CONCEPT OF METHODOLOGY FOR MAGLEV TRAIN’S MECHANICAL SUBSYSTEM’S MOVEMENTS CREATING

Authors

DOI:

https://doi.org/10.32782/mathematical-modelling/2026-9-1-28

Keywords:

magnetically levitated train, mechanical subsystem, motion quality, motion construction, coordinate aggregation, stratification of the phase space, concept of methodology

Abstract

The maglev train’s (MLT) mechanical subsystem’s (MS) motion can be interpreted as the evolution of its current state in phase space, while the construction of the subsystem’s motion can be interpreted as the initiation of this evolution. Synthesized movement must possess a set of properties that define its quality. As a rule, the MLT’s MS’s computational diagram is multidimensional and multiconnectivity. Improving the quality of movements requires optimizing them, and the criteria for such optimization may not only be inconsistent but also contradictory. These factors significantly complicate and hinder the aforementioned increase. Therefore, the objective of this study is to develop a concept of methodology for constructing the subsystem’s movements would mitigate the aforementioned difficulties. The requirement to impart a specific quality to the MLT’s MS’s motion may be interpreted as the necessity to alter its integral phase manifold under the influence of control actions. Therefore, the location of the representative state point on a particular phase surface signifies that the subsystem possesses a specific set of properties. Utilizing this fact as a pattern for constructing the motion of a subsystem may serve as the foundation for the concept of the synthesized methodology. The multidimensionality, multiconnexity, and other aspects of the subsystem’s complexity make it difficult to implement direct coordinate-based vector control of its phase coordinates. This process can be significantly reduced by using the coordinate aggregation method Due to the non-holonomic nature, multi-coupling, and significant nonlinearity of the subsystem, achieving high-quality of its motion requires the use of multi-channel controllers. If the behavior of each agreed group of coordinates is equivalent to that of a single channel, then it can be synthesized using methods that meet the quality requirements for coordinated motion. Further development of the proposed concept can be achieved by the stratification of the subsystem’s phase space into subspaces of lower dimension. Taking into account the capabilities of methods for the selective aggregation of subsystem’s state coordinates, as well as the stratification of its phase space, reveals a number of expedient elements within the concept currently being developed. The primary criteria for selecting specific elements from among these are the subsystem’s motion requirements and the resources that can be allocated to their synthesis. In principle, it is possible to control the phase coordinates of a subsystem (whether independent or aggregated) sequentially – either individually or in groups – or in parallel. In turn,, the goals of the corresponding movements can be achieved both sequentially and in parallel. Each of these approaches has both advantages and disadvantages. In combination with the adopted method of influencing the subsystem’s phase coordinates, either a sequential or a parallel approach may be adopted to achieve the objectives of the synthesized motion. Each of these methods, in turn, has its own advantages and disadvantages. An analysis of the described elements of the methodology for constructing the MLT’s MS’s movements leads to the conclusion that these elements possess the property of coherence, and that their combination possesses the quality of sufficiency for creating of the sought-after methodology. The use of this methodology will eliminate the difficulties arising from the need to synthetic accounting for the specifics of adequate appropriate computational schemes of the MS under consideration and the criteria used in optimizing the designed motions. This achieves the objective of this phase of the research.

References

Поляков В. О., Пославський С. Ю. Бажані атрактори зображуючої точки стану як патерни побудування поздовжнього руху механічної підсистеми магнітолевітуючого поїзда. Прикладні питання математичного моделювання. 2025. Т. 8, № 2. С. 236–244. DOI: https://doi.org/10.32782/mathematical-modelling/2025-8-2-24

Sun Y., Li J., Wang Z., He X., Fu Q., Zou Y. Distributed formation-aggregation control algorithm for a cluster of quadrotors. Journal of the Franklin Institute. 2023. V. 360, Iss. 3. P. 1560–1581. DOI: https://doi.org/10.1016/j.jfranklin.2022.12.002

Barzel B., Liu YY., Barabási AL. Constructing minimal models for complex system dynamics. Nature Communications. 2015. Iss. 6, 7186. DOI:https://doi.org/10.1038/ncomms8186

Zhu Q., Wang S.-M., Ni Y.-Q. A Review of Levitation Control Methods for Low- and Medium-Speed. Maglev Systems. 2024. Iss. 14. P. 8–17. DOI: https://doi.org/10.3390/buildings14030837

Rogers B., Fricke G., Devendra P. Garg D. P. Aggregation and Rendezvous in an Unbounded Domain without a Shared Coordinate System. Proc. Of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). 2011. P. 1437–1442. URL: https://scispace.com/pdf/aggregation-and-rendezvous-in-an-unbounded-domain-without-a-4h2edmvzaq.pdf

Sevinov J. U., Abdishukurov M. S., Bobomurodov N. X. Synthesis Problem of adaptive Control Systems for multi-channel and multi-mode object ti-mode Objects. Chemical Technology. Control and Management. 2023. № 5 (113) P. 57–63. DOI: https://doi.org/10.59048/2181-1105.1508

Поляков В. О., Хачапурідзе М. М. Побудова руху магнітолевітуючого поїзда як багатозв’язкової системи. Наука та прогрес транспорту. 2011. № 36. С. 29–33. URL: https://stp.ust.edu.ua/article/download/8705/7518/13108

Proctor J. L, Brunton S. L., Kutz J. N. Dynamic mode decomposition with control. Optimization and Control. 2021. V. 1. Mon. DOI: https://doi.org/10.48550/arXiv.1409.6358

Yongduan S., Kai Z., Hefu Y. Control of Nonlinear Systems Stability and Performance. CRC Press, 2025. 323 p. ISBN 9781032755274. URL: https://www.routledge.com/Control-of-Nonlinear-Systems-Stability-and-Performance/Song-Zhao-Ye/p/book/9781032755274

Zhang Z., Liu X. Recent Advances in Nonlinear Control Theory and System Dynamics. Mathematics. 2026. Special issue. URL: https://www.mdpi.com/journal/mathematics/special_issues/73379189O8#

Hu J., Wang P., Xu C., Zhou H. Yao J. High accuracy adaptive motion control for a robotic manipulator with model uncertainties based on multilayer neural network. Control. 2022. V. 24. Iss. 3. P. 1503–1514. DOI: https://doi.org/10.1002/asjc.2546

Published

2026-07-01