flutter suppression

8/2/2019 Flutter Suppression

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Table 1 - Sensitivity to Aeroelastic Frequency and Control Effectiveness - Symmetric Mode (Dynamic Pressure = 300 sf)1

&ain = -4dB

~

ob=bendingmode freauency uT=torsionmode frequency S = stable U=unstable

PredictedSensitivity to Modeling ErrorsSensitivity analyses were performed to address the impact of

several forms of modeling error. Two analyses which hadimportant implications for the success of the FSS control lawwillbe discussed here. The first sensitivity analysis addressedthe effects of uncertainties in control surface effectiveness andthe aeroelastic frequencies of the tw o structural modes that ledto flutter. The second sensitivity analysis addressed the effect ofperforming flutter suppression in combination with rapid rolling

maneuvers.The nonlinear simulation model was used to evaluate theStability of the closed-loop system at a dynamic pressure of300 psf subject to simultaneous variations in the frequencies ofthe two key aeroelastic modes and variations in controleffectiveness. This was accomplished by separating theaerodynamic stiffness terms from the in vacuo vibrationfrequencies and perturbing the aerodynamic stiffnesses byf 1 0 percent. Variations in control effectiveness wereapproximated by varying control law gain by f4 B.

The results of this analysis applied to the symmetricdynamics are presented in Table 1. The results suggest that thesymmetric controller was somewhat sensitive to a simultaneousincrease in the bending mode frequency and decrease in thetorsion mode frequency. The instability associated with thelower left hand matrix elements in Table 1 denotes thissensitivity. With the above noted exception, the controller was

predicted to be robust to errors in the critical aeroelastic modefrequencies and control effectiveness.The second sensitivity analysis was performed to assess Ihe

possibility that performing both flutter suppression and rollcontrol might require more control activity than the actuatorswould be able to produce. The approach to assess possibleinteractions was toconsider th e impact of a worst case scenarioas follows. The FSS contro: iaws used the TEOsurfaces as theirprimary control. The deflection limits imposed on the rollingmaneuver controller commands were f 1 0 degrees. A typicalrolling maneuver involved initiating a roll, sustaining it for ashort period, and then stopping in less than 1.0 second from thetime of initiation. Based on these factors, a worst case rollcommand (from the perspective ofthe FSS) was chosen to be a10 degree doublet to the TEO surface with a period of about 1 Osecond.A simulation of the AFW wind-tunnel model was driven by

the roll doublet and wind-tunnel turbulence while the FSScontroller was operating at a dynamic pressure of300psf. Sincethe model was free to roll the antisymmetric control channel wasopen. Consequently, the FSS controller generated onlysymmetric commands whereas the roll controller generatedpurely antisymmetric commands.

During the simulated roll maneuver some rate limitingoccurred. However, the limiting only affected one side of theAFW wind-tunnel model at each instant and only for very short

periods of time on the order of0.05second. For comparison.the time to double amplitude ofthe flutter mode at a dynamic

pressure of300 psf is approximately 0.14 second. When the rollcommand requiredmaximum control surface rate (to initiate orstop the roll), one TEO surface moved up and the other moveddown at the rate limit. The symmetric flutter suppression

controller simultaneously commanded control deflections thatcaused both TEQ control surfaces (left and right) to move in thesame direction. Therefore, the side that was commanded byboth controllers to move in the same direction experienced ratelimiting. The other surface, however, operated below the ratelimit. The flutter suppression control law never becamecompletely ineffective due to rate limiting. It did. however,momentarily loose some effectiveness since it was, in effect,only operating on one side of the vehicle at a time. As a result,

some ofthe gain margin was "used up" during the periodofratelimiting. The FSS controller had no difficulty maintainingsystem stability subject to the simulated worse case roll doublet.

Wind-Tunnel Test ResultsTwo wind-tunnel tests were performed using the FSS

controller. The first test (Fall 1989)was aimed at performingplant estimation, flutter clearance tests, and validating theperformance of active flutter suppression controllers and rollingmaneuver controllers individually. The second test (winter1991) was aimed at more extensive flutter suppression androlling maneuver control tests, and validating the combinationof flutter suppression and rolling maneuver control.

The FFS control law succeeded in suppressing the singlesymmetric flutter mode when the vehicle was free to roll andsimultaneously suppressing two flutter modes (symmetric andantisymmetric) when the vehicle was fixed in roll. The flutter

dynamic pressure was increased by over 24 percent when themodel was fixed in roll and by over 23 percent when the modelwas free to roll.

In the fixed-in-roll case, oscillatory structural deflectionscaused loads that were in excess ofpreset safety limits. Theexcessive loads occurred at a dynamic pressure of272 psf atwhich point testing was curtailed. The experimental datasuggest that the controller stability limit had not been reached,the controller was providing sufficient damping to maintainstability. The oscillations, though sustained enough to exceedthe safety limits, were stable.

In the free-to-roll case, the maximum dynamic pressure of thewind-tunnel (290 sf ) was reached making further increases indynamic pressure impossible. However, the FSS controller wasperforming as predicted. Extrapolation of the experimental datapredicted that the dynamic pressure could have been increasedto approximately 330 psf before closed-loop instability would

occur. It should be noted. however, that safety limits wouldlikely be exceeded before the stability limit could be attained, aswas the casewhen the model was fixed in roll.

The control activity that was required to achieve thedemonstrated levels offlutter suppression was less than half thedesign requirement. Figure 10 presents a comparison of theactual and predicted RMS control activity for the free -to-rollcase. The peakRMS control rate was less than 15 degrees persecond, which is well below the predicted level. This is anindication that the turbulence model used in the controlsynthesis was conservative at dynamic pressures above 200 psf.It is possible that higher gains could have been used to exploitthe available control activity and improve controllerperformance. However, the gain values were based more onobtaining uniform stability margins than on limiting control

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5 0 I00 150 200 250 10 0 150DVNAYK: PRESSURE (W)Figure 10 Comparison ofcontrol activity (roll brake off).

I E ~ . L * ~ M I

Figure 11 Comparison of Nyquist plots - Z ~ P(g's).activity. Higher gains would also have led to smaller stabilitymargins which would have beenundesirable.

Another measure of performance of the FSS controller wasthe level ofstability indicated by the Nyquist plots depicted inFigure 11. These plots were obtained from experimental datausing the method described in Wieseman. et al. (1992) andPototzky. et al. (1990). Plots for the symmetric AFWffSSsystem at three dynamic pressures are presented: 175 psf. whichis well below open-loop flutter; 225 psf, which is very close toopen-loop flutter; and 275 psf, which is well beyond open-loopflutter. Plots for the antisymmetric AFWFSS system at threedynamic pressures are also presented: 150 psf, which is wellbelow open-loop flutter: 200 psf. which is very close to open-loop flutter; and 250psf, which iswell beyond open-loop flutter.Nyquist plots based on the mathematical model of the AFWwind-tunnel model are shown for comparison.

The demonstrated gain margins are well in excess of the

-14dB required. The positive phase margins exceeded the14 4

requirement. but the negative phase margins were slightlysmaller than -30degrees. Some ofthediscrepancy between thepredicted and actual phase margins can be attributed to theeffects ofdigital implementation of the controller . The phaseshift between the predicted and experimental results is almostentirely attributable to a time delay ofone-half sample period,approximately 0.0025 second. Th e predicted Nyquist plotsincluded an approximation of the effective time delay whichwas conservative by approximately one-half sample period.

The FSS controller was combined with a rolling maneuvercontroller [Moore,et al. (1992)J to demonstrate the ability toperform flutter suppression while performing rapid rollingmaneuvers. The test involved performing rapid rollingmaneuvers over a range ofdynamic pressures both below andabove flutter. At a dynamic pressure of260 psf(25 psf beyondopen-loop flutter). the rollingmaneuver controller accomplisheda 90degree roll. starting from rest, in less than 0.5 second. Thetime to double amplitude of the flutter mode at this dynamicpressure was approximately 0.24 second. The fluttersuppression controller had no difficulty maintaining stabilityduring the rolling maneuver. The control activity and vehicleresponses suggested no significant differences between the FSSperformance in either steady ormaneuvering flight.

DiscussionPlant identification was performed during both wind-tunnel

tests. The experimentally determined open-loop flutter dynamicpressures were 235 and 219 psf for the symmetric andantisymmetric modes, respectively. The experimentallydetermined flutter frequencies were 9.6 and 9.1 Hertz for thesymmetric and antisymmetric modes, respectively. Theantisymmetric flutter mode data corresponds to the conditionwhen themodel was fixed in roll. Notice that the predictedvalues differ from those estimated wing experimentaldam. Thepredicted flutter dynamic pressures were nonconservative in thatthey overpredicted the observed values. The error in thepredicted flutter frequencies were 16.7 and 19.8 percent for thesymmetric and antisymmetric modes. respectively.

Transfer functions for key input-output pairs at subcriticaldynamic pressures (i.e. below flutter) were determined prior toclosing the loop with the FSS controller. This allowed thecontrol designers to study the accuracy of the design models andto assess the impact ofmodeling errors before. the FSS controllerwas used to suppress flutter. Similar transfer functions weredetermined after the control loops were closed to evaluate theaccuracy of the model at post-flutter conditions using themethod described in Wieseman, et al. (1992) and Potokky. et al.

Figure 12 presents two representative transfer function plotsfor the tip accelerometer response due to andsymmetric TEOcontrol surface deflection with ihe model fixed in roll. Theanalytical resulls correspond lo the mathematical modelobtained by linearizing the nonlinear simulation model atconditions consistent with the test data. The experimental datawas obtained from the 1991 wind-tunnel test Figure 12(a)corresponds to a dynamic pressure of 150 psf. which is wellbelow the flutter dynamic pressure. The plot in Figure 12@)corresponds to a dynamic pressure of225psf, which is slightlyabove the actual flutter dynamic pressure.

In both cases there is general agreement, however, there arealso notable differences between the experimental data and theanalytical results. One of the most notable differences is theshift in the frequencies of the key aeroelastic modes. InFigure 12@) the poles, which corresponded in vacuo to the firstbending and first torsion modes, occur at frequencies below thepredicted values. As a result, flutter occurred at a frequencyapproximately 1.8 Hertz lower than predicted. Similardiscrepancies occurred for the symmetric responses [Waszakand Srinalhkumar (1991)).

Another difference between the analytical and experimentalfrequency responses are the peak magnitudes. The differencesnearthe flulter frequency varyfrom 3 to 10 dR over a range ofdynamic pressure from IS0 psf to 225 psf. As a result, theactual control effectiveness in the flutter frequency range wasconsiderably less &an what was predicted. This effect isclearly

(1990).


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flutter suppression

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