A Closed-Form Observer for the 3D Inductionless MHD and Navier-Stokes Channel Flow
R. Vazquez, E. Schuster and M. Krstic
IEEE Conference on Decision and Control
San Diego, California, December 13-15, 2006
Abstract
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We present a PDE observer that estimates the
velocity, pressure, electric potential and current fields in a
magnetohydrodynamic (MHD) channel flow, also known as
Hartmann flow. This flow is characterized by 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 so-called MHD approximation
in a low magnetic Reynolds number regime. Our observer
consists of a copy of the linearized MHD equations, combined
with linear injection of output estimation error, with observer
gains designed using backstepping. Pressure, skin friction and
current measurements from one of the walls are used for output
injection. For zero magnetic field or non-conducting fluid, the
design reduces to an observer for the Navier-Stokes Poiseuille
flow, a benchmark for flow control and turbulence estimation.
The observer design for non-discretized 3-D MHD or Navier-
Stokes channel flow has so far been an open problem.