The work objective is to develop a special model of the complex distributed object – the cement production – on the basis of the colored timed Petri nets including its analysis and estimation of effectiveness and correctness. Various kinds of the Petri nets together with the methods of their determination and performance dynamics are considered. An operation algorithm is formulated in the matrix form for the colored timed Petri nets. On the basis of the colored timed nets, a mathematical model that allows predicting the cement production volume for a defined period is built. The discussed model is realized in the C++ language. The simulation results are compared to the factual data. It is found that the implemented model with a reasonable degree of accuracy predicts the output volume of the cement production. The developed methods are operable and applicable in the manufacturing process simulation as part of an automated control system of the technology parameters.
model, simulation, colored timed Petri net, cement production, algorithm, production processes.
В работе рассмотрена методика создания модели на примере сложной распределенной системы — технологического процесса функционирования цементного производства. Процесс выпуска цемента является одним из примеров недетерминированных динамических параллельных производственных систем, проблема моделирования которых связана как с возможной хаотичностью системы, так и с необходимостью учитывать динамику подсистем.
Для описания и анализа таких систем могут применяться сети Петри [1–3] и их разновидности, например, нечеткие [4], временные [5–6], раскрашенные [7].
В [8–10] рассмотрены окрестностные модели обжига клинкера цементного производства. В [11] при моделировании процесса функционирования цементного производства использованы временные сети Петри, достоинствами которых являются динамическое отражение состояний моделируемой системы и возможность анализа свойств полученной модели.
1. Peterson, J. Teoriya setey Petri i modelirovanie system. [Petri Net Theory and the Modeling of Systems.] Moscow: Mir, 1984, 264 p. (in Russian).
2. Kotov, V. E. Seti Petri. [Petri nets.] Moscow: Nauka, 1984, 160 p. (in Russian).
3. Vasiliev, V. V., Kuzmuk V. V. Seti Petri: parallel´nye algoritmy i modeli mul´tiprotsessornykh system. [Petri nets: parallel algorithms and models of multiprocessor systems.] Kiev: Naukova dumka, 1990, 213 p. (in Russian).
4. Leonenkov, A.V. Nechetkoe modelirovanie v srede MATLAB i fuzzyTECH. [Fuzzy modeling in MATLAB and fuzzyTECH software environment.] St.Petersburg: BKhV-Peterburg, 2005, 736 p. (in Russian).
5. Voyevoda, A. A. Vremennye seti Petri i diagrammy UML. [Timed Petri nets and UML activity diagrams.] Scien-tific Bulletin of NSTU, 2009, no. 4(37), рр. 169-174 (in Russian).
6. Wang, J. Timed Petri Nets: Theory and Application. Norwell: Kluwer Academic Publishers, 1998, 296 p.
7. Ekhlakov, Y. P., Tarasenko, V. F., Zhukovsky, O. I. Tsvetnye seti Petri v modelirovanii sotsial´no-ekonomicheskikh sistem. [Color Petri nets in modeling of socio-economic systems.] Proceedings of TUSUR University, 2013, no. 3 (29), pp. 83-92 (in Russian).
8. Shmyrin, A. M., Sedykh, I. A., Scherbakov, A. P., Yartsev, A. G. Nalichie ekstremumov parametricheskogo uravneniya pechi obzhiga klinkera. [The presence of clinker furnace parametric equation extrema.] News of Higher Educa-tional Institutions of the Chernozem Region, 2015, no. 1(39), pp. 62-67 (in Russian).
9. Shmyrin, A. M., Sedykh, I. A., Scherbakov, A. P., Yartsev, A. G. Issledovanie okrestnostnoy modeli pechi obzhiga klinkera s uchetom dopustimykh znacheniy parametrov. [Research of a neighborhood model of a clinker kiln taking into account admissible parameter values.] Vestnik LSTU, 2015, no. 2(24), pp. 11-14 (in Russian).
10. Shmyrin, A. M., Sedykh I. A. Algoritmy identifikatsii i upravleniya funktsionirovaniem okrestnostnykh sistem, poluchennykh na osnove setey Petri. [Algorithms of identification and operational control of neighborhood systems built on the basis of Petri nets.] Large-scale Systems Control, 2009, iss. 24, pp. 18 - 33 (in Russian).
11. Blyumin, S.L., Shmyrin, A.M., Sedykh, I.A., Filonenko, V.Y. Okrestnostnoe modelirovanie setey Petri. [Neigh-borhood modeling of Petri nets.] Lipetsk: LEGI, 2010, 124 p. (in Russian).
