The usefulness of viscosity for the robustness of boundary feedback control of an unstable fluid flow system
Résumé
The potential lack of robustness to delays and characteristic velocities is a well known feature of boundary feedback control of hyperbolic systems. We consider the case of a one-dimensional fluid system with the flow rate as control input located at one boundary and the density as measured output located at the other boundary. Using a simple model where friction and viscosity are neglected, the system is open-loop unstable but it can be stabilized by a dynamic controller that involves a delayed output feedback. However this control is not robust with respect to delay uncertainties. Our main contribution is to show that this lack of robustness is actually an artefact which stems from the assumption that the fluid viscosity is negligible when modelling the fluid motion. In the presence of a small unknown viscosity in the model, it appears that the non-robust feedback for the inviscid case is actually a perfectly robust stabilizer for the viscous system and that there is an intrinsic uniform margin of stability which is independent of the viscosity value even if it is asymptotically small.
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