IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/95928.html
   My bibliography  Save this paper

The optimal control problem for output material flow on a conveyor belt with input accumulating bunker

Author

Listed:
  • Pihnastyi, Oleh
  • Khodusov, Valery

Abstract

The article is devoted to the synthesis of optimal control of the 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 determining 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.

Suggested Citation

  • Pihnastyi, Oleh & Khodusov, Valery, 2019. "The optimal control problem for output material flow on a conveyor belt with input accumulating bunker," MPRA Paper 95928, University Library of Munich, Germany, revised 07 Jan 2019.
  • Handle: RePEc:pra:mprapa:95928
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/95928/1/MPRA_paper_95928.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dieter Armbruster & Daniel E. Marthaler & Christian Ringhofer & Karl Kempf & Tae-Chang Jo, 2006. "A Continuum Model for a Re-entrant Factory," Operations Research, INFORMS, vol. 54(5), pages 933-950, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pihnastyi, Oleh & Kozhevnikov, Georgii & Ivanovska, Olha, 2022. "Maxwell-Element Model for Describing Conveyor Belt Stresses," MPRA Paper 112560, University Library of Munich, Germany, revised 01 Jan 2022.
    2. Pihnastyi, Oleh & Burduk, Anna, 2022. "Analysis of a Dataset for Modeling a Transport Conveyor," MPRA Paper 116161, University Library of Munich, Germany, revised 26 Nov 2022.
    3. Pihnastyi, Oleh & Khodusov, Valery, 2020. "Development of the controlling speed algorithm of the conveyor belt based on TOU-tariffs," MPRA Paper 104681, University Library of Munich, Germany, revised 12 Nov 2020.
    4. Pihnastyi, Oleh & Khodusov, Valery & Kozhevnikov, Georgii & Bondarenko, Tetiana, 2021. "Analysis of dynamic mechanic belt stresses of the magistral conveyor," MPRA Paper 110216, University Library of Munich, Germany, revised 05 Feb 2021.
    5. Pihnastyi, Oleh & Khodusov, Valery & Kotova, Anna, 2022. "The problem of combined optimal load flow control of main conveyor line," MPRA Paper 113787, University Library of Munich, Germany, revised 05 Jun 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Helbing, Dirk & Armbruster, Dieter & Mikhailov, Alexander S. & Lefeber, Erjen, 2006. "Information and material flows in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 1-1.
    2. Klug, Florian, 2014. "Modelling and analysis of synchronised material flow with fluid dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 404-417.
    3. Apostolos Kotsialos, 2010. "A hydrodynamic modelling framework for production networks," Computational Management Science, Springer, vol. 7(1), pages 61-83, January.
    4. Pihnastyi, Oleh & Parachnevych, Oksana, 2018. "On the formulation of the problem of optimal control of production parameters using a two-level model of the production process," MPRA Paper 88761, University Library of Munich, Germany, revised 01 Sep 2018.
    5. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    6. Herty, M. & Ringhofer, C., 2007. "Optimization for supply chain models with policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 651-664.
    7. Pihnastyi, Oleh & Yemelianova, Daria & Lysytsia, Dmytro, 2020. "Using PDE-model and system dynamics model for describing multi-operation production lines," MPRA Paper 103975, University Library of Munich, Germany, revised 31 Aug 2020.
    8. Пигнастый, Олег & Ходусов, Валерий, 2017. "Диффузионное Описание Производственного Процесса [Diffusion description of the production process]," MPRA Paper 89250, University Library of Munich, Germany, revised 01 Nov 2017.
    9. Пигнастый, Олег, 2015. "О Выводе Кинетического Уравнения Производственного Процесса [Derivation of kinetic equations of the production process]," MPRA Paper 93529, University Library of Munich, Germany, revised 07 Aug 2015.
    10. Tanmay Sarkar, 2016. "A numerical study on a nonlinear conservation law model pertaining to manufacturing system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 655-671, December.
    11. Mapundi Banda & Michael Herty, 2012. "Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws," Computational Optimization and Applications, Springer, vol. 51(2), pages 909-930, March.
    12. Pihnastyi, Oleh & Korsun, Roman, 2016. "The construction a kinetic equation of the production process," MPRA Paper 92073, University Library of Munich, Germany, revised 19 Mar 2016.
    13. Пигнастый, Олег, 2014. "Основы Статистической Теории Построения Континуальных Моделей Производственных Линий [Fundamentals Of The Statistical Theory Of The Construction Of Continuum Models Of Production Lines]," MPRA Paper 95240, University Library of Munich, Germany, revised 20 Aug 2014.
    14. Dong, Ming & He, Fenglan, 2012. "A new continuous model for multiple re-entrant manufacturing systems," European Journal of Operational Research, Elsevier, vol. 223(3), pages 659-668.

    More about this item

    Keywords

    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;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L23 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Organization of Production

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:95928. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.