Centralised Versus Decentralised Active Control of Boundary Layer Instabilities

Abstract

We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer.We distribute evenly in the spanwise direction up to 72 localized 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 spanswise 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. 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. Our results reveal that the best performance is obtained for a control unit which (i) is sufficiently wide to account for the full spanwise scale of the wavepacket when it reaches the actuators and (ii) is designed to account for the perturbations which 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.