy exchange of matter and information.The indicated super systems are nonlinear, multidimensional, and multiply connected, in which complex transient processes occur and critical and chaotic regimes arise.The control problems of such dynamic systems are very relevant, difficult and practically inaccessible to the existing control theory [1].The purpose of this work is to describe a synergetic method for obtaining solutions to systems of nonlinear equations [2].
A huge number of various chemical processes are implemented in the chemical industry and related industries, differing in the type of chemical reaction, thermodynamic parameters, kinetic characteristics (conversion scheme, kinetic model), phase composition of the starting reagents and reaction mixture, as well as the design and type of reactors.In many cases, the reactor subsystem is central in the general scheme for converting the starting reagents into target products and to a large extent determines the resources and energy saving, the economic efficiency of the production process as a whole, and the degree of satisfaction of consumer demand for certain products.In the class of linear systems, to ensure robustness, adaptive automatic control systems with parameter adjustment, inertialess state controllers, robust systems based on typical PID controllers, and fuzzy control systems are used [3].However, these approaches are ineffective in the synthesis of control systems for essentially nonlinear objects.The ADAR method, developed in the framework of the synergetic theory of control, seems to be promising in this regard.Synergetic methods based on nonlinear dynamics and nonequilibrium thermodynamics allow both successful research of various chemical-technological processes and efficient control of them [4].The design procedure based on synergetic control theory follows the analytical design of aggregated regulators (ADAR) method [5].

Research methods and the received results
A chemical reactor is a volume-type apparatus equipped with a mechanical stirrer and cooling jacket (Fig. 1).The device operates in isothermal mode.The multistep series-parallel reaction is carried out in the reactor as follows: For the mathematical formalization of the process, we introduce the following notation: (1) hydrogen sulfide.
Taking into account the notation (1), the chemical reactions will take the following form

Matrix of stoichiometric coefficients
The corresponding kinetic equations are presented in Table 1.
The resulting matrix is a matrix of stoichiometric coefficients, which formally represents the rate of change of the components of a chemical reaction.According to the law of the acting masses and the matrix of stoichiometric coefficients (Tab.1), the kinetic equations corresponding to the chemical transformation scheme (3) for the process can be expressed by the equations x -are the concentrations of reagents; 3 x , 4 x , -concentration of reaction products; stage speed constants [8].
A mathematical model of the dynamics of a chemical reactor consists of material balance equations for each component in the reactor, heat balance equations of the reaction mixture and the coolant in the shirt: where is the rate of reaction on components., we use the ADAR method on the basis of parallel-series combination of invariant manifolds [9][10][11].

Macro variables
Let us introduce aggregate macrovariables to consideration, the first of which determines the relationship of x with controlled variable x and the second reflects the technological requirement to the volume of reaction system as follows ( x is somewhat function, which should be determined at subsequent procedure of synthesis.Macrovariables (6) should follow the solution of principal functional equation of ADAR method (5).
Let us introduce the macrovariables and of equation ( 6) to functional equation ( 5) for the synthersis of control principle, . As result, we obtain the following equations:

Conclusion
Thus, the problem of synthesizing control algorithms for chemical reactors was solved using the ADAR method of the synergetic control theory.The ADAR method is considered one of the new modern methods of algorithmic synthesis of control systems and is based on the analytical synthesis of control laws without linearization of the nonlinear mathematical model of the plant.Nonlinear and vector laws of concentration and temperature control are obtained by ADAR's method.The computer model showed the controllability and asymptotic stability of the closed system "chemical reactor regulator" under various external and internal influences.The results obtained make it possible to increase the efficiency of the ADAR method and solve the problems of algorithmic synthesis of nonlinear, multidimensional and multiply connected technological objects.The proposed laws for the synthesis of control laws for chemical reactors can be used in the algorithmic synthesis of control of chemicaltechnological systems.
-1 ) chemical reactions of the corresponding direction.The rate of change of each i x component has the following form[12]:The kinetics of the reaction is described by a system of equations E3S Web of Conferences 458, 01025 (2023) EMMFT-2023 https://doi.org/10.1051/e3sconf/202345801025where 1 x , 2

Fig. 1 .
Fig. 1.Software package for diesel fuel hydrotreatment proces Transient graphs of the control system for the hydrotreatment of diesel fuel

Fig. 2 .
Fig. 2. Transient characteristics of control and output parameters when a step pulse is applied.

Fig. 3 .
Fig. 3. Transient characteristics of control and output parameters when applying a step effect.