Reduced Order Model of Cylinder Wake with Direct Adaptive Feedback Control

This paper demonstrates a very systematic approach for feedback flow controller design. Open loop forcing and unforced CFD simulation training data is used to build a reduced order model via the Double Proper Orthogonal Decomposition (DPOD) process. Nonlinear system identification is then used realize a very simple, low dimensional plant. The model has the ability to simulate interior points on the forcing envelope and also predict closed loop dynamics if the model is developed correctly. For simplicity, the model and controller development strategy is shown for a relatively well know flow field, the two dimensional, circular cylinder wake. This paper shows the validity of neural network (ANNARX) models to recreate closed loop simulations while only trained from open loop forcing cases. Direct adaptive feedback control is then applied to the ANN-ARX model. Once satisfying results are seen on the model, the feedback controller is scaled up to a CFD simulation. This control design technique is not limited to laminar two-dimensional flows, but also has capability to model and control more turbulent, non-linear three dimensional flows.