Approximate Subspace Iteration for constructing internally balanced reduced order models of unsteady aerodynamic systems

Baker, Myles L.; Mingori, D. L.; Goggin, Patrick

doi:10.2514/6.1996-1441

Cited by 32 publications

(27 citation statements)

References 13 publications

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“…However, in case of a very largedimensional system, extracting eigenmodes can be computationally very expensive. Thus, we use another method, such as the method of balanced modes (Baker et al, 1996) or the proper orthogonal decomposition (POD) which will be explained in detail in Section 2. The second technique to determine ROM is the input/output model.…”

Section: Introductionmentioning

confidence: 99%

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Liberge

Hamdouni

2010

Journal of Fluids and Structures

128

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Section: Introductionmentioning

confidence: 99%

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Liberge

Hamdouni

2010

Journal of Fluids and Structures

128

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“…Hall, 12 Florea and Hall, 13 and Romanowski and Dowell 14 investigated a technique that generates a reduced-order model of the system from the aerodynamic eigenmodes. Baker et al 15 applied a similar approachusing singularvalue decompositionand internal balancingto reduce the number of states even further by consideringonly the states that are important for observability and controllabilityof the aerodynamic system. Although this work was focused primarily on reduction of high delity aerodynamic analyses (like computational uid dynamic solutions), it could be applied to the present type of problem in which the aerodynamic forces are derived from a less elaborate method, such as the doublet lattice method.…”

Section: Theoretical Developmentmentioning

confidence: 99%

Reduced-Order Dynamic Aeroelastic Model Development and Integration with Nonlinear Simulation

Winther

Goggin

Dykman

2000

Journal of Aircraft

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Piloted and batch simulations of the aeroservoelastic response are essential tools in the development of advanced ight control systems. In these simulations the number of differential equations must be suf ciently large to yield the required accuracy, yet small enough to enable real-time evaluationsof the aircraft ying qualities. The challenge of these con icting demands is reinforced by nonlinearities in the quasi-steady equations of motion and by the complex characteristics of the oscillatory forces. Our solution to the problem is based on a unique formulation that eliminates the need for auxiliary state variables to represent the unsteady aerodynamics. We also address transformations from the mean ight path axes to a body axes coordinate system and describe how the structural dynamic equations of motion are integrated with the quasi-steady, nonlinear, six-degree-of-freedom plant model. The uni ed model, which accurately preserves the roots of the dynamic aeroelastic system, includes provisions for control surface inputs and atmospheric turbulence. Nomenclature A, B= matrices in state-space formulation e = vector of generalized body axes coordinates F m = aerodynamic generalized force f, g, h = aircraft displacements in mean ight path system G NL = solution to nonlinear six-degree-of-freedom equations M m = inertial generalized force P = vector derived in p transform p, q, r = aircraft angular rates about body axes q = dynamic pressure S m = structural generalized force T = transformation matrix U = mean air ow velocity u, v, w = aircraft linear rates along body axes X, Y, Z = aircraft mean ight path axes system X ,Ȳ ,Z = aircraft body axes system z = state variable vector in body axes system a m,n = real part of aerodynamic approximation b m ,n = imaginary part of aerodynamic approximation c m, n = element of structural damping matrix D G = linear equations added to G NL d = vector of inputs " = vector of generalized mean ight path coordinateś = state variable vector in mean ight path system j m,n = element of structural stiffness matrix k = complex eigenvalue l m, n = element of mass matrix r = real part of eigenvalue U I = imaginary part of eigenvector U R = real part of eigenvector x = circular frequency

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“…However, this still becomes impractical for large systems, and iterative techniques must be employed to find the balancing transformation. 9,14 The remainder of this Note will examine the accuracy loss incurred by balanced model reduction and a physical interpretation of the vorticity distributions corresponding to the most significant modes.…”

Section: Model Developmentmentioning

confidence: 99%

“…The present work follows an approach introduced by Baker 8 and Baker et al 9 and bases the model reduction on observability and controllability concepts from control theory. 10,11 The key feature of this approach is that the reduced-order model is expressed in terms of coordinates that are optimal to a particular input/output mapping, rather than an energy optimal basis as in the POD, or a basis corresponding to lightly damped behavior as in the eigenanalysis.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Model Reduction Through Balanced Realization

2004

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Approximate Subspace Iteration for constructing internally balanced reduced order models of unsteady aerodynamic systems

Cited by 32 publications

References 13 publications

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Reduced-Order Dynamic Aeroelastic Model Development and Integration with Nonlinear Simulation

Aerodynamic Model Reduction Through Balanced Realization

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