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Using a two-level dynamic PDE model to synchronize the performance of technological equipment of a production line

Author

Listed:
  • Pihnastyi, Oleh
  • Ivanovska, Olha

Abstract

The problem of designing a system for optimal operational control of random deviations in the productivity of technological equipment is considered. To construct an algorithm for optimal control of the performance of technological equipment, a PDE model of a production flow line was used. The Lyapunov functions method was used to determine the value of the optimal control of the technological equipment performance. The production line is considered by a distributed dynamic system. Equations are written for the flow parameters of the production line in small perturbations. A criterion for the quality control of the performance of technological equipment of a production flow line has been introduced. Based on this criterion, the Lyapunov function is determined for the considered production system. Taking into account the form of the Lyapunov function, control actions are obtained that correct the performance of the technological equipment. The introduced control made it possible to ensure the synchronization of the productivity of the technological equipment of the production line and the asymptotic stability of the given planned state of the flow parameters of the production line for the steady and transient operation mode.

Suggested Citation

  • Pihnastyi, Oleh & Ivanovska, Olha, 2021. "Using a two-level dynamic PDE model to synchronize the performance of technological equipment of a production line," MPRA Paper 111138, University Library of Munich, Germany, revised Sep 2021.
    • Handle: RePEc:pra:mprapa:111138
    as

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    File URL: https://mpra.ub.uni-muenchen.de/111138/1/MPRA_paper_111138.pdf
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    References listed on IDEAS

    as
    1. Pihnastyi, Oleh, 2017. "Analytical methods for designing technological trajectories of the object of labour in a phase space of states," MPRA Paper 91737, University Library of Munich, Germany, revised 2017.
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    1. 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.
    2. Пигнастый, Олег, 2018. "Синтез Программного Управления Операционными Параметрами Поточной Линии [Synthesis of program control of operational parameters of a production line]," MPRA Paper 102418, University Library of Munich, Germany, revised 25 May 2018.

    More about this item

    Keywords

    production line; production control system; PDE-model; continuous production; synchronized production line; work in progress; distributed production 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
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L72 - Industrial Organization - - Industry Studies: Primary Products and Construction - - - Mining, Extraction, and Refining: Other Nonrenewable Resources

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