Nonlinear flow control based on a low dimensional approximation of the Navier-Stokes equation*

Nonlinear control design is shown to be a critical enabler for robust model-based supression of a flow instability. The onset of oscillatory vortex shedding is chosen as a well investigated benchmark problem of flow control. A low-dimensional POD Galerkin model is adopted from earlier studies of the authors as a control-oriented fluid flow representation. Several strategies of nonlinear controller design are employed, both, to the Galerkin model and to the flow via a direct numerical simulation of the Navier-Stokes equations (NSE). Examples are input-output linearization, Lyapunov-based, backstepping, LPV-type controlles, etc., and physically motivated controllers. Whereas the first test-bed is easily mastered by the formal methods, the application to the NSE is more critical, due to robustness issues.