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A comparative study on the control of friction-driven oscillations by time-delayed feedback

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Abstract

We perform a detailed study of two linear time-delayed feedback laws for control of friction-driven oscillations. Our comparative study also includes two different mathematical models for the nonlinear dependence of frictional forces on sliding speed. Linear analysis gives stability boundaries in the plane of control parameters. The equilibrium loses stability via a Hopf bifurcation. Dynamics near the bifurcation is studied using the method of multiple scales (MMS). The bifurcation is supercritical for one frictional force model and subcritical for the other, pointing to complications in the true nature of the bifurcation for friction-driven oscillations. The MMS results match very well with numerical solutions. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control effectiveness.

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Authors and Affiliations

  1. Mechanical Engineering Department, Indian Institute of Technology, Kanpur, 208016, India

    Ashesh Saha, Bishakh Bhattacharya & Pankaj Wahi

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  1. Ashesh Saha
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  2. Bishakh Bhattacharya
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  3. Pankaj Wahi
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Correspondence to Pankaj Wahi.

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Saha, A., Bhattacharya, B. & Wahi, P. A comparative study on the control of friction-driven oscillations by time-delayed feedback. Nonlinear Dyn 60, 15–37 (2010). https://doi.org/10.1007/s11071-009-9577-x

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  • DOI: https://doi.org/10.1007/s11071-009-9577-x

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