Browsing by Author "Papadakis, George"

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    Design of poiseuille flow controllers using the method of inequalities
    (Springer Science Business Media, 2009-02-01T00:00:00Z) McKernan, John; Whidborne, James F.; Papadakis, George
    This paper investigates the use of the method of inequalities (MoI) to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral (PI) controllers. In the second one, the MoI is combined with McFarlane and Glover’s H ∞ loop-shaping design procedure in a mixed-optimization appro
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    Linear quadratic control of plane Poiseuille flow-the transient behaviour.
    (Taylor and Francis, 2007-12) McKernan, John; Whidborne, James F.; Papadakis, George
    This paper describes the design of optimal linear quadratic controllers for single wavenumber-pair periodic 2-D disturbances in plane Poiseuille flow, and subsequent verification using a finite-volume full Navier-Stokes solver, at both linear and non-linear levels of initial conditions selected to produce the largest linear transient energy growth. For linear magnitude initial conditions, open and closed-loop finite-volume solver results agree well with a linear simulation. Transient energy growth is an important performance measure in fluid flow problems. The controllers reduce the transient energy growth, and the non-linear effects are generally seen to keep energy levels below the scaled linear values, although they do cause instability in one simulation. Comparatively large local quantities of transpiration fluid are required. The modes responsible for the transient energy growth are identified. Modes are shown not to become significantly more orthogonal by the application of control. The synthesis of state estimators is shown to require higher levels of discretiation than the synthesis of state-feedback controllers. A simple tuning of the estimator weights is presented with improved convergence over uniform weights from zero initial estimates.
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    A linear state-space representation of plane Poiseuille flow for control design: a tutorial.
    (Inderscience , 2006-01-01T00:00:00Z) McKernan, John; Papadakis, George; Whidborne, James F.
    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
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    Minimizing transient energy growth in plane Poiseuille flow
    (Professional Engineering Publishing, 2008-01-01T00:00:00Z) Whidborne, James F.; McKernan, John; Papadakis, George
    The feedback control of laminar plane Poiseuille flow is considered. In common with many flows, the dynamics of plane Poiseuille flow is very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger non-linearities and lead to turbulence, even though such perturbations would, in a linear flow, eventually decay. This sensitivity can be measured using the maximum transient energy growth. The linearized flow equations are discretized using spectral methods and then considered at one wave-number pair in order to obtain a model of the flow dynamics in a form suitable for advanced control design. State feedback controllers that minimize an upper bound on the maximum transient energy growth are obtained by the repeated solution of a set of linear matrix inequalities. The controllers are tested using a full Navier–Stokes solver, and the transient energy response magnitudes are significantly reduced compared with the uncontrolled cas