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Delayed-Acceleration Feedback for Active-Multimode Vibration Control of Cantilever Beams

[+] Author Affiliations
Khaled A. Alhazza, Ali H. Nayfeh

Virginia Polytechnic Institute and State University, Blacksburg, VA

Mohammed F. Daqaq

Clemson University, Clemson, SC

Paper No. DETC2007-34793, pp. 729-738; 10 pages
doi:10.1115/DETC2007-34793
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly-coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.

Copyright © 2007 by ASME

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