Reduced Order Modelling and Boundary Feedback Control of Nonlinear Convection

Camphouse, Russell Chris; Myatt, James

doi:10.2514/6.2005-5844

Cited by 15 publications

(27 citation statements)

References 6 publications

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“…The large number of states is necessary to capture important flow features that occur at extremely small spatial scales. Although these small flow features might seem insignificant, if they are not captured, it is not possible to analyze if they are necessary in securing the closed-loop system's overall stability [10].…”

Section: Introductionmentioning

confidence: 99%

“…Presently considerable research efforts are working with feedback control law design for systems described by PDEs that need a very large number of states to accurately simulate their characteristics. However, recent advances in the design of actuators and sensors can be leveraged for better system control only if the control design methods provide a reliable low-order controller [10]. Additionally, simulation, and experimental diagnostics are making applications such as the suppression of acoustic tones in cavities, separation control for high lift, and trajectory control without the need to move hinged surfaces a possibility [11].…”

Section: Introductionmentioning

confidence: 99%

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Empirical Reduced‐Order Modeling for Boundary Feedback Flow Control

Djouadi

Camphouse

Myatt

2008

Journal of Control Science and Engineering

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This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation-(PDE-) based models in general. Specifically, the proper orthogonal decomposition (POD) of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA). This method estimates the system's Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. An H ∞ feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Empirical Reduced‐Order Modeling for Boundary Feedback Flow Control

Djouadi

Camphouse

Myatt

2008

Journal of Control Science and Engineering

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“…The goal of model reduction is to construct another nonlinear system [11] This is carried out by developing an empirical balanced truncation algorithm which is based on experimental/simulation input-output measurements of the nonlinear Galerkin model. This is introduced in the next section.…”

Section: Figure 2 Test Inputs Used To Generate For Snapshotsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Presently considerable research efforts are working with feedback control law design for systems described by PDEs that need a very large number of states to accurately simulate their characteristics. However, recent advances in the design of actuators and sensors can be leveraged for better system control only if the control design methods provide a reliable low order controller [11]. Additionally, simulation, and experimental diagnostics are making applications such as the suppression of acoustic tones in cavities, separation control for high lift, and trajectory control without the need to move hinged surfaces a possibility [12].…”

Section: Introductionmentioning

confidence: 99%

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Optical Model Reduction and Robust Feedback Control for Aerodynamics

Djouadi¹

2010

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In this project, methods of model reduction that integrate feedback active flow control with applications to nonlinear convection and turbulent flows governed by Navier-Stokes equations are developed. A new methodology which extracts boundary conditions in reduced order proper orthogonal decomposition (POD) and finite difference models is developed. A new model reduction method based on empirical data and balanced truncation was developed and applied to nonlinear Galerkin models. Based on this method a new empirical Hankel norm model reduction algorithm is proposed. These methods are applied to a prototype nonlinear convective problem governed by the two-dimensional (2D) Burgers' equation. The reduced models are used in the design of robust boundary controllers that achieve tracking, and implemented on the full order Computational Fluid Dynamics (CFD) models. POD and balanced truncation are shown to be optimal in the sense of distance minimizations in spaces of Hilbert-Schmidt (HS) operators. POD has been shown to be optimal in a broader sense than is reported in the literature. The optimality is in the sense of distance minimization in a space of integral operators under the Hilbert-Schmidt norm. A connection with balanced truncation is found. In particular, balanced truncation is shown to be optimal in the sense of distance minimization albeit in a different space of integral operators under the Hilbert-Schmidt norm when the so-called 'Curtain-Glover' balanced realization is used. This is a novel discovery as balanced truncation is usually known to be not optimal in any sense.An algorithm that combines the extended Kalman filter and expectation maximization to estimate the model coefficients from particle image velocimetry (PIV) measurements for turbulent 2D flows is developed. The algorithm is recursive and convenient for on-line implementation. The method is applied to a 2D flow control problem over the NACA 4412 airfoil using experimental data obtained from Prof. Glauser's flow control group at the University of Syracuse. The motivation for this problem is minimization of aero-optic distortion in a bluff-body flow.POD and balanced truncation are shown to minimize different n-widths of partial differential equation solutions including the Kolmogorov, Gelfand, linear and Bernstein n-widths. The nwidths are notions from metric complexity theory. They quantify inherent and representation errors due to lack of data and loss of information. Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis ...

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Data-driven identification of dynamical models using adaptive parameter sets

Wilson

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper presents two data-driven model identification techniques for dynamical systems with fixed point attractors. Both strategies implement adaptive parameter update rules to limit truncation errors in the inferred dynamical models. The first strategy can be considered an extension of the dynamic mode decomposition with control (DMDc) algorithm. The second strategy uses a reduced order isostable coordinate basis that captures the behavior of the slowest decaying modes of the Koopman operator. The accuracy and robustness of both model identification algorithms is considered in a simple model with dynamics near a Hopf bifurcation. A more complicated model for nonlinear convective flow past an obstacle is also considered. In these examples, the proposed strategies outperform a collection of other commonly used data-driven model identification algorithms including Koopman model predictive control, Galerkin projection, and DMDc.

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Reduced Order Modelling and Boundary Feedback Control of Nonlinear Convection

Cited by 15 publications

References 6 publications

Empirical Reduced‐Order Modeling for Boundary Feedback Flow Control

Empirical Reduced‐Order Modeling for Boundary Feedback Flow Control

Optical Model Reduction and Robust Feedback Control for Aerodynamics

Data-driven identification of dynamical models using adaptive parameter sets

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