Mathematical support for hierarchical digital control of a complex technological object

E. V. Larkin   ; A. V. Bogomolov   ; A. N. Privalov   ; T. A. Akimenko

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 43-55

Résumé

The paper investigates the synthesis of mathematical support for hierarchical digital control of a complex technological object based on universal controllers with flexible programming. In order to overcome the limitations on the performance of controllers operating in real time, with the complexity of control laws and the expansion of the classes of controlled objects, controllers can be divided into strategic, tactical and functional-logical hierarchical levels. The authors define the functions and construct the algorithms for processing data by the controllers of each hierarchical level. The coordinated functioning of the digital control system under study is reduced to the exchange of data between controllers of different levels, carried out programmatically, equally for controllers of all levels. The authors obtain the dependencies for calculating the estimate of the restart period of control programs operating on the Hamiltonian cycle, and the data transmission delay for the case when the proportional-integral-differentiative regulator algorithm is implemented on the controllers of the tactical and functional-logical levels. The paper highlights the features of controlling the operating modes of the controllers of the tactical and functional-logical levels due to the implementation of a neural network at the strategic level.

Détail

Keywords: digital control, control system, hierarchical control levels, controller with flexible programming, Hamiltonian cycle, semi-Markov process, neural network.

Bibliographie

[1] M. Löfving, K. Säfsten; M. Winroth, “Manufacturing Strategy Formulation, Leadership Style and Organizational Culture in Small and Medium-Sized Enterprises”, International Journal of Manufacturing Technology and Management, 30:5 (2016), 306–325 | DOI

[2] Y. Pan, K. Guo, A. Bobtsov, Ch. Yang, H. Yu, “Composite Error Learning Robot Control using Discontinuous Lyapunov Analysis”, IEEE Transactions on Automatic Control, 69:3 (2024), 1705–1712 | DOI | MR

[3] V.N. Le, A.L. Ronzhin, “Obzor intellektualnykh sistem upravleniya i robototekhnicheskikh zadach v proizvodstve akvakultury”, Morskie intellektualnye tekhnologii, 1:1 (2024), 171–180

[4] R. Meshcheryakov, “Control of hyperlinked cyber-physical systems”, Proc. 14th International Conference on Electromechanics and Robotics “Zavalishin's Readings”, Smart Innovation, Systems and Technologies, 154, 2020, 27–33 | DOI

[5] Galin R.R., Shirokii A.A., Magid E.A. i dr., “Effektivnoe funktsionirovanie smeshannoi neodnorodnoi komandy v kollaborativnoi robototekhnicheskoi sisteme”, Informatika i avtomatizatsiya, 20:6 (2021), 1224–1253

[6] R.V. Mescheryakov, “Intellektualnye robototekhnicheskie sistemy”, Datchiki i sistemy, 2024, no. 2, 12–17

[7] R.V. Mescheryakov, A.S. Shirokov, “Postanovka zadachi geterogennogo gruppovogo vzaimodeistviya robotov pri reshenii zadach umnogo sada”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya «Matematika. Mekhanika. Fizika», 16:2 (2024), 41–49

[8] O.Yu. Osipov, R.V. Mescheryakov, M.G. Shepelenko, “Proektirovanie tsifrovykh modelei elementov elektromashinnoi chasti elektromekhatronnykh modulei robototekhnicheskikh sistem”, Ekstremalnaya robototekhnika, 2017, no. 1, 160–164

[9] R. Meshcheryakov, A. Iskhakov, M. Mamchenko et al., “A Probabilistic Approach to Estimating Allowed SNR Values for Automotive LiDARs in “Smart Cities” under Various External Influences”, Sensors, 22:2 (2022), 609 | DOI

[10] A.L. Smolin, V.P. Kutakhov, A.A. Zakharova i dr., “Postanovka zadachi realizatsii modeli bespilotnoi aviatsionnoi transportnoi sistemy s ispolzovaniem tekhnologii iskusstvennogo intellekta”, Iskusstvennyi intellekt. Teoriya i praktika, 2023, no. 1 (1), 41–45

[11] I.D. Landau, G. Zito, Digital Control Systems, Design, Identification and Implementation, Springer, 2006, 484 pp.

[12] J. Aström, B. Wittenmark, Computer Controlled Systems: Theory and Design, Tsinghua University Press, Prentice Hall, 1996, 557 pp.

[13] A. N. Ivutin, E. V. Larkin, “Estimation of Latency in Embedded Real-Time Systems”, 3-rd Meditteranean Conference on Embedded Computing (MECO-2014) (Budva, Montenegro), 2014, 236–239 | DOI

[14] C. T. Kilian, Modern Control Technology: Components and systems, Thompson Delmar Learning, 2000, 644 pp.

[15] E.V. Larkin, T.A. Akimenko, A.V. Bogomolov, “Modelirovanie nadezhnosti bortovogo oborudovaniya mobilnogo robota”, Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya: Matematika. Mekhanika. Informatika, 21:3 (2021), 390–399 | MR

[16] V. Babishin, S. Taghipour, “Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements”, Applied Mathematical Modelling, 40:23-24 (2016), 10480–10505 | DOI | MR

[17] E. Larkin, A. Privalov, A. Bogomolov, T. Akimenko, “Digital Control of Continuous Production with Dry Friction at Actuators”, Smart Innovation, Systems and Technologies, 232 (2022), 427–436 | DOI

[18] E.S. Soldatov, A.V. Bogomolov, E.V. Larkin, A.S. Soldatov, “Sensornye seti kontrolya sostoyaniya aviatsionnoi tekhniki pri ispytaniyakh i ekspluatatsii”, Aviakosmicheskoe priborostroenie, 2024, no. 2, 61–68

[19] E.V. Larkin, A.V. Bogomolov, A.N. Privalov, T.A. Akimenko, “Struktura ierarkhicheskoi sistemy tsifrovogo upravleniya slozhnym tekhnologicheskim ob'ektom”, Matematicheskie metody v tekhnologiyakh i tekhnike, 2024, no. 6, 63–66

[20] A.L. Shestakov, A.A. Zamyshlyaeva, N.A. Manakova i dr., “Vosstanovlenie dinamicheski iskazhennogo signala na osnove teorii optimalnykh dinamicheskikh izmerenii”, Avtomatika i telemekhanika, 2021, no. 12, 125–137

[21] I.L. Ermolov, S.S. Graskin, S.P. Khripunov, “Models for Decision Making Support Systems in Robotics”, Studies in Systems, Decision and Control, 352 (2021), 145–149 | DOI

[22] E.V. Bychkov, S.A. Zagrebina, A.A. Zamyshlyaeva i dr., “Razvitie teorii optimalnykh dinamicheskikh izmerenii”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya «Matematicheskoe modelirovanie i programmirovanie», 15:3 (2022), 19–33

[23] E.I. Bazhenov, S.A. Mokrushin, S.I. Okhapkin, “Software for the Mobile Robot Spatial Orientation System”, Vestnik YuUrGU. Seriya «Matematicheskoe modelirovanie i programmirovanie», 14:2 (2021), 64–69

[24] A.L. Shestakov, S.A. Zagrebina, N.A. Manakova i dr., “Algoritm chislennogo nakhozhdeniya optimalnogo izmereniya, iskazhennogo inertsionnostyu, rezonansami i degradatsiei izmeritelnogo ustroistva”, Avtomatika i telemekhanika, 2021, no. 1, 55–67

[25] U. Meyer-Baese, Digital Signal Processing with Field Programmable Gate Arrays, Springer-Verlag, Berlin–Heidelbrg, 2004, 527 pp. | MR

[26] Y. C. Yeh, Y. Chu, C.W. Chiou, “Improving the Sampling Resolution of Periodic Signals by using Controlled Sampling Interval Method”, Computers Electrical Engineering, 40:4 (2014), 1064–1071 | DOI | MR