A Novel Exponential Function Based Model for an Uniaxial Magnetic Levitation System
DOI:
https://doi.org/10.17533/udea.redin.16311Keywords:
magnetic levitation, Jacobian matrix, Magnetic Bearings, nonlinear systemsAbstract
In this paper a new dynamic model for a uniaxial magnetic levitation system is developed from magnetostatic principles, which we have not found in literature. The system has two coils which are the actuators to control the position of two magnets that need to slide on a vertical axis; this configuration is used in motors with magnetic suspension and generally in any system with active magnetic bearings. Based on the Amperian model and the Biot – Savart law for this system, it was established by means of numerical calculations, the force and distance relationships between the actuators and magnets and between magnets. Once the mentioned relations were numerically determined, then exponential curve fitting was done to them, in order to obtain the nonlinear dynamic model of the magnetic suspension system. This article further presents a linearized model generated from the model previously obtained, showing that it correctly represents the system dynamics near the point of operation.
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M. Okano, T. Iwamoto, M. Senokuchi, S. Fuchino, I. Ishii. “Magnetic rail construction for a low loss superconducting magnetic levitation linear guide”. IEEE Transactions on Applied Superconductivity. Vol 14. 2004. pp. 944-947. DOI: https://doi.org/10.1109/TASC.2004.830327
R. Ravaud, G. Lemarquand, S. Babic, V. Lemarquand, C. Akyel. “Cylindrical Magnets and Coils: Fields, Forces, and Inductances”. IEEE Transactions on Magnetics. Vol. 46. 2010. pp. 3585-3590. DOI: https://doi.org/10.1109/TMAG.2010.2049026
R. Ravaud, G. Lemarquand, V. Lemarquand. “Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization”. IEEE transactions on magnetics. Vol. 45. 2009. pp. 2996-3002. DOI: https://doi.org/10.1109/TMAG.2009.2016088
M. Greconici, Z. Cvetkovic, A. Mladenovic, S. Aleksic, D. Vesa. Analytical – numerical Approach for levitation force calculation of a cylindrical bearing with permanent magnets used in an electric meter. 12th International Conference on Optimization of Electrical and Electronic Equipment. OPTIM. 2010. Romania. Brasov. pp. 197-201. DOI: https://doi.org/10.1109/OPTIM.2010.5510468
U. Hasirci, A. Bolikci, Z. Zabar, L. Birenbaum. “A novel magnetic-levitation system: design, implementation, and nonlinear control”. IEEE Transactions on Plasma Science. Vol. 39. 2011. pp. 492-497. DOI: https://doi.org/10.1109/TPS.2010.2053389
M. Subkhan, M. Komori. “New Concept for Flywheel Energy Storage System using SMB And PMB”. IEEE Transactions on Applied Superconducting. Vol. 21. 2011. pp. 1485-1488. DOI: https://doi.org/10.1109/TASC.2010.2098470
L. Mei, Z. Deng, C. Liu. A 5-dof magnetic levitation motor system with two similar hybrid magnetic bearings. 4th IEEE Conference on Industrial Electronics and Applications. China. Xian. 2009. pp. 1215-1219. DOI: https://doi.org/10.1109/ICIEA.2009.5138395
W. Hurley, W. WÖlfle. “Electromagnetic Design of a Magnetic Suspension System”. IEEE Transactions on education. Vol. 40. 1997. pp. 124-130. DOI: https://doi.org/10.1109/13.572325
A. Ahmad, Z. Saad, M. Osman, I. Isa, S. Sadimin, S. Abdullah. Control of Magnetic Levitation System Using Fuzzy Logic Control. Second International Conference on Computational Intelligence, Modelling and Simulation. Bali, Indonesia 2010. pp. 51-56. DOI: https://doi.org/10.1109/CIMSiM.2010.99
Y. Satoh, H. Nakamura, H. Katayama, H. Nishitani. Robust nonlinear adaptive control for the magnetic levitation system. Mediterranean Conference on Control and Automation. Filoxenia, Grecia. 2007. pp 1-6.
K. Kim, E. Levi, Z. Zabar, L. Birenbaum. “Restoring Force Between Two No-coaxial Circular Coils”. IEEE Transactions On Magnetics. Vol 32. 1996. pp. 478- 484. DOI: https://doi.org/10.1109/20.486535
M. Ooshima, S. Kobayashi, H. Tanaka. Magnetic Suspension Performance of a Bearing-less Motor/ Generator for Flywheel Energy Storage Systems. IEEE Power and Energy Society General Meeting. Minneapolis, US. 2010. pp 1-4. DOI: https://doi.org/10.1109/PES.2010.5589783
A. Chiba, T. Fukao, O. Ichikawa, M. Takemoto, D. Dorrell. Magnetic Bearings and Bearing-less Drives. Capítulo 1. Ed. Elsevier. Newnes, UK. 2005. pp. 34- 35.
K. Hijikata, S. Kobayashi, M. Takemoto, Y. Tanaka, T. Yoshimoto. “Basic Characteristics of an Active Thrust Magnetic Bearing With a Cylindrical Rotor Core,” IEEE Trans. Magn. Vol. 44. 2008. pp. 4167-4170. DOI: https://doi.org/10.1109/TMAG.2008.2002628
A. Rodríguez, R. Graduno, L. Vela. “PI Fuzzy Gain – Scheduling Speed Control at Startup of a Gas-Turbine Power Plant”. IEEE Transactions on Energy Conversion. Vol. 26. 2011. pp 310-317. DOI: https://doi.org/10.1109/TEC.2010.2081991
R. Ravaud, G. Lemarquand, V. Lemarquand. “Mutual inductance and force exerted between thick coils”. Progress in Electromagnetics Research. Vol. 102. 2010. pp 367-380. DOI: https://doi.org/10.2528/PIER10012806
V. Oliveira, E. Costa, J. Vargas. “Digital Implementation of a Magnetic Suspension Control System for Laboratory Experiments”. IEEE transactions on education. Vol. 42. 1999. pp. 315-322. DOI: https://doi.org/10.1109/13.804538
H. Klee. Simulation of dynamic systems with MatLab and Simulink. Cápitulo 7. Ed. CRC press. Orlando. US. 2007. pp. 611-615.
H. Khalil. Nonlinear Systems. 3rd ed. Ed. Prentice Hall. New Jersey, US. 2002. pp. 53.
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