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NASA Technical Memorandum 88275 NASA-TM-88275
19R6/)t)/JI)~96
, Eige!nsystem Synthesis for Active
Flut1ter Suppression on an
Oblique-Wing Aircraft
Gurbux s. Allag, John J. Burken, and Glenn B. Gilyard
.' August 1 98El .. ,.', ( " .' Pt"' il,j 1\. ) :-. ::J0) ; , .,". - ~j lANGLEY ReseARCH CENTI::l~ . LIBRARY, NASA W,MeTON, VIRGINIA
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National Aeronautics and /111111111111 1111 11111 111/1111111111111111111 Space Administration NF00967 NASA Technical Memorandum 88275
Eig«~nsystem Synthesis for Active
Flu1:ter Suppression on an
Obliique-Wing Aircraft
Gurbux S. Alag Western MiGhigan University, Kalamazoo, Michigan John J. Burken and Glenn B. Gilyard Ames Research Center, Dryden Flight Research Facility, Edwards, California
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National Aeronautics and Space Administration Ames Resellirch Center Dryden Flight Research Facility Edwards, California 93523 - 5000 EIGENSYSTEM SYNTHESIS FOR ACTIVE FLUTTER SUPPRESSION ON AN OBLIQUE-WING AIRCRAFT Gurbux S. Al ag* Western Michigan University Kalamazoo, Michigan and John J. Burken** and Glenn B. Gilyard** NASA Ames Research Center Dryden Flight Research Facility Edwards, California Abstract y output vector The application of the eigensystem synthesis * closed-loop eigenvalue and its li' li technique to place the closed-loop eigenvalues conjugate and shape the closed-loop eigenvectors has not been practical for active flutter suppression, minimum singular value of the return primarily because of the availability of only difference matrix one control surface (aileron) for flutter sup- pression. The oblique-wing aircraft, because of Introduct ion its configuration, provides two independent sur- faces (left and right ailerons), making the appli- The U.S. Navy and NASA are currently involved cation of eigensystem synthesis practical. This in the design and development of an unsymmetric- paper presents the application of eigensystem skew-wing aircraft capable of 65° wing sweep and synthesis using output feedback for the design flight at Mach 1.6. Such a unique configuration of an active flutter suppression system for an exhibits aeroelastic behavior distinctly dif- oblique-wing aircraft. The results obtained are ferent than that of straight, swept-back. or compared with those obtained by linear quadratic swept-forward wings and has a potential for poor Gaussian techniques.
modal response characteristics. The most serious result of such characteristics can be flutter, an Symbol s unstable motion caused by an interaction between A plant matrix structural vibrations and aerodynamic forces.
Active suppression of aerodynamic wing flutter B control matrix can result in substantial weight savings and increases in performance compared with passive C output matrix methods such as increased structural stiffness and mass balancing.
idE!ntity matrix The synthesis of modal control systems for K eigensystem gain matrix unsymmetric aircraft requires considerably more states'than are necessary for symmetric config- L partitioned matrix of specified urations because all degrees of freedom must be adequately represented in a Single formulation.
components of (liI _ A)-IB The model representing the aircraft must include rigid-body modes, flexible modes, unsteady aero-
L#
dynamics, actuators, and gust states. Control complex conjugate transpose of L laws have been formulated for active flutter con- trol using the standard linear quadratic Gaussian M partitioned matrix of unspecified (LQG) procedure;2-4 the synthesized optimal feed- components of (liI - A)-IB back control laws are of the same order as the aircraft plant. Practicalizing the control law u input vector requires order reduction by techniques such as transfer function matching, modal truncation, and V eigenvector matrix 5- 7 residualization.
Vi closed-loop eigenvector To investigate modal control synthesis strate- gies for an oblique-wing configuration, a generic a d achievable and desired eigenvectors, skew-wing aircraft model was developed for 45° Vi vi' respectively wing skew at a flight condition of Mach 0.70 at 10,000 ft altitude. At this flight condition the aircraft has an unstable flutter mode. An active * complex conjugate of Vi Vi implementable flutter control law was developed8 using the LQG design technique and modal resid- x state vector ualization to reduce the order of the controller.
However, this method increased the order of *Associate Professor, El ectrical Engineering response of the closed-loop system as compared Department. Member AlAA.
with that of the open-loop system and degraded **Aerospace Engineer.
modal control characteristics.
Eigensystem synthesis procedures are suitable aerodynamic states, actuator deflection and rate for flight control system design because they do states, and wind gust states. Eight states result not increase the order of the system. Also, the from the retained structural modes, eight from difficulty in incorporating specifications such the two-lag-term set of approximated unsteady as damping, frequency, and decoupling within a aerodynamics, six from the two actuators, and quadratic performance index makes the eigensystem two from the gust model. The five outputs con- synthesis procedure a promising design alterna- sist of pitch angle, pitch rate, and three accel- t i ve. The performance spec ifi cat ions can be erations: center of gravity and right and left interpreted in terms of desired closed-loop eigen- wingtips. The two inputs are right and left aileron deflections.
values and eigenvectors. Moore and others have shown how feedback can be used to place c10sed- For the system under consideration, the loop eigenvalues and shape closed-loop eigenvec- tors. References 10 to 12 successfully demon- following conditions hold: strate the use of an eigenstructure assignment 1. A maximum of five closed-loop eigenvalues procedure for aircraft control system design.
can be assigned arbitrarily with the stipulation The eigensystem synthesis technique using that if Ai is a complex closed-loop eigenvalue, output feedback to place ~losed-loop eigenvalues
*
its complex conjugate Ai must also be a c10sed- and shape closed-loop eigenvectors has not been loop eigenvalue.
used for active flutter suppression, primarily because of the availability of only one control 2. A maximum of five eigenvectors can be surface for flutter suppression, making eigen- altered. If the shape of a complex eigenvector vector shaping impractical. The oblique-wing aircraft, because of its configuration, provides * vi is altered, its complex conjugate Vi must two independent control surfaces (left and right be altered in the same way.
ailerons) and makes the application of eigensystem synthes; s practical.
3. For each eigenvector whose shape is altered, a maximum of two eigenvector elements This paper presents the application of can be chosen arbitrarily.
eigensystem synthesis to the design of an active flutter suppression system for a generic 4. Achievable eigenvectors must lie in the model of an oblique-wing aircraft. The results obtained are compared with those obtained by B subspace spanned by the columns of (Ail - A)-l of LQG techniques.
dimension two, which is the number of independent F1 utt~_ )?u.2.PL~s..s..i.~r:!..J!~.Lr!..\L~ijenst ruc tur:.~ control variables. A desired eigenvector v~ will in general not reside in the prescribed subspace The generic oblique-wing aircraft aerostruc- and cannot be achieved. The optimal achievable tura1 model used in the system synthesis process is a simple beam representation of the fuselage eigenvector v~ is obtained by the orthogonal and wing. The aerodynamic model was developed by d superimposing aero panels over the beams, as shown projection of vi onto the subspace spanned by in Fig. 1. The aircraft modal characteristics were developed using NASTRAN analysis. At the ( "jl_ A) -1 8 • sweep configuration (45°) and flight condition (Mach 0.70, 10,000 ft) selected, the unaugmented Given the system of equations (1) and (2) and aircraft has a flutter mode characterized as assuming an output feedback, the control input primarily wing bending. Because the intent of u is given by this paper is to demonstrate a design synthesis process, the model order was reduced considerably; 11 = Ky (3 ) the final model contained a rigid-body (primarily pitch) mode along with three elastic modes. The where K is the gain matrix of dimension 2 x 5.
model reduction process did not significantly For the closed-loop system, the following rela- affect the flutter mode characteristics. Details tionship holds: of the aircraft model formulation are given in Ref. 8.
(4) (A - BKC)Vi = "iVi The aircraft design model includes the linearized form of the unsteady aerodynamics, where vi is a closed-loop eigenvector and Ai a actuators, and gust model dynamics and can be closed-loop eigenvalue; or represented as (5 ) (Ai I - A)vi = -BKCvi BMi (1 ) x = Ax + Bu where y Cx (2 ) (6 ) M; = -KCVi where x is a 24 x 1 state vector, y is a 5 x 1 out- put vector, u is a 2 x 1 input vector, and A, B, d and C are the p1 ant, control, and output matrices, I n general, the des ired ei genvector vi does not respectively, of suitable dimensions. The reside in the achievable subspace, and an approxi- 24 states include the rigid-body mode, flexible mode deflections, flexible mode rates, unsteady mate solution by methods of orthogonal projection A time-consuming and arbitrary method for the 13 selection .of eigenvectors did lead to stabiliza- can be obtained.
tion of the aircraft. Another method, using closed-loop eigenvalues and eigenvectors obtained If through LQG design assuming full-state feedback, was used to obtain a stable closed-loop system.
(7) The closed-loop eigenvalues and eigenvectors obtained by this method were selected as the desired eigenvalues and eigenvectors for the then the achievable eigenvector vf is given by eigensystem synthesis process.
Table 2 gives the desired locations of the (8) five closed-loop eigenvalues as well as the desired eigenvectors. Five eigenvalues were located, including the unstable flutter mode, at and the gain K is given by the desired location. The achieved eigenvectors are given in Table 2. The feedback gain K was t (9) K = -M( CV) evaluated based on the achieved eigenvalues and eigenvectors. The values of K and the closed- loop eigenvalues of the aircraft are also indi- cated in Table 2.
where the superscript t denotes pseudoinverse, [i
is the compl ex conj ugate tranpose of Li , and Table 3 gives the comparative description of the rms values of response to gust input for both M (10) the LQG design8' (seventh-order controller) and the controller designed using eigensystem synthesis.
The eigensystem synthesis rms values for the sur- v (11 ) face deflections and rates are within the pre- scribed range and compare favorably with those Results obtained by the other method.
The control law synthesized by the method The controller developed by this method (K is outlined was applied to the design of an active a 2 x 5 matrix) is extremely simple to implement.
flutter suppression controller for an oblique-wing In comparison, the LQG design technique uses a aircraft. A generic 45° wing-skew structural full-order controller (the order being the same as model was developed to simulate flutter at a sub- that of the plant). Even a reduced-order sonic flight condition of Mach 0.70 and an alti- controller is difficult to implement and increases tude of 10,000 ft.
the order of the system.
Table 1 gives the eigenvalues of the open-loop However, this eigensystem synthesis approach aircraft model. The unstable eigenvalue pair at compromises robustness. Stability robustness of this flight condition (0.5 ± 14.37i) represents multi-input, multi-output feedback control systems primarily wing bending.
is characterized by the minimum singular value of the return difference matrix of the plant input or The design objective was to stabilize the output. Figure 2 shows the plots of the minimum aircraft without exceeding the specified root- singular values ~ for the controller developed in mean-square (rms) control activity so that sat- this paper and the full-state feedback controller uration would not occur. Based on actuator limitations, the rms deflection of the aileron developed using the LQG technique. A degradation was limited to 5° and the deflection rate to in robustness is evident from the plot. However, 30 deg/sec. In addition to stabilizing the air- the reduced-order controller is not as robust as craft with low surface activity, it is required the one designed using the eigensystem procedure, that the controller be robust. The controller as is evident from Fig. 2.
considered here is multi-input, multi-output: the Conclusions right and left wing control surfaces are indepen- dent of each other because of the unsymmetric nature of the aircraft. Robustness of the multi- An implementable flutter controller for a loop control system is evaluated by using the 45°-skew oblique-wing aircraft mathematical model was designed using the eigensystem synthesis tech- singular values of the return difference matrix.
nique. The controller does not increase the order of the system and is extremely simple to imple- The process of selecting desired closed-loop ment, whereas the LQG design technique uses a eigenvalues and eigenvectors for the case under full-order controller, is difficult to implement, consideration presents a problem. The selection and increases the order of the system. Work is in of desired eigenvalues and eigenvectors normally progress to improve stability margins by using is based on engineering judgment and requires a constrained optimization techniques to shape the c1 ear insi ght into physical aspects of the pl ant being controlled. Most of the physical insight singular value spectrum. A standard performance for the flutter problem is lost in the process of index is minimized while trying to satisfy minimum model reduction from the original large dimensions singular value constraints at the plant input or to the 24th-order model developed for the control output, or both.
system synthesis process.
References 8Burken, John J., Alag, Gurbux S., and Gilyard, Glenn B., "Aeroelastic Control of Obl ique-Wi ng Ai rcraft ," NASA TM-86808, 1986.
1Edwards, John W., Breakwell , John V., and Bryson, Arthur E., "Active Flutter Control Using Generalized Unsteady Aerodynamic Theory," J. Guid- 9Moore, B.C., "On the Flexibility Offered by ance Control, vol. 1, no. 1, Jan.-Feb. 1978, Full State Feedback in Multivariable Systems Beyond Closed Loop Eigenvalue Assignment," pp. 32-40.
IEEE Trans. Automat. Control, vol. 21, Oct. 1976, pp. 689-692.
2Adams, William M., Jr., and Tiffany, Sherwood H., "Design of a Candidate Flutter Suppression Control Law for DAST ARW-2," AIAA-83-2221, 10Cunningham, Thomas B., "Eigenspace Selection Aug. 1983.
Procedures for Closed Loop Response Shaping With Modal Control," Proc. 19th IEEE Conference on Decision and Control, Dec. 1980, pp. 178-186.
3Mahesh, J.K., Stone, C.R., Garrard, W.L., and Dunn, H.J., "Control Law Synthesis for Flutter 11Andry, A.N., Shapiro, E.Y., and Chung, J.C., Suppression Using Linear Quadratic Gaussian Theory," J. Guidance Control, vol. 4, no. 4, "Eigenstructure Assignment for Linear Systems," IEEE Trans. Aerospace Electron. Systems, 1981, pp. 415-422.
Sept. 1983, pp. 711-729.
4Mukhopadhyay, V., Newson, J.R., and Abel, I., 12S K.M., and Shapi ro, E. Y., "Appl ication obel, "Reduced-Order Optimal Feedback Control Law Syn- of Eigensystem Assignment to Lateral Translation thesis for Flutter Suppression," J. Guidance and Yaw Poi nt i ng Fl i ght Control," Proc. 23rd IEEE Control, vol. 5, no. 4, 1982, pp. 389-395. Conference on Decision and Control, Las Vegas, Nevada, Dec. 1984, pp. 1423-1438.
5Newsom, Jerry R., "A Method for Obtaining 13Harvey, C.A., Stein, G., and Doyle, J.C., Practical Flutter Suppression Control Laws "Optimal Linear Control," Report ONR CR 215-238-2, Using Results of Optimal Control Theory," 1977 • NASA TP-1471, 1979.
14Ly, Uy-Loi, "Robustness Analysi s of a 6Newsom, J.R., Adams, W.M., Jr., Multiloop Flight Control System," AIAA-83-2189, Mukhopadhyay, V., Tiffany, S.H., and Abel, I., Aug. 1983.
"Active Controls: A Look at Analytical Methods and Associated Tools," NASA TM-86269, 1984.
15Mukhopadhyay, V., "Stability Robustness Improvement Using Constrained Optimization Techiques," AIAA-85-1931-CP, Aug. 1985. 7Mahesh, J.K., Stone, C.R., Garrard, W.L., and Hausman, P.O., "Active Fl utter Control for Fl ex- ible Vehicles," NASA CR-159160, 1979.
Table 1 Open-loop eigenvalues 0.0000 + O.OOOOi -0.4187 + O.OOOOi -0.4229 + O.OOOOi -4.2075 + O.OOOOi -0.1612 + 5.0036i -0.1612 - 5.0036i -1.9397 + 14.0551i -1.9397 - 14.0551i 0.5011 + 14.3649i 0.5011 - 14.3649i -20.0000 + O.DOOOi -20.0000 + O.OOOOi -30.8526 + O.OOOOi -35.1822 + 0.5223i -35.1822 - 0.5223i -37.1170 + 3.5647i -37.1170 - 3.5647i -39.6927 + 0.6080i -39.6927 - 0.6080i -41.3346 + O.OOOOi -36.4000 + 37.1354i -36.4000 - 37.1354i -36.4000 + 37.1354i -36.4000 - 37.1354i Table 2 E;gensystem variables Des;red eigenvectors (from LQG method) Des;red eigenvalues 3.9999 0.0438 + 0.0049; 0.0438 - 0.0049; 0.0015 + 0.0007; 0.0015 - 0.0007; -0.0003 + 0.0000; 0.0000 -0.0317 + 0.0018; -0.0317 - 0.0018; -0.0245 + 0.0089; -0.0245 - 0.0089; -0.2355 - 5.0020; -0.2355 + 5.0020; 0.0000 0.0011 + 0.00011 0.0011 - 0.0001; 0.0023 + 0.0004; 0.0023 - 0.0004; 0.0000 0.0047 + 0.00011 0.0047 - 0.0001; -0.0004 + 0.0004; -0.0004 - 0.0004; -0.5041 - 14.3657; -0.0010 -0.0349 + 0.2177; -0.0349 - 0.2177; -0.0104 + 0.0216; -0.0104 - 0.0216; -0.5041 + 14.3657; -0.0017 + 0.1588; -0.1154 - 0.3565; -0.1154 + 0.3565; 0.0000 -0.0017 - 0.1588; 0.0000 -0.0009 + 0.0057; -0.0009 - 0.0057; -0.0075 + 0.0330; -0.0075 - 0.0330; 0.0000 -0.0014 + 0.0236; -0.0014 - 0.0236; -0.0054 - 0.0065; -0.0054 + 0.0065; 2.8445 + 16.2616; 2.8445 - 16.2616; -6.5976 - 0.9621; -6.5976 + 0.9621; 0.0746 2.4618 + 6.5556; 0.0612 1.9139 + 5.3855; 1.9139 - 5.3855; 2.4618 - 6.5556; 2.4855 + 3.2472; -0.0247 -7.3179 - 74.9682; -7.3179 + 74.9682; 2.4855 - 3.2472; 0.0829 0.9809 - 29.5832; 0.9809 + 29.5832; 10.8184 - 32.7421; 10.8184 + 32.7421; -0.0699 -2.6257 - 15.7088; -2.6257 + 15.7088; 7.1162 + 3.8695; 7.1162 - 3.8695; -2.0765 + 5.6525; -0.0578 -1.6892 - 3.9659; -1.6892 + 3.9659; -2.0765 - 5.6525; -2.6786 + 0.0123; 0.0015 6.1769 + 73.0802; 6.1769 - 73.0802; -2.6786 - 0.0123; -12.8369 + 31.1018; -12.8369 - 31.1018; -0.1024 -1.9195 + 26.9120; -1.9195 - 26.9120; 0.0000 0.0000 + 0.0001; 0.0000 - 0.0001; 0.0004 + 0.0003; 0.0004 - 0.0003; -0.0050 + 0.0055; 0.0000 -0.0003 + 0.0001; -0.0003 - 0.0001; -0.0050 - 0.0055; -0.0766 + 0.0740; 0.0000 -0.0006 - 0.0016; -0.0006 + 0.0016; -0.0766 - 0.0740; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; 0.0009 - 0.0001; 0.0009 + 0.0001; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; 0.0016 + 0.0130; 0.0016 - 0.0130; -0.0001 - 0.0001; -0.0001 + 0.0001; -0.1878 + 0.0159; -0.1878 - 0.0159; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; 0.0000 - 0.0000; 0.0000 + 0.0000; 0.0000 0.0000 - 0.0000; 0.0000 + 0.0000; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; Ach;eved closed-loop Ach;eved eigenvectors eigenvalues 0.0015 + 0.0007; -0.0003 + O.OOOO;a 3.9999 0.0438 + 0.0049; 0.0438 - 0.0049; 0.0015 - 0.0007; -0.0317 + 0.0018; -0.0317 - 0.0018; -0.0245 + 0.0089; -0.0245 - 0.0089; -0.4187 + 0.0000; 0.0000 0.0023 + 0.0004; 0.0023 - 0.0004; -0.4229 + 0.0000; 0.0000 0.0011 + 0.0001; 0.0011 - 0.0001; 0.0000 0.0047 + 0.0001; 0.0047 - 0.0001; -0.0004 + 0.0004; -0.0004 - 0.0004; -3.6775 + 0.0000; -0.0349 + 0.2177; -0.0349 - 0.2177; -0.0104 + 0.0216; -0.0104 - 0.0216; -0.2355 + 5.0020;a -0.0010 0.0000 -0.0017 - 0.1588; -0.0017 + 0.1588; -0.1154 - 0.3565; -0.1154 + 0.3565; -0.2355 - 5.0020;a -0.0009 + 0.0057; -0.0009 - 0.0057; -0.0075 + 0.0330; -0.0075 - 0.0330; -1.3818 + 12.9445; 0.0000 -0.0054 - 0.0065; -0.0054 + 0.0065; 0.0000 -0.0014 + 0.0236; -0.0014 - 0.0236; -1.3818 - 12.9445; 2.8445 + 16.2616; 2.8445 - 16.2616; -6.5976 - 0.9621; -6.5976 + 0.9621; -0.5041 + 14.3657;a 0.0746 2.4618 + 6.5556; 2.4618 - 6.5556; O. 0612 1.9139 + 5.3855; 1.9139 - 5.3855; -0.5041 - 14.3657;a 2.4855 + 3.2472; -0.0247 -7.3179 - 74.9682; -7.3179 + 74.9682; 2.4855 - 3.2472; -23.1705 + 0.0000; 10.8184 + 32.7421; 0.0829 0.9809 - 29.5832; 0.9809 + 29.5832; 10.8184 - 32.7421; -21.2819 + 13.9913; -0. 0699 -2.6257 - 15.7088; -2.6257 + 15.7088; 7.1162 + 3.8695; 7.1162 - 3.8695; -21.2819 - 13.9913; -1.6892 - 3.9659; -1.6892 + 3.9659; -2.0765 - 5.6525; -2.0765 + 5.6525; -34.5807 + 1.0410; -0.0578 0.0015 6.1769 + 73.0802; 6.1769 - 73.0802; -2.6786 - 0.0123; -2.6786 + 0.0123; -34.5807 - 1.0410; -1.9195 - 26.9120; -12.8369 + 31.1018; -12.8369 - 31.1018; -39.5120 + 1.8798; -0.1024 -1.9195 + 26.9120; 0.0000 - 0.0001; 0.0004 + 0.0003; 0.0004 - 0.0003; 0.0000 0.0000 + 0.0001; -39.5120 - 1.8798; -0.0050 + 0.0055; -0.0050 - 0.0055; 0.0000 -0.0003 + 0.0001; -0.0003 - 0.0001; -39.9263 + 0.0000; -0.0766 + 0.0740; 0.0000 -0.0006 - 0.0016; -0.0006 + 0.0016; -0.0766 - 0.0740; -30.2236 + 29.6354; 0.0009 - 0.0001; 0.0009 + 0.0001; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; -30.2236 - 29.6354; 0.0000 0.0000 + 0.0000; 0.0000 - 0.0000; 0.0016 + 0.0130; 0.0016 - 0.0130; -49.9016 + 16.2655; 0.0000 -0.0001 - 0.0001; -0.0001 + 0.0001; -0.1878 + 0.0159; -0.1878 - 0.0159; -49.9016 - 16.2655; 0.0000 0.0000 + 0.0000; 0.0000 - 0.00001 0.0000 - 0.0000; 0.0000 + 0.0000; -33.5655 + 41.6373; 0.0000 + 0.0000; 0.0000 - 0.0000; 0.0000 - 0.0000; 0.0000 + 0.0000; 0.0000 -33.5655 - 41.6373; E;gensystem feedback gain matrix, K 0.0000 0.0004 -0.0006 -0.0001 0.0002 0.0000 0.0009 -0.0010 -0.0001 -0.0001 aSee desired eigenvalues.
Table 3 Root-mean-square responses at flutter conditions Right wing Left wi ng 0, deg 0, deg/sec 0, deg 0, deg/sec
-------
Full-state feedback 1.58 7.91 0.28 3.58 Full-order controller 1.58 12.58 0.41 5.64 with Kalman estimator Full-order controller 2.06 11.21 0.41 5.02 with robust Kalman estimator Reduced-order 1. 51 10.04 0.41 4.90 controller Eigensystem 0.62 4.81 0.69 8.46 synthesis
. -
Vertical fin Fig. 1 Generia modeL (aero paneL8 and node points). vertiaaL fin 8hown in X-Y pLane.
\ Full·state feedback \ controller 1.1 /r, .......
.; ---
-.:::---- 1.0 Eigensystem / I .9 controller J " Minimum .8 VI /' singular I I value, .7 Q
LOG reduced-order \1
controller ~II .6 .5
l
.4 10 100 Frequency, rad/sec Fig. 2 Minimum singuLar vaLues of the return dif- ferenoe matrix.
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-88275 4. Title 81,d Subtitle 6. Report Date EIGENSYSTEM SYNTHESIS FOR ACTIVE FLUTTER SUPPRESSION August 1986 ON AN OBLIQUE-WING AIRCRAFT 6. Performing Organization Code 8. Performing Organizetion Report No.
7. Authorls) Gurbul( S. Alag,* John J. Burken, and Glenn B. Gilyard H-1359 10. Work Unit No.
9. Performing Organization Name and Address RTOP 533-02-91 NASA Ames Research Center 11. Contract or Grant No.
Dryden Fl i ght Research Facil ity P.O. BOl( 273 Edwards, CA 93523-5000 13. Type of R~port and Period Covered 12. Sponsoring Agency Name and Address Technical Memorandum National Aeronautics and Space Administration 1~. Sponsoring Agency Code Washington, D.C. 20546 15. Supplementarv Note:1 Prepared as AIAA-86-2243-CP for presentation at the AIAA Guidance, Navigation, and Control Conference, Williamsburg, Virginia, August 18-20, 1986.
·Western Michi9an University, Kalamazoo, Michigan 16. Abstr.,:t The application of the eigensystem synthesis technique to place the closed-loop eigenvalues and shape the closed-loop eigenvectors has not been practical for active flutter suppression, primarily because of the availability of only one control surface (aileron) for flutter suppression. The oblique-wing aircraft, because of its configuration, provides two independent surfaces (left and right ,3f1erons), making the application of eigensystem synthesis practical.
This paper presents the application of eigensystem synthesis uSing output feedback for the design of an active flutter suppression system for an oblique-wing aircraft. The results obtained are compared with those obtained by linear quadratic Gaussian techniques.
17. Key Words ISuggestlld by Author(s)) 18. Distribution Statement Active flutter suppression Unclassified - Unlimited Ei genstructure Ob 1 i que-wi ng ai rc raft STAR category 08
19. Security aaull. (of this report) 20. Securitv ClaSlIiI. (of this page)
121. N~. 01 Pages
1 . Price Unc lils ~ ifi ed Unclassified A02 FoZ' 8ate bl the Nat1.cmal. Technical. In ol'l7rl'tion SeMoe S rin ieLd y V'loZ' nia 22161. • p gf :f