reduced order model of a blended wing body aircraft configuration

REDUCED ORDER MODEL OF A BLENDED WINGBODY AIRCRAFT CONFIGURATION

F. Stroscher1, Z. Sika2, and �O. Petersson1

1Institute of Lightweight Structures, Technical University Munich15 Boltzmannstr., Garching b. M�unchen 85747, Germany

2Czech Technical University in PragueFaculty of Mechanical Engineering

4 Technicka, Praha 6, Czech Republik

This paper describes the full development process of a numerical simula-tion model for the ACFA2020 (Active Control for Flexible 2020 Aircraft)blended wing body (BWB) con¦guration. Its requirements are the pre-diction of aeroelastic and §ight dynamic response in time domain, withrelatively small model order. Further, the model had to be parame-terized with regard to multiple fuel ¦lling conditions, as well as §ightconditions. High e¨orts have been conducted in high-order aerodynamicanalysis, for subsonic and transonic regime, by several project partners.The integration of the unsteady aerodynamic databases was one of thekey issues in aeroelastic modeling.

NOMENCLATURE

Symbols

A, B, C, D State-space matricesA0, A1, A2, D, E, R Minimum-state approximation matricesAIC Aerodynamic in§uence coe©cientsc Reference chord lengthCp Unsteady pressure coe©cientsF Flight dynamic forcesFJKS Di¨erentiation matrix from k-set to j-set degrees

of freedom (DOF)G Spline matrix between aerodynamic and struc-

tural DOFJ Aircraft inertia tensor

Progress in Flight Dynamics, GNC, and Avionics 6 (2013) 635-650 DOI: 10.1051/eucass/201306635 © Owned by the authors, published by EDP Sciences, 2013

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article available at http://www.eucass-proceedings.eu or http://dx.doi.org/10.1051/eucass/201306635

http://www.eucass-proceedings.eu

http://dx.doi.org/10.1051/eucass/201306635

PROGRESS IN FLIGHT DYNAMICS, GNC, AND AVIONICS

k Reduced frequencyK Sti¨ness matrixm Aircraft massM Mass matrix; §ight dynamic momentsMa Mach numberp Roll rateq Pitch rateQ Generalized aerodynamic forces (GAF)r Yaw rates Laplace variableSKJ Integration matrix from j-set to k-set DOFT� Mode shape transformation matrixu x-velocity in body axesv y-velocity in body axesV Velocities in body axesV∞ Free-stream velocityw z-velocity in body axes, vertical gust velocityxl Lag statesX X-positionY Y -positionZ Z-positionα Angle of attackβ Sideslip angleδ Control surface de§ectionη Modal de§ection— Pitch angle� Yaw angle, mode shapes on panel control points� Roll angle, mode shapes on structural DOFŸ Rates in body axes

Subscripts/Superscripts

a Aerodynamic axesAE Aeroelasticb Body axesc Control modesCFD Computational §uid dynamics (CFD)D Drag forcee Elastic modesFD Flight dynamicg Gust modesG Gust forces

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FLEXIBLE AIRCRAFT CONTROL

h Rigid body + elastic modesl Roll momentL Lift forcem Pitch momentn Yaw momentr Rigid body modesT TrimY Side force

1 INTRODUCTION

Today, active control and load alleviation is in use in military and more lim-ited in civil transport aircraft. However, this technique still promises signif-icant improvements for fuel e©ciency, fatigue life, and ride comfort. Somefuture aircraft con¦gurations, like the BWB, might even rely on active con-trol to remain airworthy. An unacceptably high vibration level in the cabin

Figure 1 Exterior surface of BWB aircraft con¦guration. Dimensions are in millime-ters

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of such aircraft might be reduced to the requirements on comfort of todayaircraft, or even better. The ACFA2020 BWB aircraft con¦guration (Fig. 1)shall fully be exploited by active control design, in order to demonstrate bestpossible performance of load alleviation and ride comfort of such aircraft con-cepts.Active control design optimization in aircraft con¦guration design demands

for low-order simulation models, recovering the relevant aircraft dynamics fora manifold of mass distributions and §ight conditions. Highly §exible aircraftshow signi¦cant interaction of the rigid-body §ight dynamics and aeroelasticdynamics, which poses challenging tasks in active control and load alleviation.Thus, fully coupled §ight dynamics and aeroelastic equations of motion

(EOM) have to be employed. The full range of possible mass distributions,given by fuel tank ¦lling, is captured by a parametric ¦nite element model(FEM) of the aircraft primary structure. The coupled §ight-dynamic and aeroe-lastic EOM are then set up, based on the eigendynamics of the FEM and ahigh-order CFD unsteady aerodynamic database. The parametric space of themodel is augmented by multiple §ight conditions, covering the whole §ight en-velope.

2 STRUCTURAL MODEL PARAMETERIZATION

Within the ACFA2020 project, a FEM of the BWB aircraft primary structurewas developed and applied in aeroelastic modeling. The FEM level of detail iscomparably low, but su©cient for the prediction of structural dynamic response

Figure 2 Finite element model of the BWB aircraft structure (a) and fuel tanklayout (b)

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in the considered frequency range. A full span model was applied in aeroelasticmodeling to directly take into account asymmetric turbulence excitation. Thefuel tanks (Fig. 2) are represented by concentrated mass elements connected tothe structure.The possible loading conditions of the aircraft have been de¦ned over the full

range of fuel tank ¦lling level, from empty to full. Further, the fuel distributionover tanks in wing and fuselage was considered, providing a useful margin ofx-position of the aircraft center of gravity (CoG). Three con¦gurations of fueldistributions are considered (CG1-3) for 11 steps of fuel ¦lling (0: 0% 10: 100%).The range of possible CoG x-positions, measured from the aircraft nodes, de-pending on fuel ¦lling, is shown in Fig. 3.

Figure 3 Center of gravity x-position of the considered mass variants: 1 ¡ CG-1;2 ¡ CG-2; and 3 ¡ CG-3

Modal analysis was performed for all mass con¦gurations of the FEM, leadingto individual modal bases applied in aeroelastic modeling (see subsection 4.1).The elastic modal de§ections [�e] are mass-normalized, leading to unitary modalmass matrices [Mstruct]. To represent §ight dynamics by the rigid body modes,its de§ections are normalized to 1 m for translational modes, respectively, 1 rad.

3 AERODYNAMIC ANALYSIS

Steady aerodynamic analysis of the rigid aircraft as well as unsteady aerody-namic analysis of the §exible aircraft have been performed with simpli¦ed aswell as high-order aerodynamic methods in subsonic and transonic regime. Thedatabases have been combined and included in §ight-dynamic and aeroelasticmodeling.

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3.1 Steady Aerodynamic Analysis of the Rigid Aircraft

A steady aerodynamic database for the rigid BWB aircraft con¦guration wascomputed by project partners with di¨erent aerodynamic methods. Up to Machnumber 0.6, a subsonic three-dimensional (3D) panel method was applied forcomputation of static polars, §ap derivatives, as well as dynamic derivatives.The transonic regime was covered by steady aerodynamic analysis with CFDmethods. Static polars and §ap derivatives could be obtained by CFD analy-sis for a reduced set of angle of attack and sideslip angle conditions. However,dynamic derivatives have not been computed by CFD methods, thus had to beextrapolated from the subsonic aerodynamic database. The §ap layout of theBWB aircraft, applied in aerodynamic analysis, is shown in Fig. 4.

Figure 4 Panel mesh (a) and subdivision into gust zones (b)

3.2 Unsteady Aerodynamic Analysis of the Flexible Aircraft

The unsteady aerodynamic analysis was performed with the subsonic panelmethod ZONA7, implemented in the aeroelastic toolkit ZAERO [1]. The liftingsurfaces, the winglets, and the fuselage of the BWB aircraft have been modeledby wing panels, as shown in Fig. 4. Groups of panels in span and longitudi-nal directions build up gust zones, which account for individual gust downwashinputs in the simulation model.As usual in aeroelastic analysis, the unsteady aerodynamic database is com-

puted for modal coordinates, i. e., modal aerodynamic forces with regard tomodal de§ection. In order to account for the unsteady aerodynamics of controlsurfaces, additional control modes are introduced, which are de¦ned by de§ec-tion of corresponding aerodynamic panels. Further, gust unsteady aerodynamicforces are included by a downwash distribution over the aircraft.

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The aeroelastic database is computed in frequency domain, assuming har-monic oscillation of mode shapes, control surface de§ections, and gust down-wash over a prede¦ned frequency range. A nondimensional, so-called reducedfrequency is applied here:

{Cp} = [AIC(ik,Ma]T {w}

with k = ωc/(2V∞).A full matrix of aerodynamic in§uence coe©cients for each panel, with

regard to de§ection of another panel is computed by the program.Further detail on the unsteady aerodynamic foundation of ZAERO can be

found in [1]. The complex AIC relate normal wash w to unsteady pressure coef-¦cients Cp on aerodynamic panels, which are normalized by dynamic pressure.Note that the AIC are independent from structural properties and dynamic pres-sure.Generalized aerodynamic forces, denoted by Q, are the unsteady aero-

dynamic forces on modal coordinates. By the use of an integration matrix SKJ,the pressure coe©cients Cp are converted to aerodynamic forces in the 6 DOFdirections of each panel at the panel control points [1]. For the transformationof the 6 DOF displacements at the panels control points to normal wash, thedi¨erentiation matrix FJKS is employed. As the panel control points do notcoincide with structural grid points, displacements and forces have to be trans-formed from structural to aerodynamic DOF by a spline matrix G. Now, thedisplacements are the generalized right-hand side by the modal matrices, de¦nedon panel control points:

[Qh(ik)] =[Qr(ik)Qe(ik)

]

= [�r �e]T [G]T [SKJ]T [AIC(ik)]T [�r �e �c �g]

with

[�r �e] = [FJKS(ik)]T [G] [�r �e] .

Here, �r and �e are computed from rigid-body modes �r and structural modes�e, de¦ned on structural DOF. The control modes �c are directly de¦ned onpanel coordinates; �r, �e, and �c are composed of real numbers, i. e., the de-§ection of the individual panel control points are in phase. Di¨erently, thegust modes �g have to be expressed by complex numbers, as there are vari-able phase angles for gust input on all aerodynamic panels. This approachtakes into account that gusts downwash hits the individual parts of the lift-ing surface with correct time delays, as the gust is travelling through the air-craft.Concluding, the aerodynamic forces are subdivided into columns for rigid-

body, elastic, §ap, and gust perturbations. Finally, the aerodynamic forces are

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Figure 5 First two symmetric structural mode shapes

generalized left-hand side by the modal matrices for rigid-body modes and struc-tural modes.For the transonic regime, the generalized aerodynamic forces of some impor-

tant structural modes have been corrected with results from an unsteady CFDsimulation. Eight mode shapes, namely, the pitch and plunge mode, �CFDr ,the ¦rst ¦ve symmetric and the ¦rst anti- symmetric mode shape, �CFDe , werechosen for CFD analysis. Due to limited computational resources, one inter-mediate mass con¦guration for the extraction of mode shapes for CFD analysiswas chosen, meaning all fuel tanks were ¦lled by 50%. The resulting generalizedaerodynamic forces were transformed afterwards to all other modal bases, usedfor the reduced order model (ROM). The ¦rst two symmetric mode shapes areshown in Fig. 5.Further, the GAF from CFD analysis were computed for perturbations (right-

hand side generalization) of §aps 1, 2, 5, 5′′, and 6, represented by the §ap modes�CFDc . The projection (left hand side generalization) of the resulting unsteadypressures is now performed on the full set of rigid body and elastic mode shapes�CFDh :

[QCFDh (ik)

]=[�CFDh

]T[G]T [SKJ]T [AIC(ik)]T

× [FJKS(ik)]T [G] [�CFDr �CFDe �CDFc

]. (1)

(Note that Eq. (1) represents an equivalent computation of GAF with the panelmethod, but does not re§ect the process for CFD-computed GAF.)Equation (1) yields a subset of columns of the full GAF with regard to the

full modal basis. The same columns of the previously computed GAF are nowreplaced by the columns computed by CFD analysis. This results into a CFD-corrected GAF database with regard to the mode shapes of the intermediate masscon¦guration (CFD variant) of the aircraft structure. It should be noted thatsome correction factors had to be applied to the CFD-computed GAF columns,due to di¨erent modal de§ection and the application of a half-span model inCFD analysis.

642


3.2.1 Transformation of computational §uid dynamics correctedgeneralized aerodynamic forces to structural mass variants

The modi¦ed GAF for the high-speed aerodynamic regime are computed for theeight selected mode shapes, only. To recover these forces also for the modal basesof all 33 mass variants, a transformation rule for GAF has to be de¦ned. Let[Qahh] be the GAF with regard to de§ection of the mode shapes [�

ah] and [Q

ahc]

with regard to control surface de§ection. Then, the GAF[Qbhh

]with regard to

de§ection of the mode shapes[�bh], and

[Qbhc

]with regard to control surface

de§ection, are:[Qbhh(ik)

]=[T baφ

]T[Qahh(ik)]

[T baφ

];

[Qbhc(ik)

]=[T baφ

]T[Qahc(ik)]

with[T baφ

]as the least squares solution of the equation

⌊�ah⌋⌊T baφ

⌋=⌊�bh⌋.

The above transformation yields a mathematically correct solution, only ifa complete modal basis is used, meaning as many modes as DOF of the ¦niteelement model. Here, just 80 modes are inside the modal basis, but showed asu©ciently accurate solution of the transformation.

3.2.2 Approximation of aerodynamic forces in the Laplace domain

In order to derive equations of motion in the time-domain, the GAF are approxi-mated in the Laplace-domain by the Minimum-State Method [2]. By replacing iωwith the Laplace variable s, the approximation equation in the Laplace domainbecomes:

[Qh(s)] =[Qr(s)Qe(s)

]

=[Ar0Ae0

]

+c

2V∞

[Ar1Ae1

]

s+(

c

2V∞

)2 [Ar2Ae2

]

s2+[Dr

De

](

[I]s− 2V∞c[R])−1[E]s.

The rational function approximation is a well-known source of modeling er-rors, in particular, when approximating gust columns. An appropriate num-ber of roots (size of R), as well as constraint setting for approximation (real-and/or imaginary part ¦tting for one reduced frequency) is crucial for suc-cess.The approximation matrices A0, A1, A2, D, E, and R are directly applied to

the time-domain simulation model, to account for unsteady aerodynamic forceswith regard to modal, control surface, and turbulence perturbations.

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4 TIME-DOMAIN SIMULATION MODEL

The simulation model was implemented in the well-known simulation environ-ment Matlab Simulink, which was also preferably used for control design inthe ACFA2020 project. The aerospace blockset was taken advantage of, for aneasy implementation of some standard §ight dynamics blocks, like the 6 DOFNewton Euler EOM.

4.1 Equations of Motion

The time-domain simulation model represents the nonlinear 6 DOF Newton-Euler §ight-dynamic equations of motion as well as aeroelastic equations ofmotion. Flight dynamics and structural (aeroelastic) dynamics are coupledby unsteady aerodynamic forces, whereas inertial coupling is not considered,assuming the aircraft dynamics on mean axes. For the sake of low modelorder, control surface dynamics are not directly computed in the simulationmodel, but represented by appropriate transfer functions from control com-mands to control de§ection inputs. The §ight dynamic DOF, X , Y , Z, �,—, and � are de¦ned over body axes, as shown in Fig. 6, denoted by the sub-script B.The §ight dynamics Newton Euler EOM are the force and moment balance

equations:

m{‘Vb +Ÿb × Vb − Tbege

}= FFD + FFDAE + F

FDG ;

J ‘Ÿb +Ÿb × JŸb =MFD +MFDAE +M

FDG

Figure 6 De¦nition of NED-system (x0, y0, z0), body axes (xB, yB, zB), Euler angles(�,—,�), wind axes (xA, yA, zA), angle of attack αA, and sideslip angle βA

644


with aerodynamic forces and moments due to §ight dynamic motion,

FFD

= q∞SrefTba

⎛

⎝

⎧⎨

⎩

CDCYCL

⎫⎬

⎭+

⎧⎨

⎩

CDpCY pCLp

⎫⎬

⎭p+

⎧⎨

⎩

CDqCY qCLq

⎫⎬

⎭q +

⎧⎨

⎩

CDrCY rCLr

⎫⎬

⎭r +

⎧⎨

⎩

CDδCY δCLδ

⎫⎬

⎭δ

⎞

⎠ ;

MFD = q∞Srefc

2Tba

⎛

⎝

⎧⎨

⎩

ClCmCn

⎫⎬

⎭+

⎧⎨

⎩

ClpCmpCnp

⎫⎬

⎭p+

⎧⎨

⎩

ClqCmqCnq

⎫⎬

⎭q +

⎧⎨

⎩

ClrCmrCnr

⎫⎬

⎭r

+

⎧⎨

⎩

ClδCmδCnδ

⎫⎬

⎭δ

⎞

⎠+ (ARP− COG)× FFD ,

and aeroelastic coupling forces/moments and gust forces/moments,

{FFDAE

MFDAE

}

= −qAre0η − q∞(c

2V

)

Are1 ‘η − q∞(c

2V

)2

Are2�η − q∞Drxa ;

{FFDAE

MFDAE

}

= − 1Vq∞Arg0wg − q∞

(c

2V 2

)

Arg1 ‘wg .

The aeroelastic EOM are comprised by the modal inertial and elastic forceson the left-hand side, as well as aerodynamic forces due to §ight-dynamic, elas-tic, control surface, and turbulence perturbation, on the right-hand side of thefollowing equation:

[Mstruct] {�ηe}+ [Kstruct] {ηe} = [Ae0]

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

0{ηe}{δc}1V∞{wg}

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+(

c

2V∞

)

[Ae1]

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

{ ‘ηr}{ ‘ηe}{ ‘δc}1V∞{ ‘wg}

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+(

c

2V∞

)2

[Ae2]

⎧⎪⎪⎨

⎪⎪⎩

{�ηr}{�ηe}00

⎫⎪⎪⎬

⎪⎪⎭

+ [De] {xl} . (2)

The rigid-body modes ηr account for aerodynamic forces due to §ight-dynamic motion [3, 4]. For the coupling of §ight dynamic motion to rigid bodymodes, ηr has to be expressed by the §ight dynamic DOF:

645


ηr =

⎛

⎜⎜⎜⎜⎜⎜⎝

−XY−Z−�—−�

⎞

⎟⎟⎟⎟⎟⎟⎠

; ‘ηr =

⎛

⎜⎜⎜⎜⎜⎜⎝

−uv−w−pq−r

⎞

⎟⎟⎟⎟⎟⎟⎠

; �ηr =

⎛

⎜⎜⎜⎜⎜⎜⎝

− ‘u‘v− ‘w− ‘p‘q− ‘r

⎞

⎟⎟⎟⎟⎟⎟⎠

.

The aeroelastic EOM are augmented by a lag equation, which accounts fortime delays of unsteady aerodynamic forces:

{ ‘xl} =(2V∞c

)

[R] {xl}+ [E]

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

{ ‘ηr}{ ‘ηe}{ ‘δc}1V∞{ ‘wg}

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

.

The ¦rst-order di¨erential equation is solved for the lag states, which are coupledto the aeroelastic EOM, Eq. (2).Unsteady aerodynamic forces are computed for rigid-body and elastic modes

(see section 3), which are de¦ned on a body ¦xed coordinate system (Fig. 7).Thus, the aerodynamic response of the rotational rigid-body modes about y-and z-axis is equal to a corresponding change in angle of attack α or sideslipangle β. Therefore, aircraft attitude (�,—,�), which does not change the aircraftheading with regard to the air§ow, may not be represented by the rotational

Figure 7 Positions over wingspan for cut forces outputs (a) and acceleration sensorpositions over airframe (b)

646


rigid-body modes. Instead, perturbations of α and β are taken into account byvelocity proportional aerodynamic forces of the rigid-body translations in y- andz-axis directions. Note that the contribution of Ae0 to the aerodynamic couplingfrom §ight dynamics to structural dynamics is omitted in Eq. (2) for the abovedescribed reason [3].

4.2 Sensor System

Besides §ight dynamic measurement outputs, like alpha/beta probes and CoGaccelerations, structural sensors are integrated into the model, to be applied forload alleviation in active control design. These are several acceleration sensors(with regard to body axes) distributed over wingspan and wingchord, as wellas cutforce and moment sensors at 14 positions over wingspan for left and rightpart of the aircraft (see Fig. 7).

4.3 Trimming and Linearization

In ACFA2020, the requirement for control design was a linear state-space modelof the BWB aircraft of reasonably low order. Thus, the nonlinear simulationmodel was linearized at trimmed steady horizontal §ight condition. The consid-ered operating points are all possible combinations of fuel ¦lling, CoG position,Mach number, and dynamic pressure. For each of them, a linear state-spacemodel, covering §ight-dynamic and aeroelastic response, as well as required in-puts and outputs, was derived. The operating point state and input vectors forlinearization are computed by a trim routine.The trim routine is divided into two steps:

(i) §ight dynamics longitudinal trim:

mg = CL0(αT , β = 0,Ma) + 2CLδ1(αT , β = 0,Ma)δT+ 2CLδ2(αT , β = 0,Ma)δT ; (3)

mg(xARP − xCoG) = Cm0(αT , β = 0,Ma) + 2Cmδ1(α, β = 0,Ma)δT+ 2Cmδ2(αT , β = 0,Ma)δT + 2 (zARP − zengine)Fthrust ; (4)

(ii) steady aeroelastic trim:

ηT = −K−1ee q∞

(c

2V

)

Aer1

{Vb,TŸb,T

}

(5)

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where

Vb,T =

⎧⎨

⎩

cos (αT )V∞0

sin (αT )V∞

⎫⎬

⎭; Ÿb,T =

⎧⎨

⎩

000

⎫⎬

⎭. (6)

Lateral trim was not conducted, because no asymmetries of neither the air-craft nor its §ight path had to be considered. To satisfy the longitudinal momentand lift equations, the elevators (§aps 1 and 2) and angle of attack were used astrim variables.Equations (3) (6) are solved iteratively until convergence of the trimmed

angle of attack αT and the trimmed elevator angle δT . The resulting trim inputand state vectors is applied as operating condition for linearization.

4.4 Order Reduction

There are several methods how to reduce the order of the time-domain sim-ulation model suitable for the control algorithm design [5, 6]. In spite of thedi¨erent reduction concepts, there are always two basic possibilities, either thestate truncation, denoted by subscript ST, or the singular perturbation approxi-mation, denoted by subscript SPA. Let the original state space model be dividedas follows (states corresponding to index 1 are the preserved ones, 2 are thereduced ones):

[A BC D

]

=

⎡

⎣A11 A12 B1A21 A22 B2C1 C2 D

⎤

⎦ .

Then, the reduced order state space model obtained by state truncation ofany type is: [

A BC D

]

ST=[A11 B1C1 D

]

.

The singular perturbation approximation variant of the reduced modelpreserves the DC-gains of an original system and generally can be written as

[A BC D

]

SPA=[A11 −A12A−1

22 A21 B1 −A12A−122 B2

C1 − C2A−122 A21 D − C2A−1

22 B2

]

.

The preserving of the transfer functions for DC-gains and for the low fre-quencies is important in context of the low-order model approximation and,consequently, preserving of the rigid body and §ight dynamics motion compo-nents. Therefore, the SPA [7] variant of the reduction has been always cho-sen.The concept focused on four-order reduction is the balanced reduction [6]

based on the given inputs and outputs with the chosen model dimension. This

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Figure 8 Comparison between original (1) and reduced (2) transfer functions

variant has been used as the reference one. The balanced reduction is verystraightforward especially for the pure structural models with the proportionaldamping. The airplane model, however, also consists of the states with the highdamping and even real poles. The evaluation of the ¦nal damping values ofparticular modes is relatively complex. The computational experiments showthat the pure balanced reduction can discard some important states, like the¦rst bending mode, some of the lag states, or even some §ight mechanic states.Therefore, also other approaches have been applied.The ¦rst variant of the control design ROM contains all §ight mechanics

states, all lag states, and states of the ¦rst (lowest) 19 elastic modes. The sim-pli¦ed variant of the control design ROM takes separately the symmetrical andantisymmetrical components including all §ight mechanics states, all lag states,and states of the ¦rst (lowest) 4 elastic modes. The example of comparison be-tween original (80 states) and reduced input output (only 2 symmetrical modes)transfer functions is shown in Fig. 8.

5 CONCLUDING REMARKS

The results of aerodynamic and structural dynamic analysis of the BWB aircraftcon¦guration have been applied to a §ight-dynamic and aeroelastic modeling pro-cess. An easily applicable way for integrating results of unsteady CFD analysisinto the full aerodynamic database was found. Aerodynamic coupling of §ightdynamics and aeroelasticity, which is a key issue for §exible aircraft dynamicsmodeling, was accounted for by representing §ight-dynamic motion by rigid-body modes. The time-domain equations of motion have been augmented bytwo-dimensional turbulence and control surface inputs as well as §ight-dynamicand structural outputs.

649


In a second step, the simulation model was trimmed and linearized at pre-de¦ned operating points over the §ight envelope. A model order reduction wasapplied to the linear models to provide a su©ciently accurate ROM for the con-trol design process.

REFERENCES

1. ZONA Technology. 2008. ZAERO Theoretical Manual.

2. Karpel, M. 1981. Design for active and passive §utter suppression and gust allevia-tion. Technical Report CR-3482. NASA.

3. Looye, G. 2005. Integration of rigid and aeroelastic aircraft models using the resid-ualised model method. Forum (International) on Aeroelastisity and Dynamics.M�unchen, Germany.

4. Kier, T.M., and G.H. Looye. 2009. Unifying manoeuvre and gust loads analysismodels. Forum (International) on Aeroelastisity and Dynamics. Seattle, USA.

5. Obinata, G.O., and B.D.O. Anderson. 2001. Model reduction for control systemdesign, communications and control engineering. Springer.

6. Gawronski, W.K. 2004. Advanced structural dynamics and active control of struc-tures. N.Y.: Springer-Verlag, Inc.

7. �Sika, Z, J. Zav�rel, and M. Val‚a�sek. 2009. Residual modes for structure reductionand e©cient coupling of substructures. Bull. Appl. Mech. 5(19):54 59.

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reduced order model of a blended wing body aircraft configuration

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