A Closed-Form Full-State Feedback Controller for Stabilization of 3D Magnetohydrodynamic Channel Flow
R. Vazquez, E. Schuster, M. Krstic
ASME Journal of Dynamic Systems, Measurement and Control, 131, 041001 (2009)
Abstract
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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 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 non-discretized 3-D MHD
channel flow has so far been an open problem.