fuselag,e roll attltude angle ... roll, pitch and yau ratâ¬s. - maln rotor radlua. - t.ai I rotor radiue. - dlatance along track r tlm⬠..... bob-up, a vertlcal height change ...
0360-5450/90 $3.00-+-0.00 PergarnonPressplc
VerticaYol. 14, No. 2, pp. 185-200,1990 Printed in Great Britain
DEVEIOPUENT
AND VERIFICATION
HELICOPTEN,
D.G.
OF AN ALGORITHM
INVERSE
FOR
SITIIULATIONS
THOMSON and
R.
BRADLEY
DepartDent
of Acroepace Englneerlng University of Glaagou Glasgow
-
Abstract
The
control
manoeuvre
a defined vehicle's
dleplacements
requlred
may be calculaEed by of motlon. A computer
equatlons perform to
for
a
helicopter
inveree package,
to
eolutlon
of has
fly the been
HELINV, soluEions, or inverae simulatlons, for a (NOE) aerles of nap-of-the-earth gives manoeuvres. This a uniqu€ opportunfty Eo etudy almulated conErol strategiea ln conatralned paper, fliSht. The algorlthm, descrlbed in thls uses a eix degreee of developed
freedom found
for
nonllnear varlouB
manoeuvrea. discuaaion
maEhematical helicopter
Some of
the
algorlthm.
The In
calculatlons. reBults
euch
of
lnverse
model
which
allows
solutlona
configuraElons
flylng a wide preaenEed, are along potential applicabillty
typlcal resulEs llmlt.ations and method ls addltlon,
verifled flighl
by data
uae is
of
used
to range wlth of
be of a the
time reaponse to validate t.he
slmulatlons.
NOMENCI.ATURE -
b cQ
number of bladee = maln rotor torque coefflcient o maln rotor thruat coefficient r tal1 rotor thruat coefficlent - acceleratlon due to gravity . altitude - height of main rotor hub above fuselage point ref. - height of tall roEor hub above fueelage polnt ref.
%
cTt. I h hR ht. rxx'rvv'rzz
r*"
L , M , N LA, MA, NA 1t. KF Il
momenta product
of inertla of lnertia external pitchlng ro11lng, and yawing rnomenta = external aerodynamic momenta - tall rotor distance fron fuselage point reference . blade flapping sEiffness - hellcopter masa , -
Pr Qr r R
-
roll,
-
maln
Rtt s
-
t
r tlm€ = t.ranglational
v
-
v x , v , z
r
along, fl1ght
yau
the
r
xr
xry,z
*"g
-
axes earth fixed along x,y,z poaition centre of gravLty pt" fwd. of fuselage ref.
F Frc
-
velocitieF body
axea
Frs
, ,s 6
external.
conponents flxed
coef f 1c ient E fu3elage pitch attitud€ angle r maln rotor pltch collectlve angle - maln rotor cvclic lateral pitch angle . naln rotor longiEudinal pitch angle cyclic
e eo €rc 0r" '
tal1 rotor angle
collectlve
-
normalised hub rofor
components velocity
p
-
o
: .
deneity solidily
o the
x t
o forces
components
angle fueelage s!.deellp maln rotor longitudlnal angle flapplng . maln rolor lateral flapping, angle * angle of climb - forward of rotor strraIt t1lt - main rotor profile drag
9otr
velocity
earth
acceleration
!7t
x,yrz
aerodynamlc
-
rat€s
f1lght acceleration extern6l forces 6long xt yt z body axes
o velocity
2
and
rotor radlua t.ai I rotor radiue dlatance along track
xA, YA, zA Yr
pitch
it, it,;
Qtt
along axes
185
lyr
!2
-
fuselag,e
of air of main roll
pitch of
rotor
attltude
track angle yaw attltude fuselage maln rotor speed tail rotor speed
angle an8,l.e
BnnPlEY D' G Tnorr'tsoNand R' 186 INTRODUCTION
I.
lE is Possible -t" "-"-111tt,:*rJr""ti;1"r?;t"::i:";:ll rn convenrronar simulation rn 8'ener:r':oiiigtt"tio""r sequence' con.rol changee' aircraft
An
"o.rrg'tt"tio;'""t"-"-""t
liill3.,1l,",::;:: durlns "f{"li:*i:.,"-,lli#-""':":"i1":':'+"i:'*1"fit"".'""rt:il,;l;t:l: ;1';":::1";:';;"""n'"' perrormanee :l1T ii,l"llll: l:"::'""T$;;ii,"'"i'"!':':", JT"":-J.)','ff":,::\ fi,i,lii#-i""'-{'"':il;'T'"'H::"1;':"Ji""""T::; ;i:::","o"::x" 2l
or
ln';;";;;;t
{31
'"'i"ii!^'iZ
[1, ElemenEs) clearlylnverse""titt-'oL--'lafundamenta'-tttnttottofsuchanex€rc13e' stEempEs
Most
aE
solvlng
equations
aircraft
handllns
c
qualltlea
"t"-"-ttol
have
inveraely
."::::.
been-ba3ed
on
"f
wing af"raf: ^ ::1"""1i"t::"hi;tt*ttT"?"""""""t""'"it""":-"{:l'llt;'fi: aimulationsof trxeJ (4l,.us:: greu more complex for example Jonm ltnearised equattons
models, o, ,o".o.'ii
rl.l"
effects'
urr.
t oou' -t 't-",n
; : ra" t] h. fe; ;m , atical As m
oJ
,.
lnverac reccntry'
t-"
: l 1 y ^ nurnerlcal calculate. rn in lnverae .t":l"dt' develoPnentof i"n"
otr-t?,i* :" T::"r:", :#::iI;';:lrli.'i;;';o;1o aoruEiona became,o.,'"" or nol"tf"tt.""""#J;t:i.'r'."t'".-.J.". uith rhe increaaed ".i"t-t*tttt, solutions, tn"t "i*it'-o-J""*i"t"t"-L"'l'r"'"".1""r'.o"":::';"T"T;'"""t"i irave deeisners
eyst€m control u'v"' "'d:t'"^"-t"i"*:tf'"#:?'""':;:"i[ilt;; svstJms'tn" '"'i-o' AutomaticFtishE t;l;;;i a general a.rnor:"::::l"t"fftl?"".t"'.t*J-nr".oir." l": Karoand susiura rui"i"".-i""eloped 8nd. fevel fl1ght t".
;;;;;;;'
,T"I ::tol:, theory, ehould "rr'o*--ttt"t exampre they cite "tttt"nt
