Document
NASA Technical Memorandum 86808 NASA-TM-8680819860016868
Aeroelastic Control of Oblique-Wing
Aircraft
John J. Burken, Gurbux S. Alag, and Glenn B. Gilyard
....
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111111111111111111111111111111111111111111111 National Aeronautics and NF00057 Space Administration 3 117601308 6716 NASA Technical Memorandum, 86808
Aeroelastic Control of Oblique-Wing
Aircraft
John J Burken Ames Research Center, Dryden Flight Research FaCIlity, Edwards, California Gurbux S Alag Western Michigan UniVersity, Kalamazoo, Michigan Glenn B Gilyard Ames Research Center, Dryden Flight Research FaCIlity, Edwards, California
NI\S/\
National Aeronautics and Space Administration Ames Research Center Dryden Flight Research FaCIlity Edwards, California 93523 AEROELASTIC CONTROL OF OBLIQUE-WING AIRCRAFT John J. Burken* NASA Ames Research Center Dryden F11ght Research Facl11ty Edwards, Callfornla Gurbux S. A1ag** Western Mlchigan Unlverslty Kalamazoo, Mlchlgan Glenn B. Gl1yard* NASA Ames Research Center Dryden F11ght Research Facl11ty Edwards, Ca11fornla ABSTRACT f(t) forclng functlon 1n tlme dOmaln The U.S. Navy and NASA are currently lnvo1ved J quadrat1c cost cr1terlOn In the deslgn and development of an unsymmetrlc- skew-wlng alrcraft capable of 65° wlng sweep and K regulator galn matr1x, or genera1- f11ght at Mach 1.6. A generlc skew-wlng alrcraft lzed stlffness matrlx model was developed for 45° wlng skew at a f11ght L, Ll condltlon of Mach 0.70 and 3048 m a1tltude. At robust and ordlnary Kalman estlma- thlS f11ght condltlon the alrcraft has a wlng tor galn matrlces, respectlve1y flutter mode. An actlve lmp1ementab1e control law M genera11zed mass matrlx was developed uSlng the 11near quadratlc Gausslan deslgn technlque. A method of modal resldua11za- tlon was used to reduce the order of the control- pressure dlstr1butlon of the Jth PJ ler used for flutter suppresslon. mode SYMBOLS Q state welghtlng matrlx , A plant matrlX Q(S) matrlx of approxlmated aerodynamlc force coefflclents coefflclent matrlces of unsteady aerodynamlc force approxlmatlon Q1J(S) the (1 ,J) element of a matrlx of functlons due to a mode A, B, C, D reduced-order controller state- q vector of genera11zed coord1nates space matrlces R control welghtlng matrlx control and nOlse dlstrlbutlon matrlces, respectlve1y s Laplace operator modal system lnput matrlces T moda 1 matrlX correspondlng to the low- and hlgh-frequency parts of A 1nput vector u lag coefflclents Uc controller output C state-space output matrlx Vg gust ve10clty modal system output matrlces x, X state vector and estlmated state correspondlng to the low- and vector, respect1vely hlgh-frequency parts of A output vector Y D genera11zed damplng matrlx mode shape of the 1th mode Zl forclng functlon In the s plane F(s) * Aerospace Englneer.
Oa, control surface def1ect1on and OaC ** Assoclate Professor, E1ectrlcal surface command, respectlvely Englneerlng Department.
random whlte nOlse excltatlon n TIll, paper 15 declared a work ot the U S Goyernment and thcrdorc IS In the public domam a gust cal1brat1on factor 3. robust output feedback control law determ1nat10n; m1n1mum slngular values of the return d1fference matr1x 4. reduced-order (pract1cal) control law formulat1on; and A slm1lar1ty transform matr1x 5. evaluat10n of the pract1cal control law.
low- and h1gh-frequency parts of A, respectlVely MATHEMATICAL MODELS w1ng gust 1nput A1rcraft Model The gener1c obl1que-w1ng a1rcraft model used zero-mean wh1te n01se errors in 1n the system synthes1s process cons1sts of a the measurements slmple beam representat10n of the fuselage and w1ng. The structural model and the aerodynam1c INTRODUCTION panel1ng requ1red for the unsteady aerodynam1cs are represented 1n F1g. 2.
Interest 1n obl1que-w1ng a1rcraft des1gns has surfaced per1od1cally Slnce the 1940s. However, The a1rcraft modal character1st1cs were devel- not unt1l recently has the 1nterest, technology, oped uS1ng NASTRAN analys1s. At the selected and m1SS1on of an obl1que-w1ng des1gn evolved 1nto sweep conf1gurat10n (45°) and fl1ght cond1t10ns a full-scale fl1ght research program. The U.S.
(Mach 0.70, 3048 m alt1tude), the unaugmented Navy and NASA are currently 1n the des1gn and a1rcraft has a flutter mode character1zed as pr1- development stage of 1mplement1ng an obl1que w1ng mar1ly w1ng bend1ng but w1th some tors1on. The on an F-8 fuselage (F1g. 1) and evaluat1ng the 1n-vacuum mode shape character1st1cs of the w1ng conf1gurat10n to a maX1mum sweep of 65° and to alone are presented 1n F1g. 3 for the mode that Mach 1.6.
lS driven to the flutter cond1t10n w1th 1ncreas1ng dynam1c pressure.
The unsymmetr1c conf1gurat10n and forward sweep of one sem1span result 1n aeroelast1c Because the 1ntent of th1S paper lS to pre- behaV10r d1st1nctly d1fferent than that of sent a des1gn synthes1s process, the model order stra1ght, swept-back, or swept-forward w1ngs.
was reduced cons1derably; the f1nal model con- It should be noted that 1n add1t1on to unsym- ta1ned a r1g1d-body (pr1mar11y p1tch) mode along metr1c model1ng character1st1cs, unsymmetr1c w1th three elast1c modes. The model reduct10n conf1gurat1ons w1ll tYP1cally have slgn1f1- process d1d not slgn1f1cantly affect the flutter cantly larger plant formulat10ns Slnce all mode character1st1cs.
degrees of freedom must be adequately repre- sented. Separat10n of an unsymmetr1c model The formulat1on of the complete, 1ntegrated 1nto two smaller models (as 1S poss1ble for (structures, aerodynam1cs, and controls) state- symmetric and ant1symmetr1c modes of a sym- space model for use 1n the analys1s and des1gn metr1c a1rcraft) lS not poss1ble, because the process follows that of Peele and Adams [2]. The response mot10n lS coupled and not separable.
aeroelastic equat10ns of mot10n for the flex1ble a1rcraft can then be represented as To evaluate the analyt1cal tools requ1red for the analys1s of an obl1que-w1ng conf1gurat1on, a gener1c skewed-w1ng model was developed. Th1S
Mq + Dq + Kq = f(t) (1)
model was used for the control system synthes1s procedure descr1bed 1n th1S paper. The conf1g- where the matr1ces M, 0, and K are the general1zed urat10n selected has a w1ng skew of 45° at a mass, damp1ng, and st1ffness matr1ces, respec- fl1ght cond1t10n of Mach 0.70 and 3048 m alt1tude t1vely, q lS the vector of general1zed coord1- (a dynam1c pressure of 23,892 N/m2).
nates, and f(t) 1S the vector of unsteady aero- dynam1c forces; the dots denote d1fferent1at1on.
Th1.s paper demonstrates the control synthes1s Transform1ng to the Laplace doma1n Y1elds des1gn process requ1red to develop a pract1cal control law for stab1l1zat1on of the flutter mode.
(Ms2 + Os + K)q(s) = F(s) (2) Th1S process 1nvolves where s lS the Laplace operator and F(s) 15 the 1. formulat1on of the state-space model aerodynam1c forc1ng funct10n 1n the s plane. The 1nclud1ng 1ndependent w1ng actuators, a Dryden unsteady aerodynam1c forces can be expressed as gust model [1], and s-plane approx1mat1ons of unsteady aerodynam1cs; F(s) = Q(s)q(s) (3) 2. opt1mal full-state control law determ1nat10n; where the matrlx Q(s) contalns the generallzed It lS assumed that the actuators have suffl- aerodynamlc force coefflclents. The lndlvldual Clent power throughout the frequency range of elements of Q(s) are functl0ns of both alrcraft lnterest and that aerodynamlc hlnge moments and mode shapes and pressure changes resultlng from lnertlal cross coupllng do not affect control motlon In the varl0US modes. The elements are surface posltion.
deflned as Gust Model The followlng second-order Dryden gust model [1] was also lncorporated In the mathemat- where zl(x,y) lS the mode shape of the ith mode ical model: and PJ(x,y,s) lS the pressure dlstrlbutlon of the ~ = a 0.273(1 + 4.1145) Jth reduced frequency determined from a 11ftlng (7) n (s + 0.421)2 surface theory. Under the subsonic condltl0ns relevant to thlS study, the unsteady aerodynamlc where n is random excltatlon, a lS used to call- force coefflclents (elements of Q) were computed uSlng the doublet lattlce routlne contalned In the brate the gust lntenslty (to 1 ft/sec In the cur- ISAC program [2,3]. Elght reduced frequencles rent example), and Vg lS the output gust veloclty.
were used, coverlng the range of 0 to 1.2 rad/sec.
However, thlS procedure Ylelds aerodynamlc forces State-Space Eguatlons only for pure harmonlC motl0n, and therefore only a flnlte number of frequencles can be selected.
The deslgn model lS obtalned by comblnlng the As a result, tabulated aerodynamlc forces are alrcraft (1ncludlng the 11nearlzed form of the expressed as a functlon of frequency. To apply unsteady aerodynamlcs), the actuators, and the modern control technlques, the tabulated aero- gust model dynamlcs and can be represented In the dynamlcs must be expressed In state-space form.
state-space equatl0n form as If analytlc contlnulty 1S assumed, the aerodynamlc data can be expressed as a ratlonal functlon
x = Ax + BIU + B2wg (8)
approxlmatlon [4], such as, y = Cx + IL\n (9) n
Q(s) = AO + Als + A2S2 + L Au2[S/(S + b.d]
1.=1 where x lS the state vector, wg the wlng gust lnput (unlt whlte nOlse), Wm the measurement (5) nOlse, u the control input vector (2 x 1), and y the measurement vector (3 x 1); A, Bl, B2, and C where AO to An+2 are coefflclent matrlces of are plant equatlon, control, nOlse dlstrlbutlon, unsteady aerodynaml c force and b 1. are "l ag" coef- and state-space output matrlces, respectlvely, of flclents. A least squares approach can then be sUltable dlmenslons. The state vector contalns used to determlne the matrlces AO, AI, A2, ••• , 24 states, lncludlng the rlg1d body mode, flexlble mode deflectlons, flexlble mode rates, unsteady An+2. The lag coefficlents bl, b2, ••• , bn are aerodynamlc states, actuator deflectl0n and rate selected speclflcally for the analysls; the number states, and wlnd gust states. Elght states result of lag terms and thelr values are lmportant In from the structural modes retalned, elght from the obtalnlng good approxlmatlons of the tabulated two-lag-term set of approxlmated unsteady aerody- aerodynamlcs. In the obllque-wlng deslgn model namlCS, SlX from the two actuators, and two from descrlbed in thlS paper, two lag terms were used the gust model. The three outputs are the acce- In generatlng the s-plane flt of the unsteady leratlons at the center of gravlty, rlght wlngtlp, aerodynamlcs. A typlcal flt of the approx;matl0n and left wlngtlp.
to the tabulated data for one element of the Q(s) matrlx lS presented In Flg. 4.
CONTROL LAW DESIGN Actuator Model Optlmal Controller Left and right wlng actuators were modeled The llnear quadratlc Gausslan (LOG) method lndependently because the synthesls process deter- lS vlable for the deslgn of multl-lnput multl- mlnes unlque control laws for each surface. The output controllers. The actlve control syn- followlng thlrd-order model relates the control thesls lS based on LQG theory but lS modlfled surface deflectl0n oa to the control surface com- to accommodate the hlgh-order model of the mand oac alrcraft [5,6]. The deslgn process lnvolves the followlng steps state-space model generatlon; Oa 54,080 full-state feedback deslgn, estlmatlon of states (6) from aval1able measurements, and development of 2] oac (s+20)[s2 + 2(0.7)52s + 52 reduced-order controller.
The state-space model of the alrcraft lS i = A.z + T-1ly (15) defined by Eqs. (8) and (9). A full-state feed- back control law, Uc -KTz (16) (10)
u = -Kx
where T 1S the modal matr1x and lS determlned by mlnlmlzlng a quadratlc cost func-
A = T-lAaugT
tlon [7] Aaug (A - BlK - LC) (11)
x Tz
ThlS can be expanded to where Q and Rare sU1table weight1ng matr1ces.
Because dlrect measurement of all states of an aeroelastlc system lS not feas1ble, lt 1S necessary (17) to estlmate states from ava1lable measurements. A Kalman f1lter lS used for estlmatlon of the states.
The estlmator dynam1cs are glven by (18) .
x = (A - BIK - LIC); + LlY (12)
where AI. A2. Bll. B2l. Cl, and C2 are the matr1-
where LI lS the Kalman est1mator galn matrlx and x
ces correspondlng to the low- and h1gh-frequency lS the vector of estlmated states. However, parts of the orlg1nal system matrlces. In the systems des1gned uSlng a Kalman est1mator are con- low-frequency portlon the dynam1cs are retalned, dlt10nally stable, have poor galn and phase mar- whlle In the h1gh-frequency port10n only the sta- glns, and have hlgh bandwldth [8]. The lnput t1C terms w1th zero response t1me assumed for the nOlse procedure of Doyle and Ste1n [9] can be used dynam1cs are retalned. Settlng i2 = O.
to synthes1ze a robust Kalman estlmator. Th1S procedure involves comprom1s1ng root-mean-square (rms) response act1vity aga1nst robustness. The (19) optlmal controller, Wh1Ch lS of the same order as the alrcraft model used for synthesls, and the Substltutlng Eq. (19) lnto Eq. (18), controller output uc are deflned as -1
. U = Clz - C (A B y) (20)
c l 2 2 2l x (A - BK - LC)x + Ly (13) Rewrltlng the reduced system.
(14)
- -
(21)
Alz + Blly = AZ + By
l I where L lS the robust Kalman estlmator galn matr1X.
Practlcal Controller -
Cz Dy (22) The full-order opt1mal controller cons1st1ng where of a robust Kalman est1mator together w1th Optl- mal state feedback ga1ns lmposes an unnecessarlly large 1mplementatlon cost. A reduced-order con- troller that approx1mates the full-order opt1mal controller can be found that lmposes llttle deg- radat10n 1n performance [10]. A modal resldual- B = B11 1zat10n technlque [11] can be used to reduce the order of the controller. An attempt lS made to C = C approXlmate the full-order controller w1th a lower-order approxlmat10n whlle ma1nta1n1ng the des1red character1st1cs of the orlg1nal control- ler. A slm1larlty transform A 1S employed on the full-order controller descrlbed by Eqs. (13) and (14) to obta1n A Kalman estlmator lS used to estlmate the The elgenva1ues of the reduced system are the states. The rms values for the control act1v1ty elgenva1ues retalned In the Al portlon. A block are glven 1n Table 1. The robustness, as lndl- dlagram of the plant and the reduced-order cated by the m1n1mum slngu1ar value plot of F1g. 7, controller lS presented In Flg. 5.
is relatively poor, WhlCh lS characterlstlc when uSlng an ordlnary Kalman est1mator [8J. A deslgn FLUTTER SUPPRESSION APPLICATION procedure descr1bed by Doyle and Steln [9J lS used to 1mprove the robustness of the Kalman estlmator.
The control law syntheslzed by the method ThlS method lnvo1ves app1Ylng extra process nOlse out11ned In the prevlous sectlon was app11ed to to the control lnput of the alrcraft durlng estl- the deslgn of an actlve flutter suppresslon mator deslgn. Flgure 8 shows the m1nlmum slngu1ar controller for an ob11que-wlng alrcraft. A value plot for the return dlfference matrlx for generlc 45°-wlng-skew structural model was devel- the estlmator deslgned uSlng the addltlonal nOlse oped to slmu1ate flutter at a subsonlc fllght (robust Kalman estlmator). The lmproved stabl11ty condltlon of Mach 0.70 and an altltude of 3048 m.
margln does lncrease the rms control actlv1ty (as The unstable elgenvalue palr at thlS fllght con- shown 1n Table 1), but lt lS stl11 wlthln the dltlon (0.50 ± J14.37) represents prlmarlly wlng speclfled 11mlts.
bendlng wlth some torslon.
Reduced-Order Controller The deslgn obJectlve was to stablllze the alrcraft wlthout exceedlng the speclfled rms The robust Kalman estlmator, together wlth control actlvlty so that saturatlon would not the optlma1 feedback galns, constltutes an Optl- occur. Based on actuator llmltatlons, the rms mal lmp1ementab1e controller. It lS, however, deflectlon of the alleron was llmlted to 5° and lmpractlca1 to lmp1ement thlS controller because the deflectlon rate to 30 deg/sec. In addltlon of the cost lnvo1ved. The cost of lmp1ementatlon to stabl11Z1ng the alrcraft wlth low surface can be reduced by deve10plng low-order approxlma- actlvlty, It lS requlred that the controller be tlons to the optlma1 controller; approxlmatlons robust. The controller consldered here lS are referred to as practlca1 or reduced-order mu1tl-lnput, mu1tloutput: The rlght and left wlng controllers. The reduced-order controller must control surfaces are lndependent of each other achleve closed-loop stabl11ty, have satlsfactory because of the unsymmetrlc nature of the alrcraft.
control actlvlty, and be robust.
Robustness of the mu1tl100p control system lS evaluated by uSlng the slngu1ar values of the A seventh-order controller was obtalned by return dlfference matrlx [12,13,14J.
uSlng the method of modal resldua11zatlon. Table 2 shows the elgenva1ues of the full-order robust Llnear Quadratlc Controller Deslgn controller and the elgenva1ues retalned In the reduced-order controller. Flgure 9 shows the step A full-order control law, ldentlcal to the LQG response of the full-order and reduced-order Solutlon, was obtalned flrst for comparlson pur- controllers and the extent of degradatlon ln the poses. Inltla1 values of the we1ghtlng matrlces Q response due to reduct1on.
and R of Eq. (11) were selected as null and lden- tlty, respectlve1y [6J. All stable elgenva1ues The rms control actlvlty for the reduced- remaln unchanged and all unstable elgenva1ues are order controller lS shown ln Table 1, and rotated about the lmaglnary aX1S [7J. Wlth the Flg. 10 lS a plot of mlnlmum slngu1ar values resu1tlng values of the full-state feedback galns, for th1S case. Even though there lS some the remalnlng deslgn process was executed (robust degradatlon caused by controller order reduc- output estlmatlon and controller reductlon).
tlon, the rms control actlvlty and the stabl11ty Though the rms control actlvlty of the reduced margln are consldered acceptable.
controller was wlthln speclfled 11mlts, the con- troller was not very robust. To lmprove the CONCLUSIONS robustness of the flna1 reduced controller, whlle stl11 retalnlng low surface act1vlty, parametr1c An lmp1ementab1e flutter controller for a varlatlons of Q and R were performed. A matrlx R 45°-skew ob11que-wlng alrcraft mathematlca1 model wlth values of 50,000 along the dlagona1 and a was deslgned uSlng the LQG deslgn methodology.
posltlve-deflnlte Q wlth values of 0.00001 along Kalman estlmators produced low stabl11ty marglns, the dlagona1 gave satlsfactory characterlstlcs.
however, the Doy1e-Steln procedure for robust The mlnlmum slngu1ar value of the return dlffer- estlmator deslgn can be used to lmprove these ence matrlx, ~, for full-state feedback was always marglns to acceptable values wlthout exceSSlve )1, as shown In Flg. 6, the rms control values are surface actlvlty. A modal resldua11zatl0n tech- given In Table 1.
nlque was used to obtaln a reduced-order con- troller that satlsfled the performance requlre- Full-Order Controller ments and can be lmplemented.
Because all the states are not aval1ab1e for New controllers wl11 be deslgned as lmproved feedback, lt lS requlred that all states be estl- models (based on the actual f11ght conflguratlon) mated so that regulator gains can be used. The of the ob11que wlng are made avallable. Actual controller Slze lS the same as that of the lmp1ementatlon may requlre galn schedullng as a aircraft plant, and wl1l be referred to as the functl0n of wlng skew as well as other parameters.
full-order controller.
REFERENCES 7. Kwakernaak, HUlbert, and Slvan, Raphael, "Llnear Optlmal Control Systems," Wlley- 1. Houbolt, John C., Stelner, Roy, and Pratt, Intersclence, New York, 1972.
Kerml t G., "Dynaml c Response of Al rp lanes to Atmospherlc Turbulance Includlng Fllght 8. Doyle, John C., "Guaranteed Marglns for LQG Data on Input and Response," NASA TR R-199, Regulators," IEEE Trans. Automat. Control, 1964.
vol. AC-23, no. 4, pp. 756-757, Aug. 1979.
2. Peele, Ellwood L., and Adams, Wllllam M., 9. Doyle, J.C., and Steln, G., "Robustness Wlth Jr., "A Dlgltal Program for Calculatlng the Observers," IEEE Trans. Automat. Control, Interactl0n Between Flexlble Structure, vol. AC-24, no. 4, pp. 607-610, Aug. 1979.
Unsteady Aerodynamlcs and Actlve Control," NASA TM-80040, 1979. 10. Gangsaas, D., Ly, U., and Norman, D.C., "Practlcal Gust Load Allevlatl0n and Flutter 3. Albano, Edward, and Rodden, Wllllam P., "A Suppresslon Control Laws Based on a LQG Doublet-Lattlce Method for Calculatlng Llft Methodology," AlAA-81-0021, Jan. 1981.
Dlstrlbutlons on Osclllatlng Surfaces ln Subsonlc Flows," AIAA J., vol. 7, no. 2, 11. Mahesh, J.K., Stone C.R., Garrard, W.L., and pp. 279-285, 1969. Hausman, P.O., "Actlve Flutter Control for Flexlble Vehlcles," NASA CR-159160, 4. Tlffany, Sherwood H., and Adams, Wllllam M., 1979.
Jr., "Flttlng Aerodynamlc Forces ln the 12. Safonov, Mlchael G., and Athans, Mlchael, Laplace Domaln: An Appllcatlon of a Non- llnear Nongradlent Technlque to Multllevel "Galn and Phase Margln for Multiloop LQG Constralned Optlmlzatlon," NASA TM-86317, Regulators," IEEE Trans. Automat. Control, 1984. vol. AC-22, no. 2, pp. 173-178, Apr. 1977.
5. Mahesh, J.K., Stone, C.R., Garrard, W.L., 13. Mukhopadhyay, V., and Newsom, J.R., and Dunn, H.J., "Control Law Synthesls for "Appllcatlon of Matrlx Slngular Value Flutter Suppresslon USlng Llnear Quadratlc Propertles for Evaluatlng Galn and Phase Gausslan Theory," J. GUldance Control, Marglns of Multlloop Systems," AIAA-82-1574, vol. 4, no. 4, pp. 415-422, 1981. Aug. 1982.
6. Mukhopadhyay, V., Newsom, J.R., and Abel, I., 14. ly, Uy-lOl, "Robustness Analysls of a Multl- "Reduced-Order Optlmal Feedback Control Law loop Fllght Control System," AlAA-83-2189, Synthesls for Flutter Suppresslon," J. GUld- 1983.
ance Control, vol. 5, no. 4, pp. 389-395, 1982.
Table 1 RMS responses at flutter condltlons Rlght wlng Left wlng cS, deg cS, deg/sec cS, deg cS, deg/sec Full-state feedback 0.28 1.58 7.91 3.58 Full-order controller 1.58 12.58 0.41 5.64 wlth Kalman estlmator Full-order controller 2.06 ll.21 0.41 5.02 wlth robust Kalman estlmator 1.51 10.04 0.41 4.90 Reduced-order controller Table 2 Full-order and reduced-order controller elgenvalues Full-order Reduced-order controller controll er elgenvalues elgenvalues -0.2531 + 0.00001 -0.2531 + 0.00001 -0.4578 + 0.08451 -0.4578 + 0.08451 -0.4578 - 0.08451 -0.4578 - 0.08451 -6.3566 + 0.00001 -2.5815 + 6.36171 -2.5815 + 6.36171 -2.5815 - 6.36171 -2.5815 - 6.36171 -0.3773 + 13.11041 -0.3773 + 13.11041 -0.3773 - 13.11041 -0.3773 - 13.11041 -3.4330 + 15.36501 -3.4330 - 15.36501 -20.0399 + 0.00001 -28.5469 + 9.70161 -28.5469 - 9.70161 -36.0773 + 0.32611 -36.0773 - 0.32611 -37.0844 + 2.44341 -37.0844 - 2.44341 -40.1968 + 1.37961 -40.1968 - 1.37961 -36.1567 + 37.22251 -36.1567 - 37.22251 -53.6588 + 0.00001 -34.5946 + 44.06571 -34.5946 - 44.06571
--z::::::- -
~
- ---
~---
-........... -------
-.............. ---
--------- Fig. 1 Oblique-~ng configuration.
VertIcal flO F~g. 2 Generic modeL (aero paneLs and node points). VerticaL f~n shown in X-I pLane.
o 0 Tabulated data • ApprOXImate data WIOg dIsplacement -1
o
-2~----------~------------~ ImaglOary Wmg rotation -5 Left RIght wmgtlp Real wIOgtlP Fig. 3 In-vacuum f1utter mode shape character- Fig. 4 Unsteady aerodyn~cs compa~son.
ist~cs at 2.239 Hz, 45° skew.
+ Y Plant
1+------ ....... Controller
Fig. 5 ctosed-toop system with ~educed-orde~ cont~oHe~.
Mlmmum 105 10,.----_ singular value, 1 04 Q 1.03 Minimum .8 singular value, Q 6 1.01 10 100 10 100 Frequency, rad/sec Frequency, rad/sec F~g. 6 M~nimum singuta~ vatues fo~ futt-state F~g. 7 Min~mum s~nguLa~ vaLues fo~ fuLt-orde~ feedback. cont~otte~ with KaLman estimato~.
Reduced·order controller (7 states) O~r-------------------- _ Full order controller (24 states) -2 1.0 ,..------.. Controller - 4 output signal, - 6 deg Mlmmum 8 -8 smgular value, -1.0 Q 6 -1.2 41...-_.L...-....L-.L...L~..LI.J._---''--.L...-L......L..J...L.1..I.J -141...---L---~---J----~----- 1 10 100 02345 Frequency, rad/sec Time, sec F~g. 9 step ~esponse compa~~son of futt-orde~ Fig. 8 M~nimum s~nguta~ vatues fo~ futt-orde~ cont~otte~ with ~obust KaLman est~mato~. cont~otte~ and ~educed-orde~ controtte~.
1 0 ,....-------., ..
MInimum 8 singular value, Q 4~--~~~UW~~--~~~~~ 1 10 100 Frequency, rad/sec F~g. 10 M~n~mum s~nguZa~ vaLues fo~ ~educed orde~ controLZe~.
3. RecIpient's Catalog No
1 Report No I 2 Government Accession No
NASA TM-86808 5 Report Date 4 Title and Subtitle AEROELASTIC CONTROL OF OBLIQUE-WING AIRCRAFT June 1986 6 Performing Organization Code 8. Performing Organization Report No 7. Author(s) John J. Burken, Gurbux S. Alag,* and Glenn B. Gllyard H-1346
1--------------------------------; 10 Work Unit No
9 Performing Organization Name and Address RTOP 533-02-91 NASA Ames Research Center 11 Contract or Grant No Dryden Flight Research Facility P.O. Box 273 Edwards, CA 93523-5000 13 Type of Report and Penod Covered 12. Sponsoring Agency Name and Address Technlcal Memorandum Natl0nal Aeronautlcs and Space Administratlon 14 Sponsonng Agency Code Washington, D.C. 20546 15 Supplementary Notes Prepared for presentatlon at the 1986 Amerlcan Control Conference, Seattle, Washington, June 18-20, 1986.
*Western Mlchigan Unlverslty, Kalamazoo, Michlgan 16. Abstract The U.S. Navy and NASA are currently lnvolved in the design and development of an unsymmetric-skew-wlng alrcraft capable of 65 wing sweep and fllght at Mach 1.6. A generlc skew-wing aircraft model was developed for 45 wlng skew at a fllght conditl0n of Mach 0.70 and 3048 m altltude. At this flight condltlon the alrcraft has a wlng flutter mode.
An actlve implementable control law was developed uSlng the llnear quadratic Gausslan deslgn technlque. A method of modal reslduallzation was used to reduce the order of the controller used for flutter suppressl0n.
17 Key Words (Suggested by Author(s)) 18 Dlstnbutlon Statement Actlve flutter suppreSSlon UnClaSSlfled - Unllmlted Obllque-wlng alrcraft Robust reduced-order controller STAR category 08 20 Security Classlf (of thiS page) 19 Security Oasslf (of thiS report) 21 No of Pages 22 Price UnClaSSlfied UnClaSSlfled 10 A02 For sale by the National Technical Info~ation Service, SpringfieLd, Virginia 22161.