01-25208 structural dynamics, and materials conference

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

\01-2520842nd AIAA/ASMOASCBAHS/ASC Structures,

Structural Dynamics, and Materials Conferenceand Exhibit

Seattle, WA 16-19 April 20012001-1467

ACTUATOR SATURATION AND ITS INFLUENCE ON VIBRATIONREDUCTION BY ACTIVELY CONTROLLED FLAPS

R. Cribbs* and P.P. FriedmanntDepartment of Aerospace Engineering

University of MichiganAnn Arbor, Michigan 48109-2140

Abstract

The influence of actuator saturation on the vi-bration reduction abilities of an actively controlledflap is investigated. An aeroelastic model of a fourbladed hingeless rotor with a free wake is used forthe analyses. Three methods for constraining flapdeflections are studied at two limiting values, twoand four degrees, of maximum flap deflection. Re-sults indicate that neither scaling nor clipping ofthe optimal control flap deflection to the maximumflap deflection provides acceptable vibration reduc-tion. A newly developed control method with sat-uration constraints shows exceptional reduction ofvibrations. This new control method reduces vibra-tions to similar levels as the unconstrained optimalcontrol while constraining maximum flap deflectionsto the limiting values.

Nomenclature

Blade lift curve slopeBlade chordTrailing edge flap chordCoefficient of dragHelicopter coefficient of weightWeighting multiplier for Wuweighting matrixBlade bending stiffnesses in flapand lead-lag4/rev vibratory hub shears in

longitudinal, lateral and verticaldirections, respectivelyQuadratic performance index forvibration control

Cdo

EL,, EL

FHX, FHY, FHZ

J

* Postdoctoral Scholar; currently Dynamics Engineer, Siko-rsky Aircraft, Stratford, CT 06497, Member AIAA

tFrangois-Xavier Bagnoud Professor of Aerospace Engi-neering, Fellow AIAA, Member ASME, AHS

Copyright ©2001 by Richard C. Cribbs and Peretz P.Friedmann. Published by the American Institute of Aero-nautics and Astronautics, Inc. with permission.

1/5 Blade lengthLcs Trailing edge flap length?7i Blade mass distribution per unit

lengthMHX, MHY, MHZ 4/rev vibratory hub moments

in rolling, pitching and yawing,respectively

rib Number of bladesR Rotor radiusT Jacobian of the vibration re-

sponse with respect to the con-trol input

u Vector of control inputsu* Vector of optimal control inputsWu Matrix of weights on control am-

plitudesWz Matrix of weights on vibration

amplitudesWAU Matrix of weights on the rate

of change of control amplitudesfrom one control iteration to thenext

xcs Location along blade span aboutwhich trailing edge flap is cen-tered

XFA, XFC Horizontal offset of fuselageaerodynamic center and fuselagecenter of gravity from hub

z Vector of vibration amplitudesZFA, ZFC Vertical offset of fuselage aero-

dynamic center and fuselage cen-ter of gravity from hub

Pp Blade precone angle7 Lock number8 Flap deflectionSumit Flap deflection limiting valueSNC^NC Cosine and sine amplitudes of

Nth harmonic of flap deflection,respectively

1American Institute of Aeronautics and Astronautics


<5opt Optimal flap deflectionIJL Advance ratio<j Rotor solidity ratio^ Blade azimuth angleH Rotor angular velocity

Introduction

In recent years, researchers have investigated ac-tively controlled trailing edge flaps as a means forvibration control in helicopter rotors.1"3 In this ap-proach, appropriate control inputs to the flap modifythe aerodynamic loads on the blade to reduce the ro-tor vibratory hub loads. Earlier research has shownthat the partial span, trailing edge flap, shown inFig. 1, produces the same amount of vibration re-duction as individual blade control (IBC) that isimplemented by moving the entire blade by pitchinputs provided at its root in the rotating system.4

However, the actively controlled flap requires almostan order of magnitude less power for its operation.Furthermore, the practical implementation of the ac-tively controlled flap does not require the extensivemodifications to the swashplate that are describedin Ref. 5.

For practical implementation, the trend has beento use adaptive materials such as piezoelectric ormagnetostrictive actuator devices to actively controlthe flap. This type of actuation has been consideredby several researchers including Spangler and Hall,6

Bernhard and Chopra,7 Fulton and Ormiston,8 andPrechtl and Hall.9 The force and stroke producingcapability of adaptive materials based actuation islimited. Therefore, the actual flap deflections thatare achievable with this type of actuation are ex-pected to fall short of the angles required for maxi-mum vibration reduction. Thus, these actuators willbe unable to produce the control authority requiredfor optimal vibration reduction, and the actuator islikely to encounter saturation.

In this study, the consequences of imposing limitson the flap deflection produced by the actuator areexamined. The influence of such limits, typicallydenoted as saturation in the control terminology,on vibration reduction capability is assessed. Threemethods of constraining flap deflections to limitingvalues are studied. Two methods for limiting flapdeflection amplitudes given an optimal flap deflec-tion history for vibration reduction are: (1) clippingof the optimal flap deflection such that deflectionsgreater than a prescribed value are simply set to theprescribed maximum value, and (2) uniformly scal-ing down the amplitudes of the flap input harmonics

so that the flap amplitude never exceeds the limitingvalue. A third flap deflection limiting methodologyis developed and studied. In this method, the con-trol procedure is modified to allow the controller toautomatically adjust the control weighting matrix.The weighting matrix is adjusted iteratively untilthe flap deflection is properly constrained.

The issue of flap saturation has not been studiedin the literature before, yet it plays a very importantrole in the practical implementation of vibration re-duction using the actively controlled flap (ACF).

Mathematical Model and Method of Solution

The mathematical model employed in this studyrepresents a rotor with a number of flexible, hin-geless blades each of which contains a partial spantrailing edge flap as shown in Fig. 1. The modelwas developed in an earlier study by de Terlizzi andFriedmann.10

Structural Dynamic Model

Each rotor blade is modeled by beam-type fi-nite elements capable of representing a compositerotor blade with a swept tip. The blade struc-tural dynamic model was developed by Yuan andFriedmann.11 The model has provisions for an arbi-trary cross-sectional shape which is allowed to varyalong the span. The model accounts for trans-verse shear and out of plane warping and can modelanisotropic material behavior and composite cou-pling effects.

Aerodynamic Model

The aerodynamic model has two main compo-nents, calculation of the spanwise aerodynamic loadsacting on the blade and the calculation of thenonuniform inflow distribution over the rotor.

The blade section aerodynamic loads are deter-mined using two different aerodynamic models. Forthe quasi-steady loads acting on the blade/flapcombination, a modification of Theodorsen's quasi-steady aerodynamic theory which includes the influ-ence of the trailing edge flap as developed by Millotand Friedmann1 is used. To model the unsteadycompressible airloads acting on the blade/flap com-bination, the aerodynamic theory developed by Myr-tle and Friedmann3 is employed.

The nonuniform inflow distribution is calculatedfrom a free wake model that has been extractedfrom the comprehensive rotorcraft analysis tool,CAMRAD/JA,12 and modified to be compatible

American Institute of Aeronautics and Astronautics


with the aeroelastic response analysis employed inthis study. It consists of a wake geometry model anda wake computation model that, given the wake ge-ometry, calculates the induced velocity distribution.The free wake geometry routine was initially devel-oped by Scully13 and the wake calculation modelwas developed by Johnson.14 The model is based ona vortex lattice approximation of the wake.

Trailing Edge Flap

Actively controlled flaps have been incorporatedinto the model in a manner described in Ref. 10.Control inputs provided to the flap consist of a com-bination of 2/rev, 3/rev, 4/rev and 5/rev flap de-flections. These inputs are typically obtained froma control law15 based on the minimization of aquadratic performance index composed of vibrationand control amplitudes.

Method of Solution

A modal analysis is implemented using eight freevibration modes of a rotating beam, 3 flap, 2 lead-lag, 2 torsional and 1 axial mode. Either a har-monic balance technique or a time domain solutionis used to solve the blade response equations de-pending on whether or not unsteady aerodynamicsare employed. In the harmonic balance technique,the blade motions and trim equations are convertedinto a system of nonlinear algebraic equations andare then solved simultaneously by the IMSL non-linear algebraic solver DNEQNF.16 In the time do-main aeroelastic response solution, the equations ofmotion are numerically integrated using the generalpurpose Adams-Bashfort ordinary differential equa-tion solver DE/STEP.

Control

Control Algorithm

The control algorithm used in this study is onethat is typically used in HHC and IBC studies and isdescribed in detail in Ref. 15. It is based on the min-imization of a performance index that is a quadraticfunction of vibrations Zi and control inputs HI. Thequadratic function is given by:

— 7 . ^̂ y y • —I— 11 . \\/ 11 • —I— /\ <] i ~\\7 A. /\ i"? • l l i— 1 Z^l I "'2. 11 Lt/l ' i~-^ % * ̂ /\ 11 <—± LL i \ )

where A^ — ui - Ui-i. The weighting matrices,Wz, Wu and WAU, used in this study are diago-nal and assign the relative importance of the vari-ous vibration components and control inputs. A*7 •

constrains the rate of change of the control from onecontrol iteration to the next.

The optimal control is found by setting the gradi-ent of the performance index J with respect to thecontrol Ui to zero:

(2)

The solution of this equation results in the optimalcontrol u\ that minimizes J. It is assumed in thisstudy that the control inputs and vibration levelsare known.

To determine the gradient of the performance in-dex with respect to the control, it is necessary toknow the gradient of the vibrations with respect tothe control. To this end, the vibrations are linearizedabout the current control input Ui

whereT =

dz_du

(3)

(4)

The transfer matrix T is the Jacobian of the vibra-tion response with respect to the current control in-put. This Jacobian is calculated numerically usingthe finite difference method.

Substituting this model of the vibration responseinto the performance index and minimizing with re-spect to the control produces the optimal control forthe given control step:

ui+i = ~J

where- T Wu + WAu

(5)

(6)

This procedure is started by setting the initial opti-mal control input to zero and repetitively applyingEq. 5 until the optimal control input converges. Theresulting control vector is the optimal control vectorfor the given weighting matrices.

Vibration Measure and Control Input

In this study, the control law is used to simultane-ously reduce the 4/rev components of the hub loads.Therefore, the vibration vector z contains the sineand cosine components of the three 4/rev hub shearsand the three 4/rev hub moments.

The vibration control is implemented through anactively controlled trailing edge flap on the blade.The flap deflection is composed of 2, 3, 4 and 5/revharmonic components and can be expressed as:

/ -;

N=2[6Nccos(Nil>) (7)



It is assumed that all four rotor blades are identicaland that the actively controlled flap on each bladeexecutes the same motion for a given blade azimuthangle.

The control input u used for vibration reductionin the control algorithm is the vector containing thecosine and sine amplitudes of the N/rev nap deflec-tion harmonics. This vector is given by:

(8)

Constraining Flap Deflection

Three different methods for limiting flap deflectionto account for actuator saturation are studied. Twoof these methods take the computed unconstrainedoptimal control and obtain the limited flap deflec-tion history in one step through either truncation oramplitude scaling. The first method simply clips theflap deflection at the limiting amplitude for any op-timal control command that exceeds this maximumvalue. The flap deflection is thus described by:

6iimit, \6opt(i/j)\ > 8iimit

(9)or if the limit of minimum deflection differs from thelimit of maximum deflection,

< Smin

(10)

The second method for limiting flap deflection uni-formly scales down the optimal control flap deflec-tion. Each harmonic component of the optimal flapdeflection is scaled by a common factor to limit themaximum flap deflection to the desired amplitude.For this case, the flap deflection is described by:

(11)max(\Sopt\)

where max(\6opt\) is the maximum amplitude of theoptimal flap deflection over the entire range of bladeazimuth values.

In the first two limiting methods, no constraintsare imposed on the flap deflection through the useof the weighting matrix, Wu, in the optimal controlcalculation. Though the sole purpose of the weight-ing matrix, Wu, is to constrain flap deflections, it isnot possible to know a priori the proper weightingmatrix that constrains the flap deflection amplitudeto be within prescribed limits. A third flap ampli-tude limiting method was developed where a new

control procedure automatically adjusts the weight-ing to properly constrain the flap deflection ampli-tude. The structure of the new procedure is com-pared to the two previous limiting methods in Figure2.

In the new control procedure, the optimal controlu* is calculated for a given set of parameters in thesame way as in the old method. However, after theoptimal control is obtained, the maximum and min-imum flap deflections for the given control are calcu-lated. The maximum and minimum flap deflectionsare compared to the prescribed limiting values and atest is performed to determine whether the flap de-flections are properly constrained. This test consistsof ensuring that the maximum flap deflection is lessthan the limiting maximum value and the minimumflap deflection is greater than the limiting minimumvalue. An additional test is performed such thatthe difference between one of the flap deflection ex-tremes, minimum or maximum, and its correspond-ing limiting value must be within a user defined cdegrees. This additional criterion ensures that theflap is not over constrained and allows the full al-lotted control authority for vibration reduction. Ifthe flap deflection is overconstrained or undercon-strained, the weighting matrix is appropriately mod-ified to relax or tighten the flap deflection constraint.The new weighting matrix is input into the opti-mal control calculation routine and the procedurerepeats until the flap is properly constrained.

For this new control procedure, a simple form ofthe weighting matrix is used. The weighting matrixis assumed to be a scalar times the identity matrix.The weighting matrix is therefore described by:

W — r Tu — ^-wu-*- (12)

All harmonic components of the flap deflection areequally weighted. The controller manipulates thescalar multiplier to provide the proper flap con-straints. If the flap deflection is over constrained,the controller reduces the value of cwu and a newoptimal control is calculated. If the flap deflection isunderconstrained, the controller increases the valueof cwu and a new optimal control is calculated. Theiterative procedure reduces or increases cwu until theoptimal control converges to the desired deflectionlimits within a prescribed tolerance.

Results

Simulations were performed for both a low speedcondition, fi — 0.15, and a higher cruise speed con-dition, IJL — 0.30, using quasi-steady aerodynamics.



The results are obtained for a four bladed rotor con-sisting of straight, hingeless blades having the prop-erties given in Table 1. Each actively controlledtrailing edge flap has a chord length one quarter thatof the blade chord and a span of 12% of the bladespan, centered about the 3/4 blade span location.

Low Speed Results

For the \JL = 0.15 flight condition, vibratory hubloads for a number of test cases are shown in Fig-ures 3 and 4. Two values of maximum flap deflectionare investigated for their influence on vibration re-duction capabilities of the actively controlled flap.Results with a maximum flap deflection of 2 degreesare shown in Figure 3 while Figure 4 provides resultswith a maximum flap deflection of 4 degrees. Theuncontrolled, or baseline, 4/rev vibratory hub shearsand moments are presented in the figures along withthe results from four actively controlled flap simula-tions. The unweighted control results are obtainedby setting the control weighting matrices Wu andWAU identically to zero matrices. This produces abest case scenario for vibration reduction with nolimitation on either control amplitude or the rate ofchange of control amplitude from one control itera-tion to the next.

The flap deflection history as a function of az-imuth for the unweighted optimal control is shownin Fig. 5. The flap deflection is shown for the rangeof azimuth values from 0 to 360 degrees. Flap de-flection is periodic in this study so the flap deflectionis identical for each successive rotor revolution. Asseen in Fig. 3, the unweighted control flap deflectionsignificantly reduces vibratory hub loads from thebaseline values. Hub loads are reduced by a mini-mum of 24% for the yawing moment to a maximumof 98% for the vertical shear. Overall hub vibrationis reduced to 8% of the uncontrolled level. Howeverthe flap deflection history indicates that flap deflec-tion amplitudes of up to 19.5 degrees are required.This is much greater than what is currently achiev-able by adaptive materials based actuation of theflap.

The effects on vibration levels of limiting the flapdeflection to a maximum of 2 degrees through eitherthe clipping, scaling or automatic weighting meth-ods, as described previously, are shown in Fig. 3.With the clipping method, or 'truncated control',vibratory hub loads are reduced by a maximum of49% in yawing moment to an increase in verticalshear of 12%. The overall hub vibration level is re-duced by only 15%. The flap deflection history forthis control is shown in Figure 6. The flap deflection

history for the uniform scaling of the unweighted flapdeflection amplitude to a maximum of 2 degrees isshown in Fig. 7. This control input reduces vibra-tion levels from as little as 0% in the yawing mo-ment to as much as 15% in the lateral and verticalshears. Overall hub vibration is reduced to 87% ofthe uncontrolled value. Clearly neither of these flapdeflection limitation methods do a good job in re-ducing hub vibrations. The overall vibrations arefrom 10.7 to 11.0 times greater than the unweightedcontrol. The flap deflection history for the auto-matic weighting method is shown in Fig. 8. Withthe automatic adjustment of the control weightingmatrix, vibrations are reduced by a minimum of 8%in yawing moment to a maximum of 91% in longitu-dinal shear. Overall hub vibration is reduced to 36%of the uncontrolled level. Vibrations with the auto-matic weighting method are less than half of thoseobtained with either of the other two deflection lim-iting methods.

The effects on vibration levels of limiting the flapdeflection to a maximum of 4 degrees through thethree limiting methods are shown in Figure 4. Withthe unweighted flap deflection truncated at 4 de-grees, shown in Fig. 9, vibratory hub loads are re-duced by a minimum of 8% in vertical shear to amaximum of 90% in lateral shear. Overall hub vibra-tion is reduced to 54% of the uncontrolled value. Theflap deflection history for the uniform scaling of theunweighted flap deflection amplitude to a maximumof 4 degrees is shown in Fig. 10. With this control,vibratory hub loads are reduced by a minimum of 8%in pitching moment to a maximum of 30% in lateralshear. Overall hub vibration is reduced to 76% ofthe uncontrolled level. With the automatic adjust-ment of the weighting matrix to constrain maximumflap deflection to 4 degrees, vibratory hub loads arereduced by a minimum of 2% in yawing moment toa maximum of 97% in vertical shear. Overall hub vi-bration is reduced to 18% of the uncontrolled value.The flap deflection history for this control is shownin Fig. 11.

With a 4 degree deflection limitation, the clippingand scaling control methods reduce vibrations be-low the levels obtained with a 2 degree flap limita-tion. However, neither method reduces vibrationsto even half of the uncontrolled levels. The controlwith automatic adjustment of the weighting matrixproduces overall vibration levels that are one third ofthe clipping method vibrations and one fourth of thescaling method vibrations with the same maximumflap amplitude of 4 degrees.



High Speed Results

For the p, — 0.30 flight condition, vibratory hubloads are shown in Figures 12 and 13. As in the lowspeed case, two values of maximum flap deflectionare investigated for their influence on vibration re-duction capabilities of the actively controlled flap.Results with a maximum flap deflection of 2 degreesare shown in Figure 12 while Figure 13 shows re-sults with a maximum flap deflection of 4 degrees.The uncontrolled 4/rev vibratory hub shears andmoments are plotted in the figures along with theresults from four actively controlled flap simulationsas studied in the low speed case. The flap deflectionhistory for the unweighted optimal control is shownin Fig. 14. The flap deflection history indicates thatflap deflection amplitudes of up to 9.2 degrees arerequired for vibration reduction. Hub loads are re-duced by a minimum of 84% for the pitching momentto a maximum of 97% for the vertical shear. Overallhub vibration is reduced to 9% of the uncontrolledlevel.

The effects on vibration levels of limiting the flapdeflection to 2 degrees are shown in Fig. 12. The flapdeflection history for the unweighted optimal controltruncated at two degrees is shown in Fig. 15. Withthe truncated control, vibratory vertical shear is re-duced by 34% while all other components are greaterthan the uncontrolled values. The overall hub vibra-tion level is actually increased by 5%. The flap de-flection history for the unweighted control uniformlyscaled to a maximum of 2 degrees is shown in Fig. 16.This control input reduces vibration levels from aslittle as 21% in lateral shear and yawing momentto as much as 27% in longitudinal shear. Overallhub vibration is reduced to 76% of the uncontrolledvalue. As with the low speed case, neither of theseflap deflection limitation methods do a good job inreducing hub vibrations.

The flap deflection history for the automati-cally adjusted weighting matrix method is shown inFig. 17. With this control, vibration levels are re-duced by a minimum of 64% in pitching moment toa maximum of 91% in longitudinal shear. Overallhub vibration is reduced to 15% of the uncontrolledlevel. This vibration reduction is significantly bet-ter than either of the other two deflection limitingmethods. The overall vibration is less than a fifththe level of the other two methods.

The effects on vibration levels of limiting the flapdeflection to a maximum of 4 degrees through thethree limiting methods are shown in Figure 13. Withthe unweighted flap deflection truncated at 4 de-grees, shown in Fig. 18, vibratory hub loads are re-

duced by a minimum of 12% in lateral shear to amaximum of 85% in vertical shear. Overall hub vi-bration is reduced to 59% of the uncontrolled value.The flap deflection history for the uniform scaling ofthe unweighted flap deflection amplitude to a maxi-mum of 4 degrees is shown in Fig. 19. With this con-trol, vibratory hub loads are reduced by a minimumof 38% in rolling moment to a maximum of 49% inlongitudinal shear. Overall hub vibration is reducedto 59% of the uncontrolled level. The flap deflec-tion history for the control with the automatic ad-justment of the weighting matrix to constrain maxi-mum flap deflection to 4 degrees is shown in Fig. 20.With this control, vibratory hub loads are reducedby a minimum of 79% in pitching moment to a maxi-mum of 97% in vertical shear. Overall hub vibrationis reduced to 10% of the uncontrolled value. This re-duction in overall hub vibration is nearly the same asthat of the unweighted optimal control but requiresa maximum flap deflection that is less than half thatof the unweighted optimal control. This overall vi-bration level is one sixth that of the vibrations fromeither of the other two limited flap amplitude controlmethods with the same maximum flap deflection of4 degrees.

It is evident that neither of the two simple flap de-flection limiting methods, clipping or amplitude scal-ing, provides the optimal control flap deflection fora given maximum amplitude of deflection. The au-tomatic adjustment of the control weighting matrixperforms much better in vibration reduction thanthe two other methods of deflection limiting.

Concluding Remarks

Simulations on a rotor with actively controlledtrailing edge flaps were conducted to investigatethe influence on vibration reduction of actuatorswith limited ability to produce flap deflection. Thestudy considered a four bladed rotor with hingeless,isotropic blades incorporating fully coupled flap-lag-torsional dynamics. Simultaneous reduction of thevibratory hub moments was achieved through theminimization of a quadratic performance index con-sisting of weighted squares of vibration magnitudesand control amplitudes. Three means of limitingthe maximum flap deflection were investigated. Themost important conclusions obtained in this studyare summarized below:

1. The actively controlled, partial span, trailingedge flap with no constraints on control effortprovides significant reduction of the 4/rev vi-bratory hub loads. For both low and high speed



cases, overall vibrations were reduced to lessthan 10% of the uncontrolled levels. This un-weighted control required flap deflections thatare unachievable with the current state of theart in adaptive materials based actuation. Atan advance ratio of p, — 0.15, flap deflections ofup to 20 degrees were required. These deflec-tions are much greater than the expected max-imum deflections with current adaptive materi-als of less than 5 degrees.

2. Two simple methods for limiting the amplitudeof flap deflection were investigated, clipping andamplitude scaling. Neither method proved ac-ceptable for vibration reduction. Scaling theoptimal unweighted control down to a limitingmaximum deflection reduced all six componentsof the vibratory hub loads for both speed con-ditions considered in this study but the vibra-tion reduction was only marginal. The clip-ping method of limiting flap amplitude actuallycaused increased vibration levels in many hubload components. Even with a maximum flapdeflection of 4 degrees, neither method could re-duce vibrations to one half of the uncontrolledvalue.

3. A new control procedure for vibration reductionwith limited flap deflection authority was devel-oped. In this procedure, the control weight-ing matrix is adjusted automatically by thecontroller until the resulting flap deflection iswithin prescribed limits. With this method, vi-brations are significantly reduced at both for-ward flight speeds considered in the study.Overall hub vibration was reduced to 10% of theuncontrolled level at p, — 0.30 with a maximumflap deflection of 4 degrees. This reduction invibrations is nearly the same as that achievedby the unweighted optimal control that requiredflap deflections of 9.2 degrees.

References

[1] Millott, T. A. and Friedmann, P. P. , "Vibra-tion Reduction in Helicopter Rotors Using anActively Controlled Partial Span Trailing EdgeFlap Located on the Blade," NASA CR-4611,1994.

[2] Milgram, J. and Chopra, I. , "Heli-copter Vibration Reduction with Trail-ing Edge Flaps," Proceedings of the 35thAIAA/ASME/ASCE/AHS/ASC Structures,

Structural Dynamics and Materials Conference,New Orleans, LA, April 1995.

[3] Myrtle, T. and Friedmann, P. P. , "UnsteadyCompressible Aerodynamics of a FlappedAirfoil with Application to Helicopter Vi-bration Reduction," Proceedings of the 38thAIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference,Kissimmee, FL, April 1997, pp. 224-240.

[4] Friedmann, P. P. and Millott, T. A. , "VibrationReduction in Rotor craft Using Active Control:A Comparison of Various Approaches," Journalof Guidance, Control, and Dynamics, Vol. 18,No. 4, 1995, pp. 664-673.

[5] Splettstoesser, W. R. , Schultz, K. J. , vander Wall, B. ', Buchholz, H. , Gembler, W. ,and Niesl, G. , "The Effect of Individual BladePitch Control on BVI Noise - Comparison ofFlight Test and Simulation Results," Proceed-ings of the 24th European Rotorcraft Forum,Marseilles, France, September 1998, pp. AC.07l-AC.07-15.

[6] Spangler, R. L. and Hall, S. R. , "PiezoelectricActuators for Helicopter Rotor Control," Pro-ceedings of the 31st AIAA Structures, Struc-tural Dynamics and Materials Conference, LongBeach, CA, April 1990, pp. 1589-1599.

[7] Bernhard, A. and Chopra, I. , "Trailing EdgeFlap Activated by a Piezo-Induced Bending-Torsion Coupled Beam," Journal of the Amer-ican Helicopter Society, Vol. 44, No. 1, January1999, pp. 3-15.

[8] Fulton, M. V. and Ormiston, R., "Small-ScaleRotor Experiments with On-Blade Elevens toReduce Blade Vibratory Loads in ForwardFlight," Proceedings of the 54th Annual Forumof the American Helicopter Society, Washing-ton, DC, May 1998, pp. 433 - 451.

[9] Prechtl, E. F. and Hall, S. R. , "Design of aHigh Efficiency Discrete Servo-Flap Actuatorfor Helicopter Rotor Control," Proceedings ofthe 1998 SPIE Conference on Smart Structuresand Integrated Systems, San Diego, CA, March1997.

[10] de Terlizzi, M. and Friedmann, P. P. , "Aeroe-lastic Response of Swept Tip Rotors Includingthe Effects of BVI," Proceedings of the 54th An-nual Forum of the American Helicopter Society,Washington, DC, May 1998, pp. 644-663.



[11] Yuan, K. A. and Friedmann, P. P. , "Aeroelas-ticity and Structural Optimization of Compos-ite Helicopter Rotor Blades with Swept Tips,"NASA CR-4665, 1995.

[12] Johnson, W. , A Comprehensive AnalyticalModel of Rotorcraft Aerodynamics and Dynam-ics, Vol. I: Theory Manual. Johnson Aeronau-tics, Palo Alto, CA, 1988.

[13] Scully, M. P. , "Computation of HelicopterRotor Wake Geometry and its Influence onRotor Harmonic Airloads," Ph.D. Disserta-tion, Aeroelastic Research Laboratory, Mas-sachusetts Institute of Technology, 1975.

[14] Johnson, W. , "Wake Model for Helicopter Ro-tors in High Speed Flight," NASA CR-177507,1988.

[15] Johnson, W. , "Self-Tuning Regulators forMulticyclic Control of Helicopter Vibrations,"NASA TP-1996, 1982.

[16] __, IMSL Library: Reference Manual. IMSLInc., Houston, TX, 1980.

Table 1: Soft-in-plane Isotropic Rotor Blade Data

Rotor DataEIy/mtt2R4 = 0.0106

4 = 0.0301- 0.001473

nb = 47 = 5.5a = 0.07Helicopter DataCw = 0.00515

= 0.50= 0.0

Flap DataLcs = 0.12L6xcs = 0.751/6

a = 2?rPP = 0.0cb/R = 0.055

Cdo = 0.01ZFA/R = 0.25XFA/R = 0.0

Ccs = Cb/4

DeformedBlade

DeformedElastic Axis

Undeformed

UndeformedElastic Axis

Figure 1: Fully elastic blade model incorporating apartial span trailing edge flap.

Automatic control weighting

Figure 2: Flap deflection limiting methodologies

Figure 3: Vibratory hub loads with 2 degree satura-tion - IJL = 0.15



FHX FHY FH2 MHX MHY MHZ

10

120 180

Figure 4: Vibratory hub loads with 4 degree satura-tion - p, = 0.15 Figure 7: Scaled to 2 degrees flap deflection as a

function of azimuth - ^ = 0.15

I

240

Figure 5: Unweighted flap deflection as a functionof azimuth - p, = 0.15 Figure 8: Flap deflection with 2 degree limiting au-

tomatic weighting - /x = 0.15

wr60 / 120 240

Figure 6: Unweighted flap deflection truncated at 2 Figure 9: Unweighted flap deflection truncated at 4degrees - p = 0.15 degrees - // = 0.15



108

^ 6

•o8- -4E

-6

-8

-10

Figure 10: Scaled to 4 degrees flap deflection as afunction of azimuth - IJL = 0.15

FHZ MHX MHY MHZ

Figure 13: Vibratory hub loads with 4 degree satu-ration - IJL = 0.30

A /N360

Figure 11: Flap deflection with 4 degree limitingautomatic weighting - // = 0.15

Figure 14: Unweighted flap deflection as a functionof azimuth - // = 0.30

FHX FHY MHX MHZ

Figure 12: Vibratory hub loads with 2 degree satu- Figure 15: Unweighted flap deflection truncated atration - p =. 0.30 2 degrees - ^ = 0.30



jjj 4

S 2

c

*:-8

-10

t 2 \O n \

V240

Figure 16: Scaled to 2 degrees flap deflection as a FiSure 19: Scaled to 4 degrees flap deflection as afunction of azimuth - IJL = 0.30 function of azimuth - // = 0.30

&C

360

Figure 20: Flap deflection with 4 degree limitingFigure 17: Flap deflection with 2 degree limiting automatic weighting - ji = 0.30automatic weighting - // = 0.30

Figure 18: Unweighted flap deflection truncated at4 degrees -1* = 0.30


01-25208 structural dynamics, and materials conference

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