Why may reduced order models based on global modes not work for closed loop control?

Alexandre Barbagallo (1, 2) , Denis Sipp (2) , Peter J. Schmid (1)

1 LadHyX - Laboratoire d'hydrodynamique
2 ONERA - The French Aerospace Lab [Meudon]

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.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Alexandre Barbagallo, Denis Sipp, Peter J. Schmid. Why may reduced order models based on global modes not work for closed loop control?. 19ème Congrès Francais de Mécanique, Aug 2009, Marseille, France. pp.S9 Instabilités et Transition, Contrôle d'Écoulement. ⟨hal-01053037⟩