Adaptive and Model-Based Control Theory Applied to Convectively Unstable Flows

In boundary-layer flows it is possible to reduce the friction drag by breaking the path from laminar to turbulent state. In low turbulence environments, the laminar-to-turbulent transition is dominated by local flow instabilities – Tollmien-Schlichting (TS) waves – that exponentially grows while being con- vected by the flow and, eventually, lead to transition. Hence, by attenuating these disturbances via localised forcing in the flow it is possible to delay farther downstream the onset of turbulence and reduce the friction drag.Reactive control techniques are widely investigated to this end. The aim of this work is to compare model-based and adaptive control techniques and show how the adaptivity is crucial to control TS-waves in real applications. The control design consists in (i) choosing sensors and actuators and (ii) designing the system responsible to process on-line the measurement signals in order to compute an appropriate forcing by the actuators. This system, called compen- sator, can be static or adaptive, depending on the possibility of self-adjusting its response to unmodelled flow dynamics. A Linear Quadratic Gaussian (LQG) regulator is chosen as representative of static controllers. Direct numerical simulations of the flow are performed to provide a model for the compensator design and test its performance. An adaptive Filtered-X Least-Mean-Squares (FXLMS) compensator is also designed for the same flow case and its per- formance is compared to the model-based compensator via simulations and experiments. Although the LQG regulator behaves better at design conditions, it lacks robustness to small flow variations. On the other hand, the FXLMS compensator proved to be able to adapt its response to overcome the varied conditions and perform an adequate control action.It is thus found that an adaptive control technique is more suitable to delay the laminar-to-turbulent transition in situations where an accurate model of the flow is not available.

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