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11111/11111111111111111 cnp, i98'1 N,",SA VIRGII\" 11111 1111 NF01979 2";' RESEARCH C/C- U3RARY.
1111111111111 \-lAMPTON, JAN AIRCRAFT
II
LAI~GLEY
lIBRt\RY
Cj the
~
Nf)SA of of the -::, FLEXIBLE for
d--
of of Illinois University Science 1980 University Science Faculty 1!&/f' LARGE TIlailand of Illinois POOPAKA of PHILOSOPHY fulfillment By of
~
the OF 1972 1977 Degree State OF
{{
Songkla
I to
SUPAT requirements the December NASA_CR-l63593 AlSG of Haadyai, Urbana, Master Bachelor partial the University DOCTOR Graduate College QUALITIES in Oklahoma Prince Submitted eY"'a.~f HANDLING ,vAS4 ' ......
,~ 3 1176 00164 8436 111111111111111111111111111111111111111/1/111/111/11/111111/111/
[
"--, 1980 se- is to on of rig- a An nat- with clastic re- Oklahoma quali- flexible is Philosophy of response model model elastic effect easier of extendingt~e pilot December, include the using a large it with the there large undamped des criminating by pilot to a handling AIRCRAFT in elastic the handling predictions control task the hl.D1lan make Stillwater, Doctor of qualities when done The symmetric on in interaction.
Degree: of the from interaction is model of response of interaction FLEXIBLE mode ratings the
k
handling dynamics This rigid the modified modes Degree of aircraft Location: Date of on pilot model modes LARGE the model.
variations stage.
for body pilot that OF elastic the human into amounts separate lowest frequency, flexible effects rigid shows elastic developed. the modified the study proved successful University a mathematical computer simulation. a longitudinal tracking two of Candidate The is than the standard optimal A comparison of The cannot techniques developed here large QUALITIES by predict for the this a mechanism or
~
State to with~le with parametric The of in of model task.
effects Study: can predicting induce varying studied a preliminary design qualities HANDLING 61 of in the interaction to method pilot. in Oklahoma are determined aircraft Mechanical Engineering pilot experimental data Poopaka control dynamics interaction made decomposition are frequencies the Method modes better APPROVAL Study: Study: past human the tracking body Supat in of and analytical ties flexible modes aircraft vere optimal mode ural modes sponse developed in the the handling the investigate id when much qualities Institution: Pages Name: Title Major Field: Scope Findings and Conclusions: ADVISOR'S ( J '- If '\ " AIRCRAFT FLEXIBLE LARGE ii OF Thesis Advisor ortJie-Graduate College QUALITIES , Dean Approved:
o~z~
HANDLING Thesis \ \ ,j \ ,01\ 'I for guid- mem- to grant as nec- Special typing Oklahoma have always advisor, advice con- under at in technical thankful committee who job NASA his my whose thesis by also studies to the study.
for my consultation am my I the advisory committee, for and Mulholl,md Maddali excellent of Swaim, K.
J.
extended provide her L.
study.
and project, also for were supported iii Vijay Robert chairman this is Dr.
Dr.
ACKNOWLbTQ\fENTS and to effort research and tllank Dr. Robert this advisor Teresa Tackett through problems Appreciation grateful research to on my Ebbesen R. Mrs.
talk also this like idea Reid, developing the computer programs to am for of Lynn I N. in suggestions throughout guidance and encouragement throughout would are University. Dr.
I Parts and original Karl 4018.
his manuscript.
for taken tnne tributed thanks the his Dr. State bers, essary. NSG ance ,~ !,J
.. ,j
,,", " \', 1 3 5 7 13 19 20 21 23 25 28 13 15 17 30 33 33 35 36 40 42 44 47 56 Page
. -
• .
. .
. •
• • QUALITIES • AND .
.. .
• HANDLING • .
Motion ON PERWRBATION.
. ............. • DERIVATIVES of . . • . • .
. . . . • .
. . ..... .. . . .
CONTENTS Study SINGULAR .
. . • .
IV OF of . . • INrEHACI'ION STABILI1Y TO Equations . , Equations OF • ..... • . .. .
Cases TARLE Scope Boundary • .
MODES MarION.
. .
RECCU1ENDATIONS RELATED and Model Condition.
. .
Model OF VALUES Director Model.
. ••••.
Presentation.
MarION.
AND Perturbation Description . Limitations Opinion Rating Tecllnique. ELASTIC ON of OF Definition Ill~~trated Flight Pilot Separation or MODELING Internal General Background. Objectives Plan RESULTS Small Turbulence B-1 I-Iurnan Task TIle Pilot Attitude Model Computational Algorithms The The NL'MERICAL EQUATIONS DERIVATIONS NIRODUCTI CONCWSIONS BIBLIOGRAPI~ B - A - I PAST EQUATIONS PILOT EFFECTS 1.
VI.
V.
II. IV.
III.
Chapter SELECTED APPENDIX APPENDIX -, ..I 'I ,.I \', '" 19 37 38 39 51 52 53 53 54 54 55 55 Page .
.
Cases.
.
0.85 .
a Function .
Eight Ten Cases .....
as a .
Derivatives Mach of of ~I. rot.
.
as in .
.
.
.
Ratios Iktios .
Derivatives .
Standard Modified Stability Bomber TABLES • Derivatives .
.
.
OF the the Derivatives B-1 v .
.
Damping • by by .
~Ioment for .
.
LIST .
Stability and Damping and Force .
..
. • and 8). .
4) .
.•• .
8).
4).
x Non-Dimensional (4 x (4 Prediction Prediction x 8) x 8) Force x 4) x 8) Elastic (1 x 4) Condition.
of (8 x (8 x Derivatives (l (2 (2 (2 Condition.
Frequencies Frequencies Matrix Matrix Ndn-Dimensional Specifications Flight Matrix Matrix Matrix Matrix Function Matrix of Matrix Matrix Flight /lJ Natural B-1 Natural Performance l 2 Perfonuance Dimensional Dimensional Stability Gust All Al2 A A2ilJ Bi B2/~ C C Ei I.
V.
X.
II.
IV.
VI. IX.
XI.
III.
XV.
VII.
XII.
XIV.
XVI.
VIII.
Table XIII.
XVII.
XVIII.
j 0( " 1\ '- 9 9 11 22 13 26 Page Response .
• .
.
EADI.
lot .
Pi . (EADI).
.
Response.
Ihnllan FIGURES .
.
Pilot of OF Indicator vi 6 .
Human Model LISf Rating Scale Corresponding to the Case of Director Pilot Pitch Angles Hodel Attitude History - Attitude Elastic Time and Cooper":Harper Airplane The Electronic The Sample Rigid Optimal Control Modified Optimal Control 1. 2. 3. 4.
5. 7.
6.
Figure ..
., . -< " ~ '.1 attitude the vehicle equa- the vehicle equations in ft/s2) in the vehicle display variable axis y in ty ith coefficients vector in the vehicle equations stabili coefficients coefficients vii coefficients factor element about allocated to ~LA1URE Matrix for observations factor acceleration (32.17 zone state coefficient scale of{·} inertia dead span scale attention of of physical control variable output variable aerodynamic chord disturbance variable motion wing equations of mass distribution of of of of of gravitational matrix mean moment motion motion of Gust tions director Aircraft Wing of Cost functional Mass , - Matrix - - Half width - Matrix - - Matrix - - Control - Matrix - Expected value - Feet - Longitudinal gust - Airplane - Fraction - Scalar white noise - Local - - - Vertical gust w i a w
- Iy
Aa a Ba b C C Da Ea E{·} fi ft G g ~ ~ Ag J m , , ,;/ "I . '.
, ", of properties states gust 8 ) vertical scale input mode as in same ( control the threshold element elastic the physical output vehicle viii for ith rate variations Cooper-Harper the pilot with matrix to gQst to in rate the of velocity variables the input vector angle of due due variable of q u disturbance rating vector forward speed control display pitch of vehicle of associated control covariance on on centerline info~1tion state external opinion the noise noise vector (5) area aircraft Pilot Perturbation Perturbation Perturbation Perturbation "Commanded" the along Wing Motor Motor Random State - Describing function gain - Weighting - Weighting - Generalized force - - T-second delayed - - Second - Laplace transform - Neuromuscular constant matrix - time - Steady - - Control input - - - Observation noise covariance matrix - - Observation noise - - - Display r y o a g t N P.O.R. - Q Q Q~i q qg r Sw s Tn u u u U Vm Vy vm vy xa urn Wa Ya " ..
.'"' ' ", of mode ith of the presence to mode frequency due ith mode of mode model i natural arises clastic mode mode ratio shape mode mode gust modes ix gust ith frequency of mode to i th mode undamped attack to of turbulence phugoid short-period of of angle due in quantities due . ratio I clastic mode of of g Ct natural e f phugoid short-period noise/signal 0 parameter whidl ratio angle of pitch of of of normalized display damping elastic deflection .
ith undamped ratio ratio damping varIance positive of high frequency olse Perturbation Perturbation Perturbation Perturbation N .
Multiplicative Error covariance matrix Perceptual time delay of Structural Damping Damping - Perceived - - - Elevator - - - - - - - Small - Temporal frequency - In-vacuum - Coupled - Natural frequency - Natural frequency - Coupled - - - Generalized coordinate - Slope g g 2 I Yp Ct Ct 0e e e Ie 1 Ie Pi 0i E 1 T ~ 1 W w· w.
Wph wsp r;. r;.
r;ph E;sp E;. cp: ',Y ," '" '.
of of of scale static also eco- the related air- elas- '>'lith depend Most the but simulation the pilot more support then rating qualities motion and rigid arc can perfonn is between in is of the a phase that it he precision because the design pilot to for qualities research.
handling such flight aircraft required a groundbased relations the equations such assessment ease and rigid of of task the design, simulation the piloted the handling of requirements significantly a case with which pilot's IO~J prototype, of opinion results control the and a mission a TIlUS, modeling The detennine the perturbation relatively stages of of influence to CHAPTER qualities contribute INTRODUCT typical pilot's pilot small early that qualities phase.
flight not the opinion are have been perfonn the the adjusted.
do body, handling to [1] In flying flight characteristics first past assess has been done The qualities.
or to easily rigid a1.
able the subjective et is the in such as the widely accepted Cooper-Harper airplanes mission characteristics aircraft task. prior required. use a mathematical of research rating. the handling handling Chalk pilot accurately to scale 1).
pilot's of in The To Much aircraft only on control airplanes pilot the aircraft usually some the the (Figure and dynamic which a not on an is to the ticity nomical parameters can be parameters the plane perceived ,'# " ,~ ..
' ", N Figure L The Cooper-Harper Pilot Rating Scale [1] accomPOny;nQ CCt'd",gns -Otf",.loon of rlQw"'3 ::1:.'::' on .n.",." dl\o;~OI.on 01 Il.lfhl pIIOII OIlCl/or ...cp/lOH, •• 111 • ooerahOft llla(cr CII C.encon • f ~ •• 11 be 10\1 ClI"'Q Some IIQI'loon of ,,_.eI 'eto'ft control Ugp Clefcoer"Con I",..",. O'tol COtf'lQt:"sCl.on .s f.q", •• d to_ 'or COftlrol ~ cse'-coenc.s 8 C_Clt.oll~ 1)0101 CO'"II''''.IoOft '1 "Q","" eonlrollObol." "01 ... q"uloOr!
Ucp Cltfc....c'e1 7 _.......... 10leroble 11.101 '_111"10100" - Adequol. ""'OImOnc. "CII otlo_bl. ..111 fCHrotH 01"0."0" ~IOI CornQ ... lol.O" bQwOl. perfor"'o"" •• quo.tI .... n" •• _, CiCJKtooat:Jle IIwl
--
dlfCoe<1toft _Cl •• olIl. 11'10' C_'""IOhOr!
_o. .... ~1
No 1I1odIr0ftly CiCJKt~ &cst:;"OI. !Ie,for"'1I"'. "Quo'n o.foCoeftOti dlfoOenCoft ~ CO"'O."'OhOr!
"-Cll;f~ On-.CI ""'orlftO/lce '.q .. "" _Cl.'Ol.
Yn ~III'" CIe'c""'."
CII",.CI per'er_"c.
s F'Of • S- ""IClI, ""'-t poIOI CQI"OCtIIIII."" '.q ..... II. 'er ~'O."" dI'c.-.coft de .... ., perfor"'o",.
"'!eII C(IrIIOeftIll"Oft .... ' 0 fOClor for GIXII2 dt",td ""for"'a"" ";M, .. ",;tile
[ocea.n' "'101 CQftOOenIOf."" rI'" 0 foc'Ot for
~ _______ ~M~OU==~~~~~~T~~- __ ~ __ ~_~~ ______________ -=~~~~~~ ______ ~==~~
) ( AD£OU4CY FOR SELECTED TASK OR AlACRAFT O1ARACTEJ'ISTICS ... S£L£CTED TASIC OR AEOUAEO oPERATlOft r e D£u&kOS or. TH£ PILOT PILOT - ..
.. '
-, ,;; ---------- ~ in- con- of utili- struc- sta- of de- if im- free- Milne to their in mode aero- the by a trun- of actjve is and terrain are case in of behavior for hy and handling qual- <lnJ aircraft one small this results stability for airplanes. an the lower degrees size In then the approach such as effects elastic of account as design new body, flexibility which to took the approach The a need of of derivatives order modes.
aircraft adverse is rigid kinematically constrained aerodynamic physical meaning, structure additional vehicles be control same deflections the the environments, there appreciable influence approach as pointed out to real effects designs.
to and the of an distributions with the stability vibration potential approximate the dynamics Farly attempts this of to increase BackgrolUld included as to future the of pressure dynamic airplane are dynamics, be in of aeroelastic becoming pressure stability modified the the not have any frequencies associated corrections motion.
possible body General control-configured of do of air, it static drawbacks in Because the preliminary design phase they must rigid aircraft high dynamic structures therefore changes The parts which natural in that aerodynamic in makes on calculating is that approach has been aeroelastic in equations turbulent superimposed orthogonal the major known points lighter [2-4].
with the in of qualities.
is effects that the vibration enough cornmon of derivative static assessment vehicles A set It Recent advances technology modify For flying are invalid.
various trol [4] zation these handling teraction ities ture bility imagine typical perturbation elastic making rivatives at the overall-motion frequencies is following portant dom. cated ..
' " I" '.
No [1].
evi- in multi- of with are easily too quali- dutch- for aircraft.
th~ hody environ- pertinent When motion.
analysis tr'illsient all dynamics qualities, studies included or is cannot rigid under the airplane handling total is specification criteria military pressure of flying and on This done pilot the specification and short-period, structural aerodynamic coupling of flexible frequencies. the effects the feedback control work of conq1rehensive d~lamic tactical a opinion qualities and calculations elastic airplane [6].
tory hody in with for his qualities his responses.
the tile research rigid, another, effects requirements compliance with requirements on earliest between and high rigid of handling time which have been determined aeroelastic one rather equipment, of the reference and the comprehensive the handling of to the ~ruch in interaction are of to on for ratios, qualities relatively higher-order aircraft 497).
turbulent modes motion; control one recent mode in close of (p.
table such mostly meaningless was ignored.
parameters, such as phugoid, proximity discussion interest most investigation documented damping be based sui elastic handling in for are military [5] modes should not be overlooked is elastic TIle most of are the useful an important influence airplanes largely toward of likely qualities frequencies to no criteria aeroelasticity, effects specification available exert Reference subject airplanes, will individual problem. mode that as well as elastic sponsorship this such directed Since may The has been concerned with frequencies and in phenomena handling such revision this contains only the following statement: the system.
between the various modes, of AFFDL highly ties roll for elastic It ments has been The pIe frequencies discern dynamics performance presently dent the '" ,.
" '.
'~ aero- all dy- of re- seems re- rigid is values at the of de- the hody fre- IIlnthods It of body the to then not terms cannot, a arc angle low where a order fact, establish required.
rigid is particularly eventually he in to rigid In to be separate to ranges It [8], method This study 'l1lCre motion. same pitch and hy is separate when mathematical fication much of will cannot the rahle freedom, TIle i how he of alone.
visually of present.
a given criteria reference Study and visually analytical corrections the speci specified is parameter values could be of can when hody situations in of pal'lIIl1C'ters. equations an be of can In conditions body and studied.
degrees much pilot done rigid frequencies system probably qualities was motion parameters.
however, how pilot ranges should mode rigid the develop response aircraft the motion of work aeroelastic interaction to interaction the to [7]; of response.
\vhen natural control rigid due total mode ¥as concerned only with des elastic mode dynlUnk static simUlation in desirable qualities is is by have total the equations such for example, Objectives and Scope and the experimental severe the ic these frequencies {!erivati ves input from modes when objective tell, developing handling suppression the tr that for of handling modes.
stat estimating the from affected the in of pilot-flown not boundary between as the mode motion ror of conunand perturbation specification hody key primary stabili the the use elastic possible that could body same The The and under what conditions response The rigid available dynamic significantly on quires quite when magnitudes clear namic parameters pilot sponse to specifications body structural quency when termine rigid the small an extension ground-based ...
,.
'.
" [9] in TIle flex- of long- are Numeri- the presented results pilot TIle of is techniques effects developed motion major II.
human assessed.
of the are chapter.
be TIle the condition extension can that B.
for Chapter assess in its perturbation the experimental evidences in airplane equations to flight model of and the used rating. and interaction for singular is flexihle described presented control a conclusions and recommendations appear Presentation modeling is mode some opinion also observation of for TIle of of an description are pilot optimal summarized in Appendix V.
pilot Plan derivatives by results motion TIle the are the effects of of TV past general A.
on Chapter the Derivations of in TIle under study stability [8].
.
motivated that TV.
of VI is Chapter equations Appendix extension so III.
summary in modeling simulation approach in interaction
An A airplane
values presented reference made Chapter Chapter is extension itudinal pilot mode of Chapter ible cal in are in given needed ~ , H .
'" to (3.1) an (3.2) Case the to the rigid the did not which are for to of modes the However, relevant that a fixed- command, task, were on close on simulator evalu- clastic variables [10] oscillation elasticity pitch directly ripple conclud6d its of the tracking [8].
is piloted programmed and Crother TIley Yen that symmetric that pitch in a nuisance parametric lowering merely a was display I\.
and two of O;029~2(t) trackinp. performance.
was display II included aware - [10] it are first The 7 RESULTS are and configuration were very surprising turbulence.
0c effect effects ,\'c essentially the GIAP'D:R in not PAST their the Crother of 0i - is opinion; investigated. error. 0.02S~1(t)
=
period dynamics, equations in which aircraft of attitude-director 3. - it [8], eo of were B-1
pilot CRT pitch and =
OCt) short North American Rockwell appeared as Yen performance TIIUS, = the and frequencies of dynamics of anti error docLD",1cnted researc~l for aircrat-t der,rade is work angle Figures 2 dynnmics trac1~inr.
0iC~,t) pitdl only results results.
natural in attitude-director the of and did not sir,n.ificantly version pitch In The The our response. flexible The subject longitudinal a of the early ations structural pilots the 1 significantly body undamped of included phugoid total base simulator with a depicted '" ., time to mode the Fig- scale.
in clastic original average '111is in thepilot of Sample the elastic at lhe difficult is shohTI clastic-rigid specifications resulted density, modes contributions very roots.
are dynamics. of pitch.
it free-free Case 1 This level real modes' the Cooper-Harper I.
elastic Case 6 made q~11ities sea elastic on original on two at modes.
This seriousness Table where the 6.7 the elastic from the in both e. 1, 0.85 handling was of and negative the to for rigid Case difficulty of ~fach shown cases which were combinations pitch potential on is difficult, Case 6 rad/s the arc positive of eight rigid the slopes separate tracking rating 6.93 to interaction cases into amplitudes 6 are the most condition at 1.
ratings TI10 mode was each flew large set pilot's visually established relative flight to with a splitting one the i pilots' Case 6 The pilots of rating.
this frequency clearly Note pilot mode four pitch interaction.
Four has low 4. the pilot the station. mode dynamics. frequencies were phugoid histories ure total for of where 0,025 and 0,029 Contrast work body and 4 '·,1 " 9· lee DOWN) EADI
ee
PITCH Above (FAD!)
To DIRECTOR LOCAL HORIZON- AIRCRAFT Indicator SYMBOL FLIGHT (COMMANDING FIXED Corresponding Director Attitude Attitude Airplane The Electronic 2.
Figure 3.
LINE Figure HORIZON ."
o ......
-0.0541 8 10.68 9.27 2.3893 0.0256 0.11021 10.347 0.0005306 9.7781 1.9 7 10.25 9.75 0.5517 -0.0483 0.0282 0.1129 10.234 -0.0004277 9.8978 2.3 6 6.93 6.93 0.7028 1. 3665 -0.15307 0.1919 7.3305 0.007599 6.9178 6.7 +0.17581 Real Roots 5 11.66 11.66 0.5436 2.5819 -0.0001122 0.0537 0.0773 11.801 0.0162 11. 574 2.0 13.59 4.79 0.6872 1. 5745 -0.13167 0.05284 13.270 0.1137 3.1 4 5.9702 +0.14654 Real Roots 3 6.16 21.18 0.5217 1.7691 -0.076723 0.1999 5.8669 0.0213 21.357 5.9 +0.090978 Real Roots Z 9.17 21.18 0.5235 2.5724 -0.00060267 0.0573 0.08769 8.7891 0.0213 21. 356 2.0 1 13.59 21.18 0.5339 2.806 0.0197 0.0708 0.0494 13.312 0.0215 ZI.354 1.6 # rad/sec rad/sec rad/sec rad/sec rad/sec rad/sec 1e e l,;ph wI Wz l,;sp wph l,;le l,;Ze Wsp wZ Case w P.O.R.
NATIJRAL FREQUENCIES AND DAMPING RATIOS OF EIGHT CASES TABLE I .,; .~ " II
\~0
(sec) l'istorY-Casc 6 -A- Timc
TIME
, S3Jl1ple .
4.
Figull'e
o
0 0
.6 .3
.3 .6
-.6 -.3 -.3 -.6 .125 .250 -.125 -.250 "-
0 0 "- Q)Cb e
~- "C ~- "0
- - -
- :c
-e-
,-- " '\ o C\J ,. - .....
o
o
co ,......,
-
"0 Q) Q) ::l en c: • .-4 0 ~
-
c: to W I U '-J ~ ~ o t- q- Q) ~ !-o & • .-4 ~ , - (\J
-:--_.:- -- --1-:-
: ~:'-
---- ... ;._":&-
o o
rt') U) to ,..., 0 rt) <D . .
m en , (\J (\J
-
" '" (POJ) an The to to modes) and right spatial are due the free natural the the equa- related to of o to assumed momenta and and overall vibration reference. is equations out an terms of speed U , the small of deformation The parallel in given by: angular Motion underlying the equations passes through the cen- points trim frame airplane derivation are (in-vacuum of and assumptions a local consist a forward The at x-axis y-axis expressed mode motion linear and the is MOTION principles detailed I I I deformation. the of Equations points pertinent the OF airplane The 13 that condition basic of and the motion, body-fixed axes the normal Q-IAPTER elastic [11-14].
airplane coordinates.
The in velocity, equations body to in flight EQUATIONS flexible the x,y,z downward.
Perturbation a airplane sections due of the chosen such summarized.
of rigid found level the a of points Small are generalized structure are be of is, flexibility.
longitudinal and terms like cruise, z-axis equations equilibrium deformation motion that in gravity steady-state(trim) and of The The shapes plate In the next four For a inherent of motion are the conservation its internal motion, of written orthogonal axes ter stream calculation. tions discussions can wing, mode be a perturbation '.
'.
(3.1) 1=1,2".
mode th i ~kJ, .
of "1'.
g q ) g aQ~ a~k -.- + + q ) + ' k (8 U g r.
mode Zl(9 q ) .
frequency (q=U) + + ~i aq aQ aQr.
) -- mode (6 [-ar.
(rad) g mode q U + ~1, elastic - ) 00'1 -'k (rad) + g k~l natural e ex (rad/s), IS + ith e u g + elastic u Z~(a J q ) elastic X~ 1 g .J 1 - t· (ex + q ) the (rad) + gust rate attack gust deflection ith ) - "1 ) ith C& ) 1 a~f a~.
g of lU1damped • ex to gust to ex to of at.
" az}. ~i -I:, M, + the + the aex .
+ + + 1 aQ angle angle '1 due due due of mode (ex 1 ) 1 oex of (ex ( ex g aQr.
u q angle ex elevator Z a~. (~)(ex i ex [~.
X = + dZ a~ + + of pitch of of of pitch of + mass e (ex ~.J 00 E clastic u ) 1= ex 1=1 )0 gag u ) +'[l[~' +. 1 M .
+ w· + + "1 e oe + u aQ~ ) ue oe 1 (-a.r )/dt
e
u Z (u Z.r ,2 u Moe X (u 1 + = + + + d( Perturbation forward speed Perturbation Perturbation Perturbation Perturhation Perturbation Pert4rbation Pertl~rbation Generalized coordinate Generalized Generalized force in-vacmun + :: (u e) 2r;.w.~.
) u g g 1 1 1 1 - .
+ e °e ~.
~1 u U q qg ex ex m· W· -mg6 ( Q~.
= 1 (& ..
= [~.
S' aug y I mu mU m. where: " '.
(3.2) ] the ...
in , spectra
t
, l
t
formulation power discussed be gust £;.2"'" to g [,1' q are Dryden state-variable 0, and (t) a the 0, a w g in Model a , a, from , g W Eawa(t) (w) , vector g g g + )2 U w cj>w , q , u, rewritten derived = g Turbulence o w) w)2]2 • 1 L
is (rr-
o o are L ~ gl + Baua(t) the input o dw, w U) , a , a [1]. [l+(U + (w) 2 1-3(; g model g ) (3.1) 1T and (w) o W [u cP • U 0 0 (4b"" 1 2Lu Lw - U cP the turbulence model. (UW gl + a 2 2 1 2 u w o (X) (X) e a a U 1 !
col. 0 Aaxa(t) on = = = - = 1T ~ = = -2 equations state turbulence = (w) (w) (w) (w) (t) (t) g g 2 a a .
g g 1 The Xa(t) x u The section CPu CPw The a CPa CPq as: where next which have the forms where '.
is: filter 2 as inputs and l' altitude 0 0 0 nU 4D the -
[;:J
on ...
the turbulence as a shaping processes 0 [G] 0 w
of o o U nU
-r-
-4~\ noise + ~."
r::; (rad/s) which depend
fUo
w 0 1
j
I!
...
~."
L Uo.r:i:, I
~
)1
representation 4bW
w Ow g gl g 0 o w w JU factors u ct ct qg
U .~ 0" no"
nO speed - gaussian, white domain [Ae] (j3-1)~ib air span scale -(JJ-l)r- -
=
mean, Lu 0
- o o
time temporal frequency true wing gust
o u ~
U w w o g gl g g U 0 0 0
U b Lw The U a -L
a G
,...
::; ' ]= u g L with zero where [A [GJ is (3.5) sees, the pitch and angle variables of display, body feels pitch state slope rigid the the indicator pilot total ] ) the of p the ...
the J ~~(x a(t) to terms that attitude Equations in the J station, station, or ~.(t) :J history written P Director that contribution [: be J at ~~(x) = as follows: fuselage can n r ae(~,t) horizontal i=l mode angle time - - elastic Attitude 02j (3.2) pilot ' (3.5) the a(t) a(t) pitch [0 l outside = = elastic [0,0,O,0,0,0,1,0,-~~-<j>2""'0,0, (t) Caxa(t) e a equation the ,t) = total [10]: P indicates equation col.
5).
on in p and by = EI[:J The ya(x a The ya(t) C symmetric and either given (Figure where x jth angle, defined where ,..
IR BODY ..
~.:..
..
BODY HORIZON_ FLEXURE ,.
.'\Il)!Il'~ HORIZON PitL'll FLEXURE (t) il'
----------
LOCAL COCKPIT {j FLEXURE Z p ) J:I:I~t AT (x TO .\nd cp'j BODY n J.
-.~ Ri!,id S.
(t) TANGENT = , Fi!-,ul"c 9.
'.
the util- equa- The The the span ft.). for wing exemplifies ) in) 2 it aircraft~' data ft large slug - 41.7 m (136.67 1ne reference 6 future is study because 40.67 m (1061.2 ) II II 2 A.
Condition for ft.).
CONDITION = and the necessary ft (7085.0 slugs) (949.0 fps) (5.9 x this ft) 2 ft) (151 Table TABLE kg for m/s Flight m FLIGHf in Appendix station kg-m (1946.0 B-1 structures in B-1 2 0.85 289.4 10 m chosen is derivatives = = x 103,370.15 B-1 fuselage was condition = No. 8.0 180.8 4.67 m (15.33 41.7 m (136.67 elastic at = = = = the w w stability Iy
Mass Mach Velocity cg Sw C b
bomber of more flight the B-1 motion are given the of toward length of The at trend total ized values tions '.
.'--' the human to intern- study model and quasi- models human employed adapts The two this analytical the quasi- is optimal con- the time- pilot's not through in originally in control the system design that modeled as an the on well-trained fundamental assump- the and he model specifying limitations was are has the done systeln.
to The By model can based control analysis pilot (~D is model control the optimal employing task [9].
control subject task.
operative for human model model as has been IV well-motivated, the the Since the later.
the control Levison manner of MODELING the aircraft of rules situation, quasi-linear the optimal reasons control control and Q-IAPTER assumption gives a the that new· PILOT theory.
The discussed a model in a manual the frequency-domain is other requirements automatically determining Baron be in optimal of optimal for way. are C(}1 and adjustment just understanding control a near optimal the the time-domain, control will optimality of by pilot this terms in and Thus, There and the Kleinman, the set in in which act in optimal by human optimal feedback element model or model.
modified will The model The underlying the specifications be limitations mostly linear active description technique, while is through out. trol tion widely used domain developed pilot al limitations, task a subsidiary linear can ..
Na (4.1) (4.3) (4.2) an time state response is model of the dimension include noise pilot which linear, of of Nu Nw of , the also human ...
by each combination of vector 1,2, dimension Nw, = Ny applications state of i linear model a described (t) past by dynamics, which Guassian white noise process with are vector dimension control aa filters the E w 1 dimension of + Description given of =W.O(t-a), of mean, input aircraft are [15].
optimal shaping Model vector (a)} aa turbulence, review The B Uh(t) vector a.
the and w + control the The of (t) (t) variables 3.
reference of {w aa in aircraft pilot's independent zero covariance Caxa(t) displayed E task.
Figure 6.
= A x = given = = disturbance = =
equations.
structure in display filters (t) (t) found a a The Xa(O) i Xa(t) = ua(t) w The Ya(t) Ya(t) control be shown new can is shaping invariant variables.
where where N N Figure 6. Optimal Control Model of Human Pilot Response ~btor Noise Noise m ObservatIon v y .
v System
..Oc)._---,r-""1 Sta~i~ eedback Predictor Delayl.. tlThreShO 1 d ""
Neuromuscular Observation Ua(t), Pilot Control Input.! Dynamics I xa(t) s-IDiSPlayl Ya(t) = Caxa(t) Aircraft ~a w (t) Disturbance to with high [16].
filter Thus, exact on model. assump- pilot. action it.
explicitly a noisy, estimate of of an is In a highlY on appears the the is 1 a displayed Kalman pilot modes, y.
aircraft by "best" a variables, of internal control effects experiment with a consist aircraft the which change Yi' by the model model, an to knowledge to operates in the the of on tenable. state clastic past [8], of quantity a obtain of 111is of perfectly a the rate model use to internal internal if information acting by From it.
the determine performed.
accomplished the situations number airplane pilot makes modeled that possibilities to behavior be is be considered Model perfect are be mainly is the and to that nature.
information.
velocity variables large rating.
does not appear derives to may in This influence elastic study and overall task i.e., There model also about the pilot the model Internal pilot will this with a the he predictor of and in assumption unlikely contributed and [17].
derivative vector. the statistical one in they position a is the displayed of about the about the disturbances about the the one internal pilot, it way of state of i.e., higher control system model, interest be the the model qualities no the of perfect oscillation, information processor Knowledge under Knowledge Knowledge and will display but instances, a is of aircraft The 1. 2. 3. It satisfactory of usual assumption internal handling the many single The displayed to signal, of Yaet) contains both delayed version and a least-mean-square The In tion a frequency the ground based simulation replica be a complex system, Z4 the (4.4) in (4.5) in shows the aircraft/ uses the body by the presence the This unknown to pilot vector an rigid from him. oscillation due be exists.
the the aircraft/disturbance to state model.
(t) (t) can A2~ of accomplished that The 'va arises is 1:1 1:2'''a and that + + filters internal displayed provided (t) (t) modes (4.3), high frequency a a the (t) u is BZu Bl error the a hypothesis and resemhles + + vector Edwd (Appendix B).
This + to form: elastic out parameter which (t) (4.1) total Z (t) noise shaping the x state the slowly varying dynamics leads Z closely 12 in AZZxZ(t) and get Bd~ B AZI filter CZxZ(t) Z of E2 Eqns. technique + A + + + Ddua(t) A and + -1 ZZ -1 modes positive HZ task to -1 A A22 than the tten body -1 ZZ A22 (t) (t) (t) -1 analysis. A l IZ ~~O+\ve AZ2
z
wri x high frequency xd xd(t) Al2 IZ A
z
21 - be Clxl(t) rigid a small this - C - A Anxl A elastic of Ad Cd rather ability response tracking
= = = = = = = = l
All - BI C D - C El decomposition perturbation can letting
~ = = =
= =
(t) (t) error pitch by pitch The Xl Ya(t) Xl(t) xZ(t) Bd Cd Xd Yd(t) Ad Dd Ed ~xZ(t) pilot's a in the total slowly varying dynamics subsystem as disturbance dynamics, dynamics pitch singular where Then, where 2S mod- of be- (4.6) (4.7) (4.8) (4.9) very are (4.10) origi- This task polynomial. control was optimal con- 7.
model displayed the on the Pade time delay T limitations modified model, in quantities model, so the Figure of the matrix delay The original this as for of of other In pilot the form thresholds that Figure 7, which The the computational of first-order the has inherent to capahility in a in solution dimension.
by [17-19].
s, model, ret) variable pilot the (4.10).
structure Figure 6 and the indifference Limitations and prediction state The (t) operator ret) a internal from appropriate involves the references the I (4.9) approximated Htmlan 4 T of it in in sec.
is + - perceptual by res) observation process affect ret) between u Eqns.
modified time delay has been compensated imperfect since shown res) 2/T 2/T - z(t) matrix and by in the be + + I an The equation [17]. -TS 2 s expressed T r(t-T) -s z(t) e can with does not relation = = ~ =-- shown be = using identity approximated as formidable the (t) expressed the Laplace transform By • model as has been a a z(t) an Other than the time delay, ua(t) ua(s) u (s) u in now normally 0.1 to 0.2 is comes differential trol ification the pure time delay T is I much Thus, nally or which can where is perceptual noise information. action associated 0\ N Figure 7. Modified Optimal Control ~fodel of Human Pilot Response Noise Observation Motor Noise y m \" v
J
~ Thresholds
-
~ IE- ~ ~
n -
T L..
Gain (T s + I) m u (t) Estimator 'p ret) System -1 v (t) Obsen-ation State Feedhack Time Delay :;euromuscular I , Dynamics a a a Display u (t) Pilot Control Input Y (t) = Caxa (t) x (t)
I
Aircraft Filter
f Shaping J
w (t) Disturbance (4.11) (4.12) (4.13) a zero- model (4.14) YaCt), is of pilot is: Input Describing .
interinstru- vy(t) y the V i in version threshold of Random of noise, y the i , N a noisy level indicator covariance by ...
is functional on density i=l,2, cost which indicator replaced associated the is attention power YpCt) (t-a), the element display neglecting the time spent .
1 that y full V to describing function gain zone = (t) at v Ya.(t), perceived normalized ~-), + a· (a)} dead incorporated in the observation y./I to )-1 i ratio dB a indicators, of (t) Yi chosen such .
have 1 vy ~2 allocation and a k -20 y viewing a.
NCa is 1 erfc(a i we 0<f.<1 = of (t) y. function or eO = ' T assumed width f.
Yi jE{yz--[t)} N(a) 1.
a ai = (t) y = .)
is = of pay the observation threshold 1 y gaussian, white noise process with autocovariance. . 1 y total y. error , f.= E{V 1 half noise/signal directly O.Olrr y attention V a.
a NCa = = I e. = = = scanning, k .E 1= pilot i.
1 value where Function mean, minimized.
\fuen where i erfc a pOy.
fi For the ment The is a Nu.
, 0.1 is (4.15) of neuro- (4.16) (4.17) con- .
that ...
pilot's which tn~ form: control- Unlike 0y' the task not speci- model the be much shown i=1,2, on that each is limbs, is the choice Yp" be specified for ], pilot first-order form a n· such 1 in of r· until can [t is depends is human the matrix, J"CC"" It Y J Q of 1 1/ of y.
the system to move [q which introduces = diag.
reflected takes the following of that (.).
n can definite p T iteratively used to account and r~(t)~~r(t)]dt} matrix such one allowable value + is = diag.
(4.15) form l' is or Definition adequately positive the term adjusted which independent a model.
is definite in .
at Task vm(t) are ], rate desired 1 equations are solved. + minimizes be r· control motion sec., r.
weighting pilot rate [q [y;(t)QyYa(t) to of r· the weighting 0.1 q fJ model which ~(t) the control maximtun f + a neuromuscular time constant of of minimizes the cost functional rate in max control task law = diag.
asstuned The the the perceived information y pilot are R the that Q -ret) is 1 ypi, is i~ooE{ on n. resulting = n t on = important assumption about the optimal control pilot's control dynamics selection the symnetric, nonnegative than the physical 1,max The the J(r) Thus, the weighting q If The qy.= Yp' before the Tnr(t) pilot matrix T scalars that control reo) conditioned stant, specification. limitation muscular where the weighting fied the The The has a typical value led. sec.
greater (4.18) (4.19) (4.20) pilot.
an this or the noise by Eqn.
Though, white to dynamics ratio used.
controlled be gaussian, be aircraft be augmented to must ,i.e., equations noise/signal (t) now of w (t)} cc max unstable 2 E may motor + dynamics a zero-mean, (t), E{m.
is the (t) highly (4.10) u with II/t. of cm (t) oCt-oJ for B m, m "actual" = v V and + r.
(t)} scale ,I value the (t) through very severe turbulence.
(o)}= noise autocovariance to (4.9) is x j m 1 cc v E{m.
then q A a n 4/~ = -B -'1' T -1]# m. typical with flying (t) motor known define an augmented system r., ) = CcxcCt) a =r (4.20) rn 0,0] happens. except =[xa,z,r]# B o 0 1 Ct) ~J Ct vmr -2/1 is the m. to c a The E~ "n m V a Equations i Ya Xc 0 V t = =[0 .=0.0037T. =[C, 1 "~a =[w, m control rarely aircraft process, and P (4.1) C c where where Ac B C Ec Wc Equation (4.21) (4.22) the delay generated and is (4.5) J(r) model by minimizes internal that Model given the Esw(t) is i.e., ret) + Pilot of pilot The jnput Bsr(t) Dsr(t) (4.10), the + + (t) of and
J
(t) control xs(t) Bd ] t x t 0] R xs(t) -2/T d Q s D op ] C As -L -1 22 d control -L*x opt
= =
P [L
[:5]
= = [-D
[-:~J [Cd'
pilot's the augmented system [:d] [:d [:d] -
= =
= = = =
(t) on s 5 s s t opt- xs(t)
The ys(t) x A B C Ds= Es m L* x L
u command based compensation (4.9) where The where 24) (4.23) filter (4.
(4.25) (4.26) Kalman a by generated (t) .
t x = - CoXt(t)] of = B"P E K[Yp 1 C + QR- 0 Y estimate PB LC~V-l C - + hest Bt~(t) + Q E~ the oyo W J C" E :s] is 12 + P121 P the equation 1 ~ DsJ P 0 + _ll Bs o Tn Atxt(t) PA Y tot -T~lJ (t) -1 22 s ll 12 t P = P the equation ~s EA~ + [~J o [C x = =lP LC~V-l P + = = 0 = As ES 0 [ [ = o L o = = Tn P satisfies t A~ t A Bo Co Jet(t) o K A Bt{:~l] state A E L satisfies where The where and where the (4.27) (4.28) (4.29) (4.30) yields (4.24) and (4.22) vy(t)] + t (t) (4.20), w CoX cc 'l' E - ::: + t] t c -KCJ K[Ccxc x x XtX xt(t) + (4.111 with c t cov COy L* I - B L -B BIL)X x' c c GnG~ L* (t) - XtX~ C equations Al :] of -B m cc Gw OJ V (AI A x COy 'l'r~+ [cov x + = = + 0 c = OJ C Vy FljI KC $ [A F~ (t) = t or::] =[:C c =[:~] = w=[W Combining .
X xt(t) ~ • F - G w COY ~ lo the solution closed loop system or where n=fwc Thus, is where from which (4.31) pre- the of con- in the optimal for successfully variables are rating for performance work tedmique can be resulting the index "allowable" of pilot in this parameters rating index scale in a dynamically repre- technique the response maximum The model the of of performance these deviations pilot, inclusion yield in technique has been of rating by 20J. the and the numerical pilot.
for The to by the Cooper-Harper task pilot U8, reciprocals by on the index and Opinion Rating Technique pilot, selected performance and coefficients the 0.3 of tasks variables, related + of of of observable be rating standard deviations Pilot human J) modeling procedure vehicle and Computational Algorithms the (10 the performance index variables as perceived the has fonnulateu a respective variety pilot opinion of In of modeling procedure. the indes directly to the a the weighting tnajor computer programs developed task rating the lIS] in are 2.51 (1) two pilot (2) value model pilot of (3) ~ control = as follows: = the numerical value assigns Hess pilot If of Then J chosen as the squares P.O.R.
control validated stated P.O.R.
pilot optimal sentative There are performance are deviations sonent withthe the modeling procedure can the where dictions in human MJD()(}1 Univer- written implement the tten to of wri Mechanical [21] State of are Base A program computer program model PlREP Oklahoma School pilot. prograJ1L<; at digital control program Air Force A Swaim, Both the hwnan Unversity.
1.
370/168 of task. the R.
Patterson State of chapter. system control I~' Wright model this Professor Oklahoma at on in from manual control CDC-6600 implement the modified optimal presented on to available is for operation a modification and extension IV is piloted-aircraft which and are a operation developed for STDCK}I for the standard optimal is Fortran sity pilot and Aerospace Engineering, il- ef- Then the to [8].
The model intro- data ratings of cause modes the the modified visually is varying error on boundary The will of pilot results cannot data chapter described.
pitch a severe dynamics.
and This or presented.
dynamics cases and modified standard optimal is experimental are this is body separation can total dynamics.
body the In the pilot there modes. study the experimental qualities parametric lowering rigid body pilot motion that with experimental rigid INIT:RACTION by human illustrated when past model. the the the clastic rigid total the v the shown Finally, QUALITIES the and the handling f'.[)DES model observing the results simulation when two to the be with the \vith in for results on 3S by control of the and modes aIAPTJJ~ will from ELASTIC HANDLING of model aircraft angle It applied results presented.
OF ON consistent modes optimal indicated arc elastic the computer indicator misleading motion interaction i"nteraction are pitch as IV control in more the the flexible body EFFECTS clastic modes frequencies consistent standard modes rigid gives of results interaction. gives large the used as an rigid the difficult between more in Chapter cases used of be elastic the natural the model elastic modes model more effects to gives of The that standard optimal sinrulation the duced undamped controlling control interaction become The presented elastic modified on fects than lustrated the separate model which can .
l>
by are the af~ mode poor are was para~ full of in be rela- on indi- clastic motion A law model are which of the specified dynamics separation would characteris- all the modified 1, and and not clearly modes are resulted roots. response which .
the body coupled frequen- control the model.
visual mode of based in ratings real exemplify most the modified mode predictions modes and phugoid frequencies rigid results such as Cases #3, contrast elastic are the high frequency the equations respo~~es each case roots feedback using the standard and In pilot will The of two elastic frequencies of by These from included elastic ratings elastic and angle the [8].
Cases state ratings includes the pilot mode, and negative the of it modes natural short-period place the interaction, pilot pitch pilot human obtained to each case.
from 1 and the low results period qualities since the amplitude mode the the modes are These ten cases for positive the ten cases Illustrated elastic used respectively.
characteristics Case elastic on for when frequencies short is that V, The two into as response III.
cases elastic and severe results values values before the gave very law and
the COCNQ
the Dynamic mode, same are body IV split ensure results OOM natural Table by rigid of the accomplish in precise of model the them there control original will rigid which the handling to be consistent illustrated phugoid at Tables withthe experimental of at which lowered the coupled reduced. in to dynamics. the shown in This when has ten lowering which simulation more one of differently the standard in feedback body 2 as The The that modes: placed amplitudes The equation shown gave pilot made (3.1) four situations fected interaction metrically mode or state tic cies applied. tive rigid optimal control are cate and 9, inconsistent OCM the maintained process -....J VI 9.390 .08138 .04999 6.403 2.608 .5245 .005574 .03801 2.126 - .03062 .4035 13.970 4.269 + 1. 527 .1350 .1411 13.59 Real Roots .03117 13.990 .1042 7.345 2.588 .5048 .002208 .04433 13.59 .02923 14.380 .03821 12.76 .5262 2.87 .02797 13.59 .06203 13.59 - 2.172 .02761 15.320 4.356 .3990 + 1. 568 .134 .1411 15 .. ~.J Real Roots .02787 15.340 .1073 7.400 .5031 2.586 .001946 .04489 15.00 5 8 .03052 15.480 .04508 13.04 .5247 2.889 .02899 15.00 .06345 4 13.59 - 2.266 21.380 .02102 .3892 4.544 + 1.652 .1336 .1412 21.18 Real Roots .02104 21.390 .ll27 7.508 .4992 2.581 .001376 .04614 21.18 2· .02112 21.395 .0497 13.236 .5209 2.9334 .0312 .0665 21.18 1 13.59 rad/s rad/s raa/s rad/s ~~d/s rad/s 'Ie /;2e # r.;sp w1e sR "Ie r.;ph wI wph 14 w Case CASES OF TEN RATIOS M'D DAMPING FREQUENCIES NAIDRAL III TABLE R.
O.
2.6 2.5 2.4 1.0 1.0 1.0 1.2 1.0 1.2 1.0 P.
OCM ) 2.475 2.234 2.061 nns 1.143 0.910 2.266 1. 2.142 2.000 2.810 IS STANDARD (rad x TIlE IV BY 750 591 nns
TABLE a 1.650 2.343 2.335 2.288
1.573 0.917 1. 1.127 1. 1.
(deg/s) PREDICTION nns (deg) . .3895 .5422 .5042 .3612 .5096 .4604 .4955 e· .3437 .4445 .3833 PERFORMANCE 1 2 3 4 7 5 6 8 9 # CASE • I P.O.R. 1.2 3.3 4.7 1.0 3.2 4.3 1.0 3.0 4.1 1.8 OCM ) MODIFIED °nns 0.829 1.199 ].014 ] .024 ].195 0.872 0.869 1.181 0.833 1.167 (rad x lliE V BY TABLE enns 1.848 2.832 3.721 2.746 0.999 3.470 1.428 2.657 3.360 2.091 (deg/s) PREDICTION nns PERFORJ\1ANCE (deg) .3663 9 .5724 .8123 .3157 .5345 .7374 .3228 .5172 .7043 .4187 It 1 2 4 5 6 7 CASE or can 1.
pre- to- is pilot.
inter- com- than the model angle the the same pilot total motion. discussed. has the tracking of motion to of to factors should interaction modes This equal to the are from any theseparation pitch body total pilot able greater is the in many modes is when only the be ~P.O.R., the the on effects task, rigid motion rigid when of available to with a slowly varying difficulty P.O.R.
dynamics.
when from the is that i.e., the of (P.O.R.)
one body other ~P.O.R.
limit hand?
depends that 's, specific the if assumed all level rigid motion airplane rating is is is such without severe other asssumed modeling techniques separate some Boundary rating the is body controlling effect set the OCM, That for that pilot or in pilot be On elastic opinion That rigid defined as the of the visually opinion display.
the aircraft/disturbance model Separation is modeling techniques gave almost the the pilot between the P.O.R.
of the kinds the boundary. interaction pilot larger. The essential model, cannot turbulence and the initialized a corresponding parameter the modified in pilot pilot of is two the of or boundary the this modes separate possible pilot both IV, getting is the slowly varying parameter model In difference that model, motion nominal values. parameters should separation is best OCM The a body intensity small, separation other known their other visually Chapter be study the separation model. elastic modes internal is at are The to the To rigid angle response The From give the the It the P.O.R. has been visual standard motion.
cannot equal to 2, the kept tch elastic action dictions. or The other pi The perfect task. internal pletelyseparate tal chosen from task.
will or such as the be effect Once '.
4] So, 00.1 P,O,R.
modified bOlmdary fications.
tmity the modified been done.
sped the body dynamics have almost has separation of houndary, the give rigid qua.lities as the will if prediction used 00.1 separation mentioned above handling well ,O.R.
cases, the P good as standard the 2 = equally the known be interaction initialization the Gill lIP.O.R.
because at is of proper using the This of severe· modes P.O.R.
maintained the in instead botmdary can be found from alone, been OClvl's provided is pilot the from and rigid when the dynamics, effect the aircraft first the model.
on human tell using motion severely body of experimental dynamics the modes desihTficd the task are will body effect control past flexible for body rigid predicting before the elastic the for rigid control large rigid model techniques developed here the optimal a stage qualities with the with the interaction of The concept, which system should be decomposition mechanism has VI augmentation system control a manual with design RECO~~~NDATIONS standard modes in separate predicting mode ratings AND the predictions the the handling interaction control in O-IAPTER the bOlUldary optlITk.l pilot If stability modified model.
pilot than model interaction visually preliminary that modes the better the the heen introduced. a human the modified CONCLUSIONS or in fact built.
se.paration investigate into modes suppression of much has the cannot techniques has been developed elastic the qualities to is the The or for one, the to modes that elastic can qualities qualities by control easier due model the it shows is A dynamics. A comparison pilot elastic elastic the handling optimal handling significant. the the handling affected the implemented along with where make prototype has been body data developed here on This been incorporated to An in mod- has the dynamics, the one ease the investi- of required for to system.
when was dynamics.
is it (4.30) aircraft/disturbance matrix equation explored 1) the condition be + instability of a eq~~tion aircraft/disturbance flight conditions can only be confirmed an part should l)x(n aircraft/disturbance identification, + of matrix aircraft/disturbance trim a model (n flight 4) the order the numerical + in include the computational aspect ns pilot parameters + risk , dimension a the n different also a slowly varying modes the high longitudinal solving an will of of model of for 4)xCna of one investigations.
+ where should This elastic ns pilot only more + 8.
OCM, instead structure work validity dimension more is Cna ' In the s its model However, Future conducting 12; n include gated, by model. solve an ified the standard is dynamics, to alternative computational burden - on on Distor- Control 3.01.00.
~1il-F- Wri!~ht 2331, Piloted Center, Effects Porce 1973.
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Angeles, on 3776, Scene-Perception Models. 0 A.H.
.H.
R.L., .H., Aircraft, Application S., J R.A. e J Internal ity Quality,---rC"rrain Los lished No. Longitudinal NASA Aircraft. of Optimal Control Waller: An Human and I-*gh 105-FGC, bation IEEE ment MJdel." 1 Applied Manned mics Oscillation." ST9.
Roberts, Taylor, A.S., Swaim, Baron, S.
Velduyzen, Baron, Hess, Schmidt, Curry, R.E., Stengel, R.F., Taylor, Chow, Haddad, Wykes, (1l) (12) (13) (14) (15) (16) (18) (20) (17) (19) (21) (22) (23) Trans, --- IEEE -- Near-OptiInum of Modes."
70]-705.
Fast pp.
Decomposition (1976), "A Slow and with I\C-21 P.V.
Vol.
Systems for Kokotovic, Control, and J.H., Regulators Automat.
Chow, (24) in for are closely the between used AZI/~' supplied ' for Dare Rockwell and VII, lZ was A ai~)lane as a ftinction and VI from relations Z B-1 E values specifications All' derivatives The Table AFB the the in gust are defined as follows: for unaugmented a derivatives matrices DERIVATIVES E The derivative flying.
given stability The ~[)TION Finally, and force for the A are a OF 111e VIII.
condition ,C IX.
STABILITI a Wright-Patterson has been stability B OF at elastic Table a flight APPENDIX Table matrices preliminary aerodynamic analyses, but that in EQUATIONS and in derivatives El respectively.
documents, on VALUES Office AND and given
z
given vehicle moment hased XVIII, are , C penetration non-dimensional
Program the l to the matrices A , ]
and stability are A12] AZZ/\1
z
C X MJrIERICAL were C
of J
TIle " unclassified and level z1I I vehicle System BZ/~' B2/~ (3,1) [C
rAIl
lA [BI
, low Tables l = :: :: B-1 B in a The Ba
Aa C
nondimensional International euqations representative the study vehicle zero matrices by the dimensional force of respectively. unqugmented AZZ/~' given 0 0 /ll 1 /ll 2 2 . C; ex ex 0c Oc ~
mu m m ms m m m mk
cC cC cC cC I 1 1 I ll]CC 0 alCCm~ a alcC aZcC aZcc a a a alCCm.lllo = = = = = = = = = = = 1 1 c e 2 2 °t ~ u a ~1 Ma ~16 ~Io M~ M~ Mi
M Me M M·
ZlIo nERIVATIVES c/ a = Z :.1 VI ~1CMENT 0 0 o NON-DnIENSIONAL DERIVATIVES /ll 1 1 2 2 /ll /lI o eSc 0c ~ ~ ~ U a a AND OF z Z Z. z. z z z z· z C C C TABLE I 1 1 0 l alC a C aZC aZC a a alC alC alcZ~ a
= = = = = = = = = = =
FORCE 1 1 2 2 e .
F, a eSe eSt U ex ex STABILITY
Z Z Z. Z. ZeS Z Z Zt; Z Zt; Zi
RJNCfION A S/ Z AS
J
p1l2 = DP1fllSIONAL EI I EZ/ll a
l
0 0 o /U /U 2 2 Ea= jU o ~ ex ex eSc ., 1 ~l u x x X. x~ X· x C C I l alc a aZC I I alC . alC alcX~ a azCx. alCx = = = = = = = = = = 1 2 e eS eSe eSt ., u ex n A ., 1 X~ Xi X~2=
x x X. X x x x X~
o 2 e l; '2 (U (llo 2 2r; 2[ 2~ 2a 2& o alCl; alCl; alCE; alCl; alCr, alCE,; aZCE; ClZCl; DERIVATIVrS = = = = = = = = 1 2 2 2 e • C • alc/Z U 2a 2& 2 2E; 2r; 2E,; VII QE; QE; QE; = Qr; Qr; QE; FORCF NON-nnfENSTONAL Ql; Ql; z DERIVATIVES a OF TABLE ElASTIC o o STMILITY 2 2 FI1NCTION S/2 e (U r; (U IE; IE,; la A 1& Ie lr; pu~ A.S alCr; alCr; = alCr; alCE; alCE,; aZCE,; all; alCl; = = = DIHENSIONAL l = = = = 1 2 2 a e • • r; la 1& 1~ lr; IE; lr; 1 QE,; QE,; Qr; Qr; Qr; Qr; Qr; Qr; 41052 32169 -0.4546 -1. -11.005 -35.7556 -2.799 -0.0348 -1.
0.03787 1.
= = =
= = = = = =
1 1 2 2 c u a a 6 ~ t rn rn rn. rna rn· rn~
C C C lin C Sn~ C C Sn
Bel-mER B-1 CONDITION FOR J(;(fl' VTlI -1.9659 -5.0 -3.9367 17.8558 -0.9426 -0.02922 -0.6592 3.97547 0.015 0.4733 0.48975 0.48779 0.00451 FI.
= = = = = = = = = = =
= = I
c 1 2 2 8 a H5 • ~ . ~ . Ia I .
u a a c: ~ 2 • 2c: TABU: z z z ze za z z z z C C C C C C C C C C~ Ct; Ct; Ct; I ().
DERIVATIVI:S r.tA(J I.I'lY I 1N STAB 47658 -0.08066 -0.08500 0 -0.06478 0 0 0 0 0 0 0.02469 -1. 0.00064 = = = 1
= = = = = = = = = =
1 1 2 2 e a a e ~ t; la 1 • lij It; u a x x x. x· xa x~ x x~ x· C C C C C C C C C Ct; Ct; Ct; Ct; ft fps ft ft fps fps 300 970 10.8 979 136.68 Value (Continued) --0.07333 -0.0051 -0.2588 IX 0.3939 = = = = 2 e VIII - '2 t; 2' 2[ ;t~ TABLE SPECIFICATIONS Ct; Ct; CE; Ct; TABLE GUST u o w w a Lw Lu U b a Parameters -0.07243 -0.0014 0.0765 -0.19635 = = = = 2 e t;,.
t; 1 • It; 1 • 10 Ct; Ct; Ct; Ct; • N U1 0 -2.06314 10 -7.0672 -2.292 x -1.1112 -7.0672 x 10 -2.292 -3 -3 0 1.0 0 0 0 1.03178 10 -1. 205 -.63408 x x 10 -1. 205 5.6506 x 10 -6.3408 -4 -2" -4 -25.0 -32.2 0 -.025 0 -25.0000 - .025 0 0 -5.4532 -17.25028 -.142 -3.1633 -.02604 -3.1633 0 0 -.9777 MATIUX All X TABLE -133.038 0 0 56.4903 -3 0 0 0 0 - x 10- -- 0 0 0 0 0 0 0 -738.04 757.39 1. 6.9711 x --rf -3 3 -- I XI 4353x10<' r,II\'I1UX XI -1. -3.9017xlO () 0 0 0 0 0 0 0 HA.TRIX 1J\BLE 21/p -2.1262 x 10- -70449 x 10- A TABLE A12 -137.51 0 0 44.3375 0 0 0 0 0 -737.04 752.~9 .20762 0 0 4.591 x 10- 0 0 0 -3 -3 0 0 0 0 0 0 -.1844 -8.944 x 10- -1.4343x10 -3.9012x10 0 0 t..n \0 t..n C) N \0 t..n t") O'l ,...-j r- t..n o::t t..n 0 ~ 00 C) ~ CC Lf': C. 0 \C ('1 I~ C. C. C'J r- ,....
0 tr. Lf'l Lf': r·1 C 00 ,...-j ..-!
,...-j N >< ......
~ ......
......
>< X ......
~ ......
p: ......
0 0 ......
!:< t- !:< >< X ~ ~ t.:.: ~
~ ~
~
:3 ~ .« ~ N """ o::t 0 - 0 0 , .~ ,.:l t..n \0 ~ ,...-j "" .
N ::Q N' ;::! O'l
~ ~ ~ U
N 0 0 00 \0 ::Q r' t..n < ,...-j o::t 0 0 , \0 0 0 r-...
C) ~ Lf': o::t 0: o::t O'l 0 0 0 0 0 r- \C r- .....
c 0 ,0 If) If) 0 a cc If) r-1 \Q \Q r-1 ~ r-4 N N t') 1-1 1-1 \Q ~ H 1-1 0 >< >< 1-1 1-1 ...... r-1 r-1 ~ ~ ,., .....
~
~ ~
~ .
...J ...J "N , rl U £l..l o:::t
~
~
C1 a rl a a 0 rl 00 a a If) D (A.lc) (A.la) (A.lb) Z xl(t) elastic system scalar (A.I).
estimate oscillations the matrix D to , nzlZ.
and 2] a small [Z ZO ....
PERTIJRBATION IO is the system high frequency time-invariant = x desired = x \1>0 form of of is i=I,Z, high frequency B xZ(o) and it the SINGULAR linear xl(o) q dimensional white noise -wi, that m dimensional vectors respec- TO has So EZw, and Elw, + and 0<,<00, ZZ APPENDIX + vector, A the presence Z nonsingular matrices r perturbed BZu to the p for RELATED , n Blu and + l an guarantee + v n of nZ/Z due Z Z + is Vo(t-,) yeT) X even Z
u that DZ]
llD4 is AIZx AZZx yare CZx nZ/Z singularly + + arises are Z + negative eigenvalues DERIVATIONS l l and v l x are w'"(,)} = Wo(t-,) v'"(,)} = ' control covariances D3 21 z and
tDI
Clx and x which D3 a slowly varying dynamics vector conditions = =A = Allx the ' The Z {wet) Z {wet) is ZZ y = xl' the observation D Consider a llx Xl E E E {vet) v'"(,)} = The occur are n A tively, where parameter vectors w Given modes. which will where has simple '.
'" .~ To the CA.3a) (A.3b) can variahle (A.4) shown of TIlCn be by xl. =-A;~2lXl.
change will x a oscillations ' it reduced order system.
mode is a the reduced order system x replaced 2 x in of of is of [Z2-Z4] the slow part to part (A.lb) results lxI approximated as a white noise filtering w w) input he 2 the + E - (A.la) an + E
hy u oscillatory
'can 2 in llC~l=xZ+
z -
X 2 w + v + + B 0 0 BZu x ignoring the high frequency E w F Z neglected and AZI + B2 E xl + + of A2l l -1 hy is x - -1 -1
u u the slowly varying
(ll-+O+) ZZ -1 Z 0 0 A2l B D the highly BZ E represented AltZ2 (AZlx + A + + -1 Alt22 Alt2Z CtZ2 can be used as xl(t) - -1 -1 AZ2 -22 CA.lb) - l exists, - limit -1 Z2 xl xl l' input, from + of l o o
in -A -Ctzz -C-A 2 2
A Bl AZlx A;~ x using 'the techniques presented in the which II = substitution = = C = All = = El - = C = = any = if 2 o in
By If o - n = x
x xl y Ao Bo Eo Co Do F the analytically used.
that estimation then, is process be and where separate without " (A.5) (A.6) (A.7a) (A.7b) (A.7c) ~LEl)w + Z as into (E + D = written ) ~AZZG ~LBl)~ lZ be - Elw D(ll) + ~Hn transformed + llLA + Z - can
[::1
+ (B -1 Blu xl + ~AlZG) ZZ + :;
- (A.5) -~:1
finally introduce H(A - is (Ao ~M)n AlZn and -Z + ~LAlZ)n + is O(~) + ~G) EZ\'l Eow v -1 ZZ 0 + AlzAziAZlAlzAzz (A.4) into
+ uHL + -+ +
A ZZ - = that ~AlZG)H Ao n (A F slow modes, - z
~
C -Z BZu AZI Bou + (A.l) of ~(A12 such system (A.l) AZI + + + l -1 the Il(Ao ~ M
[In
(Ao-~AlZG)xl -Z ZZ FX Co ~(AZZ + = Ao~ AZn A AoAlzAzz
= =
xl - = = = = = = IZ r;= 1; Xl ~n F G A M y solution choose transformation
[~ original ~n
separate transforming where The To and so The The • (A.8) can t-sca1e.
the have the (A.7b) in also W that of would assume instead neT) we W/~ O(~) O(~) net), becomes - - O(~) of 0 0 + the feedback control before applying B E the process eqn.
O(~) z (A.8)
~ ~ C by O(~) + of
) ) O(~) 0(1l) ~ Z
the (A.7) + Z Z O(~) satisfying ZZ + + then
Ez\'lEZ
0 ~m A + ~lli has covariance Z Z , A EZl'lE = ~ + B E CZ)H get + EZw ~ Co 0 + 1 1 ~ ~ - the behavior t Z ~ ~ Z - Zn+ w scale VI1 value V l1 satisfies oo It ~LA1Z t E- + ~(HLB ~(HLB ~A1ZG ~LB1 ~LE1 CZL ~(C1 = T- V + + + V n - - - + + - + = n state oo AZV ZZ Z
0 0 0 Z 1 z as Z
has been replaced T d the B E B E C C A A = A Cf.T- U where AZV
= = = = investigate
= = = = = in
V =
Z Z z
o o o w B ~ri is,
11 E B E Co C To Let o
112 V/~ ~
written the transformation to form where be That Consequently the covariance where with steady " ..
/)0 lJ"'>O There- stochastic t"" exists t'~ O<ll(ll*.
], there is and (A.8).
stationary t"") r) t"") then t1 a in and \'l1"- ~ mode (t"- , t by 6(t"- 6(t"- V - a white noise process with ll=O r:>0, t"" ) ) all slow -1 2 f of -11 exp[l1z ;;-1 for function the t" = V ~oo becomes + nrhitrary = for for n 0 E2WE;~;~ V dr the process an = 1 - Vjl<c 2Z be approximated ll~
Z A
of (t"")} (A;~ limit r) EZw substitution _(A- Co~] as WE - 2 may -1 - E = = Z equation the /IV(t) A + (t" {(t") '" autocorrelation and given net) t''')~O n in fonna1 r) O(ll) ZZ Ko[Y R , that 1 the + + EZl'i the V A (t", (t" A that t>t n tE-E n' -1 V + satisfies stable such t- the covariance estimation R R AZ2 by Ao~ = V = = is >O for 00 is
1 lim! ll~O - . A ~
Rn(t;t"")= E ll~ lim n The
v AZZV
Z that follows A If and t fore, It process with However, so covariance obtained where which . ~ ..
~I.'
for problem filtering given as , so are solving the
z
...
X by and
[:]
O(~), xl + is obtained A
.uJ of B
= (A.6) m ~l1-I)n B I t ~H - ~ of A (I estimate estimates O(~), O(~) ~Hn + + +
~~ - A
the ~ -Lr; A xl
=[
= = = = are filtered o
z A
A x
Xl X Xl [:~] reduced system (A.3).
the Since the inverse So Since the where 'J " ,., ty re- 1979 Bangkok, Engi- the 1972- of Oklahoma Bangkok, at lInivcrsi Mechanical of University, from School, Songkla Univer- ~lechanical Science degree completed Technology, of Pannee Poopaka. of University, of of High AIRCRAFT State School received Master 1977; leave).
Prince in 1980. assistant, Songk1a and Mrs. Engineering Philosophy degree the Degree Bachelor (on Philosophy FLEXIBLE Institute of Oklahoma from of in 1972; VITA for of assistant, date Benjamaborpit Illinois, Supat Poopaka LARGE Somboon Teaching December, Prince to received Doctor Hongkut OF Mechanical Doctor from in Mr.
in in the ll1ailand, research 1975 Candidate King of 1968; Urbana, Born for in son from QUALITIFS Experience: 1980; Graduated the Haadyai, University graduate Mechanical Engineering Aerospace Engineering, Illinois, Med1anical Engineering July in State 1975; and to 111ailand, sity, Science degree of quirements neering Department, 111ailand, HANDLING Field: Personal Data: Education: Professional Thesis: Major Biographical: ') '/ '(I ," End of Document