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Instability analysis for semi-active control systems with semi-active inerters

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Abstract

In this paper, the instability of semi-active control systems caused by the utilization of semi-active inerters is analyzed. The purpose of this study is to demonstrate the possibility of inducing instability by applying semi-active inerters in vibration control systems, a phenomenon which is essential for the applications of semi-active inerters but has not been drawn much attention in the existing results. A constructive method is proposed to prove the instable effect caused by switching-state semi-active inerters based on a general multi-degree-of-freedom (DOF) mass-chain system. The underlying idea in the proof is to construct a multi-DOF unstable semi-active control system with semi-active inerters based on its 1-DOF counterparts. First of all, it is theoretically proved that for a 1-DOF system, both undamped and damped cases, instability can be induced by semi-active inerters under certain switching laws. Then, following the idea of modal analysis, unstable n-DOF semi-active inerter-based system with proportional damping is constructed via coordinate transformation. Moreover, for general damping case, phase portraits are depicted to show the instability caused by semi-active inerters. In this way, the conclusion is reached that semi-active inerter can induce instability if the inertance improperly controlled, and such a finding is still valid when the inerter nonlinearities are considered. Hence, the stability issue should not be neglected in the practical application of semi-active inerters.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Vanderborght, B., Albu-Schäffer, A., Bicchi, A., et al.: Variable impedance actuators: a review. Rob. Autom. Syst. 61(12), 1601–1614 (2013)

    Article  Google Scholar 

  2. Wolf, S., Grioli, G., Eiberger, O., et al.: Variable stiffness actuators: review on design and components. IEEE/ASME Trans. Mechatron. 21(5), 2418–2430 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Savaresi, S.M., Poussot-Vassal, S., Spelta, S., Sename, O., Dugard, L.: Semi-active Suspension Control Design for Vehicles. Elsevier, Amsterdam (2010)

    Google Scholar 

  5. Chen, M.Z.Q., Hu, Y., Li, C., Chen, G.: Semi-active suspension with semi-active inerter and semi-active damper. IFAC Proc. 47(3), 11 225–11 230 (2014)

    Article  Google Scholar 

  6. Hu, Y., Chen, M.Z.Q., Xu, S., Liu, Y.: Semiactive inerter and its application in adaptive tuned vibration absorbers. IEEE Trans. Control Syst. Technol. 25(1), 294–300 (2017)

    Article  Google Scholar 

  7. Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002)

    Article  MathSciNet  Google Scholar 

  8. Brzeski, P., Perlikowski, P.: Effects of play and inerter nonlinearities on the performance of tuned mass damper. Nonlinear Dyn. 88(2), 1027–1041 (2017)

    Article  Google Scholar 

  9. Domenico, D.De, Ricciardi, G.: An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI). Earthq. Eng. Struct. Dyn. 47(5), 1169–1192 (2018)

    Article  Google Scholar 

  10. Petrini, F., Giaralis, A., Wang, Z.: Optimal tuned mass-damper-inerter (TMDI) design in wind-excited tall buildings for occupants comfort serviceability performance and energy harvesting. Eng. Struct. 204, 109904 (2020)

    Article  Google Scholar 

  11. Zhao, G., Raze, G., Paknejad, A., Deraemaeker, A., Kerschen, G., Collette, C.: Active nonlinear energy sink using force feedback under transient regime. Nonlinear Dyn. 102(3), 1319–1336 (2020)

    Article  Google Scholar 

  12. Zhang, Z., Zhang, Y.W., Ding, H.: Vibration control combining nonlinear isolation and nonlinear absorption. Nonlinear Dyn. 100(3), 2121–2139 (2020)

    Article  MathSciNet  Google Scholar 

  13. Ding, H., Chen, L.Q.: Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dyn. 100, 3061–3107 (2020)

    Article  Google Scholar 

  14. Yang, J., Jiang, J.Z., Neild, S.A.: Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators. Nonlinear Dyn. 99(3), 1823–1839 (2020)

    Article  Google Scholar 

  15. Moraes, F.H., Silveira, M., Gonçalves, P.J.P.: On the dynamics of a vibration isolator with geometrically nonlinear inerter. Nonlinear Dyn. 93(3), 1325–1340 (2018)

    Article  Google Scholar 

  16. Wagg, D.J.: A review of the mechanical inerter: historical context, physical realisations and nonlinear applications. Nonlinear Dyn. (2021). https://doi.org/10.1007/s11071-021-06303-8

    Article  Google Scholar 

  17. Zhang, X.L., Geng, C., Nie, J.M., Gao, Q.: The missing mem-inerter and extended mem-dashpot found. Nonlinear Dyn. 101(2), 835–856 (2020)

    Article  Google Scholar 

  18. Brzeski, P., Kapitaniak, T., Perlikowski, P.: Novel type of tuned mass damper with inerter which enables changes of inertance. J. Sound Vib. 349, 56–66 (2015)

    Article  Google Scholar 

  19. Smith, N., Wagg, D.J.: A fluid inerter with variable inertance properties. In: Proceedings of the 6th European Conference on Structural Control, pp. 1C8 (2016)

  20. Ning, D., Sun, S., Du, H., Li, W., Zhang, N., Zheng, M., Luo, L.: An electromagnetic variable inertance device for seat suspension vibration control. Mech. Syst. Sig. Process. 133, (2019)

  21. Málaga-Chuquitaype, C., Menendez-Vicente, C., Thiers-Moggia, R.: Experimental and numerical assessment of the seismic response of steel structures with clutched inerters. Soil Dyn. Earthq. Eng. 121, 200–211 (2019)

    Article  Google Scholar 

  22. Wang, Y., Ding, H., Chen, L.Q.: Averaging analysis on a semi-active inerter-based suspension system with relative-acceleration-relative-velocity control. J. Vib. Control 26(13–14), 1199–1215 (2020)

    Article  MathSciNet  Google Scholar 

  23. Casciati, F., Magonette, G., Marazzi, F.: Technology of Semiactive Devices and Applications in Vibration Mitigation. Wiley, Chichester (2006)

    Book  Google Scholar 

  24. Garrido, H., Curadelli, O., Ambrosini, D.: On the assumed inherent stability of semi-active control systems. Eng. Struct. 159, 286–298 (2018)

    Article  Google Scholar 

  25. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, New Jersey (1991)

    MATH  Google Scholar 

  26. Georgiou, T.T., Jabbari, F., Smith, M.C.: Principles of lossless adjustable one-ports. IEEE Trans. Autom. Control 65(1), 252–262 (2020)

    Article  MathSciNet  Google Scholar 

  27. Corless, M., Leitmann, G.: Destabilization via active stiffness. Dyn. Control 7(3), 263–268 (1997)

  28. Gladwell, G.M.L.: Inverse Problems in Vibration, 2nd edn. Springer Science and Business Media, The Netherlands (2005)

    Book  Google Scholar 

  29. Hu, Y., Chen, M.Z.Q., Smith, M.C.: Natural frequency assignment for mass-chain systems with inerters. Mech. Syst. Sig. Process. 108, 126–139 (2018)

    Article  Google Scholar 

  30. Wang, F.C., Su, W.J.: Impact of inerter nonlinearities on vehicle suspension control. Veh. Syst. Dyn. 46(7), 575–595 (2008)

    Article  Google Scholar 

Download references

Acknowledgements

This research was partially supported by the National Natural Science Foundation of China under Grants 61873129, 62073121, 62003131, National Natural Science Foundation of China-State Grid Joint Fund for Smart Grid under Grant U1966202, and the Fundamental Research Funds for the Central Universities of China under Grant B210202058.

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Authors and Affiliations

  1. College of Energy and Electrical Engineering, Hohai University, Nanjing, 211100, China

    Yinlong Hu, Tianyang Hua, Shang Shi & Yonghui Sun

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Michael Z. Q. Chen

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  1. Yinlong Hu
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  2. Tianyang Hua
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  3. Michael Z. Q. Chen
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Correspondence to Yinlong Hu.

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Hu, Y., Hua, T., Chen, M.Z.Q. et al. Instability analysis for semi-active control systems with semi-active inerters. Nonlinear Dyn 105, 99–112 (2021). https://doi.org/10.1007/s11071-021-06555-4

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  • DOI: https://doi.org/10.1007/s11071-021-06555-4

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