Research on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review model-based techniques, such as linear-quadratic regulators, and model-free adaptive methods, such as least-mean square filters. The former are supported by a elegant and powerful theoretical basis, whereas the latter may provide a more practical approach in the presence of complex disturbance envi- ronments, that are difficult to model. We compare the methods with a particu- lar focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the one-dimensional linearized Kuramoto-Sivashinsky equa- tion, that shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples are provided. 

In boundary layer flows, one may reduce skin friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien Schlichting (TS) waves In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based I.QG controller in wind-tunnel experiments In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

This manuscript demonstrates the first successful application of the delayed-x-LMS (dxLMS) control algorithm for TS-wave cancelation. Active wave cancelation of two-dimensional broad-band Tollmien-Schlichting (TS) disturbances is per- formed with a single DBD plasma actuator. The experiments are conducted in flight on the pressure side of a laminar flow wing glove, mounted on a manned glider. The stability properties of the controller are investigated in detail with

experimental flight data, DNS and stability analysis of the boundary layer. Finally, a model-free approach for dxLMS operation is introduced to operate the controller as a “black box” system, which automatically adjusts the controller settings based on a group speed measurement of the disturbance wave packets. The modified dxLMS control algorithm allows to operate the controller without a model and an adaption based on varying conditions that may occur during flight in atmosphere. 

We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude three-dimensional Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer. A three-dimensional viscous, incompressible flow developing on a zero-pressure gradient boundary layer in a low Reynolds number environment is analyzed using direct numerical simulations. In this configuration, we distribute evenly in the spanwise direction up to 72 localised objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration, the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanwise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. If n and m are the number of sensor-actuator pairs for the whole system and for a single control unit, respectively, then in a decentralised strategy, the number of interconnections deceases mn compared to a centralized strategy, which has n (2) interconnections. We find that using a semi-decentralized approach - where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction - results only in a 11 % reduction of control performance. We explain how "wide" in the spanwise direction a control unit should be for a satisfactory control performance. Moreover, the control unit should be designed to account for the perturbations that are coming from the lateral sides (crosstalk) of the estimation sensors. We have also found that the influence of crosstalk is not as essential as the spreading effect.

Reactive-control techniques have been longly investigated to control local flow instabilities in boundary-layer flows – Tollmien-Schlichting waves – that would eventually cause laminar-to-turbulence transition. Several studies have been published about the control of two-dimensional (2D) disturbances supposing a transition delay. In this study, a three-dimensional (3D) disturbance environment is considered in a 2D zero-pressure-gradient boundary-layer flow. A control- law based on a multi-input-multi-output (MIMO) filtered-x least-mean-squares (fxLMS) adaptive algorithm is introduced and its performances are analysed for increasing disturbance amplitude. Transition delay is achieved by the investigated control set-up; moreover, an energy budget is conducted in order to asses the net energy saving capabilities of the investigated control approach. Ideal as well as real actuators models are considered, focusing in particular on dielectric-barrier-discharge (DBD) plasma actuators. To our knowledge, this is the first time that drag-reduction and energy-saving capabilities are studied for reactive transition-delay techniques.