Nonlinear Flow Control Based on a Low Dimensional Model of Fluid Flow

Abstract

Nonlinear control design is shown to be a critical enabler for robust model-based suppression of a flow instability. The onset of oscillatory vortex shedding is chosen as a well investigated benchmark problem of flow control. A low-dimensional Galerkin model using a Karhunen-Lo‘eve decomposition of the flow field 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). The aim is to find methods which respect the validity of low order models. Examples are formal methods such as input-output linearization, Lyapunov-based, backstepping controllers 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.

Keywords: Flow control, Navier-Stokes equation, nonlinear control, Galerkin model, cylinder wake.