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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Fractional Order PD Control of Friction-Induced Vibrations in a Continuous System

Journal of Applied Nonlinear Dynamics 10(3) (2021) 413--429 | DOI:10.5890/JAND.2021.09.005

Tejas Kokane, Ashesh Saha

Department of Mechanical Engineering, National Institute of Technology Calicut, Kerala - 673601, India

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Abstract

Fractional-order PD (PD$^{\lambda })$ control of friction-induced vibrations in a beam-mass model is analysed in this paper. Mathematical modelling of the system with a piezo-patch actuator bonded to the beam surface is presented. Linear stability analysis is performed to determine the stability boundary corresponding to the Hopf bifurcation points. The nature of bifurcation is found to be supercritical from the non-linear analysis by the method of averaging. The role of fractional-order on the effectiveness of the controller in quenching friction-induced vibrations is thoroughly investigated. The efficacy of the controller with varying size and locations of the piezo-patch is also studied.

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