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NASA Technical Memorandum 107652
FLUTTER SUPPRESSION DIGITAL CONTROL
LAW DESIGN AND TESTING FOR THE
AFW WIND-TUNNEL MODEL
Vivek Mukhopadhyay
July 1992 N92-31350
(NASA-TM-I07o52} FLUTTER SUPPRESSIQN _[G[TAL CONTROL LAW UESIGN AND TESTING FOR THE AFW Unclas WINn-TUNNEL MODEL (NASA) 8 p G3/05 011_55
NASA
National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23665-5225 r_ e FLUTTER SUPPRESSION DIGITAL CONTROL LAW DESIGN AND TESTING FOR THE _-TUNNEL MODEL Vivek Mukhopadhyay * NASA Langley Research Center, Hampton, Virginia 23665 Abstract I. Introduction Design of a control law for simultaneously suppressing the A summary of the Active Flexible Wing (AFW) Program is mmetric and antisymmetric flutter modes of a sting mounted presented in Ref. 1. Within the operating range of the Langley ed-in-roll aeroelastic wind-tunnel model is described. _ Research Center Transonic Dynamics Tunnel, the sting mounted flutter supJ_ression control law was designed using linear _kFW aeroelastic model had both symmetric and antisymmetric quadratic Liaussian theory, and involved control law order flutter modes, in a fixed-in-roll configuration, and a symmetric reduction, a gain root-locus study and use of previous flutter mode only, when the model was in a free-to-roll experimental results. A 23% increase in the open-loop flutter Configuration. The active flutter suppression system (FSS) test dynamic pressure was demonstrated during the wind-tunnel test.
goals were to demonstrate: a) simultaneous symmetric and Rapid roll maneuvers at 11% above the symmetric flutter antisymmetric flutter suppression for the fixed-in-roll boundary were also performed when the modelwas in a free-to- configuration, and b) symmetric flutter suppression in the free- roll configuration.
to-roll configuration. An additional goal was to test a rolling maneuver loadallevjation system along with the FSS above the Nomenclature open-loop flutter boundary. Since the free-to-roll symmetric flutter and the fixed-in-roll symmetric and antisymmetric flutter A,B control law state-space matrices modes had very similar characteristics, a single FSS control law C,D control law output matrices was designed and demonstrated for both the flutter test Bo Kalman state estimator gain matrix configurations, a) and b) as stated above. This paper addresses
Co
optimal regulator gain matrix the mathematical modeling, control law design and wind-tunnel E test results.
expectation operator F,G plant state-space matrices Gw II. AFW Equations of Motion gust input matrix g gravitational acceleration constant H The description of the AFW aeroelastic wind-tunnel model and sensor output matrix I the wing-tip ballast stores, including details of the accelerometer identity matrix M Mach number sensor positions and multiple control surface actuation P estimator Riccati equation solution capabilities are provided in Ref. 2. The accelerometer sensors q and the control surface locations on the wing-plan form are dynamic pressure, psf qf shown in figure 1. The development of the aeroelastie equations flutter dynamic pressure, psf QI of motion is described in Ref. 3. The equations for the plant output weighting matrix Q2 symmetric and antisymmetric motion were developed separately, control input weighting matrix Rv using ten flexible modes for each configuration. The flexible measurement noise intensity matrix Rw gust input noise intensity mode shapes and natural frequencies were derived from a finite- S regulator Riccati equation solution element modal analysis and were corrected using ground S Laplace variable vibration test data.
T sample period, seconds t time, seconds Inches U control input vector 50 - V measurement noise vector W gust input noise O) frequency, radians/second X plant state vector Xc control law state vector measurement vector Y accelerometer output, g's 7O control surface angular position, degrees Subscripts:
•
LEI wing leading edge inboard 80 - LEO wing leading edge outboard TEI wing trailing edge inboard TEO wing trailing edge outboard tip wing tip 90 - Abbreviations: AFW active flexible wing CL closed loop !
tO0 CPE controller performance evaluation 0 10 20 Inches 30 40 5011 FSS flutter suppression system L(_ linear quadratic Gaussian OL open loop psf pounds per square foot RMLA rolling maneuver load alleviation rms mot mean square Figur_ 1. Accelerometer and control surface locations on AFW SISO single-input single-output wing plan form.
*Associate Fellow, AIAA imaginary part _¢:_: A set of state-space mathematical models --100 were developed for control law design 3. For the aeroelastic equations, the doublet-lattice oscillatory aerodynamics mode 4 --90 filter mode approximation used four aerodynamic lag terms for each flexible mode. In addition, the state-space models included corrections --80 for control surface effectiveness based on results from the 1989 mode 3 wind-tunnel test 2, and the third-order transfer functions of the 4 5 6 actuator dynamics derived from ground test of the unloaded --60 control surfaces. A Dryden gust spectrum transfer function, NO.
mode2 3
driven by a white noise process was used to simulate the random --50 100 psi .,_.._ i vertical gust of the wind-tunnel. The Complete linear equations 150 " 6 1 of motion at a specified dynamic pressure were expressed by the --40 3 200 state-space equations, 250 " J --30 300 " mode 1 dx/dt = Fx + Gu + Gww (1) 6 350 " --20 and y -- Hx+ v (2) open-loop --10 closed-loop where x is the state vector, u is the control input vector, w is the
I I
I I I__ 1 gust input noise, y is the accelerometer sensor output vector, and 0 5 10 -2o -15 -10 -5 v is the measurement noise vector. Equations (1) and (2) were scaled such that the units of the control inputs were in degrees, real pad the units of the sensor outputs were in g's, and the gust input units were in feet/second.
Figure 2. Symmetric open- and closed-loop dynamic pressure root-locus at M=0.5 (arrows indicate increasing Open-loop dynamic pressure root-locus: Using these state-space dynamic pressure).
mathematical models at six dynamic pressures, q = 100, 150, 200, 250, 300 and 350 psf, the flexible-mode toot'loci with imaginary part dynamic pressure were studied. The open-loop, dynamic -100 pressure root-locus of the first four flexible symmetric and antisymmetric modes, for the fixed-in-roll configuration, are -90 shown in figures 2 and 3, respectively. The figures 2 and 3 mode 4 filter mode _ -80 indicate that the second and third flexible mode frequencies coalesced to produce the flutter instability. The unstable mode --__"_,x 1 2_3 _7_ mode3 was primarily wing-tip torsion, for both the symmetric and the antisymmetric motions. The sixth and seventh symmetric 6 5 -60 5 6 flexible mode frequencies also tended to coalesce (not shown in figure 2). At Mach 0.5, the analytical open-loop symmetric No. Dyn. pressure mode 2 -50 flutter dynamic pressure was estimated to be 248 psf at 11.2 Hz.
100 psf 1 The analytical open-loop antisymmetrie flutter dynamic pressure I50 " 6 1 I -40 3 200 " was estimated to be 233 psf at 10.9 Hz. The closed-loop 4 250 " mode 1 -30 dynamic-pressure root-locus is also shown in figures 2 and 3 5 300 " and will be discussed later.
6 350 " -20 III. Control Law Design • open-loop -10 x closed-loop
I
I ...... 1_ I I
The flutter suppression design objective was to develop low- -20 -15 -10 -5 0 5 10 order robust digital control laws which would simultaneously suppress the symmetric and antisymmetric flutter modes of the real part model in the fixed-in-roll configuration with allowable control surface activity. The maximum permissible control surface rms Figure 3. Antisymmetric fixed-in-roll open- and closed-loop deflection and rates were 1.0 degree (at 11.2 Hz flutter dynamic pressure root-locusat M=0.5 (arrows frequency) and 75 degrees/second, respectively. From the 1989 indicate increasing dynamic pressure).
test 2, the antisymmetric flutter frequency was known to be 1.8 Hz below the theoretical value. The control law was also required to be sufficiently robust to compensate for this '_ dght and left Z tip difference.
right and left &rr=o _ _ sensor output, g input, degrees . . .
= .(_ _ .._ant,ahas,ng_ The FSS control laws were designed using linear quadratic Gaussian (LQG) theory and involved control law order reduction, a gain root-locus study, and use of previous experimental results 2. Since the symmetric and antisymmetric flutter modes had very similar characteristics for the fixed-in-roll configuration (see figures 2 and 3), a single FSS control law Sym FSS I n _ . right I was designed to suppress both the flutter modes. This control taw used the grip pair of accelerometers and the TEe pair of
control surfaces on the right and left wings. The block diagram I- c°+°"a* ' -
for digital implementation 2 of the symmetric and antisymmetric FSS control laws [s shown in Figure 4. The accderometer _ff_J__ I control law I_ left outputs from the left and right wing were passed through 25 Hz fast-order antialiasing filters, modeled by the transfer function 157/(s+157) and converted into digital data at a sampling rate of 200 Hz. The digital eontroller separated the data into symmetric Figure 4. Digital FSS control law implementation block and antisymmetric components, computed the digital control law diagram.
In the residualization procedure, only the steady state part of the outputs and then distributed the processed feedback signals to stable higher frequency dynamics in equation (5) were retained.
the right and left actuators after 0.005 seconds computational This was acco_mplished by setting the state derivative dxc2/dt to delay.
zero and solving for Xc2, provided the matrix Ao2 is Design plant model: The 68thorder antisymmetric state-space nonsingular (Ref. 4). The reduced state space model of the equations at q = 350 psf for the fixed-in-roll configuration was control law is given by equations (7) and (8).
used as the design plant model, since from the analysis and the dxc/dt = AXc + B y (7) 1989 test, the antisymmetric flutter mode was found to be most critical and was encountered at a lower dynamic pressure, than u -- Cxc+Dy (8) the symmetric flutter mode. The accelerometer sensors and where control surfaces were selected based on the frequency response xc = Xcl, B = Bol, C = Col analysis of the open-loop system. The _'Eo and Zdp and D = - Co2 Ao2 "! Bo2.
accelerometer responses were predominant at the wing-tip torsion frequencies due to the excitation from TEl and TEO This procedure introduced a direct feedthrough matrix D in control surfaces. In addition, the _tip sensor exhibited relatively equation (8). The residualized Ihh-order control law was subsequently reduced to a second-order control law by balanced low response at frequencies above 25 Hz. Therefore, ZTEO and realization and truncation of the balanced system. The balanced 2tip accelerometer sensors and TEl and TEO control surfaces realization procedure finds a linear transformation in which the were initially studied as candidates for measurement inputs and control law states have equal controllability and observability control outputs, respectively.
properties 4. The weakly controllable and observable states are then truncated. Even with the elimination of these states, the Full order LOG design: A full order LQG control law was_ resulting set of equations retained the most important input- designed using the design plant model state-space equations (i) output characteristics of the original system. This second-order, and (2). The full-order LQG control law which is given by two-input two-output control law, is given by equations (9) and equations (3) and (4), minimizes a weighted quadratic cost (10).
function defined by E[yTQly + uTQ2u], where Q1 and Q2 are the plant output and control input weighting matrices 4,5, (9) dxo/dt = Aoxc + Boy, (3)
6,61iI ,,9,1{e}
dt [-64.6 -5.2 xc + -0.45 -0.73 u = Coxc, (4) where Ao = [F - Boll + GCo] (10) {_TI_ } [--0.4 2.1 ] [ -0.06 -0.091I.' ".Zr_ 8"too = 3.6 -9.4 xc + 0.13 0.21 J[Ztlp j Bo = pHTRv -l Co = - Q2" IGTS.
The corresponding Bode diagrams of the four components of this 2x2 control law are shown in Figure 5. This figure indicates The matrices Bo and Co are the Kalman state estimator gains that the maximum gain of this control law was 2.5 deg/g (8 dB) and the full-state optimal regulator gains, respectively. The with a peak gain at 10.3 Hz. The primary stabilizing gain of this matrices P and S are the positive definite solution of the steady control law was from the sensor _tip. to the control surface 5r_o.
state dual matrix Riccati equations, given by Although this control law stabilized the symmetric and antisymmetric plant models at 350 psf, the step responses FP + PF T + GwRwGw T - pHTRv'IHp = 0 contained high frequency components. With the addition of 25 Hz antialiasing filters to each accelerometer channel, the high SF+tTS+HTQI H- SG Q2-1GTS -- 0, frequency components of the step responses were eliminated.
However, with the addition of T=0.005 second computational where Rw and Rv denote the intensity matrices of the gust delay ( modeled by the first-order Pade approximation input and measurement Gaussian white noise processes, w and (2rl'-s)/(2/T+s)), the system was marginally stable. It was also v, respectively. To obtain the LQG control law, full-state noted that, when this control law was reduced to a single-input optimal regulator gain matrix Co was first determined using a single-output (SISO) control law by retaining only the congol unit output weighting matrix, Qt = I, and a control weighting matrix Q2 = 0.001 I, where I is a 2x2 identity matrix. Then the law input Ztip and the output 8TEO the nominal design plant was Kalman state estimator gain matrix Bo was determined using Rw also stable. This simplified SISC) control law was therefore, studied further in order to compensate for the computational = 0 and Rv = I. The final selection of these weighting and noise delay effects, and possible uncertainty in the actual flutter intensity matrices for the full order control law, and the frequencies, as mentioned earlier.
subsequent order reduction process were determined after several design iterations, until a stabilizing low order controller was found for the nominal design plant model. The control law 10 F _TELr_ 1_)(Sk_O) I order reduction process is described next.
Order Reduction: The full 68th order LQG control law given by equations (3) and (4) was first biock-diagonalized, and then reduced to 11 th order by residualization of all the damped modes above 19 Hz. Equations (3) and (4) in block-diagonalized form, are shown in equations (5) and (6), where the vector Xcl represents the retained states and the vector Xc2 represents the remaining states associated with the damped higher frequency dynamics.
Phase,
,oL
d ,fx_tl, [_o 0 IJXcll+[Bo, 1
d-t"[xe2J = t Ao2J_xe2 _ L o2j y (5) Frequency, Hz u =[ Co,c .tfxc, l, ozSx¢2 j (6) Figure 5. Bode diagram of reduced, second-order control laws.
imaginary part second-order notch filter, given by the transfer function (s2+42s+44100)/(s2+84+44100 ), was added to increase the - 350 = = _ :" symmetric model gain margin to 6 dB, near 33 Hz. This filter _ "_'_. _ g ain= 0.75 deglg attenuated a 33 Hz lightly damped oscillation due to the - 3uu TEO actuator pole mode 10 CK interaction of the sixth and seventh symmetric flexible modes. A mode 9 first-order washout filter, given by the transfer function s/(s+6) was also added to remove any steady state input bias to the mode 8 sensor signal.
mode 7 mode 6 200 The resulting 5th order SISO control law in Laplace domain was discretized using the Tustin transformation z = (1 +sT/2)/(1-sT/2), where T is the sampling interval. For the - 150 200 Hz sampling rate used by the digital controller, T = 0.005 mode 5 _, seconds. With the Tustin transformation at this sampling rate, - 100 the Bode diagrams in the Laplace domain and the discrete mode 4 domain were almost identical below 15 Hz. Hence no frequency warping corrections were applied.
- 50 mode 3 mode 1Oil Dynamic-pressure root-locus: The open- and closed-loop dynamic pressure root-locus plots are compared in figures 2 and ! I I 1 I -20 -t5 -10 -5 0 5 10 3. These comparisons indicated that both the symmetric and antisymmetric models were stable, up to dynamic pressure q = real part 350 psf. The closed-loop frequency decoupling was due to Figure 6. Gain root-locus plot for negative feedback from _tip to lowering of the frequency of mode 2 to about 6.8 Hz. The frequency of mode 3 was increased to 11.6 Hz, but the damping 8TEOat 350 psf, antisymmetric fixed-in-roll ratio was only of the order 0.010 at 300 psf.
configuration (x = poles, o = zeros, * indicates gain increment by 0.1).
Sensitivity studies: The closed-loop system sensitivity was studied by perturbing the second and third modal frequencies in • L_IlI_gLL_: This simplified SISO control law (plot the state-space block-diagonalized plant model by +10% and the nominal gains by +4 dB at q = 250 psf and examining the labeled by iS'Tr.O/_tip, in figure 5) was improved further via gain closed-loop system step responses, for all possible augmentation. Therequired gain level was determined using a combinations. These studies indicated that the design could gain root-locus analysis. The output gain feedback root-locus of accommodate simultaneous gain and frequency changes for all "the design plant model at 350 psf, with qSTEO as plant input, and cases except when the second and third mode frequencies were _tip as plant output, is shown in figure 6. This root-locus perturbed to approach each other. Sensitivity studies were also indicated that, the open-loop unstable pole (mode 3) near 11 Hz done using the state-space model with and without the 25 Hz migrated into the stable left half plane, with a negative feedback antialiasing filters, with and without one cycle delay, with additional delays, and with + 6 dB gain perturbations at 250 psf.
gain of 1.3 deg/g from _qip to qSTEO. However, the actuator poles These studies indicated that the symmetric configuration could near 50 Hz become unstable at a gain of 0.75 deg/g. Therefore, tolerate one additional delay (or phase lag of 1.8 degree,VHz) at a gain level of at least 1.3 deg]g in the 8 to 12 Hz frequency half the nominal gain, but the antisymmetric configuration would range, with subsequent gain attenuation at higher frequencies become unstable with an 11 Hz oscillation. The phase and gain was necessary to stabilize the system, and accommodate the margin comparisons with the experimental results, described in f_ossible difference between the analytical and experimental the next section, indicated that this particular situation may have utter frequencies. In addition, compensation for the phase lag been encountered during the experiment. The gain toss was effects of the antialiasing filter and one cycle computational delay apparent from the experimental Bode diagram, was also required, The total phase lag introduced by these two effects, was about 40 degrees at the frequency 10 I-Iz.
IV. Summary of Test Results The gain and phase compensations were achieved by varying the Qpen-loop Flutter: Based on examination of the peak-hold data three elements of C and D in the SISO control law, and studying obtained during the wind tunnel test with the tip ballast store the gain and phase diagrams and the closed loop stability coupled, the open-loop (OL) flutter dynamic pressures were as responses. An increase in CI and decrease in IC21resulted in a follows: The free-to-roll OL symmetric flutter was at a dynamic desirable phase increase at low frequencies. An increase in D, pressure of 235 psf, at a frequency of 9.6 Hz. The fixed-in-roll reduced the phase (towards zero) at high frequencies, which was OL antisymmetric flutter was at a dynamic pressure of 219 psf, also beneficial. These three parameters were varied, until a gain- at a frequency of 9.1 Hz. These experimental symmetric and level near 1.3 deg/g (2.3 dB) was maintained over the frequency antisymmetric OL flutter dynamic pressures were, respectively, range 8 to 12 Hz, and sufficient phase lead was obtained. The 13 and 14 psf below the predicted values, and the flutter real part of the control law complex pole was also moved from - 5.2 to - 6.0 to achieve a widergain range. The high frequency frequencies were, respectively, 1.6 Hz and 1.8 Hz below the predicted values.
gain was kept below 0.75 deg/g. This modified SISO control law is given by equations (I I) and (12), assuming negative feedback.
Open-loop frequency responses: Figures 7 and 8 show the OL frequency responses of Y'tip due to iSTEO from analysis and experiment at 250 psf, forthe symmetric and antisymmetric d'-'_" = -64.6 xc + --0.73j Zap (11) (fixed-in-roll) cases, respectively. At this dynamic pressure, the OL plant is unstable. So, the OL frequency responses were computed from closed-loop (CL) experimental data, using the &trio = [ 14.4 -3.1]xc + 0.63 ztip (12) Controller Performance Evaluation (CPE 6,7) procedure. Figure 7 indicates good agreement below 9 Hz and qualitative The corresponding gain and phase plots are shown in figure 5 agreement above 12 Hz. Above 12 Hz, the magnitudes differ by and are labeled 5TEO/:gtip (SISO). The complex poles and zeros aDout 5 dB while the phase angles are nearly equal. Figure 8 of this control law were -6+_j64.6 and -30+_j56, respectively. A indicates fair agreement, below 7 Hz, and qualitative agreement 3O II sensor and control surface for FSS 2O
(9 [] sensor and control surface for RMLA
Magnitude. o gvdeo (riB) tO -2O -30
S J
.,..._.------
®
300 -- Phase.
degrees 0 -100 Augmented q / _ - / 3 , ncrease 260 - -200 _ ,_ul I I I I I I I I HOII maneuver/lll--/"l above qf 2 4 6 B 10 12 14 16 18 20 _ . -/10"/, , q, psf Frequency. Hz Figure 7. Comparison of Ztip / 8TEO Bode diagrams at 250 psf, 220 - symmetric configuration.
_ymmetr7 I I 180 -
:F
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o--.%
0.0 0.3 0.4 0.5 -1o I- _ -...1.."" " v ....
-20 _--/J"J'Y experiment Mach number
.301" i 10 I l I I ! I I
Figure 10. Summary of results for free-to-roll RMLA/FSS wind-tunnel test.
200100 _ _I ,ana_/s_s Closed-loop Tests: The active flutter suppression test results are -I00 / ,.-JU ,xpo,tmo.t _ g - - r summarized in figures 9 through 13. Figures 9 and l0 show the -200/ " I I I I ' I l I I ,J wind-tunnel test dynamic pressures versus the free stream Mach 2 4 6 8 10 t2 14 16 18 20 number. During the wind-tunnel test, in the fixed-in-roll Frequency. Hz configuration, with both the symmetric and antisymmetfic FSS control laws operating, the CL system was stable up to q = 270 Figure 8. Comparison of Yaip / iSTEO Bode diagram at 250 psf, psf, at Mach 0.46. This augmented q represents a 23% increase antisymmetric fixed-in-roll configuration.
over the eL antisymmetric qf.
above 12 Hz. Above 12 Hz, the magnitudes differ by 6 to 8 dB During the wind-tunnel test, in the free-to-roll configuration, and the phase angles differ by 10 to 20 degrees. Note, that for with the symmetric FSS control law operating, the CL system each phase diagram, the 180 degree crossing occurs near the was stable up to q = 290 psf, at Mach 0.48. This augmented q respective OL flutter frequencies, and the difference between represents a 23% increase over the OL symmetric qf as shown their predicted and experimental values is quire apparent.
in figure 10. This FSS control law also suppressed the flutter when a Rolling Maneuver Load Alleviation (RMLA 8) system 300 - was tested with rapid roll maneuvers at q = 260 psf, 11% above the OL symmetric flutter boundary. This RMLA control law used LEO and TEl control surfaces, so the interaction with the FSS control law was minimal.
260 - Augmented q/-_-- " _ .. / 23 % Increase The rms deflection and deflection rate of the fight and left side q, psf _ymmetrlc qf 1( above qf TEe control surface were computed from the data sampled at 200 Hz at each fixed-in-roll FSS test condition. If the value of 220 - the right and left differed, the maximum is plotted in figure 11.
The maximum rms deflection and rates were less than 0.4 Antlsym q/ I degrees and 25 degrees/second, respectively. These maximum 180 - rms deflection and rate demands of the actuators were well below the maximum allowable values of I deg and 75 deg/sec as q stated earlier in the paper.
I I I
o--._
The Nyquist-diagram-based gain- and phase-margins were 0.3 0.4 0.5 0.0 estimated using the CPE technique, during the experiment.
Mach number These estimates Were compared with corresponding analytical quantifies in figures 12 and 13, for the symmetric free-to-roll and the antisymmetric fixed-in-roll configurations, respectively.
Figure 9. Summary of results for fixed-in-roll FSS wind-tunnel For the symmetric, free-to-roll configuration (figure 12), the test.
analytical and experimental gain margins were above _+6 dB up
0.4 - 40 ,-
to 270 psf. The analytical positive phase margins (at or below 7
5rms Hz) were about 20 degrees, but the negative phase margins (at
6rms
or above I2 Hz) were well above 45 degrees. The analytical
deg
deg/s
phase margins were close to experimental results up to about m
0.2
270 psf.
For the antisymmetric, fixed-in-roll configuration (figure 13), the analytical negative gain margins were only -3 dB.The analytical positive phase margins (at or below 7 Hz) were about
o.o- 0-% I I I I
20 degrees, but the negative phase margins (at or above 12 Hz)
0 180 220 260 300
were 45 degrees. The analytical phase margins were close to the
q, psf experimental data at 250 psf, because the design model was
fairly accurate at frequencies below 7 Hz (see figure 8). The negative gain and phase margins at the high frequency end were Figure 11. Maximum 8q_o control surface deflection and rates primarily responsible for preserving the system stability. The demands for simultaneous symmetric and source of additional phase lag with increasing dynamic pressure antisymmetfic flutter suppression tests.
was possibly due to highly loaded actuators. The gain loss was 201 m apparent from the experimental Bode diagram shown in figure 8 in the 8 to 12 Hz frequency range.
1D B V. Conclusions
- - _
Oaln A single-input single-output control law was designed for flutter ,., I I I I I I I I mst_|n, suppression using linear quadratic Gaussian theory and involved dB v 160 18O 20O _"_0 _00 O'ynamlc pm_um, pd control law order reduction, a gain root-locus study and use of previous experimental results. The control law was digitally -10 implemented and tested. Simultaneous suppression of symmetric and antisymmetric flutter modes in close proximity was demonstrated to 23% above the open-loop antisymmetric flutter boundary when the model was in a fixed-in-roll configuration.
I _ i ! [ ] a r m l y s l m I • ,xperln_nl Symmetric flutter suppression system operating simultaneously with a rolling maneuver load alleviation system was tested to 23% above the open-loop symmetric flutter boundary, when the 2o 0 model was in a free-to-roll configuration. With this combined rrlllrgln, 0 system, rapid roll maneuvers were also performed at 11% above the symmetric flutter boundary.
References 1 Perry, B. HI, Cole, S. R and Miller, G. D., "A Summary of the _ctive Flexible Wing Program,' AIAA Paper 92-2080, presented at the 1992 Dynamics Specialists Meeting, April 16- 17, 1992.
2 Perry, B. III, Mukhopadhyay, V., Hoadley, S. T., Cole, S.
Figure 12. Gain and phase margin comparison (symmetric).
R., Buttriil, C. S. and Houck, J. A., "Digital Implementation, B Simulation and Testing of Flutter-Suppression Systems for the 2O Active Flexible Wing Wind-Tunnel Model," AIAA Paper 90- lS 1074, Proc. of 31st AIAA SDM Conference, Long Beach, CA, April 1990.
3 Buttrill, C. S., Bacon, B. J., Heeg, J. and Houck, J. A., m e,*ln "Simulation and Model Reduction for the AFW Program," mi_Dln, S d8 AIAA Paper 92-2081, presented at the 1992 Dynamics Specialists Meeting, April 16-17, 1992.
_, I I I i I I 1 l
160 180 2O0 220 240 :_kO 28O 300, 4 Maciejowski, J. M., Muhfvariable Feedback Design, Addison Wesley Publishing Co., Great Britain, 1989.
-- Dyn*mle pro.urn, _f _ Q 5 Bryson, A. E., Jr, and Ho, Y. C., Applied Optimal Control, -10 Hemisphere Publishing Corporation, Washington, 1975.
-- [ [] ,m.lysl. I
6 Pototzky, A. S., Wieseman, C. D., Hoadley, S. T. and 6O [ • expert.m! ] Mukhopadhyay, V., "Development and Testing of Methodology for Evaluating the of Performance of Multi- input/multi-output Digital Control Systems," AIAA Paper 90- Phase 20 3501, presented at the AIAA Guidance, Navigation and Control mr_tn,O Conference, Portland, Oregon, August 1990.
_'g"?2o
7 Pototzky, A. S., Wieseman, C. D., Hoadle_,, S. T. and Mukhopadhyay, V., "On-line Performance of Multi-loop Digital -40 Control Systems", Journal of Guidance, Control, and Dynamics, Vol. 15, No. 3, May-June, 1992 (TBP).
-.
8 Woods-Vedeler, J. A. and Pototzky, A. S., "Rolling -80 Maneuver Load Alleviation Using Active Controls," AIAA _ m -1(_ Paper 92-2099, presented at the 1992 Dynamics Spe_cialists Meeting, April 16-17, 1992.
Figure 13. Gain and phase margin comparison (antisymmeu'ic, fixed-in-roll).
Form Approved
REPORT DOCUMENTATION PAGE O_e _o ozo.o,aa
T _OhC reDor_lr_C bU raen for this cOllectiOn of inform&riO fl _ ._'[imil_ed t3 _verage _ _o_r D_r "-asPorse rrc]udi_g the t_me _¢r rewew_ng InstrudJo_$, _earc_'li_g e:(_$t_nCjl data source_ oather,na and mamta_nmq the data ne@_l_, and comDIetmg an¢l re_,e_ng the c311e_ion of mfcrmatlo_ r_end comments regarding t_is burden estimate or any other a_c_ of this _olle_qonof _nfor_atlOf_._nc_udmg $ugge_tiOn_ for reduohg th_s D_rcle_ to _Wlsh_hgtO_ Headquarters _er_ces, D_reC_otate fOr _nformat_on Ogera_On_, and Report_,, I2 _5 _ef_erso_ 0av_s H_g_way. Surte 12_4, A¢ ngtOn. _A 22202-4302 and to the Off,ce 3f Management and B_cfge_ =a_3_rwork Redu_On Project (07_4-0 tB8), Washington, DC 205(_3 1. AGENCY USE ONLY'(Leave blank) 2. REPORT DATE ' 3. REPORT TYPE AND DATES COVERED
Jul 7 1992 Technical Memorandum
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Flutter Suppression Digital Control Law Design and
Testing for the AFW grind-Tunnel Model WU 505-63-50-15
6. AUTHOR(S)
Vivek Mu_op_hyay
8. PERFORMING ORGANIZATION
7. PERFORMING ORGANIZATION NAME(S) ANDADDRESS(ES)
REPORT NUMBER
NASA Langley ResearchCenter
Hampton, VA 23665-5225
Tli 10. SPONSORING /MONITORING 19. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AGENCY REPORT NUMBER
National Aeronautics and Space Administration
NASA TM- 107652
Washington, DC 20546-0001
11. SUPPLEMENTARY NOTES
Presented as AIAA Paper No. 92-2095-CP at the AIAA Dynamics Specialists' Conference, Dallas, Texas, April 16-17, 1992.
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Unclassified - Unlimited
Subject Category 05
13. ABSTRACT {Maximum 200 words) Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind-tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory and involved control law order reduction, a gain root-locus study, and use of previous experimental results. A 23-percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind-runnel test.
Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.
15 NUMBER OF PAGES 14. SUBJECT TERMS Active Flexible Wing flutter suppression; aircraft aeroelastic model; 16 PRICE CODE reduced order IA_ design; symmetric and antisymmetric mode flutter;, wind-tunnel multifunction test , H. • 20. LIMITATION OF ABSTRACT 17, SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19, SECURITY CLASSIFICATION OF REPORT OF THIS PAGE OF ABSTRACT
Unclassified Unclassified
S:andard gorm 298 {Rev 2-8g) NSN 7540-0_-2B0-5500 P,e$cri_ I_y AN_ r_t_ Z39-1B 29E-_02