# dynamics

## Dynamics of Adsorption of Copper Ions in Fixed-Bed Column and Mathematical Interpretation of the First Stage of the Process

The dynamics of the adsorption process in the fixed-bed column was experimentally studied on the example of the system natural zeolite - water solution of copper salt with low concentrations, which are characteristic for wastewater treatment processes from toxic contaminants. The initial curves of the adsorption process for the height of the sorbent layer of 5 and 7 cm were constructed. The equilibrium of such processes can be described by Henry's linear equation. The adsorption process in the layer consists of two stages, which are examined in the study.

## Dynamic model of speed control in the device with a multistage gear differential and the closed-loop hydraulic systems through carriers

Aim. Development of a mathematical model of dynamic processes in speed change devices with multistage gear differential transmissions with closed-loop hydraulic systems on an example of a concrete design. Method. A device with a multistage differential has been considered, in which the gear wheel - the ring gear of the first stage is connected to the sun gear wheel of the second stage, the gear wheel - the ring gear of the second stage is connected to the sun gear wheel of the third stage, and so on, depending on the number of steps.

## Structural-functional modeling for the determination of the company's equilibrium conditions in the dynamic business environment

The article discusses algorithms for structural and functional modeling, implemented in the form of an optimal control problem in which the motion of systems is described by a first-order differential equation, to determine the optimal period of transition of the enterprise system to the planned equilibrium state and the required values of indicator indicators.  The developed model is used to predict the innovative dynamics of the enterprise, the parameters of the model are used with the help of financial and economic indicators of the PJSC "Bashtansky cheese factory".  Seven possible equil

## NEUROCONTROLLED OBJECT PARAMETERS ADJUSTMENT BY ACKERMANN'S FORMULA USAGE

Synthesis methods of controllers based on the use of frequency characteristics or root hodographs are considered classic or traditional. Frequency methods are available in practical applications, and most control systems are designed based on various modifications to these methods. A distinctive feature of these methods is the so-called robustness, which means that the characteristics of a closed system are insensitive to the minor errors of the model of the real system.

## Mathematical modelling and experimental determination of parameters of the guidance system of weaponry complex

The methodological approaches to the improvement of the control system of the vertical guidance mechanism of FM-21 multiple launch missile system to increasing its speed and positioning accuracy are confirmed. The use of the three-circuit positional structure of the control system of the guidance mechanism with a position control loop and a fuzzy corrector is justified. A mathematical model of the guiding package motion has been obtained and its reaction has been calculated.

## MANAGING THE FINANCES OF WHOLESALE AND RETAIL TRADING ENTERPRISES

The article deals with the main features and trends of financial management development of wholesale and retail trade enterprises. The comparative dynamics of wholesale trade and retail trade in Ukraine and factors that adversely affect the development of enterprises are analyzed. The main stimulating and restraining factors influencing the development of the wholesale and retail market are investigated.

## Theoretical foundations for the development of experimental equipment for determining the load capacity of speed change devices

The article gives the theoretical base for construction of equipment for experimental research of static, kinematic and dynamic characteristics of devices for speed change by epicyclic gear trains with closed circuit hydrosystems through the ring gear during the transmission by them of the periodic, shock long-term or short-term loads or their executive mechanism stoppage due to overload.

## Design of a short-time energy saving tank for light weight electric transport vehicles

The paper suggests the approach to the design of a short-time energy saving reservoir for light-weight electric transport vehicles. It is substantiated that the new product will be energysaving and will ensure gains in traction and braking force. CATIA was chosen as the most proper environment for the design as its libraries are the most suitable for machine-building.

## Modelling of the Articulated Vehicle Dynamics Taking into Account the Elastically Fastened Freight

In this article, some methodological statements of the formation of mathematical models in the problems of machine dynamics are elucidated. The presence of a cushioned freight in the form of the fastened vehicle complicates the system, so that the equations describing its oscillations are too complicated and unsuitable for practical usage. It is shown that with all the complexity of the research object, it is expedient to form the mathematical model at the level of the design diagram (model) with a relatively small number of degrees of freedom.

## Reduction of phase interactions in control processes of “arc steel-making furnace – power supply system” complex electrical technological system

The article offers system engineering solutions for enhancing the single-phase autonomy of the processes of controlling the coordinates of electrical mode (EM) in an electrical mechanical sub-system of moving the electrodes of  an electric arc steel-making furnace by including a cross-link compensator into its structure.