Linear Closed Loop Control of Fluid Instabilities and Noise Induced Perturbations: A Review of Approaches and Tools1

Abstract

This review article is concerned with the design of linear reducedorder models and control laws for closedloop control of instabilities in transitional flows. For oscillator flows, such as opencavity flows, we suggest the use of optimal control techniques with Galerkin models based on unstable global modes and balanced modes. Particular attention has to be paid to stability–robustness properties of the control law. Specifically, we show that large delays and strong amplification between the control input and the estimation sensor may be detrimental both to performance and robustness. For amplifier flows, such as backwardfacing step flow, the requirement to account for the upstream disturbance environment rules out Galerkin models. In this case, an upstream sensor is introduced to detect incoming perturbations, and identification methods are used to fit a model structure to available input–output data. Control laws, obtained by direct inversion of the input–output relations, are found to be robust when applied to the largescale numerical simulation. All the concepts are presented in a stepbystep manner, and numerical codes are provided for the interested reader.