Feedback Flow Control in Experiment and Simulation Using Global Neural Network Based Models

Abstract

For feedback control of complex spatio-temporally evolving flow fields, it imperative to use a global flow model for both flow state estimation, as well as controller development. It is important that this model correctly presents not just the natural, unforced flow state, but also the interaction of actuators with the flow for both open and closed loop situations. In order to achieve this, a novel extension of POD is introduced in this chapter, which we refer to as Double POD (DPOD). This decomposition allows the construction of a POD basis that is valid for a variety of flow conditions, which may be distinguished by changes in actuation, Reynolds number or other parameters. While traditionally the velocity field has been used as input for POD, other variables, for example the pressure or density field, may be used as well. The mode amplitudes of the DPOD spatial modes are then used as input for a system identification process, the nonlinear ANN-ARX method is employed here. The result is a dynamic model that represents both the unforced, open loop forced and closed loop flow fields with good accuracy.