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This tutorial paper presents backstepping boundary control designs for fluid systems. It starts with an introduction of an output-feedback controller for the problem of vortex shedding around a cylindrical bluff body in the flow. It is then followed by a presentation of stabilization of the thermal convection loop. Finally, the paper concludes with a control design for the turbulent channel flow.
We present a boundary control law that stabilizes the Hartman profile for low magnetic Reynolds numbers in an infinite magnetohydrodynamic (MHD) channel flow. The proposed control law achieves stability in the L2 norm of the linearized MHD equations, guaranteeing local stability for the fully nonlinear system.
We present a formula for a boundary control law which stabilizes the parabolic profile of an infinite channel flow, which is linearly unstable for high Reynolds numbers. Also known as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence, whose stabilization for arbitrary Reynolds numbers, without using discretization, has so far been an open problem. Our...
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...
In a previous work, we presented formulae for boundary control laws which stabilized the parabolic profile of an infinite channel flow, linearly unstable for high Reynolds number. Also know as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence, whose stabilization for arbitrary Reynolds number, without using discretization, had so far been an open problem...
We present an extension from 2D to 3D of a boundary control law which stabilizes the parabolic profile of an infinite channel flow. In this 3D case, we include an additional controller in the spanwise direction which, similar to the streamwise and wall normal velocity controllers, actuates solely along one boundary. The controller that acts in the wall normal direction transforms the system into a...
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