Linear control of oscillator and amplifier flows1

Schmid, Peter J.; Sipp, Denis

doi:10.1103/physrevfluids.1.040501

Cited by 21 publications

(17 citation statements)

References 43 publications

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“…The control action is then decided by means of measuring the input and acting to minimize a given quantity at the objective position. This can be accomplished using static compensators, such as the Linear Quadratic Gaussian (LQG) regulator (Barbagallo et al 2009(Barbagallo et al , 2011Juillet et al 2014;Schmid & Sipp 2016;Fabbiane et al 2017).…”

Section: Controlmentioning

confidence: 99%

On the role of actuation for the control of streaky structures in boundary layers

et al. 2019

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This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST) in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.

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Section: Controlmentioning

confidence: 99%

On the role of actuation for the control of streaky structures in boundary layers

et al. 2019

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“…A generalization of the work of Bagheri et al [7] to 3-D flows is presented in Semeraro et al [19] and was applied by Semeraro et al [20] in fully non-linear simulations to verify the possibility of delaying transition to turbulence using velocity measurements and volume forcing actuation. Limitations related to a more realistic set-up were addressed by Dadfar et al [8,21] Sipp [23]. It guarantees robust stability in convective flows and the best nominal performance [3,23,24].…”

Section: A Model Reduction and Control Of Convective Instabilitiesmentioning

confidence: 99%

“…Limitations related to a more realistic set-up were addressed by Dadfar et al [8,21] Sipp [23]. It guarantees robust stability in convective flows and the best nominal performance [3,23,24]. However, the performance of feedforward control deteriorates quickly in off-design conditions as shown in Fabbiane et al [22] and feedforward control poses challenges in the presence of additional unmodeled dynamics and disturbances as argued by Belson et al [24].…”

Section: A Model Reduction and Control Of Convective Instabilitiesmentioning

confidence: 99%

Pressure Output Feedback Control of Tollmien–Schlichting Waves in Falkner–Skan Boundary Layers

2019

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This paper investigates the use of point wall pressure measurements for output feedback control of Tollmien-Schlichting waves in Falkner-Skan boundary layers. A new approach is presented for input-output modeling of the linear dynamics of the fluid system and the integration with H 2 /LQG reduced-order control design. The pressure output at the wall is related with the global perturbation velocity field through the linearized pressure Poisson equation. A Kalman filter is subsequently used to obtain time-resolved estimates of the velocity field using pressure information at discrete points at the wall. The estimated field is in turn used to calculate an optimal state feedback control to suppress the instabilities. The controller is designed in both a feedforward, a feedback and a combined feedforward/feedback actuator/sensor configuration. It is shown that combined feedforward/feedback control gives the best trade-off between robust performance and robust stability in the presence of uncertainties in the Reynolds number and the pressure gradient. Robust performance in off-design conditions is enhanced compared to feedforward control while robust stability is enhanced compared to feedback control. Nomenclature A, B, C, D = full order /spatial continuous state-space operators A, B, C, D = reduced order state-space matrices E = perturbation energy F = state feedback gain f = body force vector L = linearized Navier-Stokes operator L = Kalman filter gain l = control penalty m = dimensionless constant characterizing the pressure gradient * Researcher, Faculty of Aerospace Engineering, h.j.tol@tudelft.nl † Assistant Professor, Faculty of Aerospace Engineering, m.kotsonis@tudelft.nl ‡ Assistant Professor, Faculty of Aerospace Engineering, c.c.devisser@tudelft.nl p = fluctuating pressure p f f = feedforward pressure measurement p f b = feedback pressure measurement Re δ = Reynolds number based on local δ * Re 0 = Reynolds number based on inflow δ * r = order of the reduced order model T = closed-loop transfer function t = time U ∞ = dimensionless external free-stream velocity u = fluctuating velocity vector U = base flow vector w = external disturbance x = dimensionless spatial coordinate z, q, p m = output signals Z = boundary to domain lifting operator δ * = displacement thickness, m ξ = similarity variable φ = control input ν = kinematic viscosity, m 2 /s η = temporal state defined at the boundary γ = estimation penalty, relative magnitude of the sensor noise ω = radial frequency ω n = natural frequency ζ = damping ratio Γ = boundary Subscripts in, out, wall = inflow boundary, outflow boundary, rigid wall h, c, d, = homogeneous, control, disturbance m, ff, fb, = measured, feedforward, feedback Superscripts e = extended * = dimensional variable 2

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“…8. The output z(t) is then directly obtained from the superposition of an open-loop behaviour with an actuating signal, and a scheme denoted as disturbance feedforward [41] results, with the objective of rejecting incoming disturbances, measured at y(t). The closed-loop control of such amplifier flow [26] may be understood in terms of the actuation leading to a perturbation profile in phase opposition with the unperturbed, open-loop behaviour of the system, causing a cancellation of the incoming wave.…”

Section: Feedforward and Feedback Control Strategiesmentioning

confidence: 99%

Closed-loop control of a free shear flow: a framework using the parabolized stability equations

Sasaki

Tissot

Cavalieri

et al. 2018

Theor. Comput. Fluid Dyn.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle IDAbstract In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A Communicated by study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations. IntroductionThe manipulation of flow dynamics through active or passive control strategies represents a challenge with several industrial and technological applications. Reduction in drag and consequently of fuel consumption, delay in the transition to turbulence of laminar flows, and reduction in noise levels are but a few of the foreseeable applications of flow control [29]. Over the last years, passive and active flow manipulation has been accomplished. Passive control has been achieved, for boundary layers, via the introduction of roughness elements, as in the work of [49] or by means of chevrons in turbulent jets which attenuate large scale structures [8,31]. For the active, open-loop case, Biringen [7] used suction and blowing in order to obtain the delay in transition in a channel flow. Koenig et al. [30] and Le Rallic et al. [32] use the continuous injection of air in the core of a turbulent jet in order to diminish the radiated acoustic emission. Active closed-loop control is also possible, as the initial stages of the transition of laminar shear flows is a linear pro...

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Linear control of oscillator and amplifier flows1

Cited by 21 publications

References 43 publications

On the role of actuation for the control of streaky structures in boundary layers

On the role of actuation for the control of streaky structures in boundary layers

Pressure Output Feedback Control of Tollmien–Schlichting Waves in Falkner–Skan Boundary Layers

Closed-loop control of a free shear flow: a framework using the parabolized stability equations

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