Browsing by Author "McKernan, John"

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    Control of plane poiseuille flow: a theoretical and computational investigation
    (Cranfield University, 2006-04) McKernan, John; Whidborne, James F.
    Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.
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    Control of plane Poiseuille flow: a theoretical and computational investigation - MATLAB code
    (Cranfield University, 2022-10-03 15:31) Whidborne, James; McKernan, John
    Feedback Control of Plane Poiseuille Flow - MATLAB Codemincode-version2.zip File contains the functions for the system matrices A,B,C and energy matrix Q for modeling linearized plane Poiseuille flow with wall-transpiration actuation and wall shear-stress measurements, which may be of use for controller synthesis. See mincode.m to begin.  Please acknowledge and reference via thesis:  Mckernan, J. Control of plane Poiseuille flow: a theoretical and computational investigation, PhD Thesis, School of Engineering, Cranfield University, 2006
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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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    Kolmogorov-Chaitin complexity of digital controller implementations.
    (Springer Science Business Media, 2006-07-01T00:00:00Z) Whidborne, James F.; McKernan, John; Gu, Da-Wei
    The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for statespace realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.
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    Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow
    (2011-01-31T00:00:00Z) Martinelli, F.; Quadrio, M.; McKernan, John; Whidborne, James F.
    Suppression of the transient energy growth in subcritical plane Poiseuille flow via feedback control is addressed. It is assumed that the time derivative of any of the velocity components can be imposed at the walls as control input and that full-state information is available. We show that it is impossible to design a linear state-feedback controller that leads to a closed-loop flow system without transient energy growth. In a subsequent step, state-feedback controllers- directly targeting the transient growth mechanism-are designed using a procedure based on a linear matrix inequalities approach. The performance of such controllers is analyzed first in the linear case, where comparison to previously proposed linear-quadratic optimal controllers is made; further, transition thresholds are evaluated via direct numerical simulations of the controlled three-dimensional Poiseuille flow against different initial conditions of physical interest, employing different velocity components as wall actuation. The present controllers are effective in increasing the transition thresholds in closed loop, with varying degree of performance depending on the initial condition and the actuation component employed.
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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
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    On minimizing maximum transient energy growth
    (2005-06-27T00:00:00Z) Whidborne, James F.; McKernan, John; Steer, Anthony J.
    The problem of minimizing the maximum transient energy growth is considered. This problem has importance in some fluid flow control problems and other classes of non-linear systems. Conditions for the existence of static controllers that restrict the maximum transient energy growth to unity are established. An explicit parametrization of all linear controllers ensuring monotonic decrease of the transient energy is derived. It is shown that by means of a Q-parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means of a Ritz approximation of the free parameter. By considering the transient energy growth at an appropriate sequence of discrete time points, the minimal maximum transient energy growth problem can be posed as a semidefinite problem. The theoretical developments are demonstrated on two numerical problems.
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    On the Minimization of Maximum Transient Energy Growth.
    (IEEE Institute of Electrical and Electronics, 2007-09-01T00:00:00Z) Whidborne, James F.; McKernan, John
    The problem of minimizing the maximum transient energy growth is considered. This problem has importance in some fluid flow control problems and other classes of nonlinear systems. Conditions for the existence of static controllers that ensure strict dissipativity of the transient energy are established and an explicit parametrization of all such controllers is provided. It also is shown that by means of a Q-parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means of a Ritz approximation of the free parameter. By considering the transient energy growth at an appropriate sequence of discrete time points, the minimal maximum transient energy growth problem can be posed as a semidefinite program. The theoretical developments are demonstrated on a numerical example.