Interpolation synthesis of thecontrollers for a multi-motorelectric drive system containingan elastically linked element
Le Quy Don Technical University
email: npdang@lqdtu.edu.vn
University of Transport Technology
email: tuanvd@utt.edu.vn
Faculty of Computer Science & Engineering, CMR Institute of Technology, Hyderabad, TS, India
email: spesinfo@yahoo.com
Faculty of Electronics and Telecommunication VNU University of Engineering and Technology
email: congls@vnu.edu.vn
Faculty of Electrical and Electronic Engineering, Phenikaa University, Hanoi 12116, Vietnam
email: tan.tranduc@phenikaa-uni.edu.vn
Partial differential equations, integral, differential, or other equations describe multi-motor automatic electric drive systems containing elastic conveyor belts. Because of the elastic and distributive nature of the system parameters, the transfer function describing them is often a complex expression, containing not only the arguments as a linear system but also the inertial and transcendental components. This makes the precise control of tension and speed synchronously much more complicated than the centralized parameter system. A promising numerical solution based on the real interpolation method will simplify the procedure for synthesizing control loops while preserving the characteristic properties of objects with distributed parameters. The objective of the study is to propose a feasible solution for synthesizing the regulators based on the real interpolation method; it allows direct operation with the original transfer function containing the inertial and transcendental components. In this paper, we proposed an approach to synthesize the control system for objects with distributed parameters using the real interpolation method to reduce computational capacity and synthesis error while preserving the properties of this object class. Building an experimental model of the two-motor electric drive system containing an elastic conveyor to verify the effectiveness of the proposed algorithm. The simulation and experimental results indicate that the control system with the received regulators operating stably and meets the required quality criteria. It proves the efficiency of the synthesis algorithm based on the real interpolation method.
Э.Я. Рапопорт, “Анализ и синтез систем автоматического управления с распределенными параметрами,” М. Высш. шк., 2005, 292 с.
В.М. Терехов, О.И. Осимов, “Системы управления электроприводов,” Москва: Издательский центр Академия , 2006, 304с.
Л.Н. Рассудов, “Электроприводы с распределенными параметрами механических элементов,” Л.: Энергоатомиздат, Ленингр. Отд-ние, 1987, 144 с.
O.F.Opeyko, “Synthesis of Robust Control System Using Double-Mass Electro-Mechanical,” Energetika. Proceedings of CIS higher education institutions and power engineering associations, no. 1, pp. 14-21, 2009.
H. Koc, D. Knittel, M. D. Mathelin, G. Abba, “Modeling and robust control of winding systems for elastic webs,” IEEE Trans. on Control Systems Technology, vol. 10, no. 2, pp. 197-208, Mar. 2002. doi: https://doi.org/10.1109/87.987065.
H. Glaoui, A. Hazzab, B. Bouchiba, I. Khalil Bousserhane, “Modeling and Simulation Multi Motors Web Winding System,” International Journal of Advanced Computer Science and Applications (IJACSA), vol. 4, no. 2, pp. 110-115, 2013. doi: https://doi.org/10.14569/IJACSA.2013.040217.
X. Chu, X. Nian, M. Sun, H. Wang, H. Xiong, “Modeling and robust decentralized control for speed-up phase of web processing systems for composite elastic web,” Journal of the Franklin Institute, vol. 357, no. 11. doi: https://doi.org/10.1016/j.jfranklin.2020.04.034.
M. Braik, “A Hybrid Multi-gene Genetic Programming with Capuchin Search Algorithm for Modeling a Nonlinear Challenge Problem: Modeling Industrial Winding Process,” Case Study. Neural Processing Letters, vol. 53, no. 1, pp. 2873-2916. doi: https://doi.org/10.1007/s11063-021-10530-w.
T. Shi, H. Liu, Q. Geng, Ch. Xia, “Improved relative coupling control structure for multi-motor speed synchronous driving system,” IET Electr. Power Application, vol. 10, no. 6, pp. 451-457. doi: https://doi.org/10.1049/iet-epa.2015.0515.
H. Subari, Ch. Shin-Horng, H. Wai-Keat, “Investigation of Model Parameter Variation for Tension Control of A Multi Motor Wire Winding System,” 10th Asian Control Conference (ASCC), IEEE. May 2015. doi: https://doi.org/10.1109/ASCC.2015.7244885.
M. D. Baumgart, L. Y. Pao, “Robust Lyapunov-based feedback control of nonlinear web-winding systems,” Proceedings of 42nd IEEE Conference on Decision and Control, pp. 6398-6405, Dec. 2003. doi: https://doi.org/10.1109/CDC.2003.1272347.
О.Н. Киселев, “Синтез регуляторов низкого порядка по критерию и по критерию максимальной робастности,” АиТ, no. 3, pp. 119-130, 1999.
S. Yixin, X. Gang, “Research of Multi - Motor Synchronous Driving System Based on Fuzzy Smith Control,” ICECE '10: Proceedings of the 2010 International Conference on Electrical and Control Engineering, IEEE, pp. 5466–5469, Jun. 2010. doi: https://doi.org/10.1109/iCECE.2010.1328.
F. Salem, E.H.E. Bayoumi, “Robust fuzzy-PID control of three-motor drive system using simulated annealing optimization,” Journal of Electrical Engineering, vol. 13, no. 3, pp. 284-292, 2011.
B. Allaoua , A. Laoufi, B. Gasbaoui, “Multi-Drive Paper System Control Based on Multi-Input Multi-Output PID Controller,” Leonardo Journal of Sciences, no. 16, pp. 59-70, Dec. 2010.
B. Bouchiba, I. K. Bousserhane, M. K. Fellaha, A. Hazzab, “Artificial neural network sliding mode control for multi-machine web winding system,” Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., Bucarest, vol. 62, no. 1, pp. 109–113, 2017.
Ch. Cong, L. Xingqiao, L. Guohai, Z. Liang, Ch. Li, Z. Buhui, "Multi-motor synchronous system based on neural network control," 2008 International Conference on Electrical Machines and Systems, Wuhan, pp. 1231-1236, 2008.
L. Guohai, L. Pingyuan, S. Yue, W. Fuliang, K. Mei, “Experimental Research on Decoupling Control of Multi-motor Variable Frequency System Based on Neural Network Generalized Inverse,” Proceedings of the IEEE International Conference on Networking, Sensing and Control, ICNSC 2008, Hainan, China, pp. 1476–1479, April 2008. doi: https://doi.org/10.1109/ICNSC.2008.4525453
A. Angermann, M. Aicher and D. Schroder, "Time-optimal tension control for processing plants with continuous moving webs," Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy, vol.5, pp. 3505-3511, 2000. doi: https://doi.org/10.1109/IAS.2000.882671.
C. Wang, Y. Z. Wang, “Research on precision tension control system based on neural network,” IEEE Transaction on Industrial Electronics, vol. 51, no. 2, pp. 381-386, 2004. doi: https://doi.org/10.1109/TIE.2003.822096.
X. Yan, W. Xing Zheng, Y. Liu, “Adaptive output-feedback tracking for nonlinear systems with rather general control coefficients”, International Journal of Robust and Nonlinear Control, vol. 29, no. 6, pp. 1660-1679, Jan. 2019. doi: https://doi.org/10.1002/rnc.4454.
L. Liu, N. Shao, M. Lin, Y. Fang, “Hamilton-based adaptive robust control for the speed and tension system of reversible cold strip rolling mill,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 4, pp. 626-643, Feb. 2019. doi: https://doi.org/10.1002/acs.2977.
N.R. Abjadi, J. Soltani, J. Askari, G.R. Arab Markadeh, “Nonlinear sliding-mode control of a multi-motor web-winding system without tension sensor,” IET Control Theory Application, vol. 3, no. 4, pp. 419-427, May 2009. doi: https://doi.org/10.1049/iet-cta.2008.0118.
D.M. Zinelabidine, K. Madjid, “Decentralized Controller Robustness Improvement Using Longitudinal Overlapping Decomposition - Application to Web Winding System,” Elektronika IR Elektrotechnika, vol. 24, no. 5, pp. 10-18, Oct. 2018. doi: https://doi.org/10.5755/j01.eie.24.5.21837
X. Chu, X. Nian, H. Wang, H. Xiong, “Distributed fault tolerant tracking control for large-scale multi-motor web-winding systems,” IET Control Theory & Applications, vol. 13, no. 4, pp. 543-548, Mar. 2019. doi: https://doi.org/10.1049/iet-cta.2018.6010.
X. Chu, X. Nian, “Robust fault estimation and fault tolerant control for three-motor web-winding systems,” International Journal of Control, vol. 94, no. 6, pp. 1-25, Mar. 2020. doi: https://doi.org/10.1080/00207179.2020.1749887.
K. Seok-Kyoon, Ch. Ki Ahn, “Observer-based decentralized pole–zero cancellation tension control with gain booster and surface stabilizer for roll-to-roll systems,” Nonlinear Dynamics, vol.105, no. 3, pp. 2313 – 2326, Jul. 2021. doi: https://doi.org/10.1007/s11071-021-06718-3.
L. Wang, D. Astolfi, L. Marconi, H. Su, “High-gain observers with limited gain power for systems with observability canonical form,” Automatica, vol. 75, pp. 16-23, Jan.2017. doi: https://doi.org/10.1016/j.automatica.2016.09.006.
J. Liu, L. Wan, D. Xiao, “Flatness Prediction of Cold Rolled Strip Based on EM-TELM,” Institute of Electrical and Electronics Engineers (IEEE), vol, 9, pp. 51484- 51493, Ap. 2021. doi: https://doi.org/10.1109/ACCESS.2021.3067363.
P. Wang, H. Wang, X. Li, “A double-layer optimization model for flatness control of cold rolled strip,” Applied Mathematical Modelling, vol. 91, pp. 863-874, Mar. 2021. doi: https://doi.org/10.1016/j.apm.2020.09.028.
L. Liu, N. Shao, S. Ding, Y. Fang, “Command Filter-based Backstepping Control for the Speed and Tension System of the Reversible Cold Strip Rolling Mill Using Disturbance Observers,” International Journal of Control, Automation and Systems, vol. 18, no. 4, pp. 1190–1201, Dec. 2019. doi: https://doi.org/10.1007/s12555-018-0697-2.
M. Bensaid, A. Ba-razzouk, M. Elharoussi and B. Rached, "Effects of Symmetrical Voltage Sags on Two Induction Motors System Coupled with An Elastic Web," IEEE 2nd International Conference on Electronics, Control, Optimization and Computer Science (ICECOCS), Kenitra, Morocco, pp. 1-6, Dec. 2020, doi: https://doi.org/10.1109/ICECOCS50124.2020.9314298.
V. Goncharov, I. Aleksandrov, V. Rudnicki, “Real Interpolation Method for Automatic Control Problems Solution,” LAP Lambert Academic Publishing, pp. 300, May, 2014.
V. Goncharov, V. Rudnicki, A. Liepinsh, "Numerical form of the automatic-control system mathematical models based on the real interpolation method approach," International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), St. Petersburg, Russia, pp. 1-6, May 2017, doi: https://doi.org/10.1109/ICIEAM.2017.8076431.
А.Р. Пантюхин, В.И. Гончаров, “Исследование возможностей численного метода синтеза систем автоматического управления объектами с большим запаздыванием,” Доклады ТУСУР, vol. 1, no. 39, 2021.
M. A. Abutheraa, D. Lester, “Computable function representations using effective Chebyshev polynomial,” Proceedings of world academy of science, engineering and technology, vol. 25, pp. 103-109.
Copyright (c) 2023 Ingeniería Solidaria
This work is licensed under a Creative Commons Attribution 4.0 International License.
Cession of rights and ethical commitment
As the author of the article, I declare that is an original unpublished work exclusively created by me, that it has not been submitted for simultaneous evaluation by another publication and that there is no impediment of any kind for concession of the rights provided for in this contract.
In this sense, I am committed to await the result of the evaluation by the journal Ingeniería Solidaría before considering its submission to another medium; in case the response by that publication is positive, additionally, I am committed to respond for any action involving claims, plagiarism or any other kind of claim that could be made by third parties.
At the same time, as the author or co-author, I declare that I am completely in agreement with the conditions presented in this work and that I cede all patrimonial rights, in other words, regarding reproduction, public communication, distribution, dissemination, transformation, making it available and all forms of exploitation of the work using any medium or procedure, during the term of the legal protection of the work and in every country in the world, to the Universidad Cooperativa de Colombia Press.