Controller development for closed-loop feedback control of flows

The aim of this study is to implement a closed-loop feedback control with a modeled controller of the flow over a NACA-4412 airfoil equipped with leading-edge zero net-mass actuators. We showed at the AIAA 2004 Portland meeting how low-dimensional methods can be effective for smart flow control. A first simple proportional feedback method was a crucial starting point for verifying the applicability of such low-dimensional methods to, not only control of flow separation over a wing, but to flow control in general. These methods based on the Proper Orthogonal Decomposition (POD) and modified Linear Stochastic Measurement (mLSM) techniques have already shown effective in extracting, estimating and representing the most energetic features of turbulent flows but the proportional feed- back control showed that these features were great candidates for applied flow control. Using only real-time measurements of unsteady pressure along the chord of the airfoil, we are able to spatially estimate the flow field above the wing at all times and sense the incipient separation. For a better understanding of the actuation effect on the flow over the NACA-4412 airfoil, Particle Image Velocimetry (PIV) measurements in a wide window above the airfoil were taken. A higher order estimation, the modified Quadratic Stochastic Estimation (mQSM) is performed here and shows more effective in representing the coherent structures in the flow. By then solving a system of ordinary differential equations based on learning samples of the estimated POD coefficients and through Low-Order Dynamical Systems (LODS) development, we are able to obtain an estimate of the evolution equation of the flow. A novel way of decomposing the velocity field enables us to explicitly include the effect of the actuation in the evolution equation of the flow around the NACA-4412 airfoil for controller development.