Vol. 9 No. 2 (2024)

Mechanical and Vehicle Engineering

Determination of the Differential Equations of a Dynamical System using Dual Description

Published:

2024-06-28

https://doi.org/10.21791/IJEMS.2024.013

Author

László Rónai

University of Miskolc, Faculty of Mechanical Engineering and Informatics, Institute of Machine Tools and Mechatronics. Hungary

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Keywords

Lagrangian Generalized Momentum PID Control

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Copyright (c) 2024 László Rónai

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Selected Style: APA

Rónai, L. (2024). Determination of the Differential Equations of a Dynamical System using Dual Description. International Journal of Engineering and Management Sciences, 9(2), 41-48. https://doi.org/10.21791/IJEMS.2024.013

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Abstract

The paper deals with the description of a mathematical model of a mechanical system using the so-called energy-based approach. The model is created using both generalized displacements and generalized momenta. The latter prescription method is less common in practice, due to its complexity. The two ways are presented through the same example mechanical problem, and a control task is also solved with the help of a PID block.

References

1. B. M. Csizmadia, E. Nándori, “Mechanika Mérnököknek – Modellalkotás –”, Nemzeti tankönyvkiadó, Budapest, ISBN 963 19 4525, 2003
2. P. E. Wellstead, “Introduction to Physical System Modelling”, Academic Press Ltd., London, ISBN 0-12-744380-0, 1979
3. A. Preumont, “Mechatronics – Dynamics of Electromechanical and Piezoelectric Systems –”, Springer, ISBN-13 978-1-4020-4695, 2006
4. J. Bokor, P. Gáspár, “Irányítástechnika járműdinamikai alkalmazásokkal”, Typotex kiadó, Budapest, 2018.
5. L. Rónai, “Investigation of the Vibrational Behavior of a Quarter-Car Model”, Lecture Notes in Mechanical Engineering, Vehicle and Automotive Engineering 4, 2022, pp. 824-834, DOI: 10.1007/978-3-031-15211-5_68
6. S. D. Cohen, A. C. Hindmarsh, “CVODE, a Stiff/Nontiff ODE Solver in C”, Computers in Physics, vol. 10, no. 2., 1996, pp. 138-143, DOI: 10.1063/1.4822377
7. A. S. McCormack, K. R. Godfrey, “Rule-Based Autotuning Based on Frequency Domain Identification”, IEEE Transctions on Control Systems Technology, vol. 6, no. 1, 1998, DOI: 10.1109/87.654876