Gain self-scheduled H1 control for morphing aircraft in.rtf

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


2/16

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*


3/16

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

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8/16

$ain DZ is referre!, althou$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


9/16

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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10/16

;i$* 7 Close!.loo resonse in orhin$ rocess*


11/16

-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


12/16

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$ne!*5he si.ulations sho+that the controlo'ecti&e of aintainin$


13/16

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


14/16

# 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


15/16

=

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


16/16

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*

Gain self-scheduled H1 control for morphing aircraft in.rtf

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