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

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/95928/1/MPRA_paper_95928.pdf
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    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.
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    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 & 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.
    5. 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.

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    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

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