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Документ Статистическая теория описания производственно-технических систем(Харківський національний університет ім. В. Н. Каразіна, 2010) Пигнастый, Олег Михайлович; Ходусов, Валерий ДмитриевичДокумент Optimal stabilization algorithm for production line flow parameters(Національний університет "Запорізька політехніка", 2020) Pihnastyi, O. M.; Khodusov, V. D.; Kazak, V. Yu.Context. A method for constructing an algorithm for stabilizing the interoperability of a production line is considered. The object of the study was a model of a multi-operational production line. Objective. The goal of the work is to develop a method for constructing an optimal algorithm for stabilizing the flow parameters of a production line, which provides asymptotic stability of the state of flow parameters for a given quality of the process. Method. A method for constructing an algorithm for stabilizing the level of interoperative backlogs of a multi-operational production line is proposed. The stabilization algorithm is based on a two-moment PDE-model of the production line, which made it possible to represent the production line in the form of a complex dynamic distributed system. This representation made it possible to define the stabilizing control in the form of a function that depends not only on time but also on the coordinates characterizing the location of technological equipment along the production line. The use of the method of Lyapunov functions made it possible to synthesize the optimal stabilizing control of the state of interoperation backlogs at technological operations of the production line, which ensures the asymptotic stability of the given unperturbed state of the flow parameters of the production line at the lowest cost of technological resources spent on the formation of the control action. The requirement for the best quality of the transition process from a disturbed state to an unperturbed state is expressed by the quality integral, which depends both on the magnitude of the disturbances that have arisen and on the magnitude of the stabilizing controls aimed at eliminating these disturbances. Results. On the basis of the developed method for constructing an algorithm for stabilizing the state of flow parameters of a production line, an algorithm for stabilizing the value of interoperation backlogs at technological operations of a production line is synthesized. Conclusions. The use of the method of Lyapunov functions in the synthesis of optimal stabilizing control of the flow parameters of the production line makes it possible to provide asymptotic damping of the arising disturbances of the flow parameters with the least cost of technological resources spent on the formation of the control action. It is shown that in the problem of stabilizing the state of interoperative backlogs, the stabilizing value of the control is proportional to the value of the arising disturbance. The proportionality coefficient is determined through the coefficients of the quality integral and the Lyapunov function. The prospect of further research is the development of a method for constructing an algorithm for stabilizing the productivity of technological operations of a production line.Документ Conveyor Model with Input and Output Accumulating Bunker(Institute of Electrical and Electronics Engineers, Inc., USA, 2020) Pihnastyi, O. M.; Kozhevnikov, G. K.; Khodusov, V. D.In this article, a model of a conveyor-type transport system with an input and output bunker is developed. The transport conveyor is presented in the form of a dynamic distributed system. It is shown that the material flow is proportional to the linear density of material distribution along the transport route. The coefficient of proportionality is the speed of the belt. When constructing the model, the assumption of the absence of oscillatory processes associated with the tension of the conveyor belt is introduced, which corresponds to the case when the function determining the speed of the belt is only a function of time. A solution is given, that determines the state of the flow parameters of the conveyor section for a given point of the transport route at an arbitrary point in time. It is shown that the state of the flow parameters for an arbitrary place in the transport route is determined by the state of the flow parameters at the input of the conveyor section, considering the transport delay. An expression is written that allows to calculate the amount of transport delay. The relationship of the transport delay value with the algorithm for controlling the conveyor belt speed is demonstrated. A system of equations for the model of a conveyor-type transport system with an input and output bunker is obtained. The behavior of the model for several characteristic cases of the functioning of the transport system is analyzed. The constructed model of the control object can be used to design highly efficient control systems for the flow parameters of the transport system with an input and an output bunker.Документ Оптимальное управление потоком материала на входе магистрального конвейера(ИД "БелГУ", 2020) Пигнастый, Олег Михайлович; Ходусов, Валерий ДмитриевичВ статье решена задача оптимального управления величиной входного потока материала магистрального конвейера с аккумулирующим бункером. Для описания магистрального конвейера использована PDE-model поточной линии. Магистральный конвейер представлен в виде сложной динамической распределенной системы. Предложен алгоритм построения оптимального управления потоком материала из аккумулирующего бункера. Алгоритм позволяет обеспечить минимальное отклонение выходного грузопотока материала от заданного планового значения. Синтез оптимальных управлений выполнен с учетом ограничений на размер аккумулирующего бункера и ограничения на величину управления. При проектировании оптимальных управлений полагается, что скорость конвейерной ленты магистрального конвейера является постоянной. Детально анализируется динамика заполнения материалом аккумулирующего бункера для разных алгоритмов управления. Представлены варианты точек переключения значения оптимального управления. Отдельно анализируются случаи оптимального управления, когда фазовая координата не достигает фазовых ограничений и когда фазовая координата находится на фазовом ограничении.