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Mathematical Model of Magnetic Field Penetration for Applied Tasks of Electromagnetic Driver and Ferromagnetic Layer Interaction

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 730))

Abstract

This paper deals with the investigations of an interaction between magnetic driver and ferromagnetic surface based on the calculation of magnetic field parameters in conditions of various thicknesses of layer. Special attention is paid for development of mathematical model of magnetic field penetration through flat soft magnetic layer. Applied aspects of developed mathematical model implementation in robotics, automation of different technological processes, renewable energy equipment and other industrial devices are discussed in the paper in details.

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References

  1. Abramovich, M., Stegun, I. (eds.): Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1979). Ed. Nauka, Moscow (In Russian)

    Google Scholar 

  2. Collon, C., Rudolph, J.: Invariant feedback control for the kinematic car on the sphere. Syst. Control Lett. 61(10), 967–972 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Drozd, J., Drozd, A.: Models, methods and means as resources for solving challenges in co-design and testing of computer systems and their components. In: Proceedings of the 9th International Conference on Digital Technologies 2013, Zhilina, Slovak Republic, 29–31 May, pp. 225–230 (2013)

    Google Scholar 

  4. Franke, M., Rudolph, J., Woittennek, F.: Motion planning and feedback control of a planar robotic unicycle model. Meth. Models Autom. Robot. 14(1), 501–506 (2009)

    Google Scholar 

  5. Gerdt, V.P., Prokopenya, A.N.: Simulation of quantum error correction with Mathematica. In: Lecture Notes in Computer Science, vol. 8136, pp. 116–129. Springer, Berlin (2013)

    Google Scholar 

  6. Gradshtein, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products. Academic press, Cambridge (1963). Fizmatgiz, Moscow (In Russian)

    Google Scholar 

  7. Greenberg, G.A.: Selected Topics of Mathematical Theory of Electrical and Magnetic Phenomena. AS of USSR, Moscow (1948). (In Russian)

    Google Scholar 

  8. Kiltz, L., Join, C., Mboup, M., Rudolph, J.: Fault-tolerant control based on algebraic derivative estimation applied on a magnetically supported plate. Control Eng. Pract. 26, 107–115 (2014)

    Article  Google Scholar 

  9. Kondratenko, Y.P.: Robotics, automation and information systems: future perspectives and correlation with culture, sport and life science. In: Lecture Notes in Economics and Mathematical Systems, vol. 675, pp. 43–56 (2015)

    Google Scholar 

  10. Kondratenko, Y., Shvets, E., Shyshkin, O.: Modern sensor systems of intelligent robots based on the slip displacement signal detection. In: Annals of DAAAM for 2007 and Proceedings of the 18th International DAAAM Symposium on Intelligent Manufacturing and Automation, Vienna, pp. 381–382 (2007)

    Google Scholar 

  11. Kondratenko, Y., Gordienko, E.: Neural networks for adaptive control system of caterpillar turn. In: Annals of DAAAM for 2011 and Proceedings of the 22nd International DAAAM Symposium on Intelligent Manufacturing and Automation, Vienna, Austria, 20–23 October 2011, pp. 305–306 (2011)

    Google Scholar 

  12. Kondratenko, Y.P., Zaporozhets Y.M.: Propulsion wheel of mobile robot, UA Patent 45369 U, Ukraine, Bulletin 21 (2009). (In Ukrainian)

    Google Scholar 

  13. Kondratenko, Y.P., Zaporozhets, Y.M., Kondratenko, V.Y.: Method of magnetically operated displacement of mobile robot, UA Patent 47369 U, Ukraine, Bulletin 2 (2010). (In Ukrainian)

    Google Scholar 

  14. Kondratenko, Y., Gordienko, E.: Implementation of the neural networks for adaptive control system on FPGA. In: Annals of DAAAM for 2012 and Proceeding of the 23th International DAAAM Symposium on Intelligent Manufacturing and Automation 23(1), 389–392 (2012)

    Google Scholar 

  15. Kratzer, A., Franz, V.: Transcendental functions. Publ. House of foreign literature, Moscow (1963). (In Russian)

    MATH  Google Scholar 

  16. Lebedev, N.N.: Special functions and their applications. Fizmatgiz, Moscow (1963). (In Russian)

    Google Scholar 

  17. Lizorkin, P.I.: A course of differential and integral equations with additional chapters of analysis. Nauka, Moscow (1981). (In Russian)

    Google Scholar 

  18. Manzhirov, A.V., Polyanin, A.D.: Handbook of Integral Equations: Methods of Solution. Publishing House, Moscow (2000). (In Russian)

    MATH  Google Scholar 

  19. Mirolyubov, N.N., Kostenko, M.V., Levinshtein, M.L., Tikhodeev, N.N.: Methods for calculating the electrostatic fields. Higher School, Moscow (1963). (In Russian)

    Google Scholar 

  20. Palagin, A., Opanasenko, V.: Reconfigurable computing technology. J. Cybernetics and Systems Analysis 43(5), 675–686 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series. Elementary Functions. Fizmatlit, Moscow (2002). (In Russian)

    MATH  Google Scholar 

  22. Prudnikov, A.P., Brankov, Y.A., Marichev, O.I.: Integrals and Series. Special Functions. Additional Chapters, vol. 3. Fizmatlit, Moscow (2003). (In Russian)

    Google Scholar 

  23. Smirnov, V.I.: A Course of Higher Mathematics, vol. 2. Nauka, Moscow (1974). (In Russian)

    Google Scholar 

  24. Tkachenko, A.N., Brovinskaya, N.M., Kondratenko, Y.P.: Evolutionary adaptation of control processes in robots operating in non-stationary environments. Mech. Mach. Theor. 18(4), 275–278 (1983)

    Article  Google Scholar 

  25. Tozoni, O.V.: Method of secondary sources in electrical engineering. Energy, Moscow (1975). (In Russian)

    Google Scholar 

  26. Vasiliev, A.N.: Scientific computing in Microsoft Excel. Publ. House, Moscow (2004). (In Russian)

    Google Scholar 

  27. Verlan, A.F., Sizikov, V.S.: Methods of Solution of Integral Equations with Computer Programs. Naukova Dumka, Kiev (1978). (In Russian)

    MATH  Google Scholar 

  28. Whittaker, E.T., Watson, J.N.: A Course of Modern Analysis. Part two. Transcendental Functions. Fizmatgiz, Moscow (1963). (In Russian)

    MATH  Google Scholar 

  29. Yanke, E., Emde, F., Lesh, F.: Special Functions: Formulas, Graphics, Tables. Nauka, Moscow (1964). (In Russian)

    Google Scholar 

  30. Zaporozhets, Y.M., Kondratenko, Y.P., Shyshkin, O.S.: Mathematical model of slip displacement sensor with registration of transversal constituents of magnetic field of sensing element. Tech. Electrodynamics 4, 67–72 (2012). (In Ukrainian)

    Google Scholar 

  31. Zaporozhets, Y.M., Kondratenko, V.Y., Kondratenko, Y.P.: Peculiarities of computer modeling of components of magnetic field near pole faces. Electron. Model. 35(2), 95–108 (2013)

    Google Scholar 

  32. Zaporozhets, Y.M., Kondratenko, Y.P.: Problems and features of control over magnetically operated drivers of mobile robots. Electron. Model. 35(5), 109–122 (2013)

    Google Scholar 

  33. Zaporozhets, Y.M.: On the problem of magnetic field penetration through flat soft magnetic layer and its applied use in field of renewable energy. Altern. Energ. Ecol. 23(163), 12–24 (2014)

    Google Scholar 

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Correspondence to Yuriy P. Kondratenko .

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Zaporozhets, Y.M., Kondratenko, Y.P., Kondratenko, V.Y. (2018). Mathematical Model of Magnetic Field Penetration for Applied Tasks of Electromagnetic Driver and Ferromagnetic Layer Interaction. In: Gil-Lafuente, A., Merigó, J., Dass, B., Verma, R. (eds) Applied Mathematics and Computational Intelligence. FIM 2015. Advances in Intelligent Systems and Computing, vol 730. Springer, Cham. https://doi.org/10.1007/978-3-319-75792-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-75792-6_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75791-9

  • Online ISBN: 978-3-319-75792-6

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