This study investigates the technological process of heating a liquid considered as a controlled cybernetic system for converting resources into a usable technological result. The work aims to solve a pressing task of choosing a single universal criterion for assessing the effectiveness of technological processes. The subject of research is the ELF (Normalized Efficiency Criterion) computing module, designed for an integral assessment of the effectiveness of cybernetic control over technological processes in discrete time. This work reports designing a computing module that converts technological input parameters and corresponding price coefficients into a system of cost indicators of costs and useful effect. The proposed system allows for the reduction of heterogeneous resources and the result of the process to a single scale, which makes it possible to formalize their joint analysis and a coordinated comparison of alternative modes. Elementary cost functions and aggregated indicators of the control cycle are introduced, on the basis of which the first-level integral accumulators are formed – accumulated costs and accumulated effect. To assess the efficiency of control over a given time interval, secondary integrators of the second level and the mode selection index are used, which reflects the excess of the integral effect over the integral costs in the inertial-accumulator sense. Within the framework of the approach, the additional benefit and resource intensity of the permissible control mode are determined, which are formed using a storage device with a reset mechanism in the case of violation of the regime conditions. The permissibility of the mode is set by the threshold rule and the procedure for resetting the final indicators in the case of its inadmissibility, which provides a diagnostically interpreted separation of the causes of zero efficiency. The proposed structure of the computing module focuses on the analysis, diagnostics, and optimization of control modes and allows for software implementation as part of cybernetic control systems

This study examines controlled technological process of heating liquid, which is considered as a cybernetic system for transforming resources into a usable technological product. The work investigates the possibility of constructing a normalized functional of deviation in the efficiency indicator in dynamic models of technological processes, used to synthesize optimal control effects. They provide a quantitative assessment of deviation of the actual efficiency from the required level and allow the application of optimal control methods. The task addressed is to find a standardized indicator of efficiency deviation E, which would ensure the dimensionlessness of this indicator and its large-scale independence. It is a dimensionless quadratic measure of difference between the total useful result and the total costs. It has been shown that the parameter E has the properties of computational constancy and could be used for analysis, normalization, and comparison of various control modes. The ELF (Normalized Efficiency Criterion) computing block has been designed, which makes it possible to convert input parameters into cost form, accumulate total costs and useful effect, form indicators of additional benefit and resource intensity, as well as calculate a normalized efficiency criterion. It is shown that ELF is an integrated indicator of efficiency as a ratio of additional benefit to the resource intensity of the permissible mode; the indicator E represents its normalized metric form. The results make it possible to assess the effectiveness of the process in a quantitative way. And the functional E shows a deviation from the required mode, which gives the opportunity to conduct an analysis and make the right decisions in the management of a technological process. The research findings could be used in any technological processes

The object of this study is the processes of optimal control over complex technical systems with input and output products distributed in time. The automatic formation of optimal control trajectories of technical systems that ensure maximum efficiency of production processes is limited by the insufficient development of the applied theory of the efficiency of complex systems. This work considers the development of the conceptual base and axiomatization of the applied theory of the efficiency of technical systems. A system of definitions and a system of axioms describing the indicators of the functioning of the cybernetic model of a technical system have been developed. The resulting system of axioms formalizes the technique and methods for determining various indicators, as well as obtaining the current value of the performance indicator of the technical system. The obtained expressions make it possible to form a subsystem for assessing the effectiveness of a technical system, invariant with respect to its internal structure and the characteristics of the transformation processes implemented by it. The universality of the proposed indicators and the structural unity of the performance evaluation subsystem make it possible to express an opinion on the cybernetic level of these decisions. An example of the practical application of the proposed system of axioms of the applied theory of efficiency is given. The proposed method for determining the efficiency indicator can be applied to arbitrary technical systems with a distributed nature of the change in input and output products. The cybernetic level of abstractions used to determine the effectiveness of complex systems makes it possible to proceed to solving the problem of formalization and full automation of the processes of optimal control over complex technical systems with distributed input and output products

The research concerns the field of optimization for technological transformation processes with a continuous supply of raw materials. The article offers an approach to the organization of the dynamic systems work with monitoring and management is carried out on the basis of specified parameters from a cybernetic view point. In order for the system to reach the optimum and maintain it with dynamically changing input parameters, a systematic calculation of the system efficiency in the current mode with subsequent correction of the control trajectory is required. For these purposes, an improved method of efficiency calculating of the continuous dynamic system operating mode was proposed, which differs from the existing one by using the parameters of the global model of the continuous process. Verification of the proposed method was carried out by testing the system interface model.

Optimization of production processes has always been one of the cornerstones for industrial enterprises seeking to improve productivity while minimizing the costs involved. A particularly difficult situation is when it is necessary to manage the process of the entire production chain with a continuous supply of raw materials. It is necessary to keep under control the actual production data, current production requirements, and adhere to the international strategy of energy saving. This paper reports a devised optimal dynamic system with a continuous supply of raw materials, which automatically changes the control trajectory in order to reduce the amount of resources used. The theoretical scientific component is represented in the form of an interface model of the system, and the research results are represented in the form of time diagrams that show the verification of the proposed model. The model provides for the interconnection of the chain of such developed dynamical systems, in which the continuity of the process is ensured by buffering systems, and the optimality of operation is enabled by adaptation mechanisms. The time diagrams can demonstrate the interaction of systems and mechanisms that generate information signals through the port sections. At each subsequent control action, the process parameter changes were made within a set range. As a result of a targeted search for permissible controls, the system, driven by the adaptation mechanism, enabled a gradual reduction in the consumption of the energy product and stabilized the intensity of the target product being processed, which made it possible to subsequently avoid shutdowns and restarts of the production line and reduce overall production costs.

This study relates to the field of verification of cybernetic estimates of the use of reserves as criteria for the effectiveness of transformative class systems with a continuous supply of a technological product. The task set here attracted even more attention after the advent of improved approaches that make it possible to automatically change the control trajectories of technological systems in real time. In such cases, the assessment of the current status of the process and the efficiency of stock management has become an integral part of the operation of the management subsystems. Therefore, the development and verification of cybernetic assessment of effectiveness for such control systems is a relevant issue. The first stage of the reported research involved the development of a cybernetic model of operation with distributed parameters. Four formal features have been proposed. Finding integral functions of these features has made it possible to obtain an idea of some quantitative characteristics of the process while finding the second time-dependent integral characteristic has made it possible to represent the physical and cybernetic parameters of the process. At the second stage, formulas for calculating the main assessment indicators were proposed; their verification was carried out under three different control trajectories, which showed the adequacy of the devised approach. The final step was to develop three variations of the efficiency formula, which is calculated at set points in time throughout the entire production cycle. Thus, cybernetic assessment of the effectiveness of the use of reserves makes it possible to formalize and fully automate the processes of optimization and adaptation of the functional systems of an enterprise

Many modern industrial production facilities consist of sequentially operating systems with a continuous supply of technological product. The task of stabilizing the qualitative and quantitative parameters of output products at all stages of such production is a very difficult task and often leads to additional time and money costs. Therefore, improving the efficiency of these processes is a relevant issue. A review of analogous solutions to this type of problem revealed the variability of their authors’ approaches. However, all of them are aimed at optimizing existing control trajectories, rather than creating a new, more accurate trajectory. Earlier, as part of the description of the basic principles of structural and parametric optimization of the management of production processes of this type, only the improved work of technological subsystems was reported. This paper describes the principles of control over the proposed dual buffering system and its interactive interaction with other technological subsystems. The introduction of buffering systems makes sequential technological subsystems more independent of each other. That makes it possible to increase the degree of freedom for each control subsystem and thereby improve the efficiency of finding the optimal mode of operation of the entire cybernetic system. A conceptual model of the dual buffering system was built, the stabilization of the quantitative parameter at the output of the buffering system was substantiated through the development of an adaptation mechanism, and simulation modeling of the synthesized system was carried out. The study shows that the use of buffering systems could improve the quality of energy utilization and reduce the wear of technological mechanisms by 14 % in general

The aim of the work is to develop a method of operations models forming by introducing restrictions on the operation parameters of the compared operational processes. Consequently, we need to formulate rules for determining of tolerance region of cost estimates for the output product of operational process consisted of short operations. Also, we need to develop the method of tolerance region determining for the parameters of short operations for compared processes. This allows to us formalize the solution of the constraints determining problem for the generated model data. Also we need to carry out test experiments of the developed method on the example of the estimated factors designed to effectiveness determining. The developed modeling method was verified by comparing the results of two operational processes. A comparison of the operational processes results with evaluating of the individual operations results of these processes is obtained. The discrepancy between the simulation results and the results of direct assessment of operations using verified indicators in the area excluded from consideration, using the developed method is observed. The developed modeling method allows to us determine the restrictions area of the simulated operations parameters. Under the conditions of this area accounting, the errors probability in modeling results of problems associated with decision making is eliminated.

Optimization of the stock management process is associated with the search for a forecasting model, a method for generation of a forecasting time series, a model of logistic operation, determining a reasonable level of reserve stocks and establishing the optimization criterion. Successful solution to the optimization problem in general can be achieved only if the whole complex of local management problems is successfully solved. In this case, the method of generation of a cointegrated time series of demand forecasting is the central element of the technology of optimal stocks management. This relates to the fact that probabilistic nature of demand is the main factor reducing efficiency of management in systems of this class. It was shown that the proposed method for improving management efficiency can be used in any economic system due to the possibility of construction of a single logistic operation model. The proposed approach is based on formation of a time series specifically designed to solve the problem of forecasting the demand in stocks buffering systems. Such a series contains both information on sales volumes and data related to consumer demand. Since consumer activity is ahead of the process of physical consumption of products, it becomes possible to use anticipatory markers in forecasting problems. The study of operational processes using a verified indicator of efficiency has confirmed the hypothesis of presence of anticipatory markers within the framework of the formed forecast time series. It has been established that the maximum management efficiency can be achieved in the case of a lower construction accuracy of the forecast model. This is due to the fact that the logistic operation model takes into account the costs of movement of products and their valuation at the operation input and output.

The development of new converting technologies and increasing the level of automation leads to an increase in the processing speed of available resources. This means that in case of inefficient or inefficient use of resources, the potential of economic advantage is lost, and the negative consequences of such losses can be identified too late. In such conditions, the requirements for the selection of the criterion of optimization and the validity of the principles of optimal control increase. Moreover, the approach used may vary depending on the daily change in prices for energy products and fluctuations in the level of demand for manufactured products. Despite the fact that such an approach seems obvious, today energy-intensive production suffers significant losses associated with the use of an inadequate model of technological operation, a subjective approach to the choice of optimization criterion and optimization method. The task of developing a method for determining the optimal trajectory of managing energy-intensive industries with a changing level of demand for final products is posed. The solution to this problem consists of several stages. At the first stage, a model of a technological operation is being created, within the framework of which all significant factors affecting the decision result are taken into account. At the second stage, a global operation model is created, the input and output products of which are converted to comparable value values. At the third stage, the optimization criterion for the continuous operation of the system and the mode of incomplete use of its production capabilities is selected. At the final stage, the control path for intermittent and continuous modes of operation is determined. Thus, the aim of research is development of a method for determining the optimal control trajectory in systems of energy-intensive systems, depending on the level of demand for the final product.

Queueing systems (QS) belong to the class of systems the quality of control over which cannot be assessed in real time. In other words, it is impossible to apply methods of classic search optimization at the stage of control design. The current practice of control design implies the acquisition of historical data required to model an operational process in order to choose its best control parameters. These parameters include: determining the size of the planning horizon, forecasting interval, the type of a forecasting model. All these parameters represent the degrees of freedom of search optimization. Upon defining these parameters, modeling process is repeated for different values of shift in the demand forecasted value towards the region of large positive values. Such a shift leads to an increase in the QS inventory levels and a decrease in the likelihood of a product deficit occurrence. Process efficiency is compromised by both the insurance stocks and a shortage of products. However, experience has shown that a certain shift in control towards an increase in the inventory levels improves the efficiency of their functioning. Thus, the task on QS inventory control implies the substantiation of choice of control parameters in the process of cyclic simulation of the operational process based on the set of historical data. Despite the long history of the subject, there is no method at present whose application would make it possible to obtain control, the parameters of which could be considered justified. This relates to that the best control parameters are determined not by examining the quality of economic models of an operational process but rather by studying the quality of quantitative models of this process. In order to further advance the theory and methods of control, we have constructed an economic-mathematical model of uncoordinated operation. The model proposed takes into consideration the result of interaction between processes in the buffering channel and processes in the client channel that aims to meet customer demand considering a factor of information impact from marketing technologies on the internal and external consumer. The structure of the constructed mathematical model has passed the validation procedure for consistency, in the process of comparing the redundant and deficient operations. A procedure for estimation optimization of the simulated process has showed a possibility to determine the optimal control parameters based on the criterion for a maximum criterion of efficiency of operational process

At present, mathematical models in the form of artificial neural networks (ANNs) are widely used to solve problems on approximation. Application of this technology involves a two-stage approach that implies determining the structure for a model of ANN and the implementation of its training. Completion of the learning process makes it possible to derive a result of the approximation whose accuracy is defined by the complexity of ANN structure. In other words, increasing the ANN complexity allows obtaining a more precise result of training. In this case, obtaining the model of ANN that implements approximation at the assigned accuracy is defined as the process of optimization. However, an increase in the ANN complexity leads not only to the improved accuracy, but prolongs the time of computation as well. Thus, the indicator «assigned accuracy» cannot be used in the problems on determining the optimum neural network architecture. This relates to that the result of the model structure selection and the process of its training, based on the required accuracy of approximation, might be obtained over a period of time unacceptable for the user. To solve the task on structural identification of a neural network, the approach is used in which the model’s configuration is determined based on a criterion of efficiency. The process of implementation of the constructed method implies adjusting a time factor related to solving the problem and the accuracy of approximation. The proposed approach makes it possible to substantiate the principle of choosing the structure and parameters of a neural network based on the maximum value for the indicator of effective use of resources

The issues of stabilization of quality parameters of dynamic processes are considered to be well studied. Traditionally, the negative feedback technology is used for this purpose. The concomitant moment of the negative feedback technique use is the need of research of the dynamic system stability in the range of admissible controls, the choice of the stabilization criterion and stabilization parameters. The examples of dynamic systems with continuous and batch technological products feed show that the introduction of negative feedback is not the only alternative allowing to stabilize the quality parameters of output products. It is shown that the problems of dynamic systems stabilization are related to the fact that control signals are transmitted as part of control signals of nonlinearity of the system technological part. In this regard, there are problems of stability and quality of stabilization. The stabilization method that is free from the influence of the technological part and the system-based sign for classifying system objects are proposed. Using this sign allows classifying the system objects relative to the technological subsystem or the control subsystem. The method also provides for the use of system-based principle to determine the optimal control parameters of the stabilization process using the verified criterion of resource efficiency. Using the proposed method allows creating automatic dynamic systems, built on a single architectural principle.

Increasing the efficiency of continuous technological processes, in practice, involves certain difficulties. The presence of these difficulties is due to the fact that the technological product quality is functionally related to energy consumption. In turn, the lack of necessary degrees of freedom, within the framework of the system under investigation, limits the optimization capabilities of control processes. To increase the degrees of freedom of control, the technological mechanism was divided into technological sections. The sections allow collecting independent modules, each of which has its own subsystem of stabilization of the technological product qualitative parameter. This approach allowed us to set different trajectories of changes in the technological product qualitative parameters within one production stage. As a result of the research, it was found that the change in the technological mechanism structure (the modules number) and the trajectory of the change in the technological product qualitative parameter made it possible to change the total energy consumption and wear of the working mechanisms of equipment. The proposed approach made possible to obtain two degrees of freedom of control: the possibility of changing the sectional structure into self-stabilizing modular systems and changing the trajectory of the technological product qualitative parameter within the production stage. The obtaining of degrees of freedom of control, in turn, allowed to change the resource efficiency of the continuous technological process and to develop the method of structural-parametric optimization. As an optimization criterion, an evaluation indicator was used, which was verified for the possibility to use it as an efficiency criterion. As a result, the optimization control capabilities are significantly increased. The principles of the approach are considered in the work with the example of one-, two- and three-step process of continuous liquid heating.

The main efforts related to enterprise creation and development are aimed at improving efficiency of resource usage in the enterprise activities. Such problem can be successfully solved only if maximum efficiency is achieved at each stage of the conversion process. In turn, solution of this problem at each separate stage relates to creation of a substantiated structure of an object of functional conversion of source products into end products during the system operation. Such an object capable of functioning with maximum efficiency of resource usage was defined by default as a "functional system". By the example of a technological process of liquid heating, the problem of synthesizing a functional system of a conversion class with a portioned supply of products of directional effect was solved. In the course of synthesis, the task of ensuring possibility of interaction of the system objects during formation of the end product with required consumer qualities was solved at the first stage. Architecture of a module for identifying system operations and determining limit values of the effective control range was developed at the second stage of synthesis. A module linking the level of demand for the end products of the system with optimal control of its productivity was created at the third stage. Application of the proposed approach has enabled creation of a functional structure with a maximum number of degrees of control freedom. In turn, this solution has made it possible to form an optimal control trajectory depending on consumer demand for end products. The proposed solution enables use of the synthesized architecture for functional systems of a conversion class with a portioned supply of source products

A solution to any problem is valuable only if the results of the solution are reliable. This axiomatic statement is trivial. However, despite the fact that this statement is undeniable, it is violated regularly in problems of operations research. This is due to the fact that the proposed evaluation criteria are not verified and possibility of using indirect methods of effectiveness evaluation of operations is not substantiated. The problem point of modeling was shown using the example of comparison of operational processes, based on equally effective operations with multiple duration. This point is related to the fact that it is necessary to take into account inter-operational losses while modeling the process, based on the use of shorter operations in relation to an alternative operational process. Ignoring these losses can lead to making a mistaken decision or to errors in verification of estimation indicators. In a number of cases the problem can be solved using specially conducted experimental studies. However, if there is a set of unverified estimation expressions or in verification problems, a formal approach can be used. Under this approach, uncertainty, arising in the process of modeling, can be removed by using the capabilities of a verified indicator itself. The developed method for modeling allows us to determine the scope of constraints on parameters of modeled operations. The probability of an error in results of modeling in problems, related to decision making, is excluded on condition of taking into account this region

Determining an indicator for the estimation of effectiveness of system operations is an important stage for optimization of technological processes of any enterprise. This step predetermines the established mode of functioning of all its system processes.The fact that all technological processes should be optimized using an agreed optimization criterion is an axiom. Such a possibility appears only in one case – if we apply the efficiency formula as an optimization criterion in all functional systems. This approach maximizes financial possibilities of the owner of an enterprise.The problem is to identify a structure that corresponds to the structure of the original efficiency formula among a set of evaluation indicators that are identical in terms of formal characteristics.There are classes of standard models of operations define now for the practical solution of this problem. Each of them has its own functional orientation. The most developed are the classes of reference models of simple operations.In relation to the classes of reference models of operations with distributed parameters, there is a solution of the problem operational processes with the same duration in time, as well as for processes with different duration of resource expense by an output.In the proposed study, we define a limited class of models of operations with distributed parameters of different duration by an input. The creation of such a class of operations is quite a difficult task, since it is necessary to take into account a time factor and to enable possibility of comparison of operational processes of different duration.To solve this problem, at the first stage, we formed global models of simple operations of different duration with predetermined rating efficiency. At the next stage, we formed reference models of operations with distributed parameters by an output of different duration by compositing.The development of the verification method by determining a class of operations with distributed parameters in terms of input of different duration in time improves reliability of verification results of the estimated indicator significantly. It is necessary to perform the verification procedure whenever we intended to use it as an indicator of effectiveness