Robust Control of Linearized Poiseuille Flow

Baramov, L.; Tutty, O.R.; Rogers, Eric

doi:10.2514/2.4859

Cited by 10 publications

(8 citation statements)

References 7 publications

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“…To obtain a finite-dimensional approximation of the above system of equations we use, as in [4], [15], [16], a Chebyshev expansion in the cross channel direction. We use a finite-difference scheme in the streamwise direction.…”

Section: A Finite Approximationsmentioning

confidence: 99%

“…In our case, we leave them zero and consider a channel sufficiently long that the conditions at its ends have an negligible effect on the relevant mid-section. Note also that if we connected with and with we would obtain the periodic case, studied in [4], [6], [15], [16].…”

Section: A Finite Approximationsmentioning

confidence: 99%

“…The scaling involving the factor was chosen because of the fact that one of the fundamental wavenumbers has length . The Chebyshev order is taken as and an analysis in [4] (where the periodic case was treated) shows that this is sufficiently accurate for frequency range of up to one radian. The control design developed below is within this range.…”

Section: (20)mentioning

confidence: 99%

“…A more usual way is, however, boundary control based on transpiration along one of the walls. Different strategies have been proposed, e.g., a simple integral control in [15], LQG control in [9], [16], control in [4], [6]. [6], [15], [16] deal with the single wavenumber case: the controlled boundary condition is assumed to be harmonically distributed along the channel wall and the measurements are taken at discrete, periodically spaced points.…”

mentioning

confidence: 99%

“…In [4], boundary control for discrete transpiration was proposed, where blowing and suction takes place only along short, periodically spaced sections of the wall. This is a model of blowing/suction panels which are being developed and considered for use in the aerospace industry.…”

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confidence: 99%

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<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow

Baramov

Tutty

Rogers

2004

IEEE Trans. Contr. Syst. Technol.

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This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice. Index Terms-control, flow control, model validation, nonperiodic flows. I. INTRODUCTION F LOW control is currently attracting considerable interest in the fluids research community. A major motivation for this is the possibility of reducing drag on a body by preventing or delaying transition from laminar to turbulent flow. The systems dealt with in these problems are, in control terms, very complex, nonlinear, and infinite dimensional, even if, in fluid mechanical terms, the structure of the flow field is simple in nature. Plane Poiseuille flow, i.e., flow between two infinite parallel plates is one of the simplest and best understood cases of fluid dynamics. Controlling this flow is, however, still an extremely challenging problem, even if it is assumed that deviations from the steady state are small enough for the governing equations to be linearized. It has become a benchmark problem for developing control algorithms for fluid flows and was considered in [4], [6], [9], [14]-[16] among others. All these references make a fundamental assumption that the flow is spatially periodic in the streamwise direction, and hence that a Fourier-Galerkin decomposition can be used to obtain independent dynamics for Manuscript

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Section: A Finite Approximationsmentioning

confidence: 99%

Section: A Finite Approximationsmentioning

confidence: 99%

Section: (20)mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow

Baramov

Tutty

Rogers

2004

IEEE Trans. Contr. Syst. Technol.

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Motion planning and trajectory tracking for three-dimensional Poiseuille flow

Cochran

Krstić

2009

J. Fluid Mech.

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We present the first solution to a boundary motion planning problem for the Navier–Stokes equations, linearized around the parabolic equilibrium in a three-dimensional channel flow. The pressure and skin friction at one wall are chosen as the reference outputs as they are the most readily measurable ‘wall-restricted’ quantities in experimental fluid dynamics and also because they play a special role as performance metrics in aerodynamics. The reference velocity input is applied at the opposite wall. We find the exact (method independent) solution to the motion planning problem using the PDE (partial differential equation) backstepping theory. The motion planning solution results in open-loop controls, which produce the reference output trajectories only under special initial conditions for the flow velocity field. To achieve convergence to the reference trajectory from other (nearby) initial conditions, we design a feedback controller. We also present a detailed examination of the closed-form solutions for gains and the behaviour of the motion planning solution as the wavenumbers grow or the Reynolds number grows. Numerical results are shown for the motion planning problem.

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Iterative design for active control of fluid flow

Veres¹,

Baramov

Tutty³

et al. 2003

International Journal of Control

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This paper considers iterative controller design for planar Poiseuille flow by model unfalsification and controller redesign. The main contribution is to show that model-unfalsification-based iterative design can be useful in flow control problems. The a priori knowledge of the dynamics of the sampled system is obtained from the analytic approximation of the Navier-Stokes equations by a Galerkin method. Pole-positions, expected model orders and feasible dynamic variations are valuable prior knowledge which can be taken into account in the uncertainty-model unfalsification-based iterative design scheme developed.

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Robust Control of Linearized Poiseuille Flow

Cited by 10 publications

References 7 publications

<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow

<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow

Motion planning and trajectory tracking for three-dimensional Poiseuille flow

Iterative design for active control of fluid flow

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Robust Control of Linearized Poiseuille Flow

Cited by 10 publications

References 7 publications

&lt;tex&gt;$H_infty $&lt;/tex&gt;Control of Nonperiodic Two-Dimensional Channel Flow

&lt;tex&gt;$H_infty $&lt;/tex&gt;Control of Nonperiodic Two-Dimensional Channel Flow

Motion planning and trajectory tracking for three-dimensional Poiseuille flow

Iterative design for active control of fluid flow

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<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow

<tex>$H_infty $</tex>Control of Nonperiodic Two-Dimensional Channel Flow