integrated optimization of control surface layout for gust load … · 2019. 2. 7. · during the...

CEAS Aeronautical Journal manuscript No.(will be inserted by the editor)

Integrated Optimization of Control Surface Layout for GustLoad Alleviation

Manuel Pusch · Andreas Knoblach · Thiemo Kier

Received: July 24, 2018 / Accepted: XXX XX, 2018

Abstract Considering active gust load alleviation(GLA) during aircraft design offers great potential forstructural weight savings. The effectiveness of a GLAcontrol system strongly depends on the layout of avail-able control surfaces, which is investigated in this ar-ticle. For the purpose of wing load reduction, a con-current optimization of controller gains and aileron ge-ometry parameters is carried out. To that end, an effi-cient update routine for the nonlinear model of a large-scale flexible aircraft with unsteady aerodynamics ispresented. Compared to a GLA system using the orig-inal aileron configuration, a 9 % performance improve-ment is achieved. Furthermore, a trade-off study is car-ried out which enables a target-oriented balancing be-tween individual load channels. The significant influ-ence of aileron size and position on overall GLA per-formance is demonstrated and hence a considerationduring the preliminary aircraft design process is rec-ommended.

Keywords Multidisciplinary Design Optimization ·Control Surface Design · Gust Load Alleviation ·Aeroservoelasticity

1 Introduction

In order to allow for a more economic and environmen-tally friendly operation of aircraft, fuel savings are im-perative. Besides the efficiency of engines and aerody-namics, the aircraft weight has a major impact on fuelconsumption [1]. For instance, a reduction of aircraft

Manuel Pusch · Andreas Knoblach · Thiemo KierInstitute of System Dynamics and ControlGerman Aerospace Center82234 Weßling, GermanyE-mail: [email protected]

weight is achieved by using new materials like carboncomposites, as it can be seen at the example of the Air-bus A350 or the Boeing 787. Another approach is todecrease the design loads of the structure [2, 3] apply-ing active control technologies. For example, the fuelconsumption of the Lockheed L-1011 TriStar aircraftcould be reduced by 3 % by means of active load allevi-ation [4]. Considering new aircraft configurations withimproved lift-to-drag ratios, a special focus has to beput on gust load alleviation (GLA), as these configura-tions are prone to have an increased sensitivity to at-mospheric disturbances. In [5], an assessment of state ofthe art GLA applications is made and its potential forweight reductions is pointed out. In industry though,advanced load alleviation functions are still often in-troduced after the preliminary design phase [6, 7, 5],where only a limited adaption of the structure is possi-ble. Hence, it is advantageous to include the load allevi-ation system as early as possible in the aircraft designcycle [8]. Promising results are achieved by multidis-ciplinary design optimization, where aircraft structureand load controller are designed simultaneously (see e.g.[9, 10]). However, less priority is put on optimization ofthe layout of multifunctional control surfaces and itsconcrete impact on load alleviation capability.

The aim of this paper is to investigate the poten-tial of simultaneously optimizing the GLA controllergains and the respective control surface layout. In or-der to gain realistic results, a flexible aircraft model ofindustrial complexity is considered in Section 2. Thenonlinear model includes unsteady aerodynamics andallows to compute cut loads for maneuvers as well asgust encounters. In avoidance of time consuming modelre-building, an efficient update procedure for controlsurface layout changes is proposed. In the derived op-timization setup (Section 3), the focus lies on simulta-

2 Manuel Pusch et al.

neously optimizing controller and aileron geometry pa-rameters to minimize the wing root bending moment.Additionally, constraints like actuator saturation, pas-senger comfort and stability requirements are consid-ered. The resulting improvement in load alleviation ca-pability is discussed in Section 4, where the optimizedaileron layout is compared with a reference configura-tion. Finally, a trade-off study is carried out to allow aglobally balanced load reduction by prioritizing singleload channels.

2 Modeling and Loads Computation

2.1 Structural and Aerodynamic Model

In order to consider both gust and maneuver loads,the integrated modeling approach from [11] is applied.The model is based on a linear finite element modelon which a modal analysis is carried out. The result-ing mode shapes are partitioned into rigid body modesΦgb and flexible modes Φgf . Taking into account theassumptions from [12], this allows to replace the lin-ear rigid body dynamics by the nonlinear equations ofmotion (EoM) from flight mechanics. Eventually, theoverall EoM can be written as[

mb(Vb + Ωb × Vb − TbEgE

)JbΩb + Ωb × (JbΩb)

]= ΦT

gbPextg (t), (1)

Mff uf + Bff uf + Kff uf = ΦTgf Pext

g (t). (2)

In Equation (1), the rigid body modes are describedin the body frame of reference by the translational ve-locity Vb and the angular velocity Ωb. Additionally,gravitational acceleration gE is taken into account byapplying a coordinate transformation TbE from the earthfixed to the body fixed frame. It is further assumed thatgE as well as the inertia tensor Jb and the aircraft massmb do not change within the considered time horizon. InEquation (2), the flexible modes uf are characterized bymeans of the modal mass matrix Mff , the modal damp-ing matrix Bff and the modal stiffness matrix Kff .

The external nodal loads Pextg include forces induced

by aerodynamics, engines or landing gears. For the pur-pose of GLA, aerodynamic forces are of major interest.In order to consider also unsteady aerodynamics, theyare obtained by means of the doublet lattice method(DLM) [13]. Applying the DLM, the lifting surfaces arediscretized by trapezoidal shaped aerodynamic boxeswith a control point j located at the three quarter chordrespectively (see Figure 1). The orthogonal componentsof the flow at these control points are collected in vj andnormalized by the free stream velocity U∞, leading to

𝑘 𝑗

𝑐𝑗

𝑈∞

Fig. 1: Aerodynamic box of chord length cj with refer-ence point k and control point j.

the downwash

wj =vjU∞

.

As a result of the DLM, the aerodynamic loads act-ing on the nodes of the structural model are given as

Paerog = Qgj(k)wj , (3)

where the aerodynamic influence coefficient (AIC) ma-trix Qgj(k) is typically computed only at discrete re-duced frequencies k [13]. To enable time domain sim-ulations, a rational function approximation (RFA) ofQgj(k) is derived using Roger’s method [14]. Accord-ing to Equation (3), the aerodynamic loads depend lin-early on the downwash wj , which consists of a gust-,modal- and control surface (CS)-component. For thegust downwash, the continuous wind field is evaluatedat each aerodynamic box and the respective orthogonalcomponents are normalized by the free stream veloc-ity. And the other two downwash components resultfrom the movements of aerodynamic boxes caused bymodal displacements and CS deflections, respectively.Note that the translations and rotations of aerodynamicboxes are generally described with respect to the mid-point k of each box (see also Figure 1) and hence, atransformation to the control point j is necessary. Amore detailed explanation on downwash computationis given in [11] and in the next subsection, where themodel updating procedure for changing the CS layoutis described. Furthermore, it has to be mentioned thatthe aerodynamic model depends on the current Machnumber, air density and free stream velocity, see also[11, 13] for details.

Eventually, the nodal loads Pg are recovered usingthe force summation method (FSM) [15]:

Pg = Pextg − Piner

g ,

where the nodal inertial loads Pinerg are obtained from

the accelerations of the rigid body and flexible modes.In comparison to that, the mode displacement method(MDM) [15] computes the nodal loads by

Pg = KggΦgf uf , (4)

Integrated Optimization of Control Surface Layout for Gust Load Alleviation 3

using the physical stiffness matrix Kgg. Generally, theMDM exhibits an inferior convergence behavior [15] andthus, it is not applied here. However, for interpretationof the results, the MDM is useful as it allows to de-termine the contributions of the corresponding flexiblemodes to the overall loads. Finally, the integrated cutloads Pc at critical cross sections, e.g. the wing root,are computed by a linear transformation which sumsup the corresponding nodal loads.

2.2 Control Surfaces

In general, the downwash wxj caused by CS deflections

ux is described by

wxj =

(D1

jk + scref/2U∞

D2jk

)Φkxux ,

where the CS matrix Φkx maps the CS deflections to themovement of individual aerodynamic boxes. The map-ping depends on the relative position of the box to therespective CS hinge and is computed applying a small-angle approximation. The differentiation matrices D1

jkand D2

jk are introduced in order to transform the boxdisplacements and movements from the reference pointk to a downwash at the control point j (see also [11]).Besides, the Laplace variable is denoted by s and thereference chord length of the aircraft is cref.

When changing the geometry of a CS, it is necessaryto rebuild the underlying aerodynamic lattice to alignit with the new boundaries of the modified CS. This, inturn, requires the AIC matrix to be recomputed and ap-proximated again by a rational function. To avoid thisrather time consuming process during optimization, analternative approach is proposed here. The AIC matrixis computed only once and the aerodynamic lattice isnot further modified. Instead, the present aerodynamicboxes are assigned to the current CSs in a proportionalmanner.

Giving an example, the size of the original CS fromFigure 2a (covered by box 4 and 6) is meant to be de-creased. In Figure 2b, the aerodynamic lattice is up-dated, leading to a new set of aerodynamic boxes requir-ing the AIC to be recomputed. In comparison to that,in Figure 2c the aerodynamic lattice is not changed butthe box assignments are weighted individually. For box4, this implies that it is weighted by a factor of 0.6 as itis covered by the new CS only by 60 %. Similarly, box6 is weighted by 100 % meaning that it is fully assignedto the CS.

In summary, each box is weighted according to thepercentage of its area overlapping with the respectiveCS. Thus, only the entries of Φkx related to the mod-ified CSs need to be updated, whereas the rest of the

2

8 7

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𝑔𝑒

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7 8 10 9

1

3 4

(c) Weighted

Fig. 2: Example of changing the size of a CS wherethe updated aerodynamic panels are compared to theoriginal aerodynamic panels with updated weights.

aircraft model remains unchanged. As the mass distri-bution and stiffness are assumed not to be influenced,the emerging approximation error is negligible for suf-ficiently small aerodynamic boxes.

2.3 Actuators and Sensors

The actuator dynamics of the CSs are modeled by afirst order low pass filter

Gacts(s) = ωc

s+ ωc,

with a bandwidth ωc = 20 rad s−1. For an active GLAat the wing, the inner and outer ailerons are primar-ily used as they can be deflected in both directionswhich allows controlling the wing lift distribution ef-fectively. In addition to that, the elevators are used tocompensate the pitching moment induced by aileron de-flections. Furthermore, the sensor signals for feedbackcontrol are the measured pitch rate qmeas and the mea-sured vertical acceleration az,meas from the inertial mea-surement unit (IMU), which is located close to the air-craft center of gravity (CoG). Both signals are readilyavailable in common aircraft and thus, no extra sensorsneed to be added.

2.4 Limit Loads Computation

In order to size the structure of an aircraft, it is nec-essary to determine the limit loads. According to thecertification requirements [3, 2], the limit loads are thelower and upper boundary of all loads occurring dur-ing aircraft operation at any time. Denoted as Pc,lowerand Pc,upper, the limit loads are determined in this pa-per by simulating extreme flight maneuvers and severeatmospheric turbulence as described in the followingsubsections.


Maneuver Limit Loads

In Table 1, trim conditions for representative steadyflight maneuvers, used to determine the maneuver limitloads, are listed. At each flight point, the steady hor-izontal flight M0 with zero pitch rate q and zero rollrate p is trimmed through the horizontal stabilizer. Ad-ditionally, the push-over maneuver M1a and the pull-up maneuver M1b are performed. Both maneuvers aretrimmed by means of elevator deflections η and differfrom each other only by the load factor nz. The loadfactors nz,min and nz,max are specified in the flight ma-neuvering envelope (V-n diagram) [3, 2] and depend onthe design airspeed. Similarly, the bidirectional rollingmaneuvers M3a and M3b are trimmed by means of theaileron deflections ξ. Moreover, sudden pilot commandsare approximated by the accelerated roll maneuversM4a and M4b, and the accelerated pitching maneuversM2a and M2b. The extreme pilot inputs are determinedby the CS deflections resulting from the previous ma-neuvers and are assumed to be established instantly.

By definition, the maximum roll rate pmax is set to15 s−1 for all operation points, which is a commonvalue for civil aircraft. Furthermore, for all maneuvers,inner and outer ailerons are deflected equally but withopposite sign on the left and right wing. In contrast,elevators are always deflected symmetrically.

Gust Limit Loads

In order to compute the structural loads in atmosphericturbulence, the “1-cos” gust model according to the cer-tification requirements [3, 2] is used. For wing loads,gusts in up- and downwards direction are considered asmost critical. Thus, time domain simulations are car-ried out for vertical gusts with different gust gradientdistances H varying from 9 m (30 ft) to 107 m (350 ft).

3 Optimization Setup

3.1 Controller Structure

For active GLA, a multiple-input multiple-output con-troller needs to be designed using the sensor and actua-tor signals described in Section 2.3. Since a concurrentoptimization of the controller and the control surfacelayout is carried out, a minimum number of controllertuning parameters is desired allowing for a smooth andfast convergence. Based on that and the findings of [16],a static gain feedback controller is chosen, where highfrequency modes are not excited due to the low-passbehavior of the actuators. As only symmetrical gustsin vertical direction are considered (see Section 2.4),

the CS deflection commands are applied equally on theleft- and right-hand side. Thus, the controller outputsare ∆ηcmd for the elevators, ∆ξinner,cmd for the innerailerons and ∆ξouter,cmd for outer ailerons. Introducingthe static gain feedback matrix K, the controller struc-ture is given as ∆ηcmd

∆ξinner,cmd∆ξinner,cmd

= K[∆az,meas∆qmeas

],

where all signals represent increments (denoted by the∆) with respect to the current trim conditions M0 givenin Table 1. For a smooth controller tuning, the inputand output signals of the controller are normalized bytheir respective maximum values. The scaled elementsof K are then collected in the controller tuner parame-ter vector DK used for optimization (see Section 3.5).

3.2 Parameterization of Ailerons

In order to evaluate the impact of the aileron layouton GLA performance, the geometry of the ailerons isparameterized. In Figure 3, different parameterizationsof the span-wise position and the span of the inner andouter ailerons are given. The parameter space is limitedby the minimum and maximum aileron position yminand ymax. While the minimum position is defined bythe planform break, the maximum position is the outerboundary of the reference aileron configuration as de-picted in Figure 7. The ailerons should not be placedfurther outside as the trailing vortex at the wing tipmay cause unfavorable effects [17]. For ailerons opti-mization, three different parameter sets Dail are tested:(1) the absolute positions y1 . . . y4, (2) the distances∆y1 . . . ∆y4, and (3) the positions y1, y3 combined withthe aileron spans ∆y2, ∆y4. Furthermore, the chord ofthe ailerons is not changed to maintain structural in-tegrity of the wing as its spars need not to be modi-fied. Note that for optimization, aileron geometry con-straints and parameter limits are introduced in order toavoid invalid configurations like overlaps or boundaryviolations.

3.3 Objective Function

Since the structural weight of a wing is largely drivenby the maximum wing root bending moment (WRBM),the main goal for GLA controller design is to reducethe increments of the WRBM due to gust encounters∆P gust

WRBM. Based on that, the objective function to beminimized is given as

V = maxF

maxH

∆P gustWRBM, (5)


Table 1: Trim table of maneuvers to compute limit loads.

ID maneuver name nz p p q q η ξM0 horizontal flight 1 0 0 0 0 0 0M1a push-over nz,min 0 0 ? 0 ? 0M1b pull-up nz,max 0 0 ? 0 ? 0M2a pilot pull ? 0 0 ? ? η(M1a) 0M2b pilot push ? 0 0 ? ? η(M1b) 0M3a roll&pull 0 ±pmax 0 ? 0 ? ?M3b roll&push 2

3nz,max ±pmax 0 ? 0 ? ?M4a pilot roll&pull 0 0 ? ? 0 ? ±ξ(M3a)M4b pilot roll&push 2

3nz,max 0 ? ? 0 ? ±ξ(M3b)

𝑦1

𝑦2

𝑦3

𝑦4

Δ𝑦3 Δ𝑦2 Δ𝑦4 Δ𝑦1

inner aileron outer aileron

𝑦min

𝑦max

𝑏/2

Fig. 3: Ailerons parameterization.

PSfrag replacements

hinge line

ymin

ymax

Fig. 4: Reference aileron layout with limits for layoutoptimization.

where F and H denote the considered discrete flightpoints and gust gradient distances, respectively. Here-inafter, the objective function V is also referred to asperformance index for GLA controller evaluation.

3.4 Constraints

Limit Loads

While reducing structural loads at some parts of theaircraft, the GLA system might induce additional loadsat other parts, e.g. at the CS mountings. Thus, it isnecessary to ensure that the limit loads of the aircraftstructure (see Section 2.4) are not exceeded at any cross

section. To that end, the constraint

C1 : Pc,lower ≤ Pc ≤ Pc,upper,

is introduced, where the c-set includes all relevant cutloads for aircraft sizing.

Passenger Comfort

Furthermore, the passenger comfort needs be consid-ered during GLA controller design. To that end, thecomfort criterion fc from [18] is applied to the verti-cal acceleration measurement az,meas of the IMU. Thecriterion is based on the ISO 2631-1 standard, whichtakes into account vibrating comfort and motion sick-ness phenomenon by weighting predefined frequencies.It is computed as the root mean square (RMS) of az,measweighted by the filter Wc(s) depicted in Figure 5. Theevaluated comfort with active GLA should not be worsethan a reference comfort determined by simulations with-out GLA. Hence,

C2 : fc(az,meas) ≤ fc(az,meas,ref).

Note that simulations without active GLA are inde-pendent of the CS configuration, as no deflections areapplied and the mass distribution is assumed to be con-stant (see also Section 2.2).

PSfrag replacements

Frequency (Hz)

Mag

nitu

de(d

B)

10−1 100 101 102−40

−20

0

20

Fig. 5: Comfort weighting filter Wc(s).


Stability

As static gain feedback does not guarantee any stabil-ity, a stability analysis is carried out on the linearizedclosed loop model of the aircraft. The resulting mini-mum damping ratio ζmin is then compared to the ref-erence value from the open loop case:

C3 : ζmin ≥ ζmin,ref.

Actuators

In order to consider actuator limitations, the allowedCS deflections are constrained by

C4 :

ηmin ≤ η ≤ ηmax

ξinner,min ≤ ξinner ≤ ξinner,maxξouter,min ≤ ξouter ≤ ξouter,max

,

where the CS deflection boundaries are obtained fromthe minimum and maximum deflections of the certifi-cation maneuvers listed in Section 2.4. This allows todefine reasonable limitations depending on the currentCS layout which limits the occurring hinge moments[19]. Furthermore, the deflection rates are limited by

C5 :

ηmin ≤ η ≤ ηmax

ξinner,min ≤ ξinner ≤ ξinner,maxξouter,min ≤ ξouter ≤ ξouter,max

,

with the maximum achievable deflection rate of all CSsbeing set to 80 s−1 in both directions.

Handling Qualities

As ailerons are also used for lateral control of the air-craft, lateral maneuverability must be maintained. Ac-cording to the certification requirements [3, 2] as wellas the handling qualities requirements [20], roll per-formance is defined by the time a certain bank anglechange can be accomplished. By defining an achievableroll rate of at least 15 s−1 (see also Section 2.4), theserequirements are generally fulfilled, not considering anychanges in the acceleration behavior. However, roll ac-celeration basically depends on actuator dynamics andmass moment of inertia [17], which are both assumednot to be affected when changing the control surfacelayout. Thus, no further handling quality constraintsare introduced here.

Rigid Body Motions

Since the deflection of the ailerons for GLA induces apitching moment, it is required to compensate the re-sulting pitching motion using the elevators. To enforce

that, the pitch rate is constrained by

C6 : qmin ≤ q ≤ qmax,

where the maximum and minimum pitch rate are de-rived from simulations without GLA.

3.5 Optimization Problem Formulation

Finally, the overall aeroservoelastic optimization prob-lem can be formulated as

minDK ,Dail

V s.t. C1 . . . C6 are satisfied, (6)

with the objective function V from Section 3.3 and theconstraints C1 . . . C6 defined in Section 3.4. The de-sign variables are the controller tuners DK from Sec-tion 3.1 and the aileron parameters Dail defined in Sec-tion 3.2. The optimization is performed with MOPS [21]using a gradient based sequential quadratic program-ming (SQP) algorithm. In each optimization step, thelimit loads (Section 2.4) of the current aircraft config-uration without GLA are computed. Subsequently, theGLA controller is derived, and the objectives and con-straints are evaluated with respect to the actual limitloads.

4 Results and Discussion

For the following results, which are based on the find-ings of [22], one single flight point F at an altitudeh = 8297 m and a Mach number Ma = 0.85 is consid-ered. The aircraft is assumed to be fully loaded with aminimum amount of fuel in the wings, which is the masscase yielding the largest wing loads during gust encoun-ters. Furthermore, up- and downwards gusts with fourdifferent gust gradient distances H = 30 ft, 150 ft, 300 ftand 350 ft are evaluated in each optimization step. Ad-ditional flight points and gusts can be taken into ac-count easily, but have been neglected to simplify resultinterpretation and to save computation time. Besides,the unsteady AIC matrix is computed at 8 frequencypoints, where the lifting surfaces are discretized by 3526aerodynamic boxes, see also Figure 6. Subsequently, theRFA is performed with a number of 6 predefined poles.Taking into account the first 40 flexible modes, thisleads to a total number of 888 states for the nonlinearaircraft model. In order to obtain satisfying optimiza-tion results, it has been found sufficient to consider theshear force, bending- and torsionalmoment at threecross sections of the wing (including the wing root) andthe root of the horizontal tail plane (HTP). Note thatdue to the symmetric excitation, the resulting loads and


Fig. 6: Aircraft model with boxes of the aerodynamicmodel (black) and nodes of the condensed finite elementmodel (red).

accelerations at the left- and right-hand side of the air-craft are identical and thus are only considered once.In summary, the optimization problem consists of 154constraints and 10 tuning parameters.

4.1 Comparison of Optimization Results

First of all, a GLA system is tuned for the referenceaileron configuration depicted in Figure 7. To that end,the optimization problem defined in Equation (6) issolved for a fixed set of aileron parameters Dail. Theresulting reference controller reduces the WRBM incre-ments forming the objective function (5) by 21 %. Sec-ond, geometry parameters of inner and outer aileronsare optimized simultaneously with controller gains. Asa result, the maximum WRBM can be reduced in to-tal by 30 %, which means that the GLA performancecan be improved by 9 % using the optimized aileron ge-ometry depicted in Figure 8. For both GLA systems,the gust gradient distance causing the largest WRBMis 300 ft, which also coincides well with Pratt’s criticalgust gradient distance of 12.5 reference chord lengths[23].

The respective time signals of the loads at the wingroot are plotted in Figure 9 for this critical gust, whichis illustrated in the background. The reduction of themaximum WRBM can be clearly seen in Figure 9. Ad-ditionally, the shear force is reduced as well, but thetorsional moment is increased. Basically, the more theWRBM is reduced, the more the wing root torsionalmoment (WRTM) is increased due to the necessaryaileron deflections. This is also depicted in Figure 10,

Fig. 7: Reference aileron layout.

Fig. 8: Optimized aileron layout.

where the gust limit loads are compared over the wholewing. For a better comprehension, in the upper part ofthe two plots the reference aileron positions are shadedand in the lower part the optimized ones are shaded.Hence, the influence of the respective aileron layout onthe torsional moment can be clearly recognized. In ad-dition to that, the arising question of balancing the twodifferent load channels is discussed in Section 4.3.

In Figure 11, the required CS deflections for load al-leviation are compared, where the deflection limits forboth layouts are also marked. As already described inSection 3.4, the deflection limitations are determinedfrom certification maneuvers and thus differ from eachother for different aileron layouts. Generally, the deflec-tion constraints, as well as the deflection rate bounds,are a major limiting factor for the achievable perfor-mance. However, it has to be noted that for the chosencontroller structure, these limitations do not necessar-ily come to effect at critical gust gradient distances butrather at very short ones.

Furthermore, the control effectiveness for roll ma-neuvers can be directly determined for both control sur-face layouts by dividing the maximum roll rate pmax =


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time [s]

win

gro

otto

rsio

nm

omen

tw

ing

root

bend

ing

mom

ent

win

gro

otsh

ear

forc

e

0 1 2 3 4 5

Fig. 9: Loads at wing root for critical gust.

15 by the deflection limitations given in Figure 11.Clearly, the optimized aileron layout provides a greatercontrol effectiveness because the overall control surfacesize is larger. The given control effectiveness is a sum ofthe effectiveness of the individual pairs of control sur-faces as it can be seen in Table 2. The outer aileronsare less effective, not only because they are smaller butalso because corresponding deflections yield a largertorsion of the outer wing. Note that at higher Machnumbers, the control effectiveness can even become neg-ative which is also known as control reversal [24].4.2 Discussion of the Optimized Aileron Layout

By varying the initial values of the controller tunersor the aileron layout, different results with similar ob-jective values are obtained. This means, that the so-lution is not unique, giving additional degrees of free-dom to the engineer. However, it appears that the in-

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reference

right wing inner → outer

win

gbe

ndin

gm

omen

t

optimized0

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reference

right wing inner → outer

win

gto

rsio

nalm

omen

t

optimized

0

Fig. 10: Bending and torsional moment on the wing forthe considered ”1-cos” gusts.

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time [s]

oute

rai

l.[d

eg]

inne

rai

l.[d

eg]

elev

ator

s[d

eg]

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

−20

0

20

−20

0

20

−10

0

10

Fig. 11: CS deflections for critical gust.


ailerons reference layout optimized layoutinner only 0.8 1.4outer only 0.4 0.1both 1.2 1.5

Table 2: Aileron effectiveness for rolling.

ner ailerons are always placed similarly as depicted inFigure 8, whereas the position and span of the outerailerons seem to have a minor influence on GLA perfor-mance. In order to find an explanation for this result,a closer look is taken on the modal displacements lead-ing to the maximum WRBM occurring at t ≈ 0.6 s, seeFigure 9. To that end, the contributions of each flexi-ble mode to the WRBM are computed according to theMDM described in Equation (4). The contributions arenormalized by the maximum occurring WRBM withoutGLA, and displayed in Table 3, where only the modeswith the highest impact are listed. For the sake of clar-ity, summing up the normalized WRBM contributionsof all flexible modes would lead to the performance in-dex V of the respective aircraft configuration. It can beseen that the WRBM is clearly dominated by the firstsymmetric wing bending mode (mode 1). Hence, theGLA system should primarily damp this mode withoutexciting any other modes, which is assumed to be cru-cial when using the reference aileron layout for GLA.Comparing the first two rows of Table 3, it is shownthat the contributions of the modes 10, 12 and 21 areincreased when using the reference aileron configura-tion. In contrast, using the optimized ailerons for GLA,modes 10 and 12 are damped instead of excited. Thereason for that can be seen in Figure 12, where the ver-tical wing displacements for the corresponding modeshapes are shown for the maximum WRBM at t ≈ 0.6 s.Again, in the upper part of the plot, the positions of thereference ailerons are marked, and in the lower part,the positions of the optimized ailerons are marked. Themode shapes 10 and 12 appear to be very similar for thismass case and it can be seen that the optimized innerailerons are placed further inward than the respectiveoscillation node. Hence, the vertical displacements ofmodes 1, 10 and 12 point in the same direction at therange of the inner ailerons. For this reason, a coordi-nated deflection of the optimized inner ailerons allowsdamping all three modes simultaneously at this instantof time. Furthermore, the undesired excitation of mode21 indicates that a compromise is made for the optimalplacement of the ailerons. Note that this interpretationis not unambiguous as, for instance, the solution of theoptimization problem also depends on many differentconstraints given in Section 3.4.

4.3 Load Balancing

As already mentioned, actively reducing the wing bend-ing moment is at the cost of an increased wing torsionalmoment. In addition to that, the loads at the HTPare increased as well due to the deflections of the el-evators for pitching moment compensation. This canalso be seen in Figures 13a and 13b, where the corre-lated gust loads of the wing root and the HTP rootare compared, respectively. A trade-off study is carriedout to identify the Pareto front between the WRBMand the WRTM. To that end, the allowable WRTM issuccessively reduced and the respective achievable GLAperformance is determined. As depicted in Figure 14,this results in a monotonic decrease of the GLA perfor-mance for both the fixed reference aileron configurationand a variable aileron configuration to be optimized. Incase the closed-loop WRTM is limited to the open-loopWRTM (no GLA), an active alleviation of the WRBMis not possible, even if the aileron layout is optimized.Furthermore, not limiting the WRTM at all does notlead to any better performance than already presentedabove. Interestingly, setting the WRTM limits to thevalues from the reference GLA system but allowing anoptimization of the aileron layout does not lead to animprovement of the GLA performance. This means thatthe reference aileron configuration is already optimal ifno further increase of the WRTM is allowed.

Similarly, limiting the bending moment at the rootof the HTP leads to a decrease of the achievable GLAperformance (not depicted). Nevertheless, selecting theWRBM as the overall GLA objective provides a higherpotential for structural weight savings than reducingthe WRTM or the loads at the HTP as discussed in Sec-tion 3.3. However, any other trade-off point may be se-lected taking into account further engineering aspects.

5 Conclusion and Outlook

The aeroservoelastic optimization framework presentedin this paper allows to simultaneously tune the con-troller and the control surface (CS) layout for the pur-pose of active gust load alleviation (GLA). An efficientupdate routine for changes of the nonlinear aircraftmodel with unsteady aerodynamics is introduced. In or-der to obtain a reasonable solution, multiple constraintsare introduced including limitations of loads at differ-ent cross sections, actuator bandwidth and passengercomfort. The resulting GLA system with an optimizedaileron geometry allows to reduce the wing root bend-ing moment (WRBM) by 30 %, whereas with the ref-erence aileron configuration only 21 % can be achieved.


aircraft configuration V mode 1 mode 10 mode 12 mode 21without GLA 100 % 93.79 % 2.72 % 1.36 % 0.82 %with GLA (reference ailerons) 79 % 69.78 % 3.54 % 1.7 % 2.07 %with GLA (optimized ailerons) 70 % 61.79 % 2.53 % 0.42 % 3.53 %

Table 3: Comparison of modal contributions to maximum WRBM.

PSfrag replacements

referencereference

referencereference

right wing inner → outervert

ical

disp

lace

men

t[m

]


ical

disp

lace

men

t[m

]


ical

disp

lace

men

t[m

]right wing inner → outerve

rtic

aldi

spla

cem

ent

[m]

optimizedoptimized

optimizedoptimized

flexible mode 21flexible mode 12

flexible mode 10flexible mode 1

×10−3×10−3

−5

0

5

10

15

−15

−10

−5

0

5

−0.04

−0.02

0

0.02

−1

0

1

2

Fig. 12: Comparison of modal displacements for maximum WRBM.

PSfrag replacements

bending moment

tors

iona

lmom

ent

0

0

(a) Correlated gust loads at wing root.

PSfrag replacements

bending moment

tors

iona

lmom

ent

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(b) Correlated gust loads at HTP root.

Fig. 13: Comparison of correlated gust loads.


PSfrag replacements

wing root torsional moment

win

gro

otbe

ndin

gm

omen

t

GLA (opt.ail.)GLA (ref.ail.)NO GLA0.7

0.8

0.9

1

Fig. 14: Comparison of achievable GLA performancedepending on WRTM limitations.

An active reduction of the WRBM leads to an increaseof the wing root torsional moment (WRTM) and thehorizontal tail plane (HTP) loads, and thus, a trade-off has to be made. On the basis of individual modeshapes, the optimal placement of the ailerons is ex-plained, where the dependency on the actual mass caseneeds to be considered. For future investigations, it isnecessary to take into account the whole design enve-lope, which increases the complexity of the optimiza-tion problem. In addition to that, the interaction ofthe GLA system with the electronic flight control sys-tem (EFCS) also has to be considered. Apart from that,further performance improvements are expected if amore advanced controller structure or additional CSslike spoilers are used. Last but not least, the concreteweight savings need to be determined in order to eval-uate the impact on the direct operating costs of theaircraft.

6 Acknowledgments

Part of the research has has been funded in the courseof the European Union’s Seventh Framework Program(FP7/2007-2013) in the Clean Sky Joint TechnologyInitiative under grant agreement CSJU-GAM-SFWA-2008-001.

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