Closed-loop feedback control of boundary layer streaks embedded in a laminar boundary layer and experiencing transient growth, which is inherent to bypass boundary layer transition, is experimentally investigated. Streaky disturbances are introduced by a spanwise array of cylindrical roughness elements, and a counter disturbance is provided by a spanwise array of plasma actuators, which are capable of generating spanwise-periodic counter rotating vortices in the boundary layer. Feedback is provided by a spanwise array of shear stress sensors. An input/output model of the system is obtained from measurements of the boundary layer response to steady forcing, and used to design and analyze a proportional-integral controller, which targets a specific spanwise wavenumber of the disturbance. Attention is directed towards a quasi-steady case in which the controller update is slower than the convective time scale. This choice enables addressing issues pertinent to sensing, actuation, and control strategy that are also relevant to the control of unsteady disturbances but without the full complexity of transient effects. The feedback controller and plasma actuators perform well, attenuating the streamwise streaks both in the vicinity of the sensors and farther downstream. The controller remains effective for a range of off-design flow conditions, such as when the free-stream velocity is varied.

This study is motivated by controlling transient growth and subsequent bypass transition of the laminar boundary layer to turbulence. In experiments employing a model problem, an active roughness element is used to introduce steady/unsteady streak disturbances in a Blasius boundary layer. This tractable arrangement enables a systematic investigation of the evolution of the disturbances and of potential methods to control them in real time. The control strategy utilizes wall-shear-stress sensors, upstream and downstream of a plasma actuator, as inputs to a model-based controller. The controller is designed using empirical input/output data to determine the parameters of simple models, approximating the boundary layer dynamics. The models are used to tune feedforward and feedback controllers. The control effect is examined over a range of roughness-element heights, free stream velocities, feedback sensor positions, unsteady disturbance frequencies and control strategies; and is found to nearly completely cancel the steady-state disturbance at the downstream sensor location. The control of unsteady disturbances exhibits a limited bandwidth of less than 1.3 Hz. However, concurrent modelling demonstrates that substantially higher bandwidth is achievable by improving the feedforward controller and/or optimizing the feedback sensor location. Moreover, the model analysis shows that the difference in the convective time delay of the roughness-and actuator-induced disturbances over the control domain must be known with high accuracy for effective feedforward control. This poses a limitation for control effectiveness in a stochastic environment, such as in bypass transition beneath a turbulent free stream; nonetheless, feedback can remedy some of this limitation.

The overarching objective motivating this work is a physical demonstration of modelbased, closed-loop control of bypass transition using plasma actuators. The present work is concerned with the closed-loop control of bypass transition using plasma actuators. This manuscripts extends the work by Hanson et al., 1, 2 who demonstrated that a spanwise array of plasma actuators can produce significant attenuation of the transient growth disturbances introduced by roughness elements. In the present work, the control loop is closed based on feedback from wall-shear stress measurements. The control signal is based on empirical modelling of the input/output flow response for several flow conditions. The latter is obtained for both the main disturbance, generated by a roughness-element array, as well as the control disturbance, forced using a spanwise plasma actuator array. The output is characterized using wall-shear-stress measurements downstream of the actuation location. The controller is designed to minimize the residual disturbance energy in the output measurements at the target instability spanwise wavenumber. The control model developed in this work was applied to three steady disturbance cases, including one that is outside of the parameter range for which the input/output model was developed. The closed-loop control model is shown to effectively attenuate the boundary layer disturbance by Ω 1,end > 95% in each case, with the initial control iteration accounting for Ω1,1 > 89%.

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