We design a controller for flow-induced vibrations of an infinite-band membrane, with flow running across the band and only above it, and with actuation only on the trailing edge of the membrane. Due to the infinite length of the membrane, the dynamics of the membrane in the spanwise direction are neglected, namely, we employ a one-dimensional (1D) model that focuses on streamwise vibrations. This framework is inspired by a flow along an airplane wing with actuation on the trailing edge. The model of the flow-induced vibration is given by a wave partial differential equation (PDE) with an antidamping term throughout the 1D domain. Such a model is based on linear aeroelastic theory for Mach numbers above 0.8. To design a controller, we introduce a three-stage backstepping transformation. The first stage gets the system to a critically antidamped wave equation, changing the stiffness coefficient's value but not its sign. The second stage changes the system from a critically antidamped to a critically damped equation with an arbitrary damping coefficient. The third stage adjusts stiffness arbitrarily. The controller and backstepping transformation map the original system into a target system given by a wave equation with arbitrary positive damping and stiffness.
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August 2015
Research-Article
Boundary Backstepping Control of Flow-Induced Vibrations of a Membrane at High Mach Numbers
Aziz Sezgin,
Aziz Sezgin
1
Department of Mechanical Engineering,
e-mail: asezgin@istanbul.edu.tr
Istanbul University Avcilar Kampusu
,Avcilar, Istanbul 34320
, Turkey
e-mail: asezgin@istanbul.edu.tr
1Corresponding author.
Search for other works by this author on:
Miroslav Krstic
Miroslav Krstic
Professor
Department of Mechanical
and Aerospace Engineering,
e-mail: krstic@ucsd.edu
Department of Mechanical
and Aerospace Engineering,
University of California
, San Diego
,La Jolla, CA 92093-0411
e-mail: krstic@ucsd.edu
Search for other works by this author on:
Aziz Sezgin
Department of Mechanical Engineering,
e-mail: asezgin@istanbul.edu.tr
Istanbul University Avcilar Kampusu
,Avcilar, Istanbul 34320
, Turkey
e-mail: asezgin@istanbul.edu.tr
Miroslav Krstic
Professor
Department of Mechanical
and Aerospace Engineering,
e-mail: krstic@ucsd.edu
Department of Mechanical
and Aerospace Engineering,
University of California
, San Diego
,La Jolla, CA 92093-0411
e-mail: krstic@ucsd.edu
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 13, 2014; final manuscript received December 10, 2014; published online April 14, 2015. Assoc. Editor: YangQuan Chen.
J. Dyn. Sys., Meas., Control. Aug 2015, 137(8): 081003 (8 pages)
Published Online: August 1, 2015
Article history
Received:
May 13, 2014
Revision Received:
December 10, 2014
Online:
April 14, 2015
Citation
Sezgin, A., and Krstic, M. (August 1, 2015). "Boundary Backstepping Control of Flow-Induced Vibrations of a Membrane at High Mach Numbers." ASME. J. Dyn. Sys., Meas., Control. August 2015; 137(8): 081003. https://doi.org/10.1115/1.4029468
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