Hybrid model reduction for compressible flow controller design

Computational fluid dynamics (CFD) has been a powerful simulation tool to gain insight and understanding of fluid dynamic systems. However, 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 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 hybrid model reduction approach that attempts to combine the best features of the two approaches. We first identify an input/output linear model by using the subspace identification method. We next project the difference between CFD response and the identified model response onto a set of POD basis. This trajectory is then fit to a nonlinear dynamical model to augment the input/output linear model. The resulting hybrid model is then used for control design with the controller evaluated with CFD. The proposed methodology has been applied to a 2D compressible flow passing a contraction geometry. The result indicates that near the steady state used for linear system identification, the linear system based design works well. However, far away from the steady state, the hybrid system shows much better performance.