Optimization-based feedback control of mixing in a stokes fluid flow

2009 ◽  
Author(s):  
I.J. Couchman ◽  
E.C. Kerrigan ◽  
J.C. Vassilicos
Keyword(s):  
Fluid Flow ◽  
Feedback Control ◽  
Stokes Fluid

scholarly journals Control of mixing in a Stokes’ fluid flow

2010 ◽  
Vol 20 (10) ◽  
pp. 1103-1115 ◽  
Author(s):  
Ian J. Couchman ◽  
Eric C. Kerrigan
Keyword(s):  
Fluid Flow ◽  
Stokes Fluid

Feedback Control of the Flutter of a Cantilevered Plate in an Axial Flow

2006 ◽  
Author(s):  
Olivier Doare´ ◽  
Thijs Paes ◽  
Michel Ferre´
Keyword(s):  
Fluid Flow ◽  
Feedback Control ◽  
Flow Velocity ◽  
Critical Velocity ◽  
State Space Model ◽  
Axial Flow ◽  
Good Correspondence ◽  
Critical Flow Velocity ◽  
Discrete State ◽  
System A

We investigate the experimental control of the instabilities of a plate in an axial fluid flow. In absence of control, the plate is subjected to a flutter instability once a critical flow velocity is reached. In the present work, the objective of the feedback control is to increase the critical velocity and reduce the vibration amplitude once the flutter has appeared. Initially, the plate vibration and the action of the piezoelectric sensors is modelled in order to obtain a discrete state-space model of the controlled system. A Galerkin method is used, so that the discrete coordinates are the modal amplitudes of a beam when the flow velocity is zero. The action of the actuator is classically modeled as a momentum acting on the plate. To estimate the validity of the model, frequency response measurements are performed on the system. A good correspondence is found between the model and experiments. Dissipation coefficients are experimentally evaluated. Next, the feedback control loop design is investigated. As a first approach, a PI controller system is implemented. The controllability and stability limits of the closed loop system are investigated. We choose to implement experimentally this control, as it does not require an overly precise modelisation of the disturbances acting on the plate. Impulse response of the system without flow is performed to investigate the optimal control gain. Other tests are performed to show how the controller works against disturbances from a fluid flow. Despite the strong limitations that have been previously mentionned, some encouraging results have been found. The critical velocity is increased and the amplitude of vibration is lowered.

Stabilization of Solution to Navier-Stokes Equations by Feedback Control Defined on the Boundary

2002 ◽  
Author(s):  
Andrei V. Fursikov
Keyword(s):  
Fluid Flow ◽  
Feedback Control ◽  
Stokes Equations ◽  
Time Moment ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Velocity Vector Field ◽  
Navier Stokes Equations ◽  
Real Process ◽  
Mathematical Construction

Let vˆ be a velocity vector field of steady-state fluid flow in a bounded container. We do not suppose that vˆ is stable. For each fluid flow which is close to vˆ at time moment t = 0 we propose a mathematical construction of feedback control from the boundary of the container which stabilize to vˆ this flow, i.e. which forces this flow to tend to vˆ with prescribed exponential rate. We introduce a notion of “real process” which is an abstract analog of fluid flow or (in other version) of numerical solution of Navier-Stokes equations. Real process differs from exact solution of three-dimensional Navier-Stokes equaitons on some small fluctuatons. Alhtough construction of feedback control is based on precise solving of Navier-Stokes equations, feedback control obtained by this method can react on unpredictable fluctuations mentioned above damping them. Such construction can be useful for numerical calculation because there fluctuations appear always.

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