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**Optimal control of vortex shedding using low-order models. I: Open loop model development. II: Model-based control.**
*(English)*
Zbl 0955.76026

Summary: We present an approach to develop active control strategies for separated flows, which is applied to incompressible unsteady wake behind a circular cylinder at a Reynolds number of 100. Control action is achieved via cylinder rotation. Low-order models which are amenable to control and which incorporate the full nonlinear dynamics are developed by applying the proper orthogonal decomposition (POD) technique to data provided by numerical simulation. This process involves extensions to the usual POD approach, and the results are therefore assessed for two ‘open-loop’ test cases. The predictions are found to be satisfactory for control purposes, assuming the model can be reset periodically.

In part II, optimal control theory is used to implement the model-based control. It is found that the level of wake unsteadiness can be reduced, even when the low-order model is reset on the basis of limit flow field information. The degree of reduction is dependent on the accuracy of the low-order model, and ways of refining it in the light of control simulations are considered. However, results from two straightforward approaches to this problem suggest that it is easy to ‘over-tune’ the model, resulting in less successful control.

In part II, optimal control theory is used to implement the model-based control. It is found that the level of wake unsteadiness can be reduced, even when the low-order model is reset on the basis of limit flow field information. The degree of reduction is dependent on the accuracy of the low-order model, and ways of refining it in the light of control simulations are considered. However, results from two straightforward approaches to this problem suggest that it is easy to ‘over-tune’ the model, resulting in less successful control.

### MSC:

76D50 | Stratification effects in viscous fluids |

76D17 | Viscous vortex flows |

76M10 | Finite element methods applied to problems in fluid mechanics |

76D25 | Wakes and jets |

76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |

### Keywords:

active flow control; vortex shedding; finite elements; separated flows; incompressible unsteady wake; circular cylinder; proper orthogonal decomposition technique; optimal control; model-based control
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\textit{W. R. Graham} et al., Int. J. Numer. Methods Eng. 44, No. 7, 945--990 (1999; Zbl 0955.76026)

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