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Model-free chaos control based on AHGSA for a vibro-impact system

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Abstract

For a vibro-impact system with clearance, the model-free chaos control method based on adaptive hybrid gravitational search algorithm (or AHGSA algorithm for short) is proposed. Nonparametric time-varying dynamic linear model based on pseudo-partial-derivative is established using input/output data of the controlled system, and on this basis, the optimal controller is designed according to the quadratic performance index, and the controller parameters is optimized using AHGSA algorithm. By combining the artificial bee colony search operator and chaos optimization strategy, gravitational search algorithm (or GSA algorithm for short) is improved from three aspects (i.e., population initialization, velocity and position update, gravity coefficient adjustment) to achieve a balance between the global detection ability and the local development ability. AHGSA algorithm has good optimization accuracy and efficiency: The arbitrariness is avoided in controller parameters selection, and the quality of the chaos control is ensured as well. In simulation experiment, the model-free controller optimized is used to control the chaotic motion of a single-degree-of-freedom vibro-impact system with clearance to verify the validity and feasibility of the proposed chaos control method. The simulation results show that the control effect is good, and the proposed chaos control method has the following advantages: the proposed chaos control method does not depend on the precise model of the controlled system, and the controller is easy to be designed and implemented.

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References

  1. Peterka, F., Vacik, J.: Transition to chaotic motion in mechanical systems with impacts. J. Sound Vib. 153(1), 95–115 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Natsiavas, S.: Dynamics of multi-degree-of-freedom oscillators with colliding components. J. Sound Vib. 165(2), 439–453 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wen, G.L., Xie, J.H.: Period-doubling bifurcation and non-typical route to chaos of a two-degree-of-freedom vibro-impact system. ASME J. Appl. Mech. 68(4), 670–674 (2001)

    Article  MATH  Google Scholar 

  4. Ding, W.C., Li, G.F., Luo, G.W., Xie, J.H.: Trous T2 and its locking, doubling, chaos of a vibro-impact system. J. Frankl. Inst. 349, 337–348 (2012)

    Article  MATH  Google Scholar 

  5. Luo, G.W., Zhu, X.F., Shi, Y.Q.: Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop: diversity and evolution of periodic-impact motions. J. Sound Vib. 334, 338–362 (2015)

    Article  Google Scholar 

  6. Yue, Y.: Local dynamical behavior of two-parameter family near the neimark-sacker-pitchfork bifurcation point in a vibro-impact system. Chin. J. Theor. Appl. Mech. 48(1), 163–172 (2016)

    Google Scholar 

  7. De Souza, S.L.T., Caldas, I.L., Viana, R.L.: Damping control law for a chaotic impact oscillator. Chaos Solitons Fractals 32(2), 745–750 (2007)

    Article  Google Scholar 

  8. Lee, J.Y., Yan, J.J.: Control of impact oscillator. Chaos Solitons Fractals 28, 136–142 (2006)

    Article  MATH  Google Scholar 

  9. Ding, W.C., Ma, Y.J., Wang, J.Y.: Feedback control of a vibro-impact system by states prediction. J. Vib. Eng. 20(6), 589–593 (2007)

    Google Scholar 

  10. Zhang, Q.S., Ding, W.C., Sun, C.: Delayed feedback control of chaos in a single DOF non-smooth system. J. Vib. Shock 27(1), 155–158 (2008)

    Google Scholar 

  11. Ma, Y.J., Ding, W.C., Yang, X.G.: Chaos control of a vibro-impact system with parameter adjustment. J. Vib. Shock 26(1), 24–26 (2007)

    Google Scholar 

  12. Li, Q.H., Wei, Y.Y., Tan, J.Y.: Chaos control of a vibro-impact dynamical system with two degrees of freedom. J. Guang Xi Univ. NAT SCI ED 34(2), 206–210 (2009)

    Google Scholar 

  13. Liu, Y.Y., Xu, W., Huang, D.M., Wang, L.: Dynamical analysis of a multi-degree-of-freedom vibro-impact system under position control law. Fire Control Command Control 38(11), 15–18 (2013)

    Google Scholar 

  14. Wang, Z.J.: Controlling chaos in a one-degree-of-freedom vibro-impact system by the OGY method. Southwest Jiaotong University Master Degree Thesis, Cheng Du (2013)

  15. Kuo, C.W., Suh, C.S.: Controlling bifurcation and dynamic behavior in vibro-impact system. In: Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, Montreal, pp. 14–20 (2014)

  16. Wei, X.J., Ding, W.C., Li, N.Z., Guo, W.Z.: Fault diagnosis of locomotive gearbox based on gravitational search RBF neural network. J. China Railway Soc. 38(2), 19–26 (2016)

    Google Scholar 

  17. Hou, Z.S.: Nonparametric Models and Its Adaptive Control Theory. Science Press, Beijing (1999)

    Google Scholar 

  18. Wang, W.H., Hou, Z.S., Huo, H.B., Jin, S.T.: Data-driven based controller design and its parameters tuning method. J. Syst. Sci. Complex. 30(6), 792–805 (2010)

    MathSciNet  MATH  Google Scholar 

  19. Rashedi, E., Nezamabadi, P.H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)

    Article  MATH  Google Scholar 

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11462011, 51665027 and 11732014).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Xiao-juan Wei, Ning-zhou Li, Wang-cai Ding & Cao-hui Zhang

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  1. Xiao-juan Wei
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  2. Ning-zhou Li
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  3. Wang-cai Ding
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  4. Cao-hui Zhang
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Correspondence to Xiao-juan Wei.

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Wei, Xj., Li, Nz., Ding, Wc. et al. Model-free chaos control based on AHGSA for a vibro-impact system. Nonlinear Dyn 94, 845–855 (2018). https://doi.org/10.1007/s11071-018-4397-5

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  • DOI: https://doi.org/10.1007/s11071-018-4397-5

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