Abstract
The impulsive state feedback control is used to create Neimark-Sacker bifurcation for a three-degree-of-freedom vibro-impact system with clearances. The linear control gains are determined to guarantee the existence of Neimark-Sacker bifurcation by using the explicit criteria of Neimark-Sacker bifurcation without directly using eigenvalues. Differently, the nonlinear control gains are selected to determine the direction and stability of Neimark-Sacker bifurcation by using center manifold reduction theory and normal form approach. The amplitude of the created invariant cycle from Neimark-Sacker bifurcation is analytically obtained to achieve the control of the amplitude by selecting appropriate nonlinear control gains. Numerical experiments are provided to show the effectiveness of the proposed control method.
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Acknowledgements
This chapter’s work was supported by the Applied Basic Research Program of Shanxi Province of China (No. 201801D121021).
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Xu, H., Ji, J. (2020). Creation of Neimark-Sacker Bifurcation for a Three-Degree-of-Freedom Vibro-Impact System with Clearances. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) Nonlinear Dynamics of Structures, Systems and Devices. Springer, Cham. https://doi.org/10.1007/978-3-030-34713-0_11
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DOI: https://doi.org/10.1007/978-3-030-34713-0_11
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