1、(NISl_-T_-72863) STABILITY A_D CO_ITttOLDEI_IVATIVE ESTIMATES OBTAINED FRO“I FLIGBTDATA FOR TEE BEECH 99 _IRCRAFT (N_SA) 38 pHC AO3/MF A01 CSCL 01CNASA T_.ehnical Memorandum 72863c,3/0 8g79-2013_Unclas172_ I_j STABILITY AND CONTROL DERIVATIVE ESTIMATES OBTAINEDFROM FLIGHT DATA FOR THE BEECH 99 AIRCR
2、AFTRussel R. Tanner and Terry D. MontgomeryApril 1979,.,i:IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i:!j_? NASA Technical Memorandum 72863STABILITY AND CONTROL DERIVATIVE ESTIMATES OBTAINEDFROM FLIGHT DATA FOR THE BEECH 99 AIRCRAFTRussel R. Ta
3、nner and Terry D. MontgomeryDryden Flight Research CenterEdwards, Califorr, i_Nat,onal Aeronaut,cs andSpace Adm,n,strat,onProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-STABILITY AND CONTROL DERIVATIVE ESTIMATESOBTAINED FROM FLIGHT DATA FORTHE BEECH
4、 99 AIRCRAFTRUSSEL R. TANNER AND TERRY D. MONTGOMERYDRYDEN FLIGHT RESEARCH CENTERINTRODUCTIONReliable estimates of stability and control derivatives are essentialfor flight simulations and handling quality evaluations of aircraft. Inresponse to the growing need for reliable derivative estimates, the
5、 NASADryden Flight Research Center developed a technique for obtaining the sta-bility and control derivatives of aircraft from flight data (r_f. l) anddeveloped a set of FORTRAN computer programs to implement the technique(ref. 2). This method of derivative extraction is based on a modifiedmaximum l
6、ikelihood estimator that uses the Newton-Balakrishna_ algorithmto perform the required minimization.These computer programs were used to determine the stability and controlderivatives of a modified Beech 99 alrplane. The aircraft, flown as a co-operative effort by NASA, Beech Aircraft Corporation, a
7、nd the Universityof Kansas Flight Research Laboratory, was utilized to study the effectsof separate surface stability augmentation (ref. 3). Data were obtainedwith the aircraft in a clean configuration and with one-third flap deflec-tion. This report presents the Beech 99 derivative estimates obtain
8、edwith the modified maximum likelihood technique and compares these esti-mates with predicted values.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A, B, C, D, Ran, ax, aybCL , CDC_, Cm, CnCN, CyCGCGgIX, IXZ, Iy, IZJmPqqrStTCTUVSYMBOLSSystem matrice
9、snormal, longitudinal, and lateralaccelerations, greference span, mcoefficients of lift and dragcoefficients of roll, pitch, andyaw momentcoefficients of normal and lateralforcecenter of gravitymean aerodynamic chord, mmeasurement noise spectraldensity matrixacceleration due to gravity, m/seczmoment
10、s of inertia, kg - m2cost functionalmass, kgroll rate, deg/secpitch rate, deg/secdynamic pressure, fi/mzyaw rate, deg/secwing area, m2time, secthrust coefficienttotal time, seccontrol vectorvelocity, m/secProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
11、-,-XAN, XAYXZAYZ8a, 6e, 6rq0Subscripts:p, q, r, _, 8, 6a, 6e, 6r0Superscripts:weight, kNlongitudinal, lateral, and normalaxesdistances of an and ay accelerometersforward of center of gravity, mstate vectorcomputed observation vectordistance of ay accelerometerbelow center of gravity, mmeasured obser
12、vation vectorangle of attack, degangle of sideslip, degaileron, elevator_ and rudderdeflections, degmeasurement noise vectorpitch attitude, degvector of unknownsroll attitude, degderivative with respect to indicatedquantitybiasmatrix transposeProvided by IHSNot for ResaleNo reproduction or networkin
13、g permitted without license from IHS-,-,-DESCRIPTIONOFTHEAIRPLANEANDINSTRUMENTATIONThe modified Beech 99 airplane used in this analysis is a 14-_eat, twinturboprop commercial airliner with low wings and retractable landing gear(figs. l and 2). Tables l and 2 list important geometric and mass charac-
14、teristics of the Beech 99 airplane. The test airplane was modified so thatthere were two independently operable control surfaces where there is normal-ly only one; however, only one set of rudder, aileron and elevator surfaceswas used during the test flight. The extra surfaces are shaded in figure I
15、.These extra surfaces remained in fixed positions during the flight.The instrumentation of the airplane consisted of a standard packageused for the measurement of stability and control parameters, includingthree-axis angular rate gyros, attitude gyros, and linear accelerometers,along with boom-mount
16、ed angle of attack and angle of sideslip es. Thedata were filtered with 40-hertz passive analog filters, then sompled witha 9-bit pulse code modulation (PCM) system and telemetered to a groundstation for real-time monitoring.The analysis used in the derivative extraction accounts for the effectof in
17、strument location on the measurement of linear accelerations and flowangles. The instrument locations used in the analysis of the flight dataare presented in table 3. Table 4 lists the resolutions of the instrumen-tation system used in the analysis.TEST PROCEDURES AND FLIGHT CONDITIONSThe Beech 99 a
18、irplane was flown in the cruise configuration for half ofthe maneuvers analyzed and at one-third flap setting for the remainder. Allmaneuvers were flown with the center of gravity at approximately 26 percentof the mean aerodynamic chord. Most of the maneuvers performed were simpleaileron, rudder, or
19、 elevator pulses.All data were obtained during a 2-hour flight in smooth air. F_fty-sixmaneuvers were performed for derivative estimation over an angle of attackr_ _e from 1.5 to 4.5 degrees, a velocity range from 65 to lO0 meters Qersecond and an altitude range from 1800 to 3200 meters. Table 5 lis
20、ts theflight condition corresponding to each maneuver.METHOD however, no _ priori infor-mation was used in this Beech 99 analysis. The maximum likelihood techni-que is described fully in reference I.In addition to giving derivative estimates, this method provides uncer-tainty levels for each derivat
21、ive. The uncertainty levels are proportionalto the approximation of the Cramer-Rao bounds described in reference l, andare analogous to the standard deviations of the estimated derivatives. Thelarger the uncertainty level, the more uncertain the validity of the estimatedvalue. The uncertainty levels
22、 obtained for derivatives from different maneu-vers at the same flight conditions can be compared to determine the most validestimate. The uncertainty levels provide additional information about thevalidity of the derivative estimation. Further information on the interpre-tation of uncertainty level
23、s is included in reference 4.The digital computer program used in the data analysis is capable of pro-ducing one set of derivative estimates based on multiple sets of data. Thelateral-directional derivative estimates in this report result from the simul-taneous analysis of both rudder and aileron ma
24、neuvers. Analysis of rudderand aileron maneuvers simultaneously usually results in improved derivativeestimates, as shown in reference 4.The cost functional minimized by theprogram is given in appendix A.The matrix G in this cost functional acts as a signal weighting matrix. Forthis analysis, G was
25、chosen to be diagonal with values given in table 6.RESULTS AND DISCUSSIONFor all _6 maneuvers flown with the Beech 99 airplane, the measured air-craft response compared satisfactorily with the computed response based onthe maximum likelihood estimation. A typical longitudinal maneuver is shownin fig
26、ure 3, and a typical lateral-directional double maneuver is shown infigure 4. The measured (solid-line) and computed (dashed line) response ofthe aircraft are in excellent agreement in these figures. Some maneuvers pro-duced better agreement than others; however, on the average, the agreementwas qui
27、te good.An atypical maneuver combining aileron and rudder inputs is shown infigure 5. This maneuver was performed to determine any nonlinearities inaileron effectiveness. The excellent fit in figure 5 based on a linear modelindicates that there was no significant nonlinearity in aileron effectivenes
28、s.The MMLE stability and control derivative estimates based on the analysis ofthis maneuver were in excellent agreement with estimates from more conven-tional maneuvers. The analysis of this maneuver required that the small angleapproximation (in bank angle) be removed from the mathematical model (s
29、eeappendix B. All other maneuvers were analyzed using small angle approxima-tions.The estimates for 56 maneuvers (19 primarily with elevator inputs, 21primarily with rudder inputs, 15 primarily with aileron inputs, and one withsimultaneous aileron and rudder inputs) are presented in figures 6 and 7.
30、5Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The longitudinal stability and control derivative estimates are pres-ented in figure 6, while the lateral-directional estimates are displayed infigure 7. Each symbol indicates the derivative estimate f
31、or one maneuver,and the vertical bar associated with the symbol represents the uncertaintylevel for that derivative estimate. The square symbols are used to indicateone-third flap down maneuvers. Manufacturer predicted derivatives based ona combination of analytical predictions, wind tunnel tests, a
32、nd flight testresults are shown along with the MMLE-3 derivative estimates for comparison.The manufacturers predictions of derivatives that are functions ofthrust coefficient (CN , CN , Cm , and Cn ) are indicated by dashed linesa 6e 6efor thrust coefficients of 0 and 0.1. This range of thrust coeff
33、icients in-cludes the values observed in flight (see table 3). The manufacturers pred-ictions for the derivatives that are not functions of thrust coefficient areindicated by a single dashed line. These predictions are valid for both cruiseand one-third flap down configurations. Details of the mathe
34、matics involved inthe presentation of the manufacturers derivatives are given in appendix B.LONGITUDINAL DERIVATIVESFigure 6 shows the MMLE-3 longitudinal derivative estimates for the Beech99 aircraft along with the corresponding predictions of the manufacturer.Comparison between the flight estimate
35、s and the manufacturers predictionsshows close agreement except for the derivative Cm For some unexplainedreason, the flight data did not produce consistent estimates of this deriva-tive. Other flight estimated derivatives are consistent, with the exceptionof the estimates of Cm and Cm resulting fro
36、m one maneuver at an angle ofq 6eattack of 4.25 degrees. The plots of CN_ Cmq CN_e and Cm6e are nearlyconstant with angle of attack, showing no observable effect of flap deflection.All these parameters show good agreement with the manufacturers estimates.LATERAL-DIRECTIONAL DERIVATIVESAs with the lo
37、ngitudinal derivatives, the lateral-directional deriva-tives are plotted with the manufacturers estimates (fig. 7). The deriva-tives , Cn , Cy , Cy , , and C are quite con-C_B C_p, P C_r Cnr _a 6r C_r n6rsistent with the derivative estimates of the manufacturer. C_ is for6aProvided by IHSNot for Res
38、aleNo reproduction or networking permitted without license from IHS-,-,-the most part smaller than the manufacturers estimates, while CnBand CyBare consistently larger in magnitude than the manufacturers estimates forboth cruise and one-third flap configurations. On the whole, the lateral-directiona
39、l derivative estimates are repeatable and show consistent trendswith angle of attack.CONCLUDINGREMARKSA complete set of linear stability and control derivatives for a Beech99 airliner was determined using a modified maximum likelihood estimator.The derivatives were extracted for both the longitudina
40、l and lateral-direc-tional modes. The maneuvers were flown in smooth air at angles of attackranging from 1.5 to 4.5 degrees. The first Z9 maneuvers were flown in thecruise configuration and the last 27 were flown in a one-third flap downconfiguration. The one-third flap down configuration had little
41、 effect onmost of the stability and control derivative estimates. All 56 maneuversproduced satisfactory results. In general, derivative estimates from flightdata for the Beech 99 airplane were quite consistent with the manufacturerspredictions, which are based on a combination of wind tunnel data, a
42、nalyticalestimates, and flight test data.Dryden Flight Research Centerkational Aeronautics and Space AdministrationEdwards, CA, November 27, 19787Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,Bt_JAPPENDIX AMAXIMUM LIKELIHOOD ESTIMATION PROGRAM AND
43、EQUATIONS OF MOTIONThe analysis for this report was done with the MMLE-3 computer program,an outgrowth of the MMLE program (ref. 2). MMLE-3 is a general maximum like-lihood estimation program used at the Dryden Flight Research Center. Thissection briefly describes the features of MMLE-3.The maximum
44、likelihood estimates are determined by minimizing the dif-ference between the aircraft measured response and the calculated responsedetermined by integrating the aircraft equations of motion. This responsedifference is formulated as a cost functional (discussed below). The min-imization of this func
45、tional is performed by varying the aerodynamic ;oef-ficients in the aircraft equctions of motion.In genera form, the equations uf motion are:R(t) _(t) = A(t) x(t + B(t) u(t)y(t) = C(t) x(t) + D(t) u(t) +Gq(t)The system matrices (R,A,B,C,D) can be time functions because of the varia-tions of q, V, B,
46、 and _ during the maneuvers. Time varyin matrices were notused in the analysis of the Beech 99 data, except for the maneuver shown infigure 5.The maximum likelihood estimates are obtained by minimizing thecost functionaldtwhere _ is the vector of unknowns, z is the measured response, and y_ is theco
47、mputed response based on _. MMLE-3 uses a Newton-Balakrishnan iterativealgorithm (ref. 2) to perform the minimization.The equations of motion used in this report are given below. In manycases, average values of parameters are used to obtain time invariant systemmatrices. These equations of motion us
48、e small angle approximations for 6,but not for _, B, or _. Symmetry about the XZ plane is assumed. All englesin these equations are in radians. The longitudinal state equations are: (_= - m_VS CL + q + V_ (cos O) (cos _) (cos e) + (sin B) (sin a)Provided by IHSNot for ResaleNo reproduction or networ
49、king permitted without license from IHS-,-,-_Iy = qSc CmO= q(cos )The longitudinal observation vector consists of the state vector concatenatedwith an observation of normal acceleration. The equation used for computingnormal acceleration is:_S CN + XANan = mg _ _In e)panded form, the longitudinal aerodynamic
