Volume 12, no. 2Pages 67 - 81

The Optimal Control Problem for Output Material Flow on Conveyor Belt with Input Accumulating Bunker

О.М. Pihnastyi, V.D. Khodusov
The article is devoted to the synthesis of optimal control of conveyor belt with the accumulating input bunker. Much attention is given to the model of the conveyor belt with a constant speed of the belt. Simulation of the conveyor belt is carried out in the one-moment approximation using partial differential equations. The conveyor belt is represented as a distributed system. The used PDE-model of the conveyor belt allows to determine the state of the flow parameters for a given technological position as a function of time. We consider the optimal control problem for flow parameters of the conveyor belt. The problem consists in ensuring the minimum deviation of the output material flow from a given target amount. The control is carried out by the material flow amount, which comes from the accumulating bunker into the conveyor belt input. In the synthesis of optimal control, we take into account the limitations on the size of the accumulating bunker, as well as on both max and min amounts of control. We construct optimal control of the material flow amount coming from the accumulating bunker. Also, we determine the conditions to switch control modes, and estimate time period between the moments of the switching.
Full text
conveyor; production line; subject of labour; PDE-model of production; parameters of the state of the production line; technological position; transition period; production control systems; optimal control; Pontryagin function; Lagrange function; differential constraints; accumulating bunker; distributed system.
1. Shahmejster L.G., Dmitriev V.G., Lobachjova A.K. Dinamika gruzopotokov i regulirovanie skorosti lentochnyh konvejerov [Dynamics of Traffic and Speed Control Belt Conveyors]. Moscow, Nedra, 1972. (in Russian)
2. Lauhoff H. Speed Control on Belt Conveyors - Does it Really Save Energy? Bulk Solids Handling, 2005, vol. 25, no. 6, pp. 368-377.
3. Halepoto I.A., Shaikh M.Z., Chowdhry B.S. Design and Implementation of Intelligent Energy Efficient Conveyor System Model Based on Variable Speed Drive Control and Physical Modeling International. Journal of Control and Automation, 2016, vol. 9, no. 6, pp. 379-388. DOI: 10.14257/ijca.2016.9.6.36
4. BARTEC GmbH. Available at: www.bartec-group.com (accessed 2018).
5. Pihnastyi O.M., Khodusov V.D. Model of Conveyer with the Regulable Speed. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2017, vol. 10, no. 4, pp. 64-77. DOI: 10.14529/mmp170407
6. Razumnyi Ju.T., Ruhlov A.V., Kozar A.V. Improving the Energy Efficiency of Coal Mine Conveyor Transport. Gornaja jelektromehanika i avtomatika, 2006, no. 76, pp. 24-28. (in Russian)
7. Procenko S.N. Reduced Energy Consumption in Coal Mine Conveyor Transport. Gornaja jelektromehanika i avtomatika, 2008, no. 81, pp. 31-40. (in Russian)
8. Prokuda V.N., Mishanskij Ju.A., Procenko S.N. Research and Evaluation of Cargo Traffic on the Main Conveyor Transport PSP ''Mine Pavlogradskaya'' PAO DTEK ''Pavlogradugol''. Gornaja jelektromehanika, 2012, no. 88, pp. 107-111. (in Russian)
9. Hiltermann J., Lodewijks G., Schott D.L. A Methodology to Predict Power Savings of Troughed Belt Conveyors by Speed Control. Particulate Science and Technology, 2011, vol. 29, no. 1, pp. 14-27. DOI: 10.1080/02726351.2010.491105
10. Continous conveyors. Belt conveyors for loose bulk materials. Basics for calculation and dimensioning. DIN 22101:2002-08. Available at: https://din.de (accessed 2002).
11. Semenchenko A., Stadnik M., Belitsky P., Semenchenko D., Stepanenko O. The Impact of an Uneven Loading of a Belt Conveyor on the Loading of Drive Motors and Energy Consumption in Transportation. Eastern-European Journal of Enterprise Technologies, 2016, vol. 82, no. 4, pp. 42-51. DOI: 10.15587/1729-4061.2016.75936
12. Conveyor Belt. Available at: http://conveyorbeltguide.com (accessed 2018).
13. Shahmejster L.G., Dmitriev V.G. Teorija i raschet lentochnyh konvejerov [Theory and Calculation of Belt Conveyors]. Moscow, Mashinostroenie, 1978. (in Russian)
14. Shahmejster L.G. Veroyatnostnye metody rascheta transportiruyushchih mashin [Probabilistic Methods for Calculating Transport Vehicles], Moscow, Mashinostroenie, 1983. (in Russian)
15. Demuckii V.P., Pihnastaja V.S., Pihnastyi O.M. [Stability of Functioning Mass Production and Product Promotion on The Market]. Kharkov, HNU, 2003.
16. Armbruster D., Marthaler D., Ringhofer C., Kempf K., Tae Chang Jo. A Continuum Model for a Re-Entrant Factory. Operations research, 2006, vol. 54, no. 5, pp. 933-950. DOI: 10.1287/opre.1060.0321
17. Pihnastyi O.M. Statisticheskaya teoriya proizvol'nyh sistem [Statistical Theory of Production Systems]. Kharkov, HNU, 2007.
18. Pihnastyi O.M., Hodusov V.D. [Diffusion Description of the Production Process]. Matematicheskoe modelirovanie. Informacionnye tehnologii. Avtomatizirovannye sistemy upravlenija, 2017, vol. 35, pp. 61-73. (in Russian)
19. Pihnastyi O.M., Hodusov V.D. [Model of a Single-Node Conveyor Line with a Constant Speed of Movement of Objects of Labor]. Matematicheskoe modelirovanie. Informacionnye tehnologii. Avtomatizirovannye sistemy upravlenija, 2016, vol. 32, pp. 60-74. (in Russian)
20. Pontrjagin L.S., Boltjanskij V.G., Gamkrelidze R.V. Matematicheskaya teoriya optimal'nyh processov [Mathematical Theory of Optimal Processes]. Moscow, Nauka, 1983. (in Russian)
21. Moiseev N.N. Jelementy teorii optimal'nyh sistem [Elements of the Theory of Optimal Systems]. Moscow, Nauka, 1974. (in Russian)
22. La Marca M., Armbruster D., Herty M., Ringhofer C. Control of Continuum Models of Production Systems. IEEE Transactions on Automatic Control, 2010, vol. 55, no. 11, pp. 2511-2526. DOI: 10.1109/TAC.2010.2046925