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Steady state response analysis for a switched stiffness vibration control system based on vibration energy conversion

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Abstract

A novel semi-active vibration control concept with a serial-switch-stiffness-system was previously presented in our work. Differing from conventional vibration control systems, this system does not dissipate but converts vibration energy as potential energy stored in springs and then reacts against external disturbance. As a piecewise linear system, whether or not energy conversion limit happens is an interesting nonlinear dynamic issue related to the systems steady state response. This paper formulates this issue in depth using the approach called equivalence in control. The systems control force represented by the converted vibration energy is approximately decomposed into two portions. One is responsible for low-frequency free response and the other for high-frequency switching response. An equivalent linear system suffering from a decomposed high-frequency switching force is obtained instead of the original switched system. The steady state response of the disturbed system can be delivered through linear superposition as executed in a linear system. Energy conversion limit occurring in the system under a harmonic disturbance is numerically shown by means of fast Fourier transformation. Analytical formulation and numerical simulation for open- and closed-loop control of the system are further carried out, respectively. The results give that the proposed approach is capable of solving the stead state response of the switched system accurately, and meanwhile, energy conversion limit occurs in the vibration control system indeed. Experimental discussion is also executed.

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References

  1. Nader, J.: A comparative study and analysis of semi-active vibration control systems. J. Vib. Acoust. 124(4), 593–605 (2002)

    Article  Google Scholar 

  2. Kamali, S.H., Moallem, M., Arzanpour, S.: Realization of an energy-efficient adjustable mechatronic spring. IEEE/ASME Trans. Mechatron. 23(4), 1877–1885 (2018)

    Article  Google Scholar 

  3. Opie, S., Yim, W.: Design and control of a real-time variable stiffness vibration isolator. In: Proceedings of IEEE/ASME, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 380–385 (2009)

  4. Winthrop, M.F., Bakerb, W.P., Cobba, R.G.: A variable stiffness device selection and design tool for lightly damped structures. J. Sound Vib. 287, 667–682 (2005)

    Article  Google Scholar 

  5. Onoda, J., Endo, T., Tamaoki, H., Watanbe, N.: Vibration suppression by variable-stiffness members. AIAA J. 29, 977–983 (1991)

    Article  Google Scholar 

  6. Leitmann, G.: Semi-active control for vibration attenuation. J. Intell. Mater. Syst. Struct. 5, 841–846 (1994)

    Article  Google Scholar 

  7. Irie, T., Shingu, K.: Vibraion control of variable rigidity frame structure by magnetic clutch. J. Comput. Sci. Technol. 2(3), 393–400 (2008)

    Article  Google Scholar 

  8. Leavitt, J., Bobrow, J.E., Jabbari, F.: Design of a 20000 pound variable stiffness actuator for structural vibration attenuation. Shock Vib. 2008(15), 687–696 (2008)

    Article  Google Scholar 

  9. Cunefare, K.A., Rosa, S.D., Sadegh, N., Larson, G.: State-switched absorber for semi-active structural control. J. Intell. Mater. Syst. Struct. 11, 300–310 (2000)

    Article  Google Scholar 

  10. Min, C., Dahlman, M., Sattel, T.: A concept for semi-active vibration control with a serial-stiffness-switch system. J. Sound. Vib. 405, 234–250 (2017)

    Article  Google Scholar 

  11. Dahlman, M., Min, C., Sattel, T.: A note on a double-serial switch-spring-parallel semi-active connection element. In: The 88th Annual Meeting of the International Association of/Proceedings in Applied Mathematics and Mechanics, Germany (2017)

  12. Min, C., Dahlman, M., Sattel, T.: Semi-active vibration reduction based on a sliding mode controlled serial-stiffness-switch system. In: The 89th Annual Meeting of the International Association of/Proceedings in Applied Mathematics and Mechanics, Germany (2018)

  13. Min, C., Dahlman, M., Sattel, T.: A semi-active shock isolation concept with serial-stiffness-switch system. J. Sound. Vib. 445, 117–131 (2019)

    Article  Google Scholar 

  14. Guinjoan, F., Calvente, J., Poveda, A., Martinez, L.: Large-signal modeling and simulation of switching DC–DC converters. IEEE Trans. Power Electron. 12(3), 485–494 (1997)

    Article  Google Scholar 

  15. Davoudi, A., Jatskevich, J., De Rybel, T.: Numerical state-space average-value modeling of PWM DC–DC converters operating in DCM and CCM. IEEE Trans. Power Electron. 21(4), 1003–1012 (2006)

    Article  Google Scholar 

  16. Ben-Yaakov, S.: Behavioral average modeling and equivalent circuit simulation of switched capacitors converters. IEEE Trans. Power Electron. 27(2), 632–636 (2013)

    Article  Google Scholar 

  17. Maksimovic, D.: Computer-aided small-signal analysis based on impulse response of DC/DC. IEEE Trans. Power Electron. 15(6), 1183–1191 (2000)

    Article  Google Scholar 

  18. Liou, M.L.: Exact analysis of linear circuits containing periodically operated switches with applications. IEEE Trans. Circuit Theory 19(2), 146–154 (1972)

    Article  Google Scholar 

  19. Yuan, F., Opal, A.: Noise and sensitivity analysis of periodically switched linear circuits in frequency domain. IEEE Trans. Circuits Syst. I Reg. 47(7), 986–998 (2000)

    Article  Google Scholar 

  20. Behjati, H., Niu, L., Davoudi, A., Chapman, P.L.: Alternative time-invariant multi-frequency modeling of PWM DC–DC converters. IEEE Trans. Circuits Syst. I Reg. 60(11), 3069–3079 (2013)

    Article  Google Scholar 

  21. Trinchero, R., Manfredi, P., Stievano, I.S., Canavero, F.G.: Steady-state analysis of switching converters via frequency-domain circuit equivalents. IEEE Trans. Circuits Syst. II Exp. Br. 63(8), 748–752 (2016)

    Article  Google Scholar 

  22. Min, C.: New Semi-active Vibration Control with Serial-Stiness-Switch-System Based on Vibration Energy Harvesting. Ph.D. thesis, Technischen Universitaet Ilmenau, Ilmenau, Germany (2018)

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Acknowledgements

Funding was provided by Postdoctoral Research Foundation of China and Natural Science Foundation of Shanxi Province (Grant No. 2020JQ-048).

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710054, China

    Chaoqing Min

  2. Mechatronics Group, Department of Mechanical Engineering, Technische Universität Ilmenau, 98693, Ilmenau, Germany

    Martin Dahlmann & Thomas Sattel

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  1. Chaoqing Min
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  2. Martin Dahlmann
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  3. Thomas Sattel
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Correspondence to Chaoqing Min.

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Min, C., Dahlmann, M. & Sattel, T. Steady state response analysis for a switched stiffness vibration control system based on vibration energy conversion. Nonlinear Dyn 103, 239–254 (2021). https://doi.org/10.1007/s11071-020-06147-8

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  • DOI: https://doi.org/10.1007/s11071-020-06147-8

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