McKernan, JohnPapadakis, GeorgeWhidborne, James F.2011-11-162011-11-162006-01-01John McKernan, George Papadakis, James F. Whidborne; A linear state-space representation of plane Poiseuille flow for control design: a tutorial. International Journal of Modelling, Identification and Control 2006 - Vol. 1, No.4 pp. 272 - 2801746-6172http://dx.doi.org/10.1504/IJMIC.2006.012615http://dspace.lib.cranfield.ac.uk/handle/1826/1488A method for the incorporation of wall transpiration into a model of lin- earised plane Poiseuille °ow is presented, with the aim of producing a state- space model suitable for the development of feedback control of transition to turbulence in channel °ow. The system state is observed via wall shear-stress measurements and controlled by wall transpiration. The streamwise discretisation in the linearised model is by Fourier series, and the wall-normal discretisation is by a Chebyshev polynomial basis, which is modi¯ed to conform to the control boundary conditions. The paper is intended as a tutorial on the addition of boundary control to a spectral model of a °uid continuum, to form a state-space model, as used in the emerging multidisciplinary ¯eld of °ow control by means of MEMs (microelectrical machines). The ultimate aim of such °ow control is the reduction of skin-friction drag on movingFlow controllinear systemsPoiseuille Flowstate spaceNavier-Stokes equationsArticle