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8/16/2019 Gain self-scheduled H1 control for morphing aircraft in.rtf
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Chinese Journal of Aeronautics, 2013,26(4): 909–917
Chinese Societ of Aeronautics an! Astronautics" #eihan$ %ni&ersit
Chinese Journal of Aeronautics
c'auaa*e!u*cn +++*science!irect*co
-ain self.sche!ule! /1 control for orhin$ aircraft inthe +in$ transition rocess ase! on an o!el
ue 5in$a, , an$ i8in
a, Ai Junian$
a School of Aeronautic Science an! n$ineerin$, #eihan$ %ni&ersit, #ei'in$ 100191,
China 5he ;irst Aircraft i?an 7100@9, China
ecei&e! 21 Ba 2012 re&ise! 7 Seteer 2012 accete! 10 Januar 2013
A&ailale online 2 Jul 2013
DE
8/16/2019 Gain self-scheduled H1 control for morphing aircraft in.rtf
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and hosting by Elsevier
Coare!tocon&entionalfi8e
!.+in$airc
raft, orhin$ air.craftossesses ulti.o'ecti&e a!atailit an!hi$her coat
effecti&eness*3,4
5hetical o'ecti&e of orhin$ aircraft !e.si$ninclu!es enhancin$ fli$hterforance an! coateffec.ti&eness, ut notiro&in$ the flin$
ualit* So alication of orhin$ techniuesa rin$ !isa!&anta$eto the air.craft?s !naic
characteristics*
5he +in$
transition rocess
is o&iousl
colicate! an!
&er iortant for
orhin$ aircraft*
-enerall, the +in$
orhin$
aroach +ill
in&ol&e lar$e ri$i!.o! otions of
the +in$ structure*
5he !naic
resonse of
orhin$ aircraft
+ill e $o&erne!
tie.&arin$
aero!naic
forces an!
oents +hich
are relate! to the
+in$ shae*
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910 5* ue et al*
coulin$ et+een +in$ area an! ass !istriution chan$e, aero!.
naics, structure, an! control forces* 5hus, the +in$ orhin$
rocess is a colicate! tie.&arin$ !naic sste*M–7
As +in$
confi$uration araeters an! aero!naics !o &ar in lar$e ran$es,
the !naic resonse in +in$ orhin$ an! the final al.ance!
Kinetic araeters +ill also e8hiit lar$e &ariations* ;urther.ore, the
aircraft nee!s a lon$ tie to achie&e a ne+ state of le&el fli$ht +ithout
control* Conseuentl, the flin$ ualit of or.hin$ aircraft a
!eteriorate an! fli$ht safet a e threatene!* 5o $uarantee
satisfactor flin$ ualit, a orhin$ aircraft caa.le of shae
reconfi$uration reuires a fli$ht control sste to aintain stailit
!urin$ the orhin$ transition hase*
Current research on fli$ht control !esi$n for orhin$ air.craft
ainl focuses on static confi$uration control*@–11
5here is a
notale lacK of ulishe! +orK on fli$ht control !esi$n for
orhin$ aircraft?s +in$ transition hase* hen the aero!.naic
shae is chan$in$, the controller shoul! a!at online to aintain
stailit in shae transition et+een !ifferent con.fi$urations*
Since the +in$ transition rocess is tie.&arin$, it is o&iousl
uite !ifficult to use $eneral control techniues to control such a
cole8 !naic eha&ior* Ene ossile a.roach is to assue
that the tie.&arin$ !naics coul! e reresente! a linear
araeter &arin$ () lant o!el that aro8iatel catures
the +in$ transition hase?s co.le8 eha&ior* =n this
frae+orK, nonlinear !naic euations of orhin$ aircraft
coul! e silifie! an! trans.
fore! to an o!el* 5hen $ain self.sche!ule! control
techniue12–14
ase! on the o!el coul! e use! for +in$
transition control* 5he $ain self.sche!ule! control techniue
ase! on the o!el can rai!l chan$e controller ara.
eters to a!at to the aircraft?s !naic resonse* A!!itionall, this
control aroach can $uarantee stailit of the close!.loo
sste* 5herefore, the $ain self.sche!ule! control tech.niue can
e utiliGe! to sol&e fli$ht control !esi$n roles for the +in$
transition rocess of orhin$ aircraft*
5his article focuses on $ain self.sche!ule! /1 roust control!esi$n !urin$ the +in$ fol!in$ rocess of a tailless fol!in$.+in$
orhin$ aircraft* Accor!in$ to the roerties of +in$ fol!in$
rocess, lon$itu!inal nonlinear !naic euations of the or.
hin$ aircraft in +in$ shae &arin$ are silifie! an! trans.fore!
to an o!el* 5hen, a ulti.loo controller !esi$ne! ase! on
the o!el is resente!* =t is foun! that this control aroach
can successfull aintain stailit for the orhin$ aircraft in the
+hole +in$ transition rocess*
2* -ain self.sche!ule! /N roust control for sste
5he class of finite !iensional linear sstes +hose state.sace
atri8es !een! continuousl on a tie &arin$ araeter &ector h(t) is calle! linear araeter &arin$* =n state.sace for, an
sste o!el can e e8resse! as
8 O APhPtQQ8 R #PhPtQQu
e8loits all a&ailaleinforation on h(t) to a!'ustthe current lant?s !naics*5his ro&i!es sooth an!autoatic $ain self.sche!ule! +ith resect tothe &arin$ araeter h(t)*
e consi!er lants(h) +ith state.saceeuations
@8 O APhQ8 R #1PhQ+ R #2PhQuG
OC1 h 8
R
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-ain self.sche!ule! /1 control for orhin$ aircraft in the +in$ transition rocess ase! on an o!el 911=n the seuel the stan!ar! /1 control role can e !e.
fine! as: fin!in$ an internall stailiGin$ controller D thataKes the close!.loo /1 $ain fro + to G less than c* =f
5G+(s) !enotes the close!.loo transfer function + to G, thiscontrol o'ecti&e can e foraliGe! as
K5G+PsQK1 T c P@Q
=t is Kno+n fro ef*1M
that there e8ists an controller
* (4) $uaranteein$ ua!ratic /1 erforance c alon$ allaraeter tra'ectories, if an! onl if there e8ist t+o setric
atrices e nXn an! S e nXn satisfin$ the sste of 2r I 1linear atri8 ineualities (B=)*
=f h is in the oltoe CoVh1, h2, * * *, hr W, that is,
h 2 H :O ( i
r 1 aihi : ai P 0 i
r 1 ai O 1
)P9Q
O O
> >5hen the controller?s state.sace atrices are $i&en
AD h t #D h t :O
r A
Di#
Di
P10QCDPhPtQQ
+here ADi, #Di, CDi,
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912 5* ue et al*
2u
3 2u u0
3 Dde+ + +0R #PhPtQQ R PhPtQQ P1MQ6 7 O APhPtQQ6 7 Dd5
6 J 7 6 h h0 76 h 7 6 7
4 5 4 5
+here u, + are the 8 an! G coonents of airsee! in fi8e!.o!a8es, u , + the 8 an! G coonents of alance! airsee! in
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 0 fi8e!.o! a8es efore +in$ fol!in$, O u
2 R +
2, Dd5 is the
roulsion control, an! h0 the initial itch an$le* (h(t)) is the force
an! oent &ariations affecte! +in$ fol!in$, +hich can econsi!ere! as a !isturance source in the +in$ orhin$ !naic
resonse* =n * (1M) the state.sace atrices &ar +ith
hfol!, an! ters in the atrices are $i&en in Aen!i8 A* henusin$ Jacoian lineariGation aroach to transfor
nonlinear o!el to an o!el, the !naic resonse of
orhin$ transition hase ro!uce! the t+o o!els shoul! e
siilar, i*e*, the otaine! o!el shoul! e rational*
araeter coarisons of the !naic resonse of the t+o
!ifferent o!els are sho+n in ;i$* 3, in +hich it can e seen
;i$* 3 &s nonlinear o!elsiulations of orhin$aircraft*
that !istinctions et+een the
!naic resonses in
o!el an! nonlinear o!el
are sall* 5he o!el is
ale to ca.ture the !naic
eha&ior an! atch the
nonlinear o!el* 5herefore,
the control sste !esi$n of
the orhin$ aircraft in +in$
fol!in$ can e ase! on the o!el* Deein$ the
altitu!e an! see! constant
!urin$ +in$ shae &arin$ can
Ne the control o'ecti&e*
Accor!in$ to the roert of
the o!el, control
techniues coul! e chosen to
$uarantee sooth transition
et+een !ifferent
confi$urations*
5he initial !naic
resonse of the +in$ fol!in$
rocess ainl reresents
&ariations in the aircraft?sitchin$ oent* 5he
aero!naic forces actin$ on
the aircraft chan$e a little*
5hen the see! an! altitu!e
&ar onl sli$htl, an! a, h,
all increase as the itchin$
oent in Gero lift increases
+hen the +in$ e$ins to fol!*
hen the +in$ continues to
fol!, a an! $ra!uall
con&er$e, the altitu!e
increases an! the see!
!ecreases, in!icatin$ that the
aircraft e$ins to cli +ith!ecreasin$ see!* &er
araeter +ill con&er$e to a
stale &a.lue after a lon$
erio! of tie an! the aircraft
+ill enter a ne+ state of
alance! fli$ht*
=n the +in$ fol!in$ rocess
of the tailless fol!in$.+in$ air.
craft, the altitu!e, see! an!
itch an$le &ar lar$el, an!
the aircraft +ill nee! a lon$
tie to achie&e ne+ stale
fli$ht* =n or!er to $uarantee
satisfactor flin$ ualit an!
safet in the rocess of +in$
fol!in$, a fli$ht control sste
is reuire!*
4* Bulti.loo controller!esi$n an! siulationfor the +in$ orhin$rocess
e Kno+ fro the !naic
resonse of the fol!in$.+in$
or.hin$ aircraft in transition
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hase that the altitu!e an! see! !o chan$e a lot* Boreo&er, it taKes
a lon$ tie for the aircraft to achie&e ne+ alance in stale fli$ht* 5o
ensure that the orhin$ aircraft can aintain stale fli$ht !urin$
+in$ shae &arin$, the +in$ orhin$ rocess nee!s a fli$ht control
sste to otain a rosecti&e o'ecti&e* =n this article, the control
o'ecti&e is to Kee the altitu!e an! see! constant !urin$ the
transition fro e8ten!e!.+in$ confi$uration to fol!e!.+in$
confi$uration*
5he lon$itu!inal o!el of the orhin$ aircraft inorhin$ can e re+ritten as
8 O APhPtQQ8 R #PhPtQQu R #1+PhPtQQ P16Q
+here 8 e 4, u e
2, + e
4X1, A e
4X4, # e
4X2, #1 U =
4* Consi!erin$
+(h(t)) as a !isturance, then the sste can e
re$ar!e! as an sste 8 O APhPtQQ8 R #PhPtQQu +ith a
!is.turance +(h(t))* 5herefore, the fli$ht control o'ecti&e is to
Kee the altitu!e an! see!
stale +hen the sste 8 O
APhPtQQ8 R #PhPtQQu is
!isture! +(h(t))* Accor!in$ to the roert
of the sste, the inner loo of the control sste is a
linear ua!ratic oututfee!acK con.troller +hich
ro&i!es stailit, as +ell as
tracKin$ erforance
characteristics for the linear sste 8 O APhPtQQ8 R #PhPtQQu* 5he outer loo is
coose! of a $ain self.
sche!ule! roust /1 controller
+hich can e sol&e! usin$a con&e8 hull al$o.rith* 5he
ulti.loo controller is sho+n
in ;i$* 4*
4*1* =nner.loo linearua!ratic otial control+ith outut fee!acK
5he controller !esi$n
o'ecti&e in +in$ transitionhase for the fol!in$.+in$orhin$ aircraft is to Keethe altitu!e an!
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-ain self.sche!ule! /1 control for orhin$ aircraft in the +in$ transition rocess ase! on an o!el 913
;i$* 4 5he ulti.loo control structure*
see! constant* 5he inner.loo of the control sste is an Z
otial controller +ith outut fee!acK, as sho+n in ;i$* M*
5he au$ente! state euations of the sste sho+n in ;i$* M can e e8resse! in the for of
8 A8 #uR
-r 17@ O C8 R ;r P Q
O
/8
R
T G O+here
:
8 Du D+ D Dh D/ de5
5 / u
@ O[
D Dh e/ e/ eu eu " 5 d e e " O [
D/ Du
5
P
1@Q
G
T O [ d5 "
5 " u O [de
:
ith this structure, the lant atrices are $i&en
a11
a12
a13
a14 0
)11
)12 0 0
32
a21a
22a
23a
24 0)
21
22 0 06 a31
a32 a33 a34 0 31 32 0 0 76 a
42a
43a
44 0
41
420 0
76 a41 7
A6
0 1 0 u0 0 0 0 0 07
196 7
O 6 7 P Q6
0 0 0 0 20 0 0 07
6 0 76
0 0 0 0 0 2 0 07
6 0 76 7
60 0 0 0 1 0 0 0
76 0 76
1 0 0 0 0 0 0 07
6 0 76 7
4 M
;i$* M =nner.loo oututfee!acK controlstructure*
2
0 0
30 0
6 0 0 76 0 0 7
6 7
# 6 0 0 7O 6
20 0
7
6 76 7
60 2
76 76
0 07
6 76 76 76 7
4 0 0 M
2
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0C
O6 0 0 0 0 1 0 0 06
0 0 0 0 0 0 066
1 0 0 0 0 0 06
66 0 0 0 0 0 0 0 06
4
0 0 0 0 1 0 0 0 0
/ O
1 0 0 0 0 0 0 0 0
; O
0 0 1 0 0 0 5
0 0 0 0 1 0
- O
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 Accor!in$ to ;i$* M, the control
D DD
e/
u O DZ O 0 0h 0
=n the au$ente! !escrition, th
Deu an! Deu are unKno+n, an! neeaccetale close!.looerforance*
5o sol&e the outut $ain
role, Ste&ens an! e+is21
!e.&ise! the con&ersion fro
tracKin$ to a re$ulator
role, usin$ a ne+ set of
!e&iation &ariales* 5o aKe
oth the er.ror !e&iation e\PtQ
an! the stea!.state error e
sall, the out.ut $ain D is
selecte! to iniiGe the
erforance in!e8 (=)
1 1 1
J O ]0 Pe\5e\ R u\
5Au\Q!t R e
5e2 2
+ith 0, P 0* 5heotiiGation role can esol&e!nuericall usin$ aniterati&e roce!ure throu$hauno& euations*
22,23
As the state.saceatrices of the o!elchan$e +ith
the +in$ fol! an$le hfol!, the
otial outut $ain DZ +ill also
chan$e +ith correson!in$ hfol!*
Fe&ertheless, a tie.in&ariant
http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page5
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$ain DZ is referre!, althou$h onl a suotial solution +oul! e
achie&e! in such a case* 5he erforance of the close!.loo sstein the +in$ fol!in$ rocess can e achie&e! outer.loo self.
sche!ule! /1 roust control !esi$n* /ere +e select the otial
outut fee!acK $ain in e8ten!e!.+in$
confi$uration as the inner.loo $ain:
DZ O16 M 6@ 7 0 14 0 03 0 0
0 : 0:
:0 :0 1M:@ 1@:9
P27Q
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914 5* ue et al*
4*2* Euter.loo $ain self.sche!ule! /1 roust control follo+in$ forulas for the state.sace !ata of the control.ler are otaine!:
5he close!.loo sste +ith Z outut fee!acK inner.loo AD h t #D h t 4 A
Di#
Di
controller is foun! to e CDPhPtQQ toic controller enforces stailit an! /
1 erforanceP P: o&er the entire araeter oltoe H an! for aritrar ara.
AcPhPtQQ O APhPtQQ #PhPtQQDZC:eter &ariations*
5he $ain self.sche!ule! /1 control role consists in 4*3* Close!.loo siulationfin!in$ an controller
u O DPhQ P29Q 5he resultin$ $ain self.sche!ule! /1 roust Controller ase!
to aKe the altitu!e an! see! reain constant !urin$ the on the o!el is alie! at the orhin$ aircraft?s +in$+in$ orhin$ rocess* 5he reference inut
r O [ r D/ r Du "5 O 0, an! the outer.loo control structure
is sho+n in ;i$* 6*hen usin$ con&e8 hull al$orith to !esi$n the con.
troller, if there are n &ariale eleents in Ac(h(t)) an! #(h(t)),
the con&e8 hull +ill ha&e 2n &ertices* 5he calculation +ill e
colicate! if n is i$* 5herefore, +e assue that the eleents
in Ac(h(t)) an! #(h(t)) !o not chan$e as the &ar in &er sallran$e* =n other +or!s, +e onl consi!er the eleents that &ar
in lar$e ran$es !urin$ the +in$ fol!in$ rocess*
;ro the silifie! euations of orhin$ aircraft +e
fin! that the &ariale eleents a22 an! a32 in Ac(h(t)) &ar inlar$e ran$es, +hich oth !een! on the aero!naic chan$es
!urin$ the +in$ fol!in$ rocess* /ereafter, the araeter &ec.a
22
tor of the lant is !enote! as hPtQ :O a32 * An!a
22a
22ina
22a8 1:3392 0:M212P30Q a32 [ a32in a32a8 " O [ 0:061@ 0:0344 "
[ " O [ "
So h(t) ran$es in the oltoe H e CoVhi, i U 1, 2, 3, 4W* 5he
&ertices hi are the &alues of h(t) at the four &ertices of the
h1 O a22in a22a8 h3 O
araeter o8: a32inh
2 O a32in
a22in
h4 O
a22a8
*=t is clear that the state.sace a.a32a8 a32a8tri8 Ac(h(t)) ran$es in a oltoe of atrices +hose &ertices
are the ia$es of the &ertices h1, h2, h3, h4* =n other +or!s,
AcPhPtQQ 2 CofAi :O APhiQ i O 1 2 3 4$ P31Q
;inall, a foral e8ression for the controller is!eri&e! sol&in$ the con&e8 !ecoosition role* 5he
;i$* 6 Euter.loo controlstructure*
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;i$* 7 Close!.loo resonse in orhin$ rocess*
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-ain self.sche!ule! /1 control for orhin$ aircraft in the +in$ transition rocess ase! on an o!el 91M
shae transition hase* 5he resonse of the aircraft in close!.
loo siulation is sho+n in ;i$* 7* =t is clear that the see! is
alost constant an! the altitu!e !ecreases aout 0*7 to thea8iu !urin$ the +in$ fol!in$ rocess* 5he can oth con.&er$e in 10 s after the +in$ finishes fol!in$* Since the +in$area !ecreases after it fol!s, the an$le of attacK +ill increaseto achie&e a ne+ alance* =n a!!ition, the chan$es in ele&ator !eflection an! throttle are oth +ithin accetale ran$es* =t is
o&ious that the $ain self.sche!ule! /1 roust controller
ase! on the orhin$ aircraft?s o!el can eliinate the!isturance cause! +in$ fol!in$ an! $uarantee con.stant.see! an! altitu!e fli$ht !urin$ the +in$ transition rocess*
;i$* @ Close!.loo resonse in araeter erturation !urin$
+in$ fol!in$ rocess* 4*4* oustness &erification
=n this article the
aero!naics in +in$ fol!in$
otaine! C;< is assue!
to e uasi.stea!, an!
unstea! aero!na.ics is
i$nore!* Conseuentl, theaero!naics in the nonlin.
ear o!el of the orhin$
aircraft is not o!ele!
recisel, an! not e8actl the
sae +ith aero!naics in
actual fli$ht con!itions* =n
other +or!s, the aero!naic
o!el of the +in$ fol!in$
rocess is uncertain +ithin a
ran$e* 5hus it is ior.tant for
the controller to ha&e the
ailit to ro&i!e stailit in
site of o!elin$ errors !ue
to uno!ele! !naics an!lant araeter &ariations*
5he unre!ictale anner
of the o!el can e !escrie!
araeter erturation*
/ere +e use the araeter
ertura.tion of the
aero!naic force an!
oent coefficients to !e.
scrie o!el araeter
erturation* 5he
aero!naic coefficient
erturation is !een!ent on
the an$le of attacK* hen the
an$le of attacK is i$$er, theerturation +ill e $reater*
5hus the erturations of
aero!naic force an! o.
ent coefficients are set to e
@C
00:@ 0:M
pa C1@0
O P Q p C<
0O P1:2 R 0:M a C
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ertura.tion* 5he otion of the orhin$ aircraft con&er$es
slo+er after +in$ fol!in$ is colete!* &en so, the fli$ht control
ss.te can still ensure that the see! &ariation in the +in$ or.
hin$ rocess is sall, an! that the altitu!e &aries less than 1 *
5his eans the $ain self.sche!ule! /1 roust control sste can
aintain $oo! roustness un!er o!elin$ uncertaint of
aero!naics*
5.Conclusion
(1)5he o!el for the fol!in$.+in$ orhin$ aircraft in+in$ fol!in$ is !eri&e! fro lon$itu!inal nonlinear !naic
euations usin$ Jacoian lineariGation aroach* 5he
o!el inclu!es the
&ariants of aero.
!naic force an!
oent cause!
+in$ fol!in$, +hich can
e re$ar!e! as a
!isturance source*
5he !naic resonse
is siulate! usin$ the
nonlinear o!el an!
o!el* =t is sho+nthat the lon$itu!inal
o!el otaine!
Jacoian lineariGation
aroach can cature
the orhin$ aircraft?s
cole8 eha&ior in the
+in$ transition rocess*
(2)=n or!er to ensure thatthe orhin$ aircraftflies at a $i&en altitu!ean! see! in the +in$fol!in$ rocess,
an inner.loo otialua!ratic oututfee!acK an! outer.
loo $ain sche!ule! /1roust controller ase!on con&e8 otiiGational$orith is !esi$ne!*5he si.ulations sho+that the controlo'ecti&e of aintainin$
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916 5* ue et al*
see! an! altitu!e chan$e onl sli$htl +hen the +in$@
a31 O
SG
fol!in$ rocess can e achie&e! &ia the ulti.loo con. ,= SG2 1
trol aroach* 5he orhin$ aircraft can rai!l return q0SC
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# A1 31
SC<
q cSC de
2 2
q 0 de 0 O 31 32 P Q O = S G 2
R = S G2
6 7
T
6
41
42
7 0
6 7 O
4 M
+11
= T
125
d
2
O
+21
= SG
2 3
0
O
+31 22
O
6 7
S G 6 7 +41 32
5d
2 6 7 O =
S
G 4 M :
=
0 42
a11 O
2
O = SG
A6
@1 SG
: P Q
q0SC
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=
a13
2
+0 2SG
1 2 O =
S
GP Q Y
U1 Y U2 q cS
22S
18
S1G
2S28
S2G
2 0
R =
SG
R R S
G 1
2
= S + 0 q c SC 2 G 0
Ca
= S G P R 4 Q C0C
0C
a0
C
de0 $S sin h0
Ca
deG
P R a R R Q
=
S
G
a14 ,$ cos
h
0 $S cos 0 0
2 2 G h
+41
O = S G
R = S G O
A7
P A2
Q:
P Q
:1 1
q0SC R qu0SPC
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16* ue 5, an$ >, Ai JZ* on$itu!inal ultio! !naic
characristics of ].+in$ orhin$ aircraft* Acta Aeronaut Astro.
naut Sin 201031(4):679–@6 ^Chinese_*
17. Barcos A, #alas -* inear araeter &arin$ o!elin$ of the#oein$ 747–100L200 lon$itu!inal otion* A=AA.2001.4347 2001*
18. Duar A, An!ersen B* A coarision of o!ellin$techniues for aircraft, control* A=AA.2000.44M@ 2000*
19. Barcos A, #alas -J*