James H. Myatt

Optimal Feedback Control of Vortex Shedding Using Proper Orthogonal Decomposition Models

We treat the question of control of two-dimensional incompressible, unsteady wake flow behind a circular cylinder at Reynolds number Re = 100. Two finite-dimensional lower order models based on proper orthogonal decomposition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used for obtaining stabilizing feedback control systems. An expression for the region of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control function and penalty methods are presented

PROPER ORTHOGONAL DECOMPOSITION MODELING OF A CONTROLLLED GINZBURG-LANDAU CYLINDER WAKE MODEL

A short computational program was undertaken to evaluate the effectiveness of a closed-loop control strategy for the stabilization of an unstable bluff-body flow. In this effort, the nonlinear one-dimensional GinzburgLandau wake model at 20% above the critical Reynolds number was studied. The numerical model, which is a nonlinear partial differential equation with complex coefficients, was solved using the FEMLAB/MATLAB package and validated by comparison with published literature. Based on computationally generated data obtained from solving the unforced wake, a low-dimensional model of the wake was developed and evaluated. The lowdimensional model of the unforced Ginzburg-Landau equation captures more than 99.8% of the kinetic energy using just two modes. Two sensors, placed in the absolutely unstable region of the wake, are used for real-time estimation of the first two modes. The estimator was developed using the linear stochastic estimation scheme. Finally, the loop is closed using an PID controller that provides the command input to the variable boundary conditions of the model. This method is relatively simple and easy to implement in a real-time scenario. The control approach, applied to the 300 node FEMLAB model at 20% above the unforced critical Reynolds number stabilizes the entire wake for a proportional gain of 0.06. While the controller uses only the estimated temporal amplitude of the first mode of Im(A(x,t)), all higher modes are stabilized. This suggests that the higher order modes are caused by a secondary instability that is suppressed once the primary instability is controlled.

Flow Control Research and Applications at the AFRL's Air Vehicles Directorate

This paper summarizes many of the Air Vehicles Directorate’s activities in flow control. Recent and current projects are reviewed, and an attempt is made to forecast future activities and air vehicle applications for flow control. Our ultimate objective is to identify and develop flow control sub-systems that can effectively and efficiently improve the performance of air vehicle systems. These schemes must not only buy their way onto the aircraft by improving performance, but must do so in an uncomplicated, maintainable, and dependable manner. While this emphasis on matchmaking between methods, devices, and applications will be maintained, research in promising higher risk methods of flow control is often warranted, given that they may provide revolutionary performance improvements for future air vehicles. There are several hubs of flow control activity in the Air Vehicles Directorate, and this paper attempts to capture the essence of the research and development pursuits in each of these groups. The projects described are being accomplished through a combination of in-house, contracted, and cooperative efforts, with team members from the airframers, small businesses, and academia.

Boundary Feedback Flow Control: Proportional Control with Potential Application to Aero-Optics

A large percentage of the losses in performance and effectiveness of airborne optical systems are caused by turbulence. In an effort to reduce these adverse effects in airborne optical systems, we are exploring the use of both openand closed-loop flow control over a cylindrical turret. A series of experiments were performed at a Reynolds number of 2 10, based on the turret’s diameter and freestream velocity, which corresponds to aMach number of 0.3. The three-dimensional turret contained an actuation system that consists of 17 synthetic jets placed upstream from the leading edge of the aperture. Initially, a large database containing no control and open-loop control was obtained. These data sets provide a rich ensemble for the development and application of a simple proportional closed-loop control with the use of proper orthogonal decomposition. Surface pressuremeasurements were acquired across the aperture region for all cases studied. Results from the open-loop test demonstrate a reduction of 19.6% in the root-mean-square values when compared to the baseline case. The closed-loop flow control results show that the root-mean-square pressure fluctuations are reduced by 25.7%, the integral scales are significantly reduced, and the flow is driven toward homogeneity.

Flow and Aero-Optics Around a Turret Part II: Surface Pressure Based Proportional Closed Loop Flow Control

As focused light passes through turbulent ∞ow the light is distorted and the intensity is reduced. An extended study using active ∞ow control to afiect the turbulent region over the a ∞at aperture of a 3-D hemispheric turret was conducted in the Air Force Research Laboratory’s Subsonic Aerodynamic Research Laboratory (SARL) wind tunnel at WrightPatterson Air Force Base. The SARL experiments were performed at a Mach number of :3, which gives Reynolds number on the order of 2;000;000. At these Reynolds numbers the ∞ow becomes highly complex and more challenging to study. A large database from previous work containing no control and open loop control cases provided a rich ensemble for plant model development based on low dimensional techniques such as the split-POD method of Camphouse (2007). PIV velocity data was acquired along with simultaneously sampled surface pressure data at various planes across the turret with and without control. Control authority was acquire by actuators mounted upstream of the aperture that generated a momentum ∞ux in the ∞ow around the turret. Simple proportional closed-loop control was performed using the bandpass flltered temporal POD mode coe‐cients of the surface pressure as the feedback signal. This paper shows that the active control reduced the root mean squared of the pressure ∞uctuations, shrunk the integral scales, and drove the ∞ow towards homogeneity.

Reduced Order Modelling and Boundary Feedback Control of Nonlinear Convection

A distributed parameter model of a nonlinear two-dimensional convective system is formulated. Proper orthogonal decomposition is used to construct a reduced order state-space model of the system. Open-loop simulations of the full and reduced models are compared to demonstrate the validity of the reduced model. A linear quadratic regulator control problem is formulated for the system under boundary control. Control efiectiveness is demonstrated in reduced and full order simulations.

A SNAPSHOT DECOMPOSITION METHOD FOR REDUCED ORDER MODELING AND BOUNDARY FEEDBACK CONTROL.

Abstract : In this paper, we develop a reduced basis construction method that allows for separate consideration of baseline and actuated dynamics in the reduced modeling process. A prototype initial boundary value problem, governed by the two-dimensional Burgers equation, is formulated to demonstrate the utility of the method in a boundary control setting. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics. A tracking control problem is specified using a linear quadratic regulator formulation. Comparisons of feedback control effectiveness are done to demonstrate benefits in control effectiveness obtained from separate consideration of actuated dynamics during model reduction.

Feedback Control for a Two-Dimensional Burgers' Equation System Model

In this paper, we consider the problem of controlling a system governed by a two-dimensional nonlinear partial differential equation. Motivation for the problem is the development of control methodologies for fluid flow, where the dynamics of the system are governed by the nonlinear Navier-Stokes equations. An initial boundary value problem described by the twodimensional Burgers’ equation is formulated to model a right-travelling shock over an obstacle. We focus on implementing feedback control via Dirichlet boundary conditions on the obstacle. We formulate a control problem for the system model, and examine two different methods of finding the control. The first method involves obtaining the solution of an algebraic Riccati equation. The second method involves obtaining a steady-state solution of the Chandrasekhar equations. Numerical approximations are developed to numerically simulate solutions of the problem with and without control. Numerical examples are presented to illustrate the efficacy, as well as the shortcomings, of the control method. Additionally, the influence of boundary condition on the functional gains, and the resulting controls, is demonstrated through numerical examples. Avenues of future work are presented.

Adaptive feedback linearizing control of proper orthogonal decomposition nonlinear flow models

This paper treats the question of feedback linearizing control oftwo-dimensional incompressible, unsteady wake flow. For definiteness,flow past a circular cylinder is considered, but the design approachpresented here is applicable to other flow control problems. Twofinite-dimensional lower-order models based on Proper OrthogonalDecomposition (POD) of dimension N with N actuators are considered.Models I and II are obtained using control function and penalty functionmethods, respectively. Control action can be achieved by a combinationof suction, injection, and synthetic jets. For the design ofcontrollers, it is assumed that the system matrices of the POD modelsare unknown. Nonlinear adaptive control systems for the two models arederived. For model I, nontrivial zero-error dynamics exists, which playa key role in the stability of the closed-loop system. But for model II,global adaptive trajectory control is achieved. In the closed-loopsystem, the mode amplitudes asymptotically follow the referencetrajectories. Simulation results for a 4-mode POD model obtained usingthe penalty function method are presented. These results show that inthe closed-loop system, unsteadiness in the mode amplitudes can besuppressed in spite of large uncertainties in the flow model.

Flow characteristics of active control around a 3D turret

At high speeds the wake of a hemisphere turret is completely separated and fully turbulent. Within this region of separated flow large density fluctuations develop. The problem comes in with attempting to propagate light through the turbulent wake of the turret. As the a light beam passes through the wake and the shear layer of the turret, the beam becomes distorted. Distortion of the beam causes the intensity of the light to be reduced making a laser less effective. By manipulating the flow around the turret, in particular the region just over the laser aperture, the loss of light intensity can be minimized. Active flow control has been shown in pervious work to alter the flow characteristics around an object. In the effort to delay the onset of stall around an airfoil at high angles of attack Glauser et al (2004) and Ausseur et al (2005) were successful at showing that utilizing an active flow control system was a very effective means of control. The active flow control included open and closed loop control. For the closed loop control, a low dimensional analysis of the velocity field around the airfoil and the surface pressure along the airfoil, was fed back into a simple proportional controller. Closed loop flow control reduced the onset of stall as the angle of attack was increased. and the system also consumed less power to prevent stall than the open loop control. A pervious experiment perform under similar conditions and procedures was performed in the Syracuse University windtunnel. In this experiment open loop flow control was test on a quarter sized turret at a low freestream speed. After a large database of surface pressure and velocity measurements where obtain it was seen that there was a reduction in the unsteady fluctuating characteristics. In an effort to take this a step further and improve on the open loop control, the next step was to investigate the effects of open loop and closed loop control upon the flow and aero-optics of the system at a much higher Reynolds number. Like the pervious work before, the surface pressure based proportional closed loop control was found to have a positive effect upon the wake of the turret.