The controller with installed polling program model for vector control systems
Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 127-138.

Voir la notice de l'article provenant de la source Math-Net.Ru

An approach to digital controller's programs design, that perform the functions both sensors and actuators polling control, and control actions calculation, id worked out. Three types of control action computation vector algorithms: the solving systems of difference equations, calculation the digital convolution and PID controller are investigated: It is shown that the controller, as a real physical device, when implementing a polling program on it, is a time-setting element, and provides not only a specified peripheral devices polling period, but also time delays between transactions. An estimation of time intervals using the semi-Markov model of the polling algorithm with a Hamiltonian transaction management cycle is made. The model of a closed linear vector control system shows the influence of time delays on such system characteristics as overshoot and time to reach steady state. A method has been developed for polling algorithm synthesis using a control system matrix model that takes into account the real characteristics of the controller as the device included in the vector feedback loop.
Keywords: vector control, polling algorithm, transaction, time delay, semi-Markov process.
@article{CHEB_2024_25_2_a7,
     author = {E. V. Larkin and V. S. Salnikov and S. A. Skobel'tsyn},
     title = {The controller with installed polling program model for vector control systems},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {127--138},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a7/}
}
TY  - JOUR
AU  - E. V. Larkin
AU  - V. S. Salnikov
AU  - S. A. Skobel'tsyn
TI  - The controller with installed polling program model for vector control systems
JO  - Čebyševskij sbornik
PY  - 2024
SP  - 127
EP  - 138
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a7/
LA  - ru
ID  - CHEB_2024_25_2_a7
ER  - 
%0 Journal Article
%A E. V. Larkin
%A V. S. Salnikov
%A S. A. Skobel'tsyn
%T The controller with installed polling program model for vector control systems
%J Čebyševskij sbornik
%D 2024
%P 127-138
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a7/
%G ru
%F CHEB_2024_25_2_a7
E. V. Larkin; V. S. Salnikov; S. A. Skobel'tsyn. The controller with installed polling program model for vector control systems. Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 127-138. http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a7/

[1] Malin Löfving M., Säfsten K., Winroth M., “Manufacturing strategy formulation, leadership style and organizational culture in small and medium-sized enterprises”, IJMTM, 30:5 (2016), 306–325 | DOI

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

[3] Larkin E. V., Ivutin A. N., “Estimation of Latency in Embedded Real-Time Systems”, 3-rd Meditteranean Conference on Embedded Computing (MECO-2014) (2104, June 15-19, Budva, Montenegro), 2014, 236–239

[4] Kilian C. T., Modern control technology: Components and systems, Thompson Delmar Learning, 2000, 608 pp.

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

[6] Aström J., Wittenmark B., Computer Controlled Systems: Theory and Design, Tsinghua University Press; Prentice Hall, 2002, 557 pp.

[7] Meyer-Baese U., Digital signal processing, Springer-Verlag, Heidelbrg–Berlin, 2004, 523 pp. | MR | Zbl

[8] Yeh Y.-C., Chu Y., Chiou C. W., “Improving the sampling resolution of periodic signals by using controlled sampling interval method”, Computers Electrical Engineering, 40:4 (2014), 1064–1071 | DOI | MR

[9] Ang K. N., Chong G., Li Y., “PID control system analysis, design and technology”, IEEE Transactions of control systems technology, 13:4 (2005), 559–576 | DOI

[10] O'Dwier A., “PID compensation of time delay processes 1999-2002: a survey”, Proceedings of the American control conference (USA, Denver, Colorado, 2003), 1494–1499

[11] Larkin E. V., Nguyen V. S., Privalov A. N., “Simulation of digital control systems by nonlinear objects”, Lecture Notes on Data Engineering and Communications Technologies, 124, 2022, 711–721 | DOI

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

[13] Bielecki T. R., Jakubowski J., Niewȩgłowski M., “Conditional Markov chains: Properties, construction and structured dependence”, Stochastic Processes and their Applications, 127:4 (2017), 1125–1170 | DOI | MR | Zbl

[14] Ching W. K., Huang X., Ng M. K., Siu T. K., Markov Chains: Models, Algorithms and Applications, International Series in Operations Research Management Science, 189, Springer Science + Business Media, NY, 2013, 241 pp. | MR | Zbl

[15] Janssen J., Manca R., Applied Semi-Markov processes, Springer US, 2006, 310 pp. | MR | Zbl

[16] Toshiharu Sugie, “Simple explanation of Routh-Hurwitz criterion for undergraduate education”, Systems, control and information, 65:7 (2021), 257–270

[17] Bodoson M., “Explaining Routh-Hurwitz criterion: A tutorial presentation”, IEEE Control systems magazine, 40:1 (2020), 45–51 | DOI | MR

[18] Wu M., He Y., She J. H., Liu G. P., “Delay-dependent criteria for robust stability of time-varying delay systems”, Automatica, 40:8 (2004), 1435–1439 | DOI | MR | Zbl

[19] Zhang X. M., Min W. U., Yong H. E., “Delay dependent robust control for linear systems with multiple time-varying delays and uncertainties”, Control Decision, 19:5 (2004), 496–500 | MR | Zbl