Why may reduced order models based on global modes not work for closed loop control?
Résumé
In this article, we use a reduced model based on global modes to stabilize a globally unstable cavity flow. We show that although the full-state control is successful, the partial state controller cannot stabilize the perturbations. We introduce the notion of full-state measurement control to analyze this failure and show that it is due to a lack of information of the reduced model about the stable subspace. In particular, the input-output behavior is identified as the key parameter to be captured by the reduced model. A criterion is then derived in order to select the stable global modes which are likely to contribute to the input-output behavior. These critical modes are found to be impossible to compute because of the non-normality of the Navier-Stokes operator, which leads us to the conclusion that global modes are not suitable for control based reduced models.
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