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PDF (655 KB) - AIAA - American Institute of Aeronautics and ...

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(4) time delay case

(4) time delay case where the °ight is executed witha nominal center of gravity and a time delay of 100 ms.Five quantitative criteria are given for each segment(A, B, C, D) of the °ight path:² performance;² quality;² safety;² control; andTable 1Segment A Criteria ComparisonCases P A Q A S A C A R AGARTEUR 0.0764 0.5432 0.0038 0.0037 0.0309nominal 0.0766 0.5482 0.0041 0.0031CG fwd 0.0743 0.5269 0.0104 0.0031CG aft 0.0792 0.5744 0.0091 0.0032delay 0.0794 0.5770 0.0096 0.0032average 0.0774 0.5566 0.0083 0.0032 0.0347² robustnessSegment A Criteria EvaluationThe performance criterion de¯nes the lateral deviationboundary of 20m to account for the e®ect ofturbulence, and the boundary of 100m during enginefailure:P A = 1 ³2maxeyb (t)t 0·t·t a 100 + e yb(t a )´(1)20where e yb (t) denotes the lateral deviation in bodycoordinates.The quality criterion considers the maximum lateralacceleration of 0:2g:Q A =³ ny (t)´maxt 0·t·t a 0:2(2)The safety criterion sets the limit of the maximumangle of attack ® of 12 deg:S A =³ j®(t)j´3maxt 0·t·t a 12(3)The control criterion concerns the rudder actuatore®ort to stabilize the aircraft after engine failure isrecovered:C A =Z tat 0± 2 R dt (4)The maximum di®erence between the lateral deviationof the trajectories with nominal and perturbedcenter of gravity (CG forward, CG backward) and withthe time delay is de¯ned as:³´¢ eyb (t) = max je ybmax (t)¡e yb (t)j; je ybmin (t)¡e yb (t)j(5)and the robustness criterion sets the limit of maximalallowable deviations and the limit at the end of thissegment:R A = 1 2³ max¢eyb (t)t 0·t·t a 10+ ¢ eyb(t a )´2(6)The o®-line simulation results of Segment A comparedwith the published results are shown in Table 1and Figure 9.Fig. 9 Segment A Criteria Evaluation: Case (1)- nominal, (2) - CG fwd, (3) - CG aft, (4) - delay,(5) - averageSegment B Criteria EvaluationThe performance criterion de¯nes the maximum lateraldeviation of 200m due to the turn and the lateraldeviation of 20m at the end of the segment:P B = 1 2³ maxeyb (t)t a·t·t b 200 + e yb(t b )´20(7)The quality criterion considers the maximum lateralacceleration of 0:02g:Q B =³ ny (t)´maxt a·t·t b 0:02(8)The safety criterion sets the limit of the maximumangle of attack ® of 12 deg:S B =³ j®(t)j´3maxt a·t·t b 12(9)The control criterion concerns the rudder andaileron actuator e®ort:Z tb ³ ´C B = ± R 2 + ± A2 dt (10)t aThe robustness sets the limit of maximal allowablelateral deviations with perturbed center of gravity and6 of 9American Institute of Aeronautics and Astronautics Paper 2002-4473

time delays:R B = 1 2³ max¢eyb (t)t a·t·t b 20+ ¢ eyb(t a )´2(11)The o®-line simulation results of Segment B comparedwith the published results are shown in Table 2and Figure 10.Table 2Segment B Criteria ComparisonCases P B Q B S B C B R BGARTEUR 0.4964 0.7340 0.0382 0.0027 0.0161nominal 0.6090 0.7095 0.0302 0.0024CG fwd 0.6092 0.6925 0.0374 0.0024CG aft 0.6086 0.7332 0.0236 0.0025delay 0.6086 0.7356 0.0239 0.0025average 0.6089 0.7177 0.0288 0.0025 0.0156The control criterion concerns the tailplane actuatore®ort:Z tcC C = ± T 2 dt (15)t bThe robustness sets the limit of maximal allowablevertical deviations with perturbed center of gravityand time delays:R C = 1 ³2max¢ezb (t)+ ¢ ezb(t c )´(16)t b·t·t c 2 0:6The o®-line simulation results of Segment C comparedwith the published results are shown in Table 3and Figure 11.Table 3Segment C Criteria ComparisonCases P C Q C S C C C R CGARTEUR 0.3285 1.1808 0.0070 0.0150 0.4926nominal 0.3475 1.1907 0.0078 0.0160CG fwd 0.3759 1.2080 0.0109 0.0261CG aft 0.3268 1.1757 0.0054 0.0084delay 0.3271 1.1774 0.0054 0.0084average 0.3443 1.1880 0.0074 0.0147 0.5034Fig. 10 Segment B Criteria Evaluation: Case (1)- nominal, (2) - CG fwd, (3) - CG aft, (4) - delay,(5) - averageSegment C Criteria EvaluationThe performance criterion considers the maximumvertical deviation during the capture of the ¡6 degreeglide slope and the vertical deviation at the end ofthis segment. Further, speed variations should be keptsmall in spite of the change in required angle of attack:P C = 1 ³3maxezb (t)+ e zb(t c )+ jV ¡ V commandjt b·t·t c 20 64(12)The quality criterion considers the maximum verticalacceleration:³ nz (t)´Q C = max(13)t b·t·t c 0:05The safety criterion sets the limit of the maximumangle of attack ® of 12 deg:S C =³ j®(t)j´3maxt b·t·t c 12´(14)7 of 9Fig. 11 Segment C Criteria Evaluation: Case (1)- nominal, (2) - CG fwd, (3) - CG aft, (4) - delay,(5) - averageSegment D Criteria EvaluationThe performance criterion considers the maximumvertical deviation due to the wind shear and the verticaldeviation at the end of this segment:P D = 1 2³ maxezb (t)t c·t·t d 20+ e zb(t d )1:5´(17)The quality criterion considers the maximum verticalacceleration:³ nz (t)´Q D = max(18)t c·t·t d 0:2American Institute of Aeronautics and Astronautics Paper 2002-4473

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