A framework for closed-loop flow control using the parabolized stability equations

Abstract

We develop a reduced-order-model framework using the parabolized stability equations and identification techniques for the closed-loop control of unsteady fluctuations along fluidic systems. These models had been successfully applied to a turbulent jet as estimation techniques and to an incompressible shear-layer for the development of closed-loop control laws. Through this paper, we propose a further investigation of the PSE-based transfer functions, exploring its flexibility to educe different control schemes and to determine the most effective sensor/actuator positions. Emphasis is be given to the feedforward and feedback configurations for flow control, and differences are understood in terms of causality. A study of the robustness to uncertainties in Reynolds and mean flow velocity, along with external perturbations is also presented. These topics allow deeper insight into the active closed-loop flow control problem and therefore may lead to more effective schemes, particularly on what concerns the experimental implementation of closed-loop control.