Development and Implementation of an Experimental-Based Reduced-Order Model for Feedback Control of Subsonic Cavity Flows

Abstract

This work is focused on the development of a reduced-order model based on experimental data for the design of feedback control for subsonic cavity flows. The model is derived by applying the proper orthogonal decomposition (POD) in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The experimental data consist of sets of 1000 simultaneous particle image velocimetry (PIV) images and surface pressure measurements taken in the Gas Dynamics and Turbulent Laboratory (GDTL) subsonic cavity flow facility at the Ohio State University. Models are derived for various individual flow conditions as well as for their combinations. The POD modes of the combined cases show some of the characteristics of the sets used. Flow reconstructions with 30 modes show good agreement with experimental PIV data. For control design, four modes capture the main features of the flow. The reduced-order model consists of a system of nonlinear ordinary differential equations for the modal amplitudes where the control input appears explicitly. Linear and quadratic stochastic estimation methods are used for real-time estimation of the modal amplitudes from real-time surface pressure measurements.

Control of nonlinear systems represented by Galerkin models using adaptation-based linear parameter-varying models

“…Substituting (50) and (58) 4 Let , x y ε + , , ∈» then ≤ + which will be negative since from (24), (29) and (32) The fact that ˆ0 e a a = − → implies ˆ, a a → which states that the trajectories of the LPV system, whose parameter variations are controlled by the designed adaptation mechanism, will eventually approach those of the original nonlinear Galerkin model. The fact that 0 a → states that the LPV control design based on the LPV plant is indeed successful in asymptotically stabilizing the origin of the nonlinear Galerkin model.…”

“…3. This is a problem that has captured significant research interest [18,19,[22][23][24], and has been an initial motivation for this study. Air flow over a shallow cavity is characterized by a strong self-sustained resonance produced by a natural feedback mechanism.…”

“…This produces a Galerkin model that approximates the original system of nonlinear partial differential equations (PDEs). An approach of this sort has been used, among others, in feedback control of cylinder wakes [12][13][14][15][16][17], control of cavity flow [18][19][20][21][22][23][24], and optimal control of vortex shedding [25,26].…”

Linear control of oscillator and amplifier flows1

“…In order to control limit-cycle behavior, a nonlinear underlying model and a nonlinear control strategy is required. Following the system-identification approach in this article, we can postulate a nonlinear reduced-order model (e.g., using a POD-based Galerkin projection 44,45 ) motivated by the Navier-Stokes equations and determine the unknown coefficients of this model by matching the predicted output to the true output. Once verified by a testing data-set, this model can be incorporated into a nonlinear modelpredictive framework and used to manipulate limit-cycle behavior.…”

Modeling and Feedback Control for Subsonic Cavity Flows: A Collaborative Approach

“…This results in a set of ordinary non-linear differential equations, in which the control input need to be rendered explicit by means of control separation techniques. The use of POD/Galerkin methods has become increasingly popular to handle flow control problems, including control of cylinder wakes [11,26,42], flow separation [19], modeling and control of synthetic jets [27], controller order reduction [3], and cavity flow [5,6,32,46].…”