Low Order Model Identification and Controller Design for Active Flow Control

Abstract

This paper presents a model reduction and control approach for a class of active flow control problem. Computational fluid dynamics (CFD) has been used extensively to study fluid dynamic systems. It is a powerful tool to gain insight and understanding, but it is also extremely computationally intensive and thus unsuitable for control design and iteration. Various model reduction schemes have been proposed in the past to approximate the Navier-Stokes equation with a low-dimensional model. There are essentially two approaches: input/output model identification and modal decomposition based on snapshots of high-dimensional states such as proper orthogonal decomposition (POD). The former captures mostly the local behavior near a steady state and the latter is highly dependent on the snapshots of the flow state used to extract the projection. This paper presents a novel model reduction approach that attempts to combine the attractive features of the two approaches. The local behavior is first obtained through the identification of a linear (or semi-linear) time invariant model using the input/output data. To capture the large nonlinear structure, we project the difference between CFD response and the linear identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the input/output linear model. The resulting linear+nonlinear model is used to design a feedback control law. The difference between the predicted trajectory and CFD simulated trajectory under this control law is further used to refine the POD basis, until a good match is obtained. The proposed method is applied to 2D compressible flow example with outlet flow rate control for a contraction section. Preliminary results for lift control of a 2D airfoil is also included.