Управління ділянкою першої сатурації з використанням методів тензорного аналізу

В. М. Сідлецький, Є. О. Кадура

Анотація


THE METHOD OF TENSOR ANALYSIS FOR PROCESS CONTROL SYSTEMS FIRST SATURATION

V.Sidletskyy, Ie.Kadura

 

To one of the main stages of sugar production area is the first step carbonation - lime juice purification and carbon dioxide from nonsugars (juice purifying section). Juice purification scheme on the site of the first carbonation consists of the following operations: preliminary defecation (prelimer); main defecation; first carbonation device. This is a universal scheme which provides for the possibility juice purification various options that are chosen depending on the quality of the processed beet juice is quality.

Different versions of processing juice station purification involve changing of technological equipment, as an introduction to the machine and removing them from work (eg working with major defecation and without, with the return of the juice of 1 st carbonation in prelim also can work without return prelimed juice, or the use of combination cold - hot bowel movements) as well as a possible change of parameters of technological regime routine within. That is, depending on the quality of the processed beet production process (quantity and consistency of operating equipment) and technological regime will be chosen to achieve quality indicators juice on the output device first carbonation as well as technical and economic performance of the entire enterprise will be imposed restrictions on the use of resources and travel time of the process.

Changes in the process also impose requirements for management of the site. This is due primarily to the fact that the change of the technological equipment necessary to set and change the values for controls (as a result may have prolonged transients) and modify most controllers: proportional, integral and differential components. But it should be noted that when the process of doing most approaches to management may also change.

That process of cleaning juice characterized by significant variability, but is presented variability related to the manufacturing process, the same situation is with respect to the management system. For example, regulatory filing lime predefecator can occur in three ways: 1) at pH prelimed juice at the output of the device, 2) the ratio of diffuse juice / milk of lime, 3) the ratio of diffuse juice / milk of lime and adjusted to pH prelimed juice .

In turn, the contours management major defecation may regulate the supply of lime into the machine by following three approaches: 1) continuously over time, regardless of the number of processed beet and quality of juice, 2) depending on the quality of juice, 3) the flow of juice .

For the first carbonation is also characterized by three approaches to management, most widespread control circuit supply carbonation gas on the deviation of the pH at the outlet of the saturator, but the best indicators of regulation when carbonation gas is supplied to the ratio of the amount of juice to the amount of gas from the correction in pH at the outlet and by carbonation of CO2 in the gas.

That is the model of process purification juice and management of this process should take into account all the possible work, and provide an opportunity to conduct their analysis and solutions.

Therefore, in this paper the use tensor analysis methods to develop model components and calculations in the management process of cleaning juice. Tensor analysis allows to simplify the simulation almost any point region by introducing the category of multidimensional space. Developed tensor model allows to describe all tasks regardless of their complexity.

Tensor generalizes the notion of scalar, vector and matrix. This transformation rules tensor components are arranged so that we can design new tensors available on some simple rules.

Tensor analysis is a generalization of the concepts of vector analysis and allows you to combine data sets and complex nature of physical quantities that can not be described or presented in a scalar or vector. Therefore, the use of tensor method for constructing a model of the production process is the most appropriate.

Tensor analysis and tensor decomposition were applied to: the development of neural networks, artificial vision system design, signal processing, data processing and analysis.

First tensor - a mathematical object that does not depend on changing the system of coordinates, but its components by changing the coordinate system are converted by a certain mathematical laws. From tensor closely related to its rank and it can be: zero, first, second and so on rank. Tensor of zero rank - a scalar and is the result of direct measurement parameters such as temperature, density, cost. pressure and others. More complex measurements, such as spectroscopy provides a set of parameters that can be set as a vector - a tensor of the first rank. In two-dimensional space tensor of the second rank easiest represented as a matrix describing the heterogeneity of the owner and operates the input vector, changing its direction and scale. Typically, the analysis of complex data n th order tensor formed n-th rank is used to simulate the functions of a large number of variables.

The use of tensor analysis to automated system management processes for areas 1 carbonation. The advantage of tensor analysis that tensor as for facility management and control of the system is calculated only once, then transferred tensor components depending on the selected base. Moreover, if there tensors for technological apparatus or line, when necessary, models or all areas of the enterprise production tensors can add and multiply. This new tensors will be formed, that will be developed a new model tensor for both areas and the entire company.


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