Задача управления распределенными параметрами производственной поточной линией
Journal Title: Математичне моделювання - Year 2018, Vol 1, Issue 2
Abstract
THE PROBLEM OF THE CONTROL OF THE DISTRIBUTED PARAMETERS OF THE PRODUCTION LINE Pihnastyi O.M., Kozhevnikov G.K. Abstract The program control of the flow line parameters for the transient modes of production functioning is presented. When designing the control system, a distributed model of the production line (PDE-model) is used approximation. Are given the mathematical problem of software control of the distributed parameters of the production line. A criterion for the quality of the transition process has been formulated and differential relations between the flow parameters of the production line have been determined. The constraints on control and flow parameters are defined. For the initial and boundary conditions, the goal of control of the production parameters is given. In designing the control system, the equations of differential relations are used, which are determined by the system of balance equations of a two-level model of a controlled production process. By determining the optimal program for controlling the parameters of the production line, a Fourier series expansion was used. Using the Fourier decomposition, the Pontryagin function is written for the system under study. Taking into account the restrictions on the phase coordinates (the volume of the drive between the technological operations and the limitation of the rated capacity of the process equipment), the Lagrange function is constructed. The system of equations for conjugate functions is written and the coefficients of the decomposition of the optimal control are determined in a Fourier series. Optimum control of the flow line parameters is constructed taking into account the limitations of the production system on the maximum volume of hoppers between operations and the amount of the productivity of technological equipment. Possible types of controls are identified. As a comparative analysis, a calculation was performed for an optimal control program that uses the queue model M/M/1. The main features associated with the construction of a PDE-model for managing the parameters of an industrial production line are considered. When building the optimal program for controlling the parameters of the production flow line in order to synchronize the capacity equipment of the flow line, the dependence of the control on the initial conditions is shown. References [1] Berg R. Partial differential equations in modelling and control of manufacturing systems – Netherlands, Eindhoven Univ. Technol., 2004, p. 157. [2] Forrester Dzh. Osnovy kibernetiki predprijatija, M.: Progress, 1961. – 341 p. [3] Pervozvanskij A. A. Matematicheskie metody v upravlenii proizvodstvom, M.: Nauka, 1975. – 616 p. [4] Petrov B. N. Teorii modelej v processah upravlenija (Informacionnyj i termodinamicheskij aspekty),M.: Nauka, 1978. – p. 224. [5] Razumov I. M. 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Authors and Affiliations
О. М. Пигнастый, Г. К. Кожевников
Keywords
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- EP ID EP444746
- DOI 10.31319/2519-8106.2(39)2018.154231
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