A linear state-space representation of plane Poiseuille flow for control design: a tutorial.

A 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 moving