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Damping of the pendulum during dynamic stabilization in arbitrary angle position

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Trends in Advanced Intelligent Control, Optimization and Automation (KKA 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 577))

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Abstract

The paper presents an approach to dumping of the pendulum during dynamic stabilization in an arbitrary angle. The rapid oscillations of the pendulum’s suspension point cause that created effective potential has a local minimum which guarantees the stability of the pendulum. The external disturbances bring an additional energy into the system and the pendulum increases the amplitude of oscillations around its equilibrium position. The aim of this paper is to describe the damping method of this excess oscillations during dynamic stabilization of the pendulum.

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References

  • 1. Stephenson, A.: On a new type of dynamic stability. Memories and Proceeding of the Manchester Literary and Philosophical Society. 52, 1–10 (1908)

    Google Scholar 

  • 2. Stephenson, A.: On induced stability. Philosophical Magazine. 15, 233–226 (1908)

    Google Scholar 

  • 3. Lowenstern, E.R.: The stabilizing effect of imposed oscillations of high frequency on a dynamical. Philosophical Magazine. 13(84), 458–486 (1932)

    Google Scholar 

  • 4. Kapica, P.L.: Pendulum with a vibrating suspension. Usp. Fiz. Nauk. 44, 7–15 (1951)

    Google Scholar 

  • 5. Gilary, I., Moiseyev, N., Rahav, S., Fishman, S.: Trapping of particles by lasers: the quantum Kapitza pendulum. Journal of Physics A. 36(25), L409–L415 (2003)

    Google Scholar 

  • 6. Saito, H., Ueda, M.: Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate. Phys. Rev. Lett. 90(4), 040403 (2003)

    Google Scholar 

  • 7. Bullo F.: Averaging and vibrational control of mechanical systems. SIAM Journal on Control and Optimization. 41(2), 542–562 (2003)

    Google Scholar 

  • 8. Wickramasinghe, I.P.M., Berg, J.M.:Vibrational control without averaging. Automatica. 58, 72–81 (2015)

    Google Scholar 

  • 9. Wickramasinghe, I.P.M., Berg, J.M.:Vibrational control of Mathieu’s equation. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics. pp. 686–691 (2013)

    Google Scholar 

  • 10. Nakamura, Y., Suzuki, T., Koinuma, M.: Nonlinear behavior and control of a nonholonomic free-joint manipulator. IEEE Transactions on Robotics and Automation. 13(6), 853–862 (1997)

    Google Scholar 

  • 11. Wickramasinghe, I.P.M., Berg, J.M.:A Linearization-Based Approach to Vibrational Control of Second-Order Systems. In: ASME 2013 Dynamic Systems and Control Conference. (2013)

    Google Scholar 

  • 12. Arkhipova, I., Luongo, A., Seyranian, A.: Vibrational stabilization of upper statically unstable position of double pendulum. Journal of Sound and Vibration. 331(2), 457–469 (2012)

    Google Scholar 

  • 13. VanDalen, G.J.: The Driven Pendulum at Arbitrary Drive Angle. American Journal of Physics. 72(4), 484–491 (2004)

    Google Scholar 

  • 14. Ciezkowski, M.: Stabilization of Pendulum in Various Inclinations Using Open-Loop Control. Acta Mechanica et Automatica. 5(4), 22–28 (2011)

    Google Scholar 

  • 15. Ciezkowski, M.: Dynamic stabilization of the pendulum in a moving potential well. In: 21th International Conference on Methods and Models in Automation and Robotics MMAR’2016. pp. 54–58 (2016)

    Google Scholar 

  • 16. Murray, R.M., Sastry, S.S., Li Z.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    Google Scholar 

  • 17. Bryson, A.E., Ho, Y.C.: Applied Optimal Control: optimization, estimation, and control. Blaisdell, Waltham (1969)

    Google Scholar 

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Acknowledgements

The studies have been carried out in the framework of work No. S/WM/1/2016 and financed from the funds for science by the Polish Ministry of Science and Higher Education.

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Authors and Affiliations

  1. Bialystok University of Technology, Białystok, Poland

    Maciej Ciężkowski

Authors
  1. Maciej Ciężkowski
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Correspondence to Maciej Ciężkowski .

Editor information

Editors and Affiliations

  1. Department of Automatics and Biomedical Engineering, AGH University of Science and Technology , Kraków, Poland

    Wojciech Mitkowski

  2. Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland

    Janusz Kacprzyk

  3. Department of Automatics and Biomedical Engineering , AGH University of Science and Technology , Kraków, Poland

    Krzysztof Oprzędkiewicz

  4. Department of Automatics and Biomedical Engineering , AGH University of Science and Technology , Kraków, Poland

    Paweł Skruch

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Ciężkowski, M. (2017). Damping of the pendulum during dynamic stabilization in arbitrary angle position. In: Mitkowski, W., Kacprzyk, J., Oprzędkiewicz, K., Skruch, P. (eds) Trends in Advanced Intelligent Control, Optimization and Automation. KKA 2017. Advances in Intelligent Systems and Computing, vol 577. Springer, Cham. https://doi.org/10.1007/978-3-319-60699-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-60699-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60698-9

  • Online ISBN: 978-3-319-60699-6

  • eBook Packages: EngineeringEngineering (R0)

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