Modelling and control of two dimensional Poiseuille flow

Joshi, Shrey; Speyer, Jason L.; Kim, J.

doi:10.1109/cdc.1995.479102

“…A dramatic drag reduction was obtained, up to 50% with respect to the laminar flow and up to 60% with respect to the turbulent flow. Extensions of LQG (W 2 ) design and applications of H x design [25,26] to three-dimensional channel flows and three-dimensional Blasius boundary layers are in progress.…”

Section: Discussionmentioning

confidence: 99%

“…It is becoming widely accepted that even better results can be obtained by using controllers able to analyze distributed measurements and coordinate distributed actuators. However, very little has been done [24][25][26] to exploit the tools recently developed in the control community [27,28]. In particular, linear-quadratic-Gaussian (LQG) design, or, in modem terms, H 2 design, combined with model reduction techniques for multiinput-multioutout (MIMO) systems, has never been used in fluid mechanics nor plasma physics.…”

Section: Progress Over the Grant Periodmentioning

confidence: 99%

“…The size of the controller is a crucial parameter in engineering applications because of the amount of Although a rigorous mathematical framework for the designs of disturbance attenuation (H x ) linear controllers is provided by the control synthesis theory in [25,26], for this initial study LQG (Hi) synthesis is quite adequate. In general, the design of an optimal and robust linear feedback controller for the LQG (Hi) problem is divided in two parts: linear-quadratic regulator (LQR) and minimum variance estimator (Kaiman-Bucy filter).…”

Section: Model Reduction and Controller Designmentioning

confidence: 99%

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Development of Robust Boundary Layer Controllers

Speyer¹,

Kim²

2002

0

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Public reporting burden fa this collection of information isThe problem of controlling tu'',ulent boundary layers was studied using techniques employed in control system analysis and design. During the last three 'ears, the linearized Navier-Stokes equations were modified to include a boundary input of blowing/suction along the ".ML By a Galerkin method, the modified linearized Navier-Stokes equations were converted into a temporal control theoretical model, to which modem control synthesis can be applied. The resulting state space model allows a multivariable feedback design combining an array of sensors with an array of actuators along the wall. Based on this spectral decomposition, a parallel architecture for the implementation of temporal controllers allows significant decrease in computational bandwidth. For each wavenumber linear-quadratic-Gaussian multi-variable synthesis and model reduction techniques are used to derive robust feedback controllers. Controller performance was tested on a direct numerical simulation of a fully developed turbulent channel flow. Controller performance for the nonlinear flow was surprisingly good, suggesting that linear systems can be used as a basis for developing controllers for near-wall turbulence. Controllers are being developed on the basis of the three dimensional linearized Navier-Stokes equations. Both spanwise and streamwise shear sensors are considered. By a Galerkin method, a temporal state space model is determined where, for every wave number pair, a 500 state system is obtained with two inputs and four outputs. Model reduction techniques are used to reduce the state space drastically, and wave number pairs that produce the largest shear stress amplification for uncertainty induced at the wall are investigated.14. SUBJECT TERMS robust feedback flow control, control of turbulence, model reduction, shear flows, skin friction, drag reduction The problem of controlling turbulent boundary layers was studied using techniques employed in control system analysis and design. During the last three years, the linearized Navier-Stokes equations were modified to include a boundary input of blowing/suction along the wall. By a Galerkin method, the modified linearized Navier-Stokes equations were converted into a temporal control theoretical model, to which modern control synthesis can be applied. The resulting state space model allows a multivariable feedback design combining an array of sensors with an array of actuators along the wall. Based on this spectral decomposition, a parallel architecture for the implementation of temporal controllers allows significant decrease in computational bandwidth. For each wavenumber linearquadratic-Gaussian multi-variable synthesis and model reduction techniques are used to derive robust feedback controllers. Controller performance was tested on a direct numerical simulation of a fully developed turbulent channel flow. Controller performance for the nonlinear flow was surprisingly good, suggesting that linear systems can be used as a basis...

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“…(l)-(3) to a set of first-order ordinary differential equations, we make a few transformations loosely based on Refc. [24] and [26]. We write the stream function as >//= <f>+x to embed the actuator into the evolution equation, and to mate the boundary conditions homogeneous.…”

mentioning

confidence: 99%

“…However, controllers able to analyze distributed measurements and coordinate distributed actuators are regarded by th^ fluid mechanics community as essential for achieving better results. Tools for designing this class of controllers have been developed by the control community over the past two decades [25,26]. Very little has been done to exploit these tools in connection with the control of boundary layers [27][28][29] techniques for designing an optimal and robust linear feedback controller able to suppress walldisturbances leading to transitions in a two-dimensional laminar channel flow.…”

mentioning

confidence: 99%

Development of Robust Boundary Layer Controllers

Speyer¹,

Kim²

2000

0

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Public reporting burden fa this collection of information isThe problem of controlling tu'',ulent boundary layers was studied using techniques employed in control system analysis and design. During the last three 'ears, the linearized Navier-Stokes equations were modified to include a boundary input of blowing/suction along the ".ML By a Galerkin method, the modified linearized Navier-Stokes equations were converted into a temporal control theoretical model, to which modem control synthesis can be applied. The resulting state space model allows a multivariable feedback design combining an array of sensors with an array of actuators along the wall. Based on this spectral decomposition, a parallel architecture for the implementation of temporal controllers allows significant decrease in computational bandwidth. For each wavenumber linear-quadratic-Gaussian multi-variable synthesis and model reduction techniques are used to derive robust feedback controllers. Controller performance was tested on a direct numerical simulation of a fully developed turbulent channel flow. Controller performance for the nonlinear flow was surprisingly good, suggesting that linear systems can be used as a basis for developing controllers for near-wall turbulence. Controllers are being developed on the basis of the three dimensional linearized Navier-Stokes equations. Both spanwise and streamwise shear sensors are considered. By a Galerkin method, a temporal state space model is determined where, for every wave number pair, a 500 state system is obtained with two inputs and four outputs. Model reduction techniques are used to reduce the state space drastically, and wave number pairs that produce the largest shear stress amplification for uncertainty induced at the wall are investigated.14. SUBJECT TERMS robust feedback flow control, control of turbulence, model reduction, shear flows, skin friction, drag reduction The problem of controlling turbulent boundary layers was studied using techniques employed in control system analysis and design. During the last three years, the linearized Navier-Stokes equations were modified to include a boundary input of blowing/suction along the wall. By a Galerkin method, the modified linearized Navier-Stokes equations were converted into a temporal control theoretical model, to which modern control synthesis can be applied. The resulting state space model allows a multivariable feedback design combining an array of sensors with an array of actuators along the wall. Based on this spectral decomposition, a parallel architecture for the implementation of temporal controllers allows significant decrease in computational bandwidth. For each wavenumber linearquadratic-Gaussian multi-variable synthesis and model reduction techniques are used to derive robust feedback controllers. Controller performance was tested on a direct numerical simulation of a fully developed turbulent channel flow. Controller performance for the nonlinear flow was surprisingly good, suggesting that linear systems can be used as a basis...

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Nonlinear Control of Incompressible Fluid Flow: Application to Burgers' Equation and 2D Channel Flow

Baker¹,

Armaou²,

Christofides³

2000

Journal of Mathematical Analysis and Applications

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This paper proposes a methodology for the synthesis of nonlinear finite-dimensional feedback controllers for incompressible Newtonian fluid flows described by two-dimensional Navier᎐Stokes equations. Combination of Galerkin's method with approximate inertial manifolds is employed for the derivation of low-order ordinary Ž . differential equation ODE systems that accurately describe the dominant dynamics of the flow. These ODE systems are subsequently used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed-loop system to follow the reference input asymptotically. The method is successfully used to synthesize nonlinear finite-dimensional output feedback controllers for the Burgers' equation and the two-dimensional channel flow that enhance the convergence rate to the spatially uniform steady-state and the parabolic velocity profile, respectively. The performance of the proposed controllers is successfully tested through simulations and is shown to be superior to the one of linear controllers.

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Modelling and control of two dimensional Poiseuille flow

Cited by 16 publications

References 0 publications

Development of Robust Boundary Layer Controllers

Development of Robust Boundary Layer Controllers

Development of Robust Boundary Layer Controllers

Nonlinear Control of Incompressible Fluid Flow: Application to Burgers' Equation and 2D Channel Flow

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