Control Oriented Models & Feedback Design in Fluid Flow Systems: A Review

The nonlinearity and high dimension of computational fluid dynamics (CFD) models (O(104) at the low end) reflect fluid dynamics' intrinsic complexity. It is a formidable challenge, setting fluid flow control apart from conventional applications. Its implications include restrictions on model based control design, reliable state estimation, and thus, on feedback implementation. Seeking low order, design accessible models, the issue of an ample dynamic envelope, covering targeted free and actuated transients, is in the essence. We review some enablers for very low order, Galerkin models (GMs). Those include the combination of empirical proper orthogonal decomposition (POD) and physics based modes, estimation of turbulence and pressure effects, actuation models, interpolated models that cover an enhanced dynamic range, and auxiliary, phasor models, focused on sensor readings. The dynamic manifold of model validity must be respected for a meaningful use of the model, but can also be exploited, such as by a restriction to slow drift in the system's periodic behavior, enabling the use of simplifying dynamic phasor models. Finally, we shall highlight some intrinsic performance limitations in GM based feedback flow control.