Active flow control using a reduced order model and optimum control

Tang, KY; Graham, WR; Peraire, J.

doi:10.2514/6.1996-1946

Cited by 32 publications

(25 citation statements)

References 9 publications

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“…Note that the situation is different in the three-dimensional case. It can be proved that the equation eðu; f; fÞ ¼ 0 in Y 0 is equivalent with the fact that ðu; fÞ is a weak solution to (26) for given f 2 L 2 ðHÞ.…”

Section: Remarkmentioning

confidence: 99%

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Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition

Volkwein

2001

Z. angew. Math. Mech.

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The proper orthogonal decomposition (POD) is a procedure to determine a reduced basis for a reduced order model. In this article POD is formulated as a minimization problem in a general Hilbert space setting. The POD‐basis functions are given by the solution to the first‐order necessary optimality conditions. In this work POD is utilized to solve optimal control problems for a phase‐field model. The numerical results are compared with finite element solutions.

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Section: Remarkmentioning

confidence: 99%

“…Let us mention that f d is not a solution to (26). To solve the optimal control problem ðOCÞ with POD we apply the augmented Lagrangian-SQP method introduced in [15].…”

Section: A Numerical Examplementioning

confidence: 99%

Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition

Volkwein

2001

Z. angew. Math. Mech.

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“…For example, Tang and Aubry [13] suppressed the vortex shedding by inserting two small vortex perturbations in the ow; Gillies [14] used neural networks; Gunzburger and Lee [15] determined the amount of uid injected or sucked on the rear of the cylinder from a feedback law depending on pressure measurements at stations along the surface of the cylinder; Huang [16] suppressed vortex shedding by feedback sound; Joslin et al [17] showed that ow instabilities can be controlled by wave cancellation; Kwon and Choi [18], Ozono [19] and You et al [20] employed splitter plates attached to the cylinder; Park et al [21] used a pair of blowing=suction slots located on the surface of the cylinder; Sakamoto and Haniu [22] introduced a smaller cylinder near the main cylinder, with experiments conducted by changing the gap between the cylinders and the angle along the circumference from the front stagnation point of main cylinder; the ow is controlled via cylinder rotation (see e.g. References [23][24][25][26][27]); Pentek and Kadtke [28] implemented a chaos control scheme to capture and stabilize a concentrated vortex around the cylinder, the control being actuated by uniformly rotating the cylinder and actively changing the background ow velocity far from the body.…”

Section: Introductionmentioning

confidence: 99%

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Homescu

Navon

2001

Numerical Methods in Fluids

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SUMMARYAdjoint formulation is employed for the optimal control of ow around a rotating cylinder, governed by the unsteady Navier-Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time-dependent. Since the numerical control problem is ill-posed, regularization is employed. An empirical logarithmic law relating the regularization coe cient to the Reynolds number was derived for 606Re6140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re = 60 to Re = 1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A signiÿcant reduction of the amplitude of the variation of the drag coe cient is obtained for the optimized values of the rotation rate.

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“…We refer to [5,22] as two of the early works on POD much of which is in the context of fluid dynamics. For optimal control and inverse problems POD was used for a wide variety of diffusion dominated systems, for instance in [4,12,16,23]. In [14] optimal closed loop control for Burgers equation is based on POD reduction of the state equation to solve the Hamilton-Jacobi-Bellman equation.…”

Section: Highlight Papermentioning

confidence: 99%

Proper orthogonal decomposition for optimality systems

2008

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Abstract. Proper orthogonal decomposition (POD) is a powerful technique for model reduction ofnon-linear systems. It is based on a Galerkin type discretization with basis elements created from the dynamical system itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. A method is proposed which avoids this problem of unmodelled dynamics in the proper orthogonal decomposition approach to optimal control. It is referred to as optimality system proper orthogonal decomposition (OS-POD).Mathematics Subject Classification. 35K20, 65Nxx, 90C20.

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Active flow control using a reduced order model and optimum control

Cited by 32 publications

References 9 publications

Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition

Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Proper orthogonal decomposition for optimality systems

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