On the need of nonlinear control for efficient model-based wake stabilization

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input-output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.