We present a boundary feedback law that stabilizes the velocity, pressure, and electromagnetic fields in a magnetohydrodynamic (MHD) channel flow. The MHD channel flow, also known as Hartmann flow, is a benchmark for applications such as cooling, hypersonic flight, and propulsion. It involves an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field. The system is described by the inductionless MHD equations, a combination of the Navier–Stokes equations and a Poisson equation for the electric potential under the MHD approximation in a low magnetic Reynolds number regime. This model is unstable for large Reynolds numbers and is stabilized by actuation of velocity and the electric potential at only one of the walls. The backstepping method for stabilization of parabolic partial differential equations (PDEs) is applied to the velocity field system written in appropriate coordinates. Control gains are computed by solving a set of linear hyperbolic PDEs. Stabilization of nondiscretized 3D MHD channel flow has so far been an open problem.
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e-mail: rvazquez1@us.es
e-mail: schuster@lehigh.edu
e-mail: krstic@ucsd.edu
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July 2009
Research Papers
A Closed-Form Full-State Feedback Controller for Stabilization of 3D Magnetohydrodynamic Channel Flow
Rafael Vazquez,
Rafael Vazquez
Departamento de Ingeniería Aeroespacial,
e-mail: rvazquez1@us.es
Universidad de Sevilla
, Camino de los Descubrimientos, 41092 Sevilla, Spain
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Eugenio Schuster,
Eugenio Schuster
Department of Mechanical Engineering and Mechanics,
e-mail: schuster@lehigh.edu
Lehigh University
, Bethlehem, PA 18015-3085
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Miroslav Krstic
Miroslav Krstic
Department of Mechanical and Aerospace Engineering,
e-mail: krstic@ucsd.edu
University of California, San Diego
, La Jolla, CA 92093-0411
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Rafael Vazquez
Departamento de Ingeniería Aeroespacial,
Universidad de Sevilla
, Camino de los Descubrimientos, 41092 Sevilla, Spaine-mail: rvazquez1@us.es
Eugenio Schuster
Department of Mechanical Engineering and Mechanics,
Lehigh University
, Bethlehem, PA 18015-3085e-mail: schuster@lehigh.edu
Miroslav Krstic
Department of Mechanical and Aerospace Engineering,
University of California, San Diego
, La Jolla, CA 92093-0411e-mail: krstic@ucsd.edu
J. Dyn. Sys., Meas., Control. Jul 2009, 131(4): 041001 (10 pages)
Published Online: April 27, 2009
Article history
Received:
June 5, 2008
Revised:
December 15, 2008
Published:
April 27, 2009
Citation
Vazquez, R., Schuster, E., and Krstic, M. (April 27, 2009). "A Closed-Form Full-State Feedback Controller for Stabilization of 3D Magnetohydrodynamic Channel Flow." ASME. J. Dyn. Sys., Meas., Control. July 2009; 131(4): 041001. https://doi.org/10.1115/1.3089561
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