Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators

Belson, Brandt A.; Semeraro, Onofrio; Rowley, Clarence W.; Henningson, Dan S.

doi:10.1063/1.4804390

Cited by 65 publications

(108 citation statements)

References 25 publications

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“…The control of small-amplitude perturbations is analysed for the two-dimensional input-output configuration already investigated by Bagheri et al (2009a) and Belson et al (2013). In figure 2, a sketch of the computational domain is shown; the streamwise and wall-normal directions are denoted by x and y, respectively.…”

Section: Flow Casementioning

confidence: 99%

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Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using numerical simulation. Full-dimensional optimal controllers are used in combination with a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors). The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits & Luchini (2010), is used to efficiently compute the Linear Quadratic Regulator (LQR) controller; the method is iterative and allows to by-pass the solution of the corresponding Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration can be cast for the estimation problem; the dual algorithm is referred to as Adjoint of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control problem, a full dimensional, model-free, Linear Gaussian Quadratic (LQG) controllers are obtained and used for the attenuation of the disturbances arising in the boundary layer flow. Model-free, full dimensional controllers turn out to be an excellent benchmark for evaluating the performance of the optimal control/estimation design based on open-loop model reduction. We show the conditions under which the two strategies are in perfect agreement by focusing on the issues arising when feedback configurations are considered. An analysis of the finite amplitude cases is also carried out addressing the limitations of the optimal controllers, the role of the estimation and the robustness to the nonlinearities arising in the flow of the control design

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Section: Flow Casementioning

confidence: 99%

“…Note that feedback and feedforward controllers strongly differ in terms of stability properties and robustness to uncertainties of the system; these aspects are thoroughly analysed for the same configuration in Belson et al (2013).…”

Section: Input-output Systemmentioning

confidence: 99%

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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“…Due to the strong time delays characterizing the system and the placement of the actuators and sensors, from the dynamical point of view the closed-loop system corresponds to a disturbance feedforward controller, a special case of output feedback control (see, e.g., Anderson & Liu 1989). This configuration guarantees the best performance in terms of minimization of the norm z and damping of the perturbation energy amplitude (see Belson et al 2013). A parametric analysis of the performance has been carried out by varying the controller effort and the finite amplitude of the perturbation for three different configurations of actuators.…”

Section: Discussionmentioning

confidence: 99%

“…This configuration guarantees the best performance in terms of perturbation energy damping as shown by Belson et al (2013) for the corresponding two-dimensional case. An analogous result is presented by Juillet, Schmid & Huerre (2013), where it is shown that the feedforward approach is equivalent to an optimal LQG for convective flows and for sensors placed sufficiently far upstream of the actuators.…”

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confidence: 99%

Transition delay in a boundary layer flow using active control

et al. 2013

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Active linear control is applied to delay the onset of laminar-turbulent transition in the boundary layer over a flat plate. The analysis is carried out by numerical simulations of the nonlinear, transitional regime. A three-dimensional, localized initial condition triggering Tollmien-Schlichting waves of finite amplitude is used to numerically simulate the transition to turbulence. Linear quadratic Gaussian controllers based on reduced-order models of the linearized Navier-Stokes equations are designed, where the wall sensors and the actuators are localized in space. A parametric analysis is carried out in the nonlinear regime, for different disturbance amplitudes, by investigating the effects of the actuation on the flow due to different distributions of the localized actuators along the spanwise direction, different sizes of the actuators and the effort of the controllers. We identify the range of parameters where the controllers are effective and highlight the limits of the device for high amplitudes and strong control action. Despite the fully linear control approach, it is shown that the device is effective in delaying the onset of laminar-turbulent transition in the presence of packets characterized by amplitudes a ≈ 1 % of the free stream velocity at the actuator location. Up to these amplitudes, it is found that a proper choice of the actuators positively affects the performance of the controller. For a transitional case, a ≈ 0.20 %, we show a transition delay of ∆Re x = 3.0 × 10 5 .

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“…This leads to a feed-forward control strategy . As shown by Belson et al (2013), this configuration leads to better performance but it lacks robustness. Therefore, an adaptive method is used to create a closed loop on the control law via the performance outputs z l and recover robustness: this loop operates on a larger time scale than the control law K and it recovers robustness for slow changes of the plant response (Fabbiane et al 2015b).…”

Section: Control Strategymentioning

confidence: 99%

Energy efficiency and performance limitations of linear adaptive control for transition delay

2016

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A reactive control technique with localised actuators and sensors is used to delay the transition to turbulence in a flat-plate boundary-layer flow. Through extensive direct numerical simulations, it is shown that an adaptive technique, which computes the control law on-line, is able to significantly reduce skin-friction drag in the presence of random three-dimensional perturbation fields with linear and weakly nonlinear behaviour. An energy budget analysis is performed in order to assess the net energy saving capabilities of the linear control approach. When considering a model of the dielectric-barrier-discharge (DBD) plasma actuator, the energy spent to create appropriate actuation force inside the boundary layer is of the same order as the energy gained from reducing skin-friction drag. With a model of an ideal actuator a net energy gain of three orders of magnitude can be achieved by efficiently damping small-amplitude disturbances upstream. The energy analysis in this study thus provides an upper limit for what we can expect in terms of drag-reduction efficiency for linear control of transition as a means for drag reduction.

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Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators

Cited by 65 publications

References 25 publications

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Transition delay in a boundary layer flow using active control

Energy efficiency and performance limitations of linear adaptive control for transition delay

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