Analysis of root crop preparation system

. In recent years, the technical level of agricultural production has increased significantly, successfully introduced new technological techniques, means of mechanization and automation of production in crop and livestock. At the same time, further progress in this direction is impossible without systematically organized work on the development and implementation of modern automatic control systems for various processes. Works in this direction are based primarily on a detailed study of the properties of various objects of agricultural production, as the basis for the analysis and synthesis of effective automatic control systems is mathematical modeling of real processes and devices. Recently, there has been a transition from the modeling of individual devices to the modeling of complex technological schemes, which is largely due to a significant increase in the complexity and dimension of the problems to be solved. Therefore, this approach allows you to set and solve optimal control problems not only for individual devices, but for entire technological complexes, which in turn will provide a significant economic effect and will be widely used in solving many engineering problems.


Introduction
One of the most time-consuming processes on livestock farms of various forms of ownership is the preparation of feed for feeding. The task of their preparation for feeding is to ensure that as a result of mechanical (grinding, mixing) or heat treatment (steaming) to increase the content of chemical elements and digestibility of animals consumed feed mixture. This principle is the basis of both the design of machines and equipment, and the entire mode of technological process of preparation of feed on livestock farms and complexes. Therefore, increasing the efficient use of nutritional value with the introduction of intensive technologies of preparation of complete feed mixtures with the use of root crops based on high-efficiency equipment is one of the most important tasks in animal husbandry [1,2,3]. Many different components are used in animal feeding diets, and therefore the process of preparing root crops for fodder for agricultural animals is currently not fully worked out, since it is quite difficult to mechanize it with one machine. For mechanization of production processes on livestock farms and complexes use various machines and equipment that are used for the preparation, transportation and distribution of feed and are used both individually and as part of the production lines (PTL) [4,5,6].
Technological lines of preparation of root crops provide performance of operations of loading, delivery, unloading, accumulation (storage), giving, clearing or washing, grinding and the metered giving on the line of mixing [7,8,9,10]. For the successful management of technological processes performed by the working bodies of forage machines, it is no longer enough to know the individual qualitative aspects of the process. Therefore, the systematic approach and methods of mathematical modeling, which are the initial basis for the study and design of modern machines, are increasingly being used [11,12,13].
A deep study of the mechanism of technological processes of machines for the purpose of their mathematical description for the subsequent optimization of the main parameters is a rather difficult task. The fact is that in addition to comprehensive information about the influence of a large number of different factors on the process under study, it is necessary to have accurate methods of their theoretical generalization. Therefore, the use of mathematical modeling methods in engineering and scientific research is a significant step forward on the path of technological progress and scientific knowledge [14,15].
Mathematical modeling is the study of the behavior of an object in certain conditions by compiling and solving equations of its mathematical model. From a large number of definitions, in our opinion, the following is optimal: "a Mathematical model is a specific information object in the form of a system of mathematical relations, which are an approximate formal description of the properties, characteristics and relationships of the original object of arbitrary nature, which are essential for the problem solved by the subject (person)" [16,17]. Thus, each mathematical model is a structure, the components of which are: the subject (person); the problem solved by the subject; the object-the original (fragment of reality) and the language of formal description of the model by means of mathematical symbolism.
If the model is an idealization of a real object, when the determining and discarded the secondary (specific tasks) traits or characteristics. It is quite obvious that each material object can be compared with many different models that differ from one another both in their structure and the degree of detail of the properties of the object in question, and the way they are obtained (description of the data table, graph, formula, system of equations, algorithm, and the like).
A well-constructed mathematical model is generally more accessible to study than a real object. In addition, it has a remarkable property: its study gives some new knowledge about the original object. However, each model has certain limitations and assumptions associated with the problem to be solved and the properties of the original object. The quality of the resulting models can not be estimated either by structure or form. The only criterion for such an assessment can only be the reliability of the predictions of the behavior of a real object obtained on the model. Moreover, one of the possible models may be more adequate than others in a certain range of variable factors, but less accurate in another range. In this case, you can choose a less accurate model, if it is adequate in the critical (optimal) area.

Procedure for analyzing engineering solutions for complex systems
A large number of factors affecting the efficiency of technological processes in the production of livestock products, their complex nature, the difference in the evaluation criteria of significance, complex relationships, make it necessary to use a systematic approach to their production. A biotechnology system that consists of the set technological processes, ranging from preparation of feed rations, including washing and chopping root E3S Web of Conferences 176, 03007 (2020) IDSISA 2020 https://doi.org/10.1051/e3sconf /202017603007 crops to produce animal products with the help of machines and equipment to ensure their function is considered for the first time. Figure 1 shows the technological scheme of BTS delivery of root crops to the point of preparation for their washing, grinding and subsequent delivery to cattle in accordance with the diet of its feeding. It includes a trailer feeder-dispenser 1 with an inclined conveyor 2, a sink-chopper 3 and a sump 4. When considering any production from the standpoint of system analysis, it is possible to distinguish a number of elements, each of which in turn can be considered as a biotechnological system. Each of these elements (subsystems) is characterized by a complex hierarchical structure of relations, to which a systematic approach is also applicable. With regard to the technological process of preparing root crops for feeding, including delivery, washing, grinding and their use in the diet of cows, BTS should be understood as a complex hierarchical structure of orderly interdependent and interrelated devices that ensure the transformation of material (feeding rations) and energy flows in the process of obtaining and processing feed into final products -meat and milk. This relationship should be analyzed using the apparatus of graph theory [18,19,20]. On the basis of the technological scheme of BTS we will make the scheme in the form of technological operators (see Fig. 2 crops under their own weight are fed to the longitudinal chain-planed conveyor (flow L1). Due to friction between root crops during their movement along the inclined sides of the side walls of the hopper feeder-dispenser 1 and moving along the scraper conveyor located inside it, there is an initial separation of contaminants (soil impurities, stones and other heavy objects) and their removal (flow L2). Next, root crops are fed to the inclined scraper conveyor 2 (flow L3), where also due to friction between themselves and their movement there is an additional separation of contaminants and their removal (flow L4). Next, the flow of root crops L5 enters the sink, where they are finally soaked and washed in the bath from contamination, washed by a stream of purified water (stream L6), created by the pump from the sump 4. At the same time, the contaminated water (flow L7) is discharged by the pump into the sump 4 and the stones are removed from the bath by the discharge conveyor of the sink (flow L8). In the chopper falls stream L5, where the grinding of root crops in accordance with zootechnical requirements. Through the discharge tray of the shredder, root crops enter the hopper of the self-propelled feed feeder-mixer 5 (stream L9) with an electronic weighing system for all components of the diet and are then issued to agricultural animals.  ;  ;  ;  ;  ;  ;  ;  ;  ;   3  3  3  3  3  2  2  2  2  2  1  1  1   where  ij Q the i-th generalized flow associated with elements of the BTS. The set of equations compiled for all elements of the system form a system of linear equations of balances of one type of generalized BTS flows [12,21]: matrix of a system of equations, elements of which.
For the considered BTS on the basis of the law of conservation of mass it is possible to make nine equations of material balance on mass expenses of streams of processed products (root crops). The resulting system will contain ten equations of material balance with known (free) and unknown (basic) variables. It is quite difficult to choose free variables of the considered BTS equations, as it is necessary to perform a large amount of calculations. The solution of this problem can be greatly simplified if we analyze the topological properties of the BTS. In this case, each system can be put in accordance with the flow graph, which is some topological model of one type of generalized or physical flows of the system. The streaming graphs used for the analysis of technological systems which allow for structural changes for ease of analysis. The complexity of the BTS analysis consists in the large dimension of the problems, as well as in the fact that it has a recycle that makes it difficult to model such a system. Using technological processes in the form of graphs and analysis of the adjacency matrix, it is possible to carry out the decomposition of the system into subsystems of smaller dimension and to investigate the work of the BTS through its subsystems. Figure 3 shows the flow material graph for the steady-state technological mode of BTS delivery and preparation of root crops. The vertices of the graph on the total mass flow rate of physical flows correspond to the elementsFor the considered BTS on the basis of the law of conservation of mass it is possible to make nine equations of material balance on mass expenses of streams of processed products (root crops). The resulting system will contain ten equations of material balance with known (free) and unknown (basic) variables. It is quite difficult to choose free variables of the considered BTS equations, as it is necessary to perform a large amount of calculations. The solution of this problem can be greatly simplified if we analyze the topological properties of the BTS. In this case, each system can be put in accordance with the flow graph, which is some topological model of one type of generalized or physical flows of the system. The streaming graphs used for the analysis of technological systems which allow for structural changes for ease of analysis. The complexity of the BTS analysis consists in the large dimension of the problems, as well as in the fact that it has a recycle that makes it difficult to model such a system. Using technological processes in the form of graphs and analysis of the adjacency matrix, it is possible to carry out the decomposition of the system into subsystems of smaller dimension and to investigate the work of the BTS through its subsystems. Figure 3 shows the flow material graph for the steady-state technological mode of BTS delivery and preparation of root crops. The vertices of the graph on the total mass flow rate of physical flows correspond to the elementsKroot crop preparation systems that transform the total mass expenditure of physical flows, source i and effluents S of physical flows substances. Arcs meet the mass flow rates of physical flows.
In the preparation of the matrix   С its columns are arranged in ascending order of the chord numbers forming the fundamental cycles, and the rows are arranged in such a way that the rows corresponding to the chords first go, and then the branches of the tree (in ascending order of the numbers) [11].

Results and discussion
The equations of material balance based on the analysis of the operator scheme of the BTS (figure 2) and the cyclomatic matrix allow to determine the load on all elements included in the BTS. At the same time, it is advisable to choose free variables of the system based on the analysis of its topological properties. Therefore, a consistent study of the nature and strength of these connections allows you to develop and make the most rational decisions in order to improve the efficiency of the use of technology.
Analyzing the flow material graph (figure 3) we see that the delivery and preparation of root crops occur in a continuous flow. Losses of root crops mass and their nutritional properties at reduction of technological operations of BTS decrease proportionally to number of elements of system. At the same time, the time of preparation of root crops in the BTS is reduced several times compared to conventional livestock farms and complexes with similar systems. In addition, it allows us to conclude that environmental pollution in the application of BTS is minimized.

Conclusion
The mathematical models considered in this article allow a reasonable approach to the selection of the main parameters of machines and equipment for the preparation of root crops for animal feed, and in many cases to optimize them. This creates prerequisites for the development of more advanced and productive machines while ensuring the required quality of technological processes with low specific costs and metal consumption.