Simultaneous Vibration Reduction and Performance Enhancement

in Rotorcraft

Using Actively Controlled Flaps

Li Liu Peretz P. Friedmann Insung Kim Dennis S. BernsteinResearch Fellow Francois-Xavier Bagnoud Ph.D. Candidate Professor

Professor of Aerospace Engineeringryanliu@umich.edu peretzf@umich.edu iskim@umich.edu dsbaero@umich.edu

Department of Aerospace EngineeringUniversity of Michigan, Ann Arbor, Michigan

Abstract

A computational study of helicopter vibration and rotor shaft power reduction is conducted using actively-controlled trailing-edge flaps (acfs), implemented in single and dual flap configurations. Simultaneous vi-bration reduction and performance enhancement is demonstrated under level flight condition at high advanceratios, where dynamic stall effects are significant. Power reduction is achieved using the adaptive HigherHarmonic Control (hhc) algorithm in closed loop, with 2-5/rev flap control harmonics. This approach iscompared with an off-line, nonlinear optimizer lsqnonlin available in the matlab package, and favorablecomparisons are obtained. Subsequently a parametric study of flap spanwise location is conducted to de-termine the optimal flap location for power reduction. Finally the effectiveness of acf approach for powerreduction is compared with that of the conventional individual blade control (ibc) approach. The simulationresults clearly demonstrate the potential of the acf system for power reduction as well as simultaneousvibration and power reduction.

Nomenclature

c Blade chordcc Flap chordCT Rotor thrust coefficientD Matrix defined to be TTQT + RFHX4, FHY 4,

FHZ4 Nondimensional 4/rev hub shearsMHX4,MHY 4,

MHZ4 Nondimensional 4/rev hub momentsMHz1 Yawing moment about rotor hubNb Number of rotor bladesPR Rotor shaft powerR Rotor blade radiusQ Weighting matrix for objectives to be

reducedR Weighting matrix on control input

Presented at the American Helicopter Society62nd Annual Forum, Pheonix, AZ, May 9-11, 2006.Copyright c©2006 by the American Helicopter Soci-ety International, Inc. All rights reserved.

T Sensitivity, transfer matrix betweencontrol inputs and objective function

uk Control input vector, kth control stepuk,opt Optimum value of control input vec-

torxc Spanwise location of center of control

surfacezk Objective vector, kth control stepα Rotor disk angle of attackδ Flap deflection angleδNc, δNs N/rev cosine and sine amplitude of δαR Relaxation coefficient for control al-

gorithmβp Blade precone angleγ Lock numberµ Helicopter advance ratioωF , ωL, ωT Blade flap, lead-lag and torsional

natural frequenciesΩ Rotor angular speedψ Rotor azimuth angleθtw Built-in twist angle

1

σ Rotor solidity

Introduction and Background

Specifications for noise and vibration levels in ro-torcraft are continuously increasing in stringency,thus motivating research related to active noise andvibration reduction. Desirable vibration levels havebeen identified to be below 0.05g to provide pas-sengers with “jet smooth” ride. A number of ac-tive control techniques have emerged for effectivevibration reduction [1, 2], as illustrated schemati-cally in Fig. 1. These approaches generally fall intoone of two categories: (a) active control approachesaimed at reducing vibrations in the rotor before theypropagate into the fuselage, and (b) active controlapproaches implemented in the fuselage using anapproach known as active control of structural re-sponse (acsr). Within the first category of activecontrol, where the primary objective is to reduce vi-brations in the rotor, two approaches have emerged.These are (1) higher harmonic control (hhc) wherethe blades are activated in the non-rotating swash-plate by introducing pitch commands, and (2) in-dividual blade control (ibc) where each blade canbe controlled independently in the rotating frame.Several implementations of ibc are available: (i)the conventional or earliest implementation basedon pitch actuation at the blade root in the rotatingsystem, (ii) actively controlled partial-span trailing-edge flaps, and (iii) the active-twist rotor where theentire blade is twisted by piezoelectric fiber embed-ded in the blade. Additional descriptions of theseapproaches can be found in Refs. 1 and 2.

Among these approaches the hhc and ibc weredeveloped earlier and have been tested extensivelyin the wind tunnels as well as flight tests. Ex-cellent vibration reduction of more than 80% hasbeen demonstrated using these approaches. Sub-sequently, these approaches have also been consid-ered for noise control, particularly in the blade vor-tex interaction (bvi) flight regime. Potential to re-duce noise levels by 4-10dB under bvi conditionshas been demonstrated in wind tunnel tests, withvarious helicopter configurations [3–5]. It is impor-tant to note that these active control approachesrely primarily on what is known as the conventionalhhc algorithm in rotorcraft community for vibra-tion reduction [1, 2, 6, 7].

More recently, actively controlled flaps (acfs)have emerged as an efficient means of the active con-

trol of vibration due to bvi as well as the alleviationof dynamic stall induced vibrations [1,8–16]. Thesestudies on acf system implemented in both sin-gle and dual flap configurations have demonstratedvibration reduction comparable to those achievedwith hhc or conventional ibc, with no adverse ef-fects on helicopter airworthiness and significantlyless power requirement as compared to the bladeroot actuation approaches [1]. Wind tunnel testshave also shown the feasibility of the acf for vibra-tion reduction [16, 17]. During the Smart MaterialActuated Rotor Technology (smart) program con-ducted by Boeing [18, 19], a full scale piezoelectri-cally actuated flap system for vibration and noisecontrol for a five-bladed bearingless MD-900 rotorhas been tested on a whirl tower to demonstratecontrol effectiveness. In Europe, a full scale BK117with three actively controlled, piezoelectrically ac-tuated flaps has been flight tested by EurocopterGermany in the open loop mode on September 6,2005 and the flight test will continue into 2006 [20].

In Refs. 11–13, the effectiveness of acf system toreduce the vibrations in the high advance ratio flightregime, where dynamic stall effects are known to beimportant, was studied by Depailler and Friedmann.The simulation indicated that acf was successful inalleviating dynamic stall induced vibrations, thusdemonstrating the capability of the acf systemsto reduce vibrations due to multiple sources. Re-cently, a comprehensive helicopter simulation codewas developed using a unified approach for the pre-diction and active control of vibratory loads andblade-vortex interaction noise [21–25]. Considerablepotential for active noise reduction and simultane-ous vibration and noise reduction have been demon-strated using actively controlled flaps with 2-5/revcomponents on a rotor resembling the mbb BO-105hingeless rotor [22, 23]. The capability of the ACFsystem has also been demonstrated using a bear-ingless rotor configuration resembling the MD-900rotor in Ref. 24.

Despite their success for vibration and noise con-trol demonstrated in experiments as well as numer-ical studies, these active control techniques are stillmostly in preliminary flight test stages [26]. Con-cerns such as: cost, interference with the primaryflight controls, and the power usage of the systemhave thus far prevented the practical implemen-tation of such devices on a production helicopter.Therefore, it is important to study further the ca-pability of such active control devices, so as to reapthe largest potential benefit on the fairly sizeablecost associated with installing such active control

2

Figure 1: An Overview of Active Control Techniques.

systems in rotorcraft. One of the most desirableobjectives is performance enhancement with the ac-tive device, or at least prevent undue performancepenalty when deploying such a device for vibrationor noise control.

A wind tunnel study by Shaw et. al. [27], whichwas intended primarily to demonstrate the effective-ness of hhc system for vibration reduction, also pro-vided a preliminary assessment of the system forperformance enhancement. The test was conductedon a scaled three-bladed CH-47D rotor, at two cruiseairspeed of 135 knots and 160 knots (µ ≈ 0.30 and0.35), respectively. Pure 2/rev hhc inputs with 2

amplitude were used for performance enhancement,and the optimal phase angle was determined exper-imentally. It was found that the power required intrim was reduced substantially by 6% at 135 knotsand 4% at 160 knots. In another study, full-scalewind tunnel tests of a mbb BO-105 rotor were con-ducted at NASA Ames in the 40 × 80 foot windtunnel [4, 28]. An ibc system was tested in theopen-loop for vibration and noise reduction as wellas rotor power reduction. Rotor power reductionsof up to 7% were demonstrated using 2/rev ibc atadvance ratios of 0.40 and 0.45, but no power re-duction could be achieved at advance ratio of 0.30.

An analytical study conducted by Nguyen andChopra [29] examined the effects of hhc on ascaled three-bladed rotor similar to the one tested inRef. 27. A power reduction of 3.8% was obtained us-ing 2/rev hhc inputs with 2 amplitude. Cheng andCeli [30] performed a computational study of powerreduction using 2/rev hhc inputs. The rotor model

used was fairly simple, with rigid blade dynamicsand a dynamic inflow model. The study noted thatrotor power reductions were possible when usingproperly phased open-loop hhc input, at an ad-vance ratio of µ = 0.3. Reference 30 was basedon table look-up aerodynamics and a nonlinear dragmodel; and it was emphasized that power reductionscould only be obtained by simulation when a non-linear drag model was used. A subsequent study bythe same authors used numerical optimization tech-niques to determine the optimal 2/rev input, andincluded a free wake model [31]. With the additionof free wake, the amount of power reduction thatcould be simulated was almost eliminated.

Performance enhancement using the acf ap-proach has only been attempted in a few studiesthus far. A model rotor equipped with cam oper-ated trailing edge flaps was tested in wind tunnelby Straub [32]. Effect on rotor performance with2/rev flap actuation was evaluated at advance ra-tios of 0.25 and 0.30, but the results were consideredinconclusive due to issues associated with the accu-racy of the measurements obtained during the test.A preliminary computational study on rotor powerreduction for a rotor resembling the mbb BO-105was conducted in Ref. 25. In this study a single flapconfiguration with deflections limited to 4 degreeswas examined in the open loop mode, under bvi con-ditions at µ = 0.15. It was found that power reduc-tion could only be obtained when the torsional fun-damental frequency of the rotor was reduced fromthe value of the mbb BO-105 to a lower value of 2.5.

When using an acf for vibration or noise reduc-

3

tion the deflections of the flap increase the dragof the blade and therefore vibration and noise re-duction are accompanied by a performance penalty.The fundamental question is therefore whether it ispossible to use the acf system without incurring apower penalty. Motivated by this desire the overallobjective of the paper is to examine simultaneousvibration reduction and performance enhancementusing the acf based approach. Rotor power reduc-tion using acf approach, employing the hhc algo-rithm in the closed loop, will be emphasized. Basedon the concise review of previous research providedin this introduction on rotor power reduction, therotor power reduction problem at high advance ra-tio (µ = 0.35) will be considered. While the noiseaspect associated with this problem is also of inter-est, the noise emissions at such advance ratios aretypically dominated by high speed impulsive (hsi)noise [33] and this problem is computationally veryintensive and therefore will be considered in follow-on research. The specific objectives of the paper areprovided next:

• assess the potential for rotor power reductionusing the acf system by applying the hhc con-trol algorithm;

• examine the mutual interaction between powerreduction and vibration reduction;

• explore the potential of simultaneous powerand vibration reduction using the acf system;

• determine the sensitivity of power reduction toflap spanwise locations so as to optimize flapperformance;

• compare the effectiveness for power reductionusing the acf approach with conventional ibcapproach;

• conduct a study of power reduction, vibrationreduction as well as simultaneous reduction us-ing off-line nonlinear optimizers, and comparethe results with those obtained using the hhcalgorithm.

Achieving reduced vibration or noise levels with-out undue performance penalty is central to prac-tical implementation of the acf system; and it hasa key role governing the feasibility of implementingan acf system in a practical setting.

Mathematical Model

The present study is based on a comprehensiverotorcraft aeroelastic analysis tool that accounts forthe effects of dynamic stall at high advance ratios,as described in detail in Refs. 11–13. The powerreduction studies conducted in the present researchwill be carried out at a high advance ratio of 0.35,where the dynamic stall effects are important. Thefundamental ingredients of the aeroelastic model areconcisely summarized in the following subsections.

Structural Dynamic Model

The structural dynamic model consists of anisotropic hingeless rotor blade, which is cantileveredat the hub and has fully coupled flap-lag-torsionaldynamics including nonlinearities due to moderateblade deflections [8]. The aeroelastic model is capa-ble of simulating rotors with single or dual activelycontrolled partial span trailing edge flaps mountedon the rotating blade as depicted in Fig. 1. Theequations of motion are discretized using the globalGalerkin method, based upon the free vibrationmodes of the rotating blade. Three flapping modes,two lead-lag modes and two torsional modes areused when computing the numerical results givenin the results section.

Aerodynamic Model

Blade section aerodynamic loads for attached floware calculated using a rational function approx-imation (rfa) approach as described in Ref. 9.The rfa approach is a two-dimensional, unsteadytime-domain aerodynamic theory that accounts forcompressibility, variations in the oncoming velocityand a blade-flap configuration. Aerodynamic cross-sectional loads including lift, moment and flap-hinge moment can be calculated, along with chord-wise pressure distribution [21] which is required inacoustic calculations. The rfa model for the blade-flap combination is linked to a free wake model[10], which produces non-uniform inflow distribu-tion. For the separated flow regime, unsteady aero-dynamic loads are calculated using the onera dy-namic stall model described by Petot [34]. The aug-mented aerodynamic states associated with rfa at-tached flow states and onera separated flow statesare combined to produce the time-domain, statespace aerodynamic model. Furthermore, a simple,linear drag model that accounts for additional drag

4

due to flap deflection, that increases the power re-quired for the rotor to operate, is also implemented[12].

Solution Procedure

The combined structural and aerodynamic equa-tions form a system of coupled differential equa-tions that can be cast in state variable form. Theyare then integrated in the time domain using theAdams-Bashforth DE/STEP predictor-corrector al-gorithm. A propulsive trim procedure is imple-mented in level flight condition; where six equilib-rium equations (three forces and three moments)are enforced. The trim equations are solved in acoupled manner with the aeroelastic equations ofmotion. Hub vibratory loads are obtained by in-tegrating the distributed aerodynamic and inertialloads over the blades. Average rotor power is de-fined as the instantaneous power required to drivethe rotor at a constant angular velocity Ω averagedover one revolution,

PR =Ω2π

∫ 2π

0

−MHz1(ψ)dψ, (1)

where MHz1 is the total yawing moment about thehub and includes the effect of unsteadiness, com-pressibility, dynamic stall (if applicable), and theadditional drag due to flap deflection. The negativesign in front of MHz1(ψ) is due to the fact that itrepresents the torque about the rotor shaft due tothe loading on the blades, and therefore the enginemust supply a torque equal to −MHz1(ψ) to main-tain a constant angular velocity [8]. Equation 1 is ageneral expression valid for blades with or withoutactively controlled flaps.

Control Strategies

The Higher Harmonic Control (hhc) algorithm[6, 7, 14] has been used successfully for both vibra-tion and noise reduction; as well as simultaneousvibration and noise reduction. Furthermore, sev-eral variants of this algorithm, including a relaxedand an adaptive version, have been shown to im-prove the robustness of the algorithm [7]. An adap-tive form of this algorithm was successfully appliedin the closed loop noise control as well as simul-taneous vibration and noise control in Ref. 22. Inthe present study, the adaptive hhc algorithm isused for rotor power reduction, where the objective

function consists of averaged rotor power over onerevolution. For simultaneous reduction of vibrationand power, a combined objective which consists ofvibration and power components is used, and anappropriate weighting matrix is used to adjust thecontrol effort so as to achieve a desirable balance be-tween vibration and power objectives. For the prac-tical implementation of the algorithm, an appropri-ate control input weighting is chosen such that themaximum flap deflection does not exceed 4.

The hhc algorithm has been the subject of a re-cent paper [7], wherein the stability, robustness, andconvergence properties of the algorithm togetherwith a number of variants are addressed in detail.This algorithm is based on a linear, quasi-static, fre-quency domain representation of helicopter responseto control inputs. The inputs to the algorithm arecomprised of a combination of flap deflection har-monics with discrete frequencies of Nmin-Nmax/rev.The total flap deflection is given as

δ(ψ) =Nmax∑

N=Nmin

[δNc cos(Nψ) + δNs sin(Nψ)] (2)

For a four-bladed rotor, the flap deflection harmon-ics typically consist of 2-5/rev components for vi-bration reduction, as well as in noise control [22].Most studies thus far have only examined the effectsof 2/rev component for power reduction using openloop [27, 30, 31]; however, in the present study thislimitation is removed and the whole range of har-monics from 2-5/rev will be used since the feedbackcontroller based on the hhc algorithm is capable ofchoosing the most effective harmonics for the pur-pose of power reduction. These pitch deflections arerelated to the vibration or noise level magnitudesthrough a transfer matrix T, given by

T =∂zk

∂uk. (3)

The control strategy is based on the minimization ofa performance index that was originally developedfor vibration reduction [6] which is a quadratic func-tion of the quantities that are being reduced (vibra-tion or noise) zk and control input amplitudes uk:

J(zk,uk) = zTk Qzk + uT

k Ruk, (4)

The subscript k refers to the kth control step, re-flecting the discrete-time nature of the control. Thetime interval between each control step must be suf-ficient to allow the system to return to the steadystate, typically in 3–5 revolutions, so that the vi-

5

bration or power levels can be accurately measured.The optimal control law is given by:

uk,opt = −D−1TTQz0 −Tu0 (5)

whereD = TTQT + R (6)

For a well-identified linear system the algorithmconverges to the optimum value in a single step [7].However, if the helicopter cannot be perfectly repre-sented by a linear model, the optimal value will notbe reached after the first step. The convergence is-sue of the algorithm was addressed in Ref. 7, where arelaxed version of the algorithm, described conciselybelow, was developed. Traditionally, the control in-put update is represented in iterative form as shownin Eq. (7):

uk+1 = uk + ∆uk. (7)

In the relaxed variant of the algorithm, a relaxationfactor αR is introduced,

uk+1 = uk + αR∆uk, (8)

where 0 < αR < 1. This has been shown to increasethe robustness of the algorithm at the expense ofconvergence speed [7]. An adaptive version [6, 7] ofthe hhc algorithm was also shown to be useful in thenoise reduction studies in the presence of strongernonlinearities, therefore it would also be applied inthis study for power control. In the adaptive vari-ant, the transfer matrix T is identified online, us-ing a recursive least-squares technique, following themethod described in Ref. 7.

For vibration reduction (vr) studies, the vectorzk consists of 4/rev vibration levels as representedby hub shears and moments, given in Eq. (9),

zk,vr =

FHX4

FHY 4

FHZ4

MHX4

MHY 4

MHZ4

(9)

When the controller is used for power reduction theobjective vector zk is simply averaged rotor shaftpower as given in Eq. (1).

zk,pr =[PR

](10)

For simultaneous reduction (sr) problems, a com-

bined output vector is defined

zk,sr =[

zk,vr

zk,pr

]. (11)

The weighting matrix Q is used to adjust the controleffort so as to achieve a desirable balance betweenthe vibration levels and power reductions.

In order to evaluate the effectiveness of the hhcalgorithm under the high speed forward flight condi-tions, where strong nonlinearities are present char-acterized by the onset of dynamic stall, the aeroelas-tic simulation code is coupled with matlab so asto utilize the built-in nonlinear optimization solversto find potentially lower controlled values using thesame active flap configurations. The nonlinear leastsquares optimizer lsqnonlin is chosen for this pur-pose, which is a subspace trust region method andis based on the interior-reflective Newton methoddescribed in Refs. 35 and 36. This approach is in-tended for offline identification of best possible vi-bration and rotor power reduction, using the acfapproach. The results obtained using the onlineadaptive hhc algorithm, which is computationallymuch more efficient, are compared with those ob-tained with lsqnonlin to determine the perfor-mance of the algorithm. The results obtained withthe offline optimizer represent the best possible per-formance enhancement that can be achieved.

Results

The results presented in this section were ob-tained for a helicopter configuration resemblinga full-scale MBB BO-105 helicopter with a four-bladed hingeless rotor system. The properties ofthe helicopter configuration used in the computa-tions are summarized in Table 1. The characteris-tics of the actively controlled flap configurations aregiven in Table 2, including a single servo flap con-figuration and a dual servo flap configuration. Thehelicopter is in level flight condition at a relativelyhigh advance ratio of µ = 0.35, and propulsive trimis used to trim the rotor.

Rotor Power Reduction

In this section the potential of the ACF approachfor rotor power reduction is explored. First theadaptive higher harmonic control (hhc) algorithmis used for rotor power control. The effect of power

6

Table 3: Summary of rotor power reduction during Power Reduction (pr) and Simultaneous Reduction(sr).

Objective Power Reduction(pr) Simultaneous Reduction(sr)Controller hhc lsqnonlin hhc lsqnonlinFlap Config. Single Dual Single Single Dual SingleBaseline Power 0.00670286 0.00681677 0.00670286 0.00670286 0.00681677 0.00670286Controlled 0.00658692 0.00669656 0.00654460 0.00667611 0.00677104 0.00663603Reduction(%) 1.73 1.76 2.36 0.40 0.67 1.00

Table 1: MBB BO-105 hingeless blade configuration.Rotor DataNb = 4 c = 0.05498Lb

ωF = 1.12, 3.41, 7.62 Cdo = 0.01ωL = 0.73, 4.46 Cmo = 0.0ωT = 3.17 ao = 2πθtw = −8 θFP = 6.5

γ = 5.5 σ = 0.07βp = 2.5

Helicopter DataCT /σ = 0.0714 µ = 0.35Lb = 4.91 m Ω = 425rpm

Table 2: Flap configuration.cc = 0.25cSingle Servo Flapxc = 0.75Lb Lc = 0.12Lb

Dual Servo Flapx1

c = 0.72Lb L1c = 0.06Lb

x2c = 0.92Lb L2

c = 0.06Lb

reduction on vibratory loads is also examined dur-ing power reduction. The results for rotor powerreduction are summarized in Table 3.

As shown in Table 3, the rotor power can be re-duced by 1.73% and 1.76% compared to the base-line, using the single and dual flap configurations,respectively. This reduction is achieved in the pres-ence of dynamic stall, which is important under thesimulated flight condition at µ = 0.35. Note thatthe baseline power is slightly higher for the dualflap case, under the same rotor trim settings. Dur-ing the power reduction the maximum flap deflec-tions required by the controller are less than 3, asshown in Fig. 2. Furthermore, it can be seen thatthe flap deflections of the two flaps are similar inthe dual flap configuration, which also resemble theflap deflection for the single flap case.

Figure 3 illustrates that the vibratory loads dur-

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

Inboard Outboard

Figure 2: Flap deflection during power reduction.

ing power reduction are severely increased; by morethan 100%, for both the single and dual flap con-figurations. This suggests that using a single ob-jective of rotor power in the hhc controller couldresult in unacceptable vibration levels. Therefore,a combined objective which accounts for both vi-bration and power is required, such an approach isconsidered next.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

Baseline PR, 1 Flap PR, 2 Flaps

Nond

imen

siona

l 4/r

ev V

ibra

tory

Hub

Load

s

Figure 3: Vibration levels during power reduction.

Simultaneous Vibration and Rotor PowerReduction

In this section, a composite objective functionwhich combines vibratory loads and rotor powercomponents is used with the hhc algorithm, so asto achieve simultaneous reduction of both vibration

7

and power. The results shown here are obtained us-ing one weighting matrix: the vibratory hub shearcomponents are weighted by a factor of 1, whilethe vibratory hub moments and rotor power com-ponents are weighted by a factor of 10. The rotorand flap configurations as well as flight conditionsare identical to those used in the previous section.

Table 3 shows rotor power reduction of about0.4% and 0.67% for the simultaneous control, usingthe single and dual flap configurations, respectively.Obviously the amount of power reduction that canbe achieved for the combined objective is smallerthan that has been demonstrated with the controllertuned for power reduction alone. The maximum flapdeflections for these cases are less than 3, as shownin Fig. 4.

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

Inboard Outboard

Figure 4: Flap deflection during simultaneous re-duction.

The reduction of the vibratory loads during powerreduction is shown in Fig. 5. For the single flapcase, the individual hub shear and moment compo-nents are reduced between 28-78%, while the vibra-tion objective is reduced by 68%. The combinedvibration and power objective is reduced by 3.6%.Despite a slightly better power reduction during vi-bration suppression, the dual flap configuration pro-duces slightly less vibration reduction compared tothe single flap case. From these results, it can beseen that the ACF is capable of producing signifi-cant vibration reduction along with a small amountof power reduction, using small flap deflections ofless than 3.

Vibration and Rotor Power Reduction UsingOff-line Optimizer LSQNONLIN

In this section the results obtained using the non-linear optimizer lsqnonlin available in the matlabpackage are shown for vibration and power reduc-tion. These results are also compared to those ob-tained previously using the adaptive hhc algorithm,to determine its effectiveness. In the optimization of

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

Baseline SR, 1 Flap SR, 2 Flaps

Nond

imen

siona

l 4/r

ev V

ibra

tory

Hub

Load

s

Figure 5: Vibration levels during simultaneous vi-bration and power reduction.

a nonlinear objective function local minima for vi-bration or power can be obtained during the search,therefore different flap inputs are applied as initialconditions. Ten initial flap inputs are generated ran-domly with the constraint that the maximum flapdeflections not exceed 4. The best optimization re-sults using lsqnonlin are chosen among these tenflap initial inputs along with the case with zero flapinitial deflection.

The nonlinear optimizer lsqnonlin is capable ofachieving rotor power reduction of 2.36%, as shownin Table 3. This is superior to that achieved usingthe adaptive hhc algorithm; however, the perfor-mance of the adaptive hhc algorithm is reasonablygood in addition to its numerical efficiency. The flapdeflections required by the optimizer are shown inFig. 6, where the maximum flap deflection is limitedto be less than 4. The vibration levels during powerreduction are also increased significantly, shown inFig. 7, which is similar to the results shown earlierusing the hhc algorithm.

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

Figure 6: Flap deflection during power reductionusing nonlinear optimizer lsqnonlin.

For simultaneous vibration and power reduction,the rotor power is reduced by 1.0% as shown in Ta-ble 3 and the vibration objective is reduced by 55%as shown in Fig. 9. The flap deflections are shown inFig. 8 and it is evident that flap deflections are less

8

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

Baseline PR, 1 Flap, lsqnonlin

Nond

imen

siona

l 4/r

ev V

ibra

tory

Hub

Load

s

Figure 7: Vibration levels during power reductionusing nonlinear optimizer lsqnonlin.

than 4. It should be noted that a different weight-ing matrix is used here, which puts more emphasison power objective compared to the weighting ma-trix used in the hhc algorithm shown earlier. As aresult, the degree of power reduction using lsqnon-lin is larger than that obtained using the hhc al-gorithm, whereas the degree of vibration reductionis slightly less than that found with the hhc algo-rithm.

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

Figure 8: Flap deflection during simultaneous re-duction using nonlinear optimizer lsqnonlin.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

Baseline SR, 1 Flap, lsqnonlin

Nond

imen

siona

l 4/r

ev V

ibra

tory

Hub

Load

s

Figure 9: Vibration levels during simultaneouspower and vibration reduction using nonlinear op-timizer lsqnonlin.

Comparison of HHC to LSQNONLIN

A plot of the vibration objective Jvib versus thepower objective Jpower is depicted in Fig. 10. Thefigure shows the tradeoff between the competingobjectives at all control steps for both lsqnonlinand hhc algorithms. The blue circles represent thevalues of the objectives at all function evaluationsduring the course of optimization using lsqnonlin.The boundary of these objectives, represented bythe red line, shows an approximate Pareto-optimalcurve illustrating the best tradeoff between the twocompeting objectives. The grey, black and greenlines represent the power reduction, vibration re-duction and simultaneous reduction using the hhcalgorithm from the same baseline, respectively. It isquite interesting to note that the optimal vibrationreduction that can be obtained using hhc reachesthe Pareto optimal curve obtained from lsqnon-lin. Moreover, the best simultaneous vibration andpower reduction can be achieved with hhc also ap-proaches the optimal trade-off curve. However, itis evident that significantly better power reductionis obtained using lsqnonlin, as shown in Fig. 10.Overall, the performance of hhc algorithm is quitegood considering its numerical efficiency.

0 0.5 1 1.5 2 2.5 36.5

6.6

6.7

6.8

6.9

JVIB (10-5)

J POW

ER (1

0-3)

Baseline

(JVIB, JPOWER) at each function evaluation during LSQNONLIN

Approximate Optimal Tradeoff

HHC with 2−5/rev, Power ControlHHC with 2−5/rev, Vibration ControlHHC with 2−5/rev, Simul. Control with equal weighting

Figure 10: Comparison of optimization history us-ing hhc and lsqnonlin, showing Jpower vs. Jvib.

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Effect of Flap Spanwise Locations

The flap configurations used in the previous sec-tions, as shown in Table 2, are optimized for vibra-tion reduction. Therefore, it is relevant to consideralternative flap spanwise locations which emphasizeoptimizing power reduction. The effect of differentspanwise flap locations on the power reduction ca-pability is considered next. This is accomplishedby varying the location where a single servo flap iscentered. The flap has a span equal to 12% of rotorradius and its chord is 25% of the blade chord, whichis similar to the single flap configuration in Table 2.Three spanwise locations are considered, as shownin Table 4, where the flap with xc = 0.94R is locatedat the tip of the blade.

It is interesting that the baseline rotor power isreduced when the flap is moved outboard. The ro-tor power reduction is somewhat less for the flapcentered at 0.85R than for one centered at 0.75Rin terms of power reduction percentage. When theflap is located at the blade tip the power reduc-tion is greatest, almost 4%. However, the optimalflap deflection also alters significantly the rotor trimconditions, in particular rotor thrust. When com-paring this characteristic to the flap placed at theother two locations, it is evident that for the inboardlocation the influence on the rotor trim is negligible.After retrimming the rotor while keeping this opti-mal flap deflection for power control, the degree ofpower reduction that can be achieved is reduced to2%. Therefore, one has to be careful to ensure thesimilar rotor operating conditions are enforced whenconducting power control studies.

Comparison of ACF to Conventional IBC forPower Reduction

Power reduction using the conventional ibc ap-proach is also considered here, so as to compare itseffectiveness to the acf approach. The controllerused in the conventional ibc approach is also theadaptive hhc algorithm described earlier. The ibccontrol inputs also consist of a combination of 2-5/rev harmonics, similar to that used in the acfstudy. Furthermore, the maximum ibc amplitudeis restricted to be less than 1.

Using the conventional ibc approach, the rotorpower consumption is reduced to 0.00660756 fromthe baseline value of 0.00670286, representing a1.4% reduction. This is similar to the reductionachieved using the acf approach. The vibration

levels are significantly increased during power con-trol using ibc as shown in Fig. 11, a phenomenonthat was also observed during power reduction stud-ies conducted using the acf. The ibc time historiesfor power reduction are shown in Fig. 12.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

BaselinePR, Conventional IBC

Nond

imen

siona

l 4/r

ev V

ibra

tory

Hub

Load

s

Figure 11: Vibration levels during power reductionusing conventional ibc.

0 180 360−5

−4

−3

−2

−1

0

1

2

3

4

5

Azimuth(deg)

Fla

p D

efle

ctio

n(de

g)

Figure 12: Flap deflection during power reductionusing conventional ibc.

Conclusions

The results presented in this paper have demon-strated that the acf system implemented in a singleor dual flap configuration is capable of simultane-ously reducing vibration and enhancing rotor per-formance. The numerical simulations are obtainedat a relatively high advance ratio of µ = 0.35 wherethe dynamic stall effects are significant.

The primary conclusions obtained in the courseof this study are summarized below:

1. The acf is an effective device for rotor perfor-mance enhancement, where a nearly 2% powerreduction is achieved using a rotor configura-tion that resembles the MBB BO-105 under thesimulated flight conditions.

2. The rotor power reduction can be implementedby using the adaptive hhc algorithm which

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Table 4: Rotor power reduction with single flap located at various spanwise locations.

Flap Center (xc) 0.75R 0.85R 0.94RBaseline Power 0.00670286 0.00663195 0.00571054Controlled 0.00658692 0.00654061 0.00548369Reduction(%) 1.73 1.38 3.97Power After Retrim — — 0.00559408Reduction(%) — — 2.04

has been applied successfully for vibration andnoise control in previous studies.

3. The rotor power reduction is accompanied bya significant increase in vibration levels, if thecontroller is tuned only for power enhancement.

4. Simultaneous reduction of vibration and rotorpower reduction is feasible, and significant vi-bration eduction of 68% is achieved combinedwith a relatively modest amount of power re-duction of approximately 1%.

5. A nonlinear optimizer lsqnonlin available inthe matlab package is also explored for off-line identification of best possible vibration andpower reduction. Compared to lsqnonlin, theadaptive hhc algorithm provides satisfactoryperformance with superior numerical efficiency,although considerably higher level of power re-duction can be achieved using lsqnonlin.

6. A parametric study of the flap spanwise loca-tion indicates that the flap placement near theblade tip can significantly improve power en-hancement. However, the rotor trim is affectedwhen the flap is placed near the tip, which re-quires retrimming the rotor.

7. The acf system shows power enhancement ca-pability that is comparable to the power en-hancement that can be obtained with the con-ventional ibc approach.

Acknowledgments

This research was supported by the fxb Centerfor Rotary and Fixed Wing Air Vehicle Design. Par-tial support of an aro grant 02-1-0202 with Dr. G.Anderson as grant monitor is acknowledged. Partialsupport for this project by RITA under WBS: 04-B-01-01.7-A.16 is also acknowledged. The authors

want to thank Walter Sonneborn for suggesting thatperformance be emphasized in conjunction with vi-bration reduction.

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