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

Pihnastyi, Oleh and Ivanovska, Olha (2021): Using a two-level dynamic PDE model to synchronize the performance of technological equipment of a production line. Published in: Actual problems of information systems and technologies No. 1 (September 2021): pp. 133-142.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: production line; production control system; PDE-model; continuous production; synchronized production line; work in progress; distributed production system
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity; L - Industrial Organization > L7 - Industry Studies: Primary Products and Construction > L72 - Mining, Extraction, and Refining: Other Nonrenewable Resources

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