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

Authors: John McKernan, George Papadakis, James F. Whidborne

Addresses: Department of Aerospace Sciences, Cranfield University, Bedfordshire MK43 0AL, UK. ' Department of Mechanical Engineering, King's College London, Strand, London, WC2R 2LS, UK. ' Department of Aerospace Sciences, Cranfield University, Bedfordshire MK43 0AL, UK

Abstract: A method for the incorporation of wall transpiration into a model of linearised plane Poiseuille flow is presented, with the aim of producing a state-space model suitable for the development of feedback control of transition to turbulence in channel flow. 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 modified to conform to the control boundary conditions. This paper is intended as a tutorial on the addition of boundary control to a spectral model of a fluid continuum, to form a state-space model, as used in the emerging multidisciplinary field of flow control by means of Microelectrical Machines (MEMs). The ultimate aim of such flow control is the reduction of skin-friction drag on moving bodies.

Keywords: flow control; linear systems; Poiseuille flow; state space models; Navier-Stokes equations; tutorial; wall transpiration; feedback control; turbulence; channel flow; boundary control; skin-friction drag; moving bodies; fluid flow; microelectrical machines.

DOI: 10.1504/IJMIC.2006.012615

International Journal of Modelling, Identification and Control, 2006 Vol.1 No.4, pp.272 - 280

Published online: 27 Feb 2007 *

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