Formalised Statement of a Problem Dealing with Energy-Efficient Destabilisation Control of Multidimensional Technological Objects for the Case of Repeated Adjustment of Expected Performance over a Long Period of Time

The paper investigates issues related to control of complex, energy- and resource-intensive technological objects that operate in variable performance modes (in terms of product) over a long period of time. When we consider the object functioning over a period of time, we gain new ways of determining optimum technological modes that correspond to the performances required. It happens due to introduction of additional control actions that expand the region of admissible object controls and appear as a result of removing hard constraints on supporting certain technological parameters that characterise in a certain manner the processes taking place in the object. These are the so-called problems of destabilisation optimisation and destabilisation control. Implementing these in production leads to the admissible variation in these parameters being organised over a period of time in such a way that there occurs a "destabilisation mode" in terms of these parameters. As a result, additional economic benefit may emerge as compared to the traditional solution to such a problem. We investigated the problem of energy-efficient destabilisation control of multidimensional technological objects for the case of repeated adjustment of expected performance over a long period of time. We outline the general description of the problem and present a formalised problem statement featuring an integral criterion for estimating object operation quality in which the integrand is a linear function of additional control actions and object load. We note that the problem may be decomposed into a set of linear n-tier one-dimensional problems of destabilisation optimisation, which we describe in this paper

The study was supported by RFBR grants (projects no. 17-08-00457-а, no. 18-08-00555-а)

References

[1] Kosarev D.A., Remizova O.A., Syrokvashin V.V., Fokin A.L. Robust control of multidimensional linear object with delay. Izvestiya SPbGTI (TU) [Bulletin of St PbSIT(TU)], 2012, no. 17 (43), pp. 77–82 (in Russ.).

[2] Eremin E.L. Adaptive control for dynamic plant on state set of functioning. Informatika i sistemy upravleniya, 2012, no. 4 (34), pp. 107–118 (in Russ.).

[3] Eremin E.L., Shelenok E.A. Robust control for one class of multivariable dynamic plants. Automation and Remote Control, 2017, vol. 78, iss. 6, pp. 1046–1058. DOI: 10.1134/S0005117917060066

[4] Zholdoshov T.M., Omorov T.T. [Synthesis of dynamic management subsystem for stationary multidimensional object]. Tekhnicheskie nauki — ot teorii k praktike [Technical sciences: from theory to practice], 2012, no. 12, pp. 27–32 (in Russ.).

[5] Gabasov R., Kirillova F.M., Vo Thi Thanh Ha. Optimal real-time control of multidimensional dynamic plant. Automation and Remote Control, 2015, vol. 76, iss. 1, pp. 98–110. DOI: 10.1134/S0005117915010099

[6] Gayduk A.R., Kolokolova K.V. Synthesis of control systems by unstable multivariable plants. Nauchnyy vestnik NGTU [Scientific Bulletin of NSTU], 2017, no. 1 (66), pp. 26–40 (in Russ.). DOI: 10.17212/1814-1196-2017-1-26-40

[7] Muromtsev Yu.L. Full analysis methodology of energy-saving control on multi-multidimen-sional objects. Sistemy upravleniya i informatsionnye tekhnologii, 2008, vol. 32, no. 2.3, pp. 364–369 (in Russ.).

[8] Gribkov A.N. Teoreticheskie osnovy optimalnogo upravleniya mnogomernymi tekhnolo-gicheskimi obektami [Theoretical fundamentals of optimum control on multidimensional technological objects]. Moscow, MINTs Publ., 2014. 138 p.

[9] Glazkova V.V., Muromtsev D.Yu., Rudenko L.V., Shamkin V.N. [Destabilization energy-saving optimization of complex technological objects as the basis of new information management technologies. P. 1. Statement of the problem]. Ustoychivoe razvitie regionov. Mat. mezhdunar. nauch.-prakt. konf. T. 5 [Sustainable development of the regions. Proc. Int. Sci.-Pract. Conf. Vol. 5]. Tambov, FGBOU VO TGTU Publ., 2016, pp. 91–96 (in Russ.).

[10] Glazkova V.V., Muromtsev D.Yu., Rudenko L.V., Shamkin V.N. [Destabilization energy-saving optimization of complex technological objects as the basis of new information management technologies. P. 2. Algorithms for solving references]. Ustoychivoe razvitie regionov. Mat. mezhdunar. nauch.-prakt. konf. T. 5 [Sustainable development of the regions. Proc. Int. Sci.-Pract. Conf. Vol. 5]. Tambov, FGBOU VO TGTU Publ., 2016, pp. 96–100 (in Russ.).

[11] Shamkin V.N., Muromtsev D.Yu., Gribkov A.N. Using destabilization control to improve the functioning of complex multidimensional technological objects on the time interval. Journal of Engineering and Applied Sciences, 2017, vol. 12, no. 24, pp. 7198–7217.

[12] Bayas M.M., Dubovoy V.M. Efficient resources allocation in technological processes using genetic algorithm. Middle East Journal of Scientific Research, 2013, vol. 14, no. 1, pp. 1–4.

[13] Lee K., Bhattacharya R. Optimal controller switching for resource-constrained dynamical systems. International Journal of Control, Automation and Systems, 2018, vol. 16, iss. 3, pp. 1323–1331. DOI: 10.1007/s12555-017-0530-3