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Nahov S. F., Plotnikov A. P. To the Issue of Mathematical Modeling of Process of Functioning of the Instrument-making Enterprise when Usingthe Experimental Data of its Activities. Izv. Saratov Univ., Economics. Management. Law, 2016, vol. 16, iss. 2, pp. 159-?. DOI:

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To the Issue of Mathematical Modeling of Process of Functioning of the Instrument-making Enterprise when Usingthe Experimental Data of its Activities

Introduction. Automation control instrument-making enterprise (PP) relies not only on the introduction in its composition of technical means and computing devices, but also on the mathematical model of its production and economic activity. For further development and expansion of modeling capabilities to reduce oscillatory (instability) of the production process, in article we propose to combine the approach based on the use of the principles and methodology of the theory of automatic control (TAU) used in the creation of the virtual process control system of production of similar products of the enterprise instrument and the mathematical description of the dynamics of production activities, PP. Theoretical analysis. To the present time developed structural scheme of enterprise’s activity, based on the above theory, one of the key principles is the principle of backward linkages that improve the quality of management, efficiency of management decisions and thus the sustainability of production of the company. Obtained and the corresponding mathematical models, illustrating structural diagrams. However, there remains a need for further development of the mathematical interpretation of feedback reflecting the influence of the latter on the sustainability and stability of production process PP. Methods. Mathematical model PP without automated control systems, i.e. naturally without the introduction of feedback, the article claims correspond with an open loop control (PSC). Accordingly, a continuous mathematical model of PP with feedback loop reflects the PP with a closed control circuit (FOD). For him mathematical model of the production unit (PSU) corresponds to the PP model, obtained experimentally. As a model production unit PSC adopted model derived from real data of production activities of one of the claims of Saratov. Results. In article the mathematical model of the functioning of the claims covered by the feedback control, i.e. closed the instrument-making enterprise (RFP). They are reduced to normal form of differential equations assigned to them and the coefficients of the feedback and other parameters. Further these equations are presented in the form convenient for the solution in the Mathcad program produced and mathematical modeling. For comparison is given also the simulation of the original RFP, in which the algorithms are given positive and negative feedback (control). It was shown that these control algorithms do not eliminate fluctuations in the production process. Was subject to adjustment in the coefficients of the control algorithms, PP. It is shown that when negative feedback is increased and when the transmission coefficient of the feedback loop, the oscillatory (the ratio of the amplitude of the oscillatory component of the process to its systematic, relatively permanent component) is affected to a lesser extent on the work of the PP, due to the structure of mathematical model of work of the RFP. Conclusions. Proposed approach allowed the modeling of the production activity of PP under different settings and conditions in feedback control loop and to find their optimal values.


1. Nahov S. F., Plotnikov P. K., Plotnikov A. P. Sovershenstvovanie operativnogo planirovaniya deyatel’nosti priborostroitel’nogo predpriyatiya na osnove matematicheskoj interpretacii ego dinamiki [Improving operational planning activities of mechanical engineering enterprises on the basis of mathematical interpretation of its dynamics]. Izv. Saratov Univ. (N.S.), Ser. Economics. Management. Law, 2015, vol. 15, iss. 3, pp. 285–290.
2. Forrester D. Osnovy kybernetiki predpriiatiia [Fundamentals of Cybernetics of the enterprise]. Мoscow, Progress Publ., 1971. 325 p.
3. Sirazetdinov T. K. Dinamisheskoe modelirovanie ekonomisheskikh ob#ektov [Dynamic modeling of economic objects]. Kazan, FEN Publ.,1996. 224 p.
4. Plotnikov А. P. Razvitie metodologii upravleniia innovatsionnoi deiatel’nostiiu na osnove printsipa obratnykh sviazei [Development of methodology of innovation management on the basis of feedback]. Vestnik SGTU [Herald of Yuri Gagarin State Technical University of Saratov], 2008, no. 3, рр. 32–38.
5. Virtual’naia sistema upravleniia processom vypuska odnorodnoi produktsii predpriiatiia [Virtual process management system of production of similar products of the enterprise]. Patent 2571598. RF. № 2014144764; declared 05.11.2014; published 20.12.2015. Bulletin № 36. 11 p.
6. Plotnikov P. А. Otsenka ustoichivosti innovatsionnogorazvitiia mikroekonomicheskikh proizvodstvennykh system [Sustainability assessment of innovative development of microeconomic production systems. Cand. econ. sci. thesis diss.]. Saratov, 2012. 24 p.

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