282 research outputs found
Data for the paper "A Sum-of-Squares approach to feedback control of laminar wake flows" by Davide Lasagna, Deqing Huang, Sergei Chernyshenko and Owen R. Tutty.
No full textThese folders/file contain data that can be used to reproduce the figures contained in the paper "A Sum-of-Squares approach to feedback control of laminar wake flows" by Davide Lasagna, Deqing Huang, Owen Tutty and Sergei Chernyshenko, published in the Journal of Fluid Mechanics.
Each folder/file is named after the figure and panel number and typically contains columns for x-y values. The precise description of the x-y data is given in each file.</span
Data for "Expensive Control of Long-time Averages Using Sum of Squares and Its Application to A Laminar Wake Flow", Huang et al., 2016
No full textThese file contain data that can be used to reproduce the figures contained in the paper "Expensive control of long-time averages using sum of squares and its application to a laminar wake flow" by Deqing Huang, Bo Jin, Davide Lasagna, Sergei Chernyshenko and Owen Tutty available at http://arxiv.org/abs/1602.05913. Each file is named after the figure number and typically contains columns for x-y values. The precise description of the x-y data is given in each file. Files are best viewed using an UTF capable text editor/viewer.</span
Vortex pair and Chaplygin cusps
No full textAn example is given of a flow past two bodies with two trapped point vortices so that the pressure is constant over the entire body surface and the flow has no stagnation points. The flow is constructed from the flow past a pair of counter-rotating vortices by replacing the stagnation points with stagnation regions of constant pressure following the Chaplygin concept. The stagnation regions are then interpreted as bodies. The demonstration of the possibility of a flow without adverse pressure gradient on solid walls and without stagnation points adjacent to closed-streamline regions is important for the high-Reynolds-number asymptotic theory of flows with trapped vortices
Expensive control of long-time averages using sum of squares and its application to a laminar wake flow
No full textThe paper presents a nonlinear state-feedback control design approach for long-time average cost control, where the control effort is assumed to be expensive. The approach is based on sum-of-squares and semi-definite programming techniques. It is applicable to dynamical systems whose right-hand side is a polynomial function in the state variables and the controls. The key idea, first described but not implemented in (Chernyshenko et al., Phil. Trans. R. Soc. A, 372, 2014), is that the difficult problem of optimizing a cost function involving long-time averages is replaced by an optimization of the upper bound of the same average. As such, controller design requires the simultaneous optimization of both the control law and a tunable function, similar to a Lyapunov function. The present paper introduces a method resolving the well-known inherent non-convexity of this kind of optimization. The method is based on the formal assumption that the control is expensive, from which it follows that the optimal control is small. The resulting asymptotic optimization problems are convex. The derivation of all the polynomial coefficients in the controller is given in terms of the solvability conditions of state-dependent linear and bilinear inequalities. The proposed approach is applied to the problem of designing a full-information feedback controller that mitigates vortex shedding in the wake of a circular cylinder in the laminar regime via rotary oscillations. Control results on a reduced-order model of the actuated wake and in direct numerical simulation are reported
Sum-of-Squares approach to feedback control of laminar wake flows
No full textIn this paper a novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. (Phil. Trans. R. Soc. Lond. A, vol. 372, 2014, 20130350), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable and efficient approach to the solution of such optimisation problems, based on sum-of-squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at , via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is first derived using proper orthogonal decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the resolved kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, total energy efficiency and the physical control mechanisms identified are analysed in detail. Key elements of the methodology, implications and future work are finally discussed
Internal degrees of freedom of an actuator disk model
No full textActuator disk models can have internal degrees of freedom as, for example, in the case for models with lagged losses, governed by additional differential equations. Generally, being a system with distributed parameters, flow in the interblade passage has an infinite number of internal degrees of freedom. An attempt is made to estimate how many of them can be distinguished as the most important. The response of a blade row to time-periodic excitations is modeled by an actuator disk with internal degrees of freedom and by linearized Navier Stokes equations, and the results are compared. It is found that in the case of subsonic flow one internal degree of freedom can be considered as the most important, both for design and off-design regimes. In the case of transonic flow in off-design regime, two internal degrees of freedom are more important than the rest. However, for the transonic design regime, no internal degrees of freedom could be distinguished as especially significant. The physical mechanisms associated with distinguished internal degrees of freedom are investigated
Controlling fluid flows with positive polynomials
No full textA novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation oflong-time averages of key flow quantities is presented. The key idea, first outlined in Ref. [1], is that the difficulties of treatingand optimising long-time averages are relaxed by shifting the analysis to upper/lower bounds for minimisation/maximisationproblems, respectively. In this setting, control design reduces to finding the polynomial-type state-feedback controller thatoptimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controlleritself and a tunable polynomial function. A numerically tractable approach, based on Sum-of-Squares of polynomials techniquesand semidefinite programming, is proposed. As a prototypical example of control of separated flows, the mitigation of thefluctuation kinetic energy in the unsteady two-dimensional wake past a circular cylinder at a Reynolds number equal to 100,via controlled angular motions of the surface, is investigated. A compact control-oriented reduced-order model, resolving thelong-term behaviour of the fluid flow and the effects of actuation, is first derived using Proper Orthogonal Decomposition andGalerkin projection. In a full-information setting, linear state-feedback controllers are then designed to reduce the long-timeaverage of the resolved kinetic energy associated to the limit cycle of the system. Controller performance is then assessed indirect numerical simulations
Finding unstable periodic orbits: A hybrid approach with polynomial optimization
No full textWe present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedure relies on polynomial optimization to construct nonnegative polynomials whose sublevel sets approximately localize parts of the optimal UPO, and that can be used to implement a simple yet effective control strategy to reduce the UPO's instability. Precisely, we construct a family of controlled ODE systems, parameterized by a scalar k, such that the original ODE system is recovered for k=0 and such that the optimal orbit is less unstable, or even stabilized, for k>0. Periodic orbits for the controlled system can often be more easily converged with traditional methods, and numerical continuation in k allows one to recover optimal UPOs for the original system. The effectiveness of this approach is illustrated on three low-dimensional ODE systems with chaotic dynamics
A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations
No full textIn this paper we consider the role that numerical computations-in particular Galerkin approximations-can play in problems modeled by the three-dimensional (3D) Navier-Stokes equations, for which no rigorous proof of the existence of unique solutions is currently available. We prove a robustness theorem for strong solutions, from which we derive an a posteriori check that can be applied to a numerical solution to guarantee the existence of a strong solution of the corresponding exact problem. We then consider Galerkin approximations, and show that if a strong solution exists the Galerkin approximations will converge to it; thus if one is prepared to assume that the Navier-Stokes equations are regular one can justify this particular numerical method rigorously. Combining these two results we show that if a strong solution of the exact problem exists then this can be verified numerically using an algorithm that can be guaranteed to terminate in a finite time. We thus introduce the possibility of rigorous computations of the solutions of the 3D Navier-Stokes equations (despite the lack of rigorous existence and uniqueness results), and demonstrate that numerical investigation can be used to rule out the occurrence of possible singularities in particular examples. (c) 2007 American Institute of Physics
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