Optimal control of vortex shedding using low-order models. Part II?model-based control

Graham, WR; Peraire, J.; Tang, K. Y.

doi:10.1002/(sici)1097-0207(19990310)44:7<973::aid-nme538>3.0.co;2-f

Cited by 73 publications

(34 citation statements)

References 2 publications

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“…Therefore, due to the energetic optimality of convergence of the POD basis [7,8,48], the choice of POD to develop a reduced-order model of the controlled unsteady flow seems to be well adapted. A similar approach was already considered in [16,49] to control the wake flow at a supercritical Reynolds number of 100.…”

Section: A Generic Configuration Of Separated Flows: the Cylinder Wakmentioning

confidence: 99%

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

180

154

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In this paper, optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime (Re = 200). The control parameters are the amplitude and the frequency of the time-harmonic cylinder rotation. In order to reduce the size of the discretized optimality system, a Proper Orthogonal Decomposition (POD) Reduced-Order Model (ROM) is derived to be used as state equation. We then propose to employ the Trust-Region Proper Orthogonal Decomposition (TRPOD) approach, originally introduced by Fahl (2000), to update the reduced-order models during the optimization process. A lot of computational work is saved because the optimization process is now based only on low-fidelity models. A particular care was taken to derive a POD ROM for the pressure and velocity fields with an appropriate balance between model accuracy and robustness. The key enablers are the extension of the POD basis functions to the pressure data, the use of calibration methods for the POD ROM and the addition in the POD expansion of several non-equilibrium modes to describe various operating conditions. When the TRPOD algorithm is applied to the wake flow configuration, this approach converges to the minimum predicted by an open-loop control approach and leads to a relative mean drag reduction of 30% at reduced cost.

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Section: A Generic Configuration Of Separated Flows: the Cylinder Wakmentioning

confidence: 99%

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

180

154

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“…More recently, Reduced Order Models based on POD are found as being an efficient tool for flow control purpose (see [40][41][42]29,17] for examples). Indeed, the use of POD ROM allows to reduce significantly the CPU time during numerical simulation and also to reduce the memory storage, an essential feature when adjoint based optimal control methods are used.…”

Section: Improvement Of the Functional Subspacementioning

confidence: 99%

“…For example, it is possible to use a database composed by snapshots that correspond to different control laws [17] or different Reynolds numbers [43]. One efficient way to do that is either by Centroidal Voronoi Tessellations (CVT) [44] or by using an ad-hoc time-dependent control law that generates a flow representing a large band of dynamics [45,42,29]. We privilege the idea of updating the POD basis during the simulation.…”

Section: Improvement Of the Functional Subspacementioning

confidence: 99%

Enablers for robust POD models

Bergmann

Bruneau

Iollo

2009

Journal of Computational Physics

286

292

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This paper focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

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“…where the definitions of the matrices E, A, B m and B d follow directly from (8). Both E and A are n × n real matrices.…”

Section: B Linearized Aerodynamic Modelmentioning

confidence: 99%

“…Models are obtained which retain the high-fidelity aerodynamics of the CFD analysis, but which have only a few states. The proper orthogonal decomposition (POD) technique has been developed as an effective method of deriving the basis functions [5], [6] and has been widely applied to many different problems, including the derivation of active control models for vortex shedding [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Model Reduction for Active Control Design Using Multiple-Point Arnoldi Methods

Lassaux

Willcox

2003

41st Aerospace Sciences Meeting and Exhibit

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I. ABSTRACT A multiple-point Arnoldi method is derived for model reduction of computational fluid dynamic systems. By choosing the number of frequency interpolation points and the number of Arnoldi vectors at each frequency point, the user can select the accuracy and range of validity of the resulting reduced-order model while balancing computational expense. The multiplepoint Arnoldi approach is combined with a singular value decomposition approach similar to that used in the proper orthogonal decomposition method. This additional processing of the basis allows a further reduction in the number of states to be obtained, while retaining a significant computational cost advantage over the proper orthogonal decomposition. Results are presented for a supersonic diffuser subject to mass flow bleed at the wall and perturbations in the incoming flow. The resulting reduced-order models capture the required dynamics accurately while providing a significant reduction in the number of states. The reduced-order models are used to generate transfer function data, which are then used to design a simple feedforward controller. The controller is shown to work effectively at maintaining the average diffuser throat Mach number. II. INTRODUCTIONComputational fluid dynamics (CFD) has reached a considerable level of maturity and is now routinely used in many applications for both external and internal flows. Euler and NavierStokes solvers enjoy widespread use for aerodynamic design and analysis, and provide accurate answers for a variety of complex flows. However, despite ever increasing computational power, unsteady problems are computationally very expensive and time-consuming. More efficient methods for time-varying flow can be obtained if the disturbances are small, and the unsteady solution can be considered to be a small perturbation about a steady-state flow [1]. In this case, a set of linearized equations is obtained which can be time-marched to obtain the flow solution at each instant.Even under the linearization assumption, any CFD-based technique will generate models with a prohibitively high number of states. For this reason, CFD models are not appropriate for many applications where model size and cost are issues. For example, when the aerodynamic solver must be coupled to another disciplinary model, as in aeroelastic analysis or multidisciplinary optimization, CFD models cannot be used. Another application which requires low-order models is control design.The concept of using active control to enhance the stability properties of an unsteady flow has been addressed for several applications [2], [3]. In order to derive control models that will be effective, it is vital that the relevant unsteady flow dynamics are captured accurately. A model is required that will capture not only the dynamics of the disturbance to be controlled, but also the visibility offered by the sensing and the effect on the flow of the actuation mechanism. A high-fidelity CFD code can offer the degree of flow resolution that is required; however, ...

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Optimal control of vortex shedding using low-order models. Part II?model-based control

Cited by 73 publications

References 2 publications

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Enablers for robust POD models

Model Reduction for Active Control Design Using Multiple-Point Arnoldi Methods

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