A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part II: numerical simulations using state feedback

• Published in: Systems & control letters Vol. 51; no. 1; pp. 15 - 22
• Main Authors: Cathalifaud, Patricia, Bewley, Thomas R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2004; Elsevier
• Subjects: Applied sciences; Boundary-layer DNS; Computer science; control theory; systems; Control regularization; Control system synthesis; Control theory. Systems; Exact sciences and technology; Flow control; Miscellaneous; Spatially localized convolution kernels; Flow control; Boundary-layer DNS; Spatially localized convolution kernels; Control regularization; State feedback; Grid; Feedback regulation; Inverse transformation; Autoregressive model; Numerical method; Regression analysis; Modeling; Flow; Regularization method; Kernels; Control; Convolution; Infinite dimension; Regularization; Boundary layer
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/S0167-6911(03)00183-X

We present numerical results illustrating the successful state feedback control of a spatially developing boundary-layer flow system. Control is applied using the noncausal framework developed in Part I of this study. After addressing some important regularization issues related to the proper treatment of the infinite-dimensional nature and semi-infinite spatial extent of the present system, we compute the state-feedback control gains according to the equations developed in Part I at several spanwise wavenumbers β. We then inverse transform the result to obtain spatial convolution kernels for determining the control feedback. The effectiveness of the controls computed using these feedback kernels, which are well resolved on the computational grid and spatially localized in the spanwise direction, is tested using direct numerical simulation of the boundary-layer flow system. A significant damping of the flow perturbation is observed, which is of the same order as the damping that arises when applying significantly more expensive iterative adjoint-based control optimization schemes.