The Usefulness of Viscosity for the Robustness of Boundary Feedback Control of an Unstable Fluid Flow System

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 flow rate as control input located at one boundary and 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 involving delayed output feedback. However this control is not robust with respect to small modelling uncertainties. Our main contribution is to show that this lack of robustness is actually an artefact which stems from the assumption that fluid viscosity is negligible when modelling 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 becomes insensitive to the viscosity value when it is small. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.