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. Organizacija i planirovanie mashinostroitel'nogo proizvodstva, M.: Mashinostroenie, 1974. – p. 592. [6] Sokolicyn S. A. Primenenie matematicheskih metodov v jekonomike i organizacii mashinostroitel'nogo proizvodstva, L.: Mashinostroenie, 1970. – p. 345. [7] E. D. Voronina Upravlenie gibkimi proizvodstvennymi sistemami. Modeli i algoritmy, obshh. red. S. V. Emel'janov, M.:Mashinostroenie, 1987. – p. 368. [8] Shkurba V. V. & V.V. Shkurba Planirovanie diskretnogo proizvodstva v uslovijah ASU, K.: Tehnika, 1975. – p. 296, p. 6. [9] Lefeber E. Modeling, Validation and Control of Manufacturing Systems., Proceeding of the 2004 American Control Conference, Massachusetts, 2004. – p. 4583–4588. [10] Lefeber E. Controlling a re-entrant manufacturing line via the push-pull point., International Journal of Production Research 46(16), 2008. – p. 4521–4536. [11] Mac Gregor S.J. Handbook of Stochastic Models and Analysis of Manufacturing System Operations.,New York, 2013. –Vol. 192, p. 373. [12] Pihnastyi O.M. Statistical theory of production systems, Kharkіv: KhNU, 2007, p. 388 doi: 10.13140/RG.2.2.18903.78244 [13] Krasovskij A. A. Fazovoe prostranstvo i statisticheskaja teorija dinamicheskih sistem, M.: Nauka,1974, p. 232. [14] V. S. Teorija upravlenija, K: Vyshha Shkola, 1988, p. 312. [15] Moiseev N. N. Jelementy teorii optimal'nyh sistem, M.: Nauka, 1974, p. 526. [16] Pontrjagin L. S. Matematicheskaja teorija optimal'nyh processov, M.: Nauka, Gl. red. fiz.-mat. Lit., 1983, p. 392. [17] Pugachev V. S. Osnovy statisticheskoj teorii avtomaticheskih sistem, M.: Mashinostroenie, 1974, p. 400. [18] Pihnastyi O. M. The calculation of a production cycle with application of the statistical theory of industrial-technical systems, Reports of the National Academy of Sciences of Ukraine – 2009, vol.12, pp. 38 – 44. doi: 10.13140/RG.2.2.36267.54562 [19] Bellman R. Teorija ustojchivosti reshenij differencial'nyh uravnenij, M.: Izdatel'stvo inostrannoj literatury, 1954. – p. 215. [20] Kazakov I. E. Statisticheskaja teorija sistem upravlenija v prostranstve sostojanij, M.: Nauka, 1975, p. 432. [21] Armbruster D. Kinetic and fluid model hierarchies for supply chains supporting policy attributes, Bulletin of the Institute of Mathematics. – Academica Sinica, 2006, pp. 496–521. [22] Ramadge P. The control of discrete event systems, Proceedings of the IEEE vol. 77, № 1., 1989, pp. 81–98. [23] Harrison J. Brownian Motion and Stochastic Flow Systems.,New York,1995. – p. 142. [24] Demutsky, V.P. Pihnastaja, V.S. Pihnastyi, O.M. 2003. Theory of the enterprise: the stability of the functioning of mass production and promotion of products on the market. Kharkov.:KhNU, p.272. doi: 10.13140/RG.2.1.5018.7123. (in Russian) [25] Armbruster D. Continuous models for production flows., In Proceedings of the 2004 American Control Conference. – Boston, MA, USA. 2004, pp. 4589–4594. [26] Zaruba V. Ja. Jentropija tehnologicheskogo processa, [Upravlenie bol'shimi sistemami: trudy mezhdunarodnoj nauchno-prakticheskoj konferencii] “Teorija aktivnyh sistem” (TAS2011),. – Moskva: IPU RAN. – 2011. – Tom. 2. – pp 145 – 148. (In Russian)1 [27] Serebrennikov G. G. Organizacija proizvodstva, Tambov: Izd. TGTU, 2004. – p. 96. [28] Sinica L. M. Organizacija proizvodstva / L. M. Sinica. – Mn.: UP IVC Minfin, 2003. – 512 p. [29] Tian F. An iterative approach to item-level tactical production and inventory planning. / F.Tian, S.P.Willems, K.G.Kempf –International Journal of Production Economics, 2011. – vol. 133. – P. 439–450. [30] Ljapilin I. I. Vvedenie v teoriju kineticheskih uravnenij, Ekaterinburg: UGTU-UPI, 2003,p. 205. [31] Pihnastyi O.M. Using PDE-models for a unified theory of production lines., Bulletin of the Kherson National Technical University. Kherson: KhNTU. – 2014 – No. 3 (50). – pp. 405–412. doi: 10.13140/RG.2.2.15769.52326 [32] Pihnastyi O.M. The construction of the target function of the production system, Reports of the National Academy of Sciences of Ukraine, 2006, pp. 79–85. doi: 10.13140/RG.2.2.11808.28161 [33] Fel'dbaum A. A. Metody teorii avtomaticheskogo upravlenija: nauchnoe izdanie, M.: Nauka, 1971, 744 p. [34] Lysenko Ju. G. Modelirovanie tehnologicheskoj gibkosti proizvodstvenno-jekonomicheskih sistem,Doneck: DonNU, 2007, p. 238. [35] Pihnastyi O.M. Multi-moventsflowmodelproductionline, Mathematical modeling. – Dneprodzerzhinsk: DSTU. 2017. – № 1. – pp. 81–87. doi: 10.13140/RG.2.2.19038.13128 [36] Pihnastyi O.M. The task of optimal operational control of macroparameters of a production system with mass production, Dopovіdі Nacіonal'noї akademії nauk Ukraїni. – Kiїv: Vidavnichij dіm "Akademperіodika". 2006, № 5 – pp. 79–85. doi: 10.13140/RG.2.2.29852.28802 [37] Karcheva G. Problemi і perspektivi rozvitku bankіvs'koї sistemi Ukraїni: zb. nauk. pr. /NBU; Mіn-vo osvіti і nauki Ukraїni. – Sumi, 2009. – T. 26. – pp. 200–206. https://goo.gl/3HcT8P (accessed 14.05.2009) [38] Pihnastyi OM. Overview of models of controlled production processes of production line production lines, Scientific bulletins of the Belgorod State University. Belgorod: BSU. – 2015. – No. 34/1. P.137–152, doi: 10.15407/dopovidi2014.12.036 [39] Lur'e K. A. Optimal'noe upravlenie v zadachah matematicheskoj fiziki, M.: Nauka. Glavnaja redakcija fiziko-matematicheskoj literatury, 1975, p. 480. [40] Armbruster D. A continuous model for supply chains with nit buffers, SIAM Journal on Applied Mathematics, 2011, pp. 855–877. [41] Klejner G. B. Proizvodstvennye funkcii: Teorija, metody, primenenie, M.: Finansy i statistika, 1986, p. 239. [42] Val'ko V. I. Variacionnoe ischislenie i optimal'noe upravlenie, M.:MVTU im.Baumana, 2006, p. 488. [43] Jel'sgol'c L. Je. Differencial'nye uravnenija i variacionnoe ischislenie, M.: Nauka, 1969, p. 425. [44] Lavrent'ev M. Osnovy variacionnogo ischislenija, M.: Izd-vo NKTP SSSR, 1935. – Tom 2, p. 399. [45] Armbruster D. Kinetic and fluid model hierarchies for supply chains, SIAM Multiscale Model Simul. – 2004. – vol. 2 № 1, pp. 43–61.
Authors and Affiliations
О. М. Пигнастый, Г. К. Кожевников
Keywords
Related Articles
- EP ID EP444746
- DOI 10.31319/2519-8106.2(39)2018.154231
- Views 77
- Downloads 0
Вибір махових мас ланок передаточних механізмів на основі оптимізації передаточної функції
On the basis of a mathematical model of the transmission mechanism were obtained dependences which allowed calculating during design phase the corresponding mass of gearwheels that can play the role of flywheel masses of...
МАТЕМАТИЧНА МОДЕЛЬ ПРОЦЕСУ МИЙКИ ШЛІФУВАЛЬНОГО ШЛАМУ
TTHE MATHEMATICAL MODEL OF THE CLEANING OF GRINDING SLUDGE PROCESS Vernyhora V.D. Abstract Continuing pollution of the natural environment with solid, liquid and gaseous wastes of production and consumption, causing env...
Розробка математичної моделі процесу мийки шламів абразивної обробки металів в миючому розчині
DEVELOPMENT OF MATHEMATICAL MODEL OF SLUDGE CLEANING PROCESS 0F ABRASIVE METAL TREATMENT IN THE CLEANING SOLUTION Vernyhora V.D. Abstract At present engineering companies have huge problems with waste sludge obtained af...
Оптимізація роботи металургійного підприємства шляхом аналізу експлуатаційних показників роботи кар’єрних самоскидів
OPTIMIZATION OF THE WORKOF METALLURGICAL ENTERPRISES BY ANALYZING OPERATIONAL PARAMETERS OF THE WORK OF DUMPTRUCKS Sereda B.P., Mukovska D.Y. Abstract In the article a comparative analysis of the spatial performance in...
Методика оцінки фінансового стану підприємства з використанням левериджу
METHOD OF ASSESSING THE FINANCIAL CONDITION OF AN ENTERPRISE USING LEVERAGE Levchuk K.O., Romaniuk R.Ya. Abstract In the modern economy, the role of innovation is great. They provide the competitiveness of products and...