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GenHel.jl
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GenHel.jl
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# DESCRIPTION
# Open-loop aircraft dynamics.
#
# INPUT
# - dx: state derivative
# - x: current state vector
# - p: current control vector
# - t: time
#
# OUTPUT
# - xdot: system dynamics
#
# ------------------------------------------------------------------------------
function GenHel!(dx,x,p,t)
# control system mixing
controls = control_mixing(p)
# PARTITION STATE VECTOR
# fuselage states
xf=x[1:NFSTATES]
# rotor states
xr=x[NFSTATES+1:NFSTATES+NRSTATES]
# tail rotor states
xtr=x[NFSTATES+NRSTATES+1:NFSTATES+NRSTATES+NTRSTATES]
# ROTOR INTERFERENCE
# body to shaft coordinate transform
Tshaft=[cos(ITHSH*D2R) 0.0 -sin(ITHSH*D2R)
sin(ITHSH*D2R)*sin(IPHSH*D2R) cos(IPHSH*D2R) cos(ITHSH*D2R)*sin(IPHSH*D2R)
sin(ITHSH*D2R)*cos(IPHSH*D2R) -sin(IPHSH*D2R) cos(ITHSH*D2R)*cos(IPHSH*D2R)]
# body-frame velocities
u=x[1]
v=x[2]
w=x[3]
# longitudinal flap angle
beta1c=x[15]
# convert longitudinal flap angle to different sign convention and deg
A1F=-beta1c*R2D
# average harmonic inflow
lambda0=x[29]
cg=0.0
Gif=1.0-cg
temp=Tshaft*[u;v;w]
us=temp[1]
vs=temp[2]
ws=temp[3]
muxs=us/(OMEGA*R)
muzs=ws/(OMEGA*R)
chi=R2D*atan2(muxs,abs(lambda0-muzs))+A1F
alpha=atan2(w,abs(u))*R2D
beta=atan2(v,sqrt(u^2+w^2))*R2D
psif=-beta
# check these two lines
chitab=min(max(chi,0.0),100.0)
A1Ftab=min(max(A1F,-6.0),6.0)
# interpolate
itp1=interpolate((chi_tab, a1f_tab), ekxf_tab', Gridded(Linear()))
ekxf=itp1(chitab,A1Ftab)
itp2=interpolate((chi_tab, a1f_tab), ekzf_tab', Gridded(Linear()))
ekzf=itp2(chitab,A1Ftab)
itp3=interpolate((chi_tab, a1f_tab), ekxt_tab', Gridded(Linear()))
ekxt=itp3(chitab,A1Ftab)
itp4=interpolate((chi_tab, a1f_tab), ekzt_tab', Gridded(Linear()))
ekzt=itp4(chitab,A1Ftab)
#
rotor_if=zeros(8)
rotor_if[1]=-Gif*ekzf*lambda0*OMEGA*R
rotor_if[2]=Gif*ekxf*lambda0*OMEGA*R
rotor_if[3]=-Gif*ekzt*lambda0*OMEGA*R
rotor_if[4]=Gif*ekxt*lambda0*OMEGA*R
rotor_if[5]=table_lookup(alpha_tab,qlossht_tab,alpha)
rotor_if[6]=table_lookup(psivt_tab,qlossvt_tab,psif)
rotor_if[7]=table_lookup(alphaeps_tab,eps_tab,alpha)
rotor_if[8]=table_lookup(psisig_tab,sig_tab,psif)
# FUSELAGE
# external velocities zeroed out in trim and linearization
VextF=zeros(3)
VextTR=zeros(3)
VextHT=zeros(3)
VextVT=zeros(3)
# fudelage geometry [ft]
FWT = (FSCG-FSfus)/12
WWT = (WLCG-WLfus)/12
BWT = (BLCG-BLfus)/12
# gust velocities
VXGWF = 0.0
VYGWF = 0.0
VZGWF = 0.0
# NED to Body transformation
sphi=sin(xf[7])
cphi=cos(xf[7])
sthe=sin(xf[8])
cthe=cos(xf[8])
spsi=sin(xf[9])
cpsi=cos(xf[9])
TNED2body=[cthe*cpsi cthe*spsi -sthe
(sphi*sthe*cpsi-cphi*spsi) (sphi*sthe*spsi+cphi*cpsi) sphi*cthe
(cphi*sthe*cpsi+sphi*spsi) (cphi*sthe*spsi-sphi*cpsi) cphi*cthe]
# external velocities in body coordinates
Vextb=TNED2body*VextF
# interference velocities
VXIWF = rotor_if[2]+Vextb[1]
VYIWF = 0.0+Vextb[2];
VZIWF = rotor_if[1]+Vextb[3]
# air velocity inputs
VXB=xf[1]
VYB=xf[2]
VZB=xf[3]
# fuselage velocities in body axes
VXWF = VXB+VXGWF+VXIWF
VYWF = VYB+VYGWF+VYIWF
VZWF = VZB+VZGWF+VZIWF
# angle of attack and sideslip
AVXWF=abs(VXWF);
if AVXWF < 0.000001
AVXWF = 0.000001
end
ALFWFR = atan(VZWF/AVXWF)
ALFWF = R2D*ALFWFR
FVTERM = VXWF^2+VZWF^2
#
if FVTERM < 0.000001
FVTERM = 0.000001
end
RVTERM = 1/sqrt(FVTERM)
CALFWF = VXWF*RVTERM
SALFWF = VZWF*RVTERM
#
BETWFR = atan(VYWF*RVTERM)
BETWF = R2D*BETWFR
SBETWF = sin(BETWFR)
CBETWF = cos(BETWFR)
PSIWF = -BETWF
# dynamic pressure
QWF = 0.5*RHO*(VYWF^2 + FVTERM)
# fuselage aerodyanmic loading coefficients
AALFWF = abs(ALFWF)
APSIWF = abs(PSIWF)
SGNPSI = sign(PSIWF)
# functions of angle of attack
CDA = table_lookup(FUSEAOA,FUSEDA,ALFWF)
CLA = table_lookup(FUSEAOA,FUSELA,ALFWF)
CMA = table_lookup(FUSEAOA,FUSEMA,ALFWF)
# functions of sideslip
CLB = table_lookup(FUSEBETA,FUSELB,PSIWF)
CMB = table_lookup(FUSEABETA,FUSEMB,APSIWF)
CDB = table_lookup(FUSEABETA,FUSEDB,APSIWF)
CYB = table_lookup(FUSEBETA,FUSEYB,PSIWF)
CRB = table_lookup(FUSEBETA,FUSERB,PSIWF)
CNB = table_lookup(FUSEBETA,FUSENB,PSIWF)
# total coefficients
CDTOT = CDA + CDB
CLTOT = CLA + CLB
CYTOT = CYB
CRTOT = CRB
CMTOT = CMA + CMB
CNTOT = CNB
# transform forces and moments from wind axes to body axes
Tbw=[CALFWF*CBETWF CALFWF*SBETWF -SALFWF
SBETWF -CBETWF 0.0
SALFWF*CBETWF SALFWF*SBETWF CALFWF]
Ffw=-QWF*[CDTOT;CYTOT;CLTOT]
Ff=Tbw*Ffw
# check this line
Mf=Tbw*QWF*[CRTOT;-CMTOT;CNTOT]+[0.0 -WWT BWT; WWT 0.0 -FWT; -BWT FWT 0.0]*Ff
pfusNED=xf[10:12]+TNED2body'*[FWT;BWT;WWT]
# TAIL ROTOR
# absolute speed
VKT = sqrt(u^2+w^2)*fps2kts
# tail rotor twist [rad]
TWSTTR = twistTR/D2R
# ratio between main and tail rotor angular speeds
OMGRAT = 1 # OMEGA/OMEGAT
# tail rotor collective
THETTRC = controls[4]
# constants
C12TR = 0.5
C13TR = 0.333333333
C14TR = 0.25
C15TR = 0.2
C16TR = 0.166666666
C23TR = 0.666666666
C25TR = 0.4
C43TR = 1.333333333
C54TR = 1.25
C58TR = 0.625
C83TR = 2.666666666
C89TR = 0.888888888
# dynamic inflow constant
XKINF = 4.0/(3.0*pi)
# angular rates
PB=xf[4]
QB=xf[5]
RB=xf[6]
# external velocities in body frame
Vextb=TNED2body*VextTR
# tail rotor geometry [ft]
XTR = -(FSTR-FSCGB)/12.0
ZTR = -(WLTR-WLCGB)/12.0
YTR = (BLTR-BLCGB)/12.0
# body to TR transform
cgam=cos((90-CantTR)*D2R)
sgam=sin((90-CantTR)*D2R)
Tcant=[1.0 0.0 0.0
0.0 cgam sgam
0.0 -sgam cgam]
#
GTR = a0TR*NB*CHRDTR/(2.0*pi*RTR)
#
S0 = a0TR*CHRDTR*RTR^4/IbTR
S1 = BTLTR/2.0
S2 = S1*BTLTR
S3 = S2^2
S4 = S2/2
S5 = (BTLTR^3)/3.0
S6 = DELTTR*TD3TR;
CBLK = 1.0/(VBVTTR^2)
#
B2 = BTLTR^2
B3 = BTLTR*B2
B4 = B2^2
B5 = B2*B3
B6 = B3^2
B7 = B3*B4
B8 = B4^2
B9 = B4*B5
B10 = B5^2
B11 = B5*B6
B12 = B6^2
#
S10 = B2/1296.0
S11 = C83TR*BTLTR
S12 = B9/864.0
S13 = 2.0*B2
S14 = B10/1080.0
S15 = C89TR*B2
S16 = B10/2304.0
S17 = C43TR*B3
S18 = B11/1440.0
S19 = B4/2.0
S20 = B12/3600.0
S21 = -B5/108.0
S22 = -B6/144.0
S23 = -B7/180.0
S24 = B2/36.0
S25 = -C14TR+(1.0/B2)+(C12TR/B4)
S26 = (B4/162.0)-(B5/81.0)+(B6/144.0)
S27 = C43TR/BTLTR*(1.0+(1.0/B2))
S28 = (B5/108.0)-(B6/54.0)+(B7/96.0)
S29 = 1.0+(1.0/B2)
S30 = (B6/135.0)*(1.0-(2.0*BTLTR))+(B8/120.0)
S31 = C14TR+(C89TR/B2)
S32 = (B6/288.0)-(B7/144.0)+(B8/256.0)
S33 = C13TR+(C43TR/BTLTR)
S34 = (B7/180.0)-(B8/90.0)+(B9/160.0)
S35 = (B8/450.0)-(B9/225.0)+(B10/400.0)
#
BLDSTR = NB
SIGTR = BLDSTR*CHRDTR/(pi*RTR)
THT1TR = TWSTTR*D2R
#
S7 = pi*((OmegaTR*OMGRAT*RTR^2)^2)
S8 = 1.0/(OmegaTR*RTR*OMGRAT)
S9 = S7*RTR
# dynamic pressure ratio (same as for vertical tail)
idxtail = 1
xtail=-(FSTR[idxtail]-FSCG)/12.0
ytail=(BLTR[idxtail]-BLCG)/12.0
ztail=-(WLTR[idxtail]-WLCG)/12.0
qlossfac=sqrt(rotor_if[6])
ublocal=xf[1]*qlossfac+Vextb[1]+rotor_if[2]+(QB)*ztail-(RB)*ytail
vblocal=(xf[2]-D2R*xf[1]*rotor_if[8])*qlossfac+Vextb[2]-(PB)*ztail+(RB)*xtail;
wblocal=(xf[3]-D2R*xf[1]*rotor_if[7])*qlossfac+Vextb[3]+rotor_if[1]+(PB)*ytail-(QB)*xtail
# ransform velocities to orientation of tail
temp=Tcant*[ublocal;vblocal;wblocal]
ut=temp[1]
vt=temp[2]
wt=temp[3]
# advance ratios
XMUXTR = ut*S8
XMUYTR = vt*S8
XMUZTR = wt*S8
XMU2 = ((XMUXTR^2) + (XMUYTR^2))
# Bailey coefficents
BT31 = S2+(0.25*XMU2)
BT32 = S5+(S1*XMU2)
BT33 = S3+(S4*XMU2)
# additional Bailey coefficients for torque
XGAM = RHO*S0
XGAM2 = XGAM^2
BT41 = S2+(C54TR+(S10*XGAM2))*XMU2
BT42 = S5+(S11+(S12*XGAM2))*XMU2
BT43 = S3+(S13+(S14*XGAM2))*XMU2
BT44 = (S15+(S16*XGAM2))*XMU2
BT45 = (S17+(S18*XGAM2))*XMU2
BT46 = (S19+(S20*XGAM2))*XMU2
BT47 = S21*XMU2
BT48 = S22*XMU2
BT49 = S23*XMU2
BT410 = S24*XMU2
BT51 = C14TR*(1.0+XMU2)
BT52 = C13TR
BT53 = BT51
BT54 = C15TR+(C16TR*XMU2)
BT55 = C12TR+((S25+(S26*XGAM2))*XMU2)
BT56 = C23TR+((S27+(S28*XGAM2))*XMU2)
BT57 = C12TR+((S29+(S30*XGAM2))*XMU2)
BT58 = C14TR+((S31+(S32*XGAM2))*XMU2)
BT59 = C25TR+((S33+(S34*XGAM2))*XMU2)
BT510 = C16TR+((C58TR+(S35*XGAM2))*XMU2)
# vertical tail blockage factor
BLKTR = BVTTR1
if VKT < VBVTTR
BLKTR = ((1.0-BVTTR)*CBLK*(VKT^2))+BVTTR
end
TTR = 200
DWTRSS = xtr[1]
XLAMTR=XMUZTR-xtr[1]
THETTR = D2R*(THETTRC)
iter=0
err=10
# iterate for steady-state induced velocity and thrust
while abs(err)>1e-6 && iter<200
# tail rotor blade pitch [rad]
THETTR = D2R*(THETTRC-(TTR*S6)+BIASTR)
# tail rotor downwash and thrust
DWTRSS = GTR*((XMUZTR*BT31)+(THETTR*BT32)+(D2R*TWSTTR*BT33))/
(2.0*sqrt(XMU2+((XMUZTR-DWTRSS)^2))+(GTR*BT31))
XLAMTR = XMUZTR-DWTRSS
TTR_new = 2.0*DWTRSS*sqrt(XMU2+(XLAMTR^2))*RHO*S7*BLKTR
err = TTR_new-TTR
# this thrust is steady-state version, it will get overwritten for current inflow
TTR = TTR+0.5*err
iter=iter+1
end
if iter>=199
@printf("warning: TR not converged")
end
# inflow dynamics (no time delay)
VT = sqrt(XMU2+(XLAMTR^2))
CDWTR = XKINF/(OmegaTR*OMGRAT*VT)
# inflow ratio nflow ratio
XLAMTR = XMUZTR-xtr[1]
# tail rotor state derivative (check this line: 10^-6 vs 10^-9)
xtrdot=(DWTRSS-xtr[1])/(CDWTR)
# tail rotor thrust
CTHTR = GTR*((XLAMTR*BT31)+(THETTR*BT32)+(D2R*TWSTTR*BT33))
TTR = CTHTR*RHO*S7*BLKTR
# tail rotor torque
ATR = a0TR
CQTR = (((D2TR*BT55)-(ATR*BT41))*(XLAMTR^2)+((D2TR*BT56)-
(ATR*BT42))*THETTR*XLAMTR+((D2TR*BT57)-(ATR*BT43))*THT1TR*XLAMTR+
((D2TR*BT58)-(ATR*BT44))*(THETTR^2)+((D2TR*BT59)-
(ATR*BT45))*THT1TR*THETTR+((D2TR*BT510)-(ATR*BT46))*(THT1TR^2)+
(D0TR*BT51 )+D1TR*((BT52*XLAMTR)+(BT53*THETTR)+
(BT54*THT1TR)))*0.5*SIGTR
Qtr = CQTR*RHO*S9
# tail rotor drag
DTR=0.5*CDTR*RHO*(ut^2)
# tail rotor horsepower [hp]
HPTR = Qtr*OmegaTR*OMGRAT*FtLb_s2Hp
# transform tail rotor thrust, drag, torque to body frame
Ftr=Tcant'*[-DTR;0.0;-TTR]
Mtr_local=Tcant'*[0.0;0.0;-Qtr]
Mtr=[0.0 -ZTR YTR
ZTR 0.0 -XTR
-YTR XTR 0.0]*Ftr+Mtr_local
ptrNED = xf[10:12]+TNED2body'*[XTR;YTR;ZTR]
# HORIZONTAL TAIL
# horizontal tail index
idxtail=1
# equivalent airspeed used in stabilator schedule
Veq=sqrt( (x[1])^2 + (x[2])^2 + (x[3])^2 )/1.688*sqrt(RHO/rhoSLSTD)
ayg=(dx[1]-G*sin(x[7])*cos(x[8])+x[6]*x[1]-x[4]*x[3])/G
StabInc=H60_StabSched(p[3],Veq,ayg,x[5],STABSET)
# geometry [ft]
xtail=-(FSTAIL[idxtail]-FSCG)/12.0
ytail=(BLTAIL[idxtail]-BLCG)/12.0
ztail=-(WLTAIL[idxtail]-WLCG)/12.0
# external velocities in body frame
Vextb=TNED2body*VextHT
#
qlossfac=sqrt(rotor_if[5])
epsilon=rotor_if[7]
sigma=0.0
# local velocities
uHT=(xf[1])*qlossfac+Vextb[1]+rotor_if[4]
vHT=(xf[2]-D2R*xf[1]*sigma)+Vextb[2]
wHT=(xf[3]-D2R*xf[1]*epsilon)*qlossfac+Vextb[3]+rotor_if[3]
ublocal=uHT+(QB)*ztail-(RB)*ytail
vblocal=vHT-(PB)*ztail+(RB)*xtail
wblocal=wHT+(PB)*ytail-(QB)*xtail
#
if (CLELEV[idxtail] == 0.0)
cthe=cos((ITAIL[idxtail]+StabInc)*D2R)
sthe=sin((ITAIL[idxtail]+StabInc)*D2R)
else
cthe=cos(ITAIL[idxtail]*D2R)
sthe=sin(ITAIL[idxtail]*D2R)
end
cphi=cos(PHITAIL[idxtail]*D2R)
sphi=sin(PHITAIL[idxtail]*D2R)
T=[cthe sthe*sphi -sthe*cphi
0 cphi sphi
sthe -sphi*cthe cphi*cthe]
# transfrom veclocities to orientation of tail
temp=T*[ublocal;vblocal;wblocal]
ut=temp[1]
vt=temp[2]
wt=temp[3]
Vtot2=ut^2+vt^2+wt^2
Vtot=sqrt(Vtot2)
Vxz=sqrt(ut^2+wt^2)
qt=0.5*RHO*Vtot2
# tail angle of attack and sideslip
alphat=atan2(wt,ut)*R2D
sa=wt/Vxz
ca=ut/Vxz
sb=vt/Vtot
cb=Vxz/Vtot
# lift and drag coefficients
CLt=table_lookup(ALTAIL[idxtail,:],CLTAIL[idxtail,:],alphat)+CLELEV[idxtail]*StabInc
CDt=table_lookup(ALTAIL[idxtail,:],CDTAIL[idxtail,:],alphat)
Lift=qt*STAIL[idxtail]*CLt
Drag=qt*STAIL[idxtail]*CDt
#
Tw2t=[cb*ca -sb -cb*sa
sb*ca cb -sb*sa
sa 0.0 ca]
#
temp=T'*Tw2t*[-Drag;0.0;-Lift]
# horizontal tail forces and moments
Fht=temp
Mht=[ 0.0 -ztail ytail
ztail 0.0 -xtail
-ytail xtail 0.0]*Fht
phtNED=xf[10:12]+TNED2body'*[xtail;ytail;ztail]
# VERTICAL TAIL
# vertical tail index
idxtail=2
# geometry [ft]
xtail=-(FSTAIL[idxtail]-FSCG)/12.0
ytail=(BLTAIL[idxtail]-BLCG)/12.0
ztail=-(WLTAIL[idxtail]-WLCG)/12.0
# external velocities in body frame
Vextb=TNED2body*VextVT
#
qlossfac=sqrt(rotor_if[6])
epsilon=0.0
sigma=rotor_if[8]
# local velocities
uHT=(xf[1])*qlossfac+Vextb[1]+rotor_if[4]
vHT=(xf[2]-D2R*xf[1]*sigma)+Vextb[2]
wHT=(xf[3]-D2R*xf[1]*epsilon)*qlossfac+Vextb[3]+rotor_if[3]
ublocal=uHT+(QB)*ztail-(RB)*ytail
vblocal=vHT-(PB)*ztail+(RB)*xtail
wblocal=wHT+(PB)*ytail-(QB)*xtail
#
if (CLELEV[idxtail] == 0.0)
# set StabInc to 0 for vertical tail
cthe=cos((ITAIL[idxtail]+0.0)*D2R)
sthe=sin((ITAIL[idxtail]+0.0)*D2R)
else
cthe=cos(ITAIL[idxtail]*D2R)
sthe=sin(ITAIL[idxtail]*D2R)
end
cphi=cos(PHITAIL[idxtail]*D2R)
sphi=sin(PHITAIL[idxtail]*D2R)
T=[cthe sthe*sphi -sthe*cphi
0 cphi sphi
sthe -sphi*cthe cphi*cthe]
# transfrom veclocities to orientation of tail
temp=T*[ublocal;vblocal;wblocal]
ut=temp[1]
vt=temp[2]
wt=temp[3]
Vtot2=ut^2+vt^2+wt^2
Vtot=sqrt(Vtot2)
Vxz=sqrt(ut^2+wt^2)
qt=0.5*RHO*Vtot2
# tail angle of attack and sideslip
alphat=atan2(wt,ut)*R2D
sa=wt/Vxz
ca=ut/Vxz
sb=vt/Vtot
cb=Vxz/Vtot
# lift and drag coefficients (set incidence of vertical tail to zero)
CLt=table_lookup(ALTAIL[idxtail,:],CLTAIL[idxtail,:],alphat)+CLELEV[idxtail]*0.0
CDt=table_lookup(ALTAIL[idxtail,:],CDTAIL[idxtail,:],alphat)
Lift=qt*STAIL[idxtail]*CLt
Drag=qt*STAIL[idxtail]*CDt
#
Tw2t=[cb*ca -sb -cb*sa
sb*ca cb -sb*sa
sa 0.0 ca]
#
temp=T'*Tw2t*[-Drag;0.0;-Lift]
# horizontal tail forces and moments
Fvt=temp
Mvt=[ 0.0 -ztail ytail
ztail 0.0 -xtail
-ytail xtail 0.0]*Fvt
pvtNED=xf[10:12]+TNED2body'*[xtail;ytail;ztail]
# MAIN ROTOR
# define inputs to module
ur=zeros(23+NB*NSEG*3+1)
ur[1]=controls[1]*pi/180
ur[2]=controls[2]*pi/180
ur[3]=controls[3]*pi/180
ur[4:15]=xf[1:12]
ur[16:21]=dx[1:6]
# nominal rotor airspeed
ur[22]=OMEGA
ur[23]=0 #dx[IDXP[1]]
# zero out external flow velocities in trim and linearization
ur[24:23+NB*NSEG*3+1]=zeros(NB*NSEG*3+1,1)
if ur[23]!=0.0
soptval=1
end
# define blade twist at blade elements
# twist=interp1(TWISTTABR,TWISTTABTHET,RSEG)
itp = interpolate((TWISTTABR,),TWISTTABTHET, Gridded(Linear()))
twist = itp(RSEG)
# map to local variables names
beta1c=xr[3]
lambda0=xr[17]
lambda1s=xr[18]
lambda1c=xr[19]
psi1=xr[20]
# blade azimuth angles
psi=psi1*ones(4)+collect(0:(NB-1))*(2*pi/NB)
for i=1:NB
psi[i]=mod(psi[i]',2*pi)
end
# trig functions
cpsi = zeros(4)
spsi = zeros(4)
for i=1:NB
cpsi[i]=cos(psi[i])
spsi[i]=sin(psi[i])
end
# convert from IBC to MBC
LMBC2IBC=[ones(4) (-1).^collect(1:NB) cpsi spsi]
LMBC2IBCdot=OMEGA*[zeros(4,2) -spsi cpsi]
beta=LMBC2IBC*xr[1:NB]
beta_dot=LMBC2IBC*xr[NB+1:2*NB]+LMBC2IBCdot*xr[1:NB]
zeta=LMBC2IBC*xr[2*NB+1:3*NB]
zeta_dot=LMBC2IBC*xr[3*NB+1:4*NB]+LMBC2IBCdot*xr[2*NB+1:3*NB]
#
LIBC2MBC=1/NB*[ones(4)'
((-1).^collect(1:NB))'
2*cpsi'
2*spsi']
LIBC2MBCdot=OMEGA/NB*[zeros(2,4)
-2*spsi'
2*cpsi']
LIBC2MBCddot=(OMEGA*OMEGA)/NB*[zeros(2,4)
-2*cpsi'
-2*spsi']
# trig functions
cbeta = zeros(4)
sbeta = zeros(4)
czeta = zeros(4)
szeta = zeros(4)
cpsizeta = zeros(4)
spsizeta = zeros(4)
for i=1:NB
cbeta[i]=cos(beta[i])
sbeta[i]=sin(beta[i])
czeta[i]=cos(zeta[i])
szeta[i]=sin(zeta[i])
cpsizeta[i]=cos(psi[i]+zeta[i])
spsizeta[i]=sin(psi[i]+zeta[i])
end
# control inputs
theta1c=ur[1]
theta1s=ur[2]
theta0=ur[3]
# air velocity inputs
Vxb=ur[4]
Vyb=ur[5]
Vzb=ur[6]
# angular rates
p=ur[7]
q=ur[8]
r=ur[9]
# Euler Angles
sphi=sin(ur[10])
cphi=cos(ur[10])
sthe=sin(ur[11])
cthe=cos(ur[11])
spsiE=sin(ur[12])
cpsiE=cos(ur[12])
Tbody2NED=[cthe*cpsiE (sphi*sthe*cpsiE-cphi*spsiE) (cphi*sthe*cpsiE+sphi*spsiE)
cthe*spsiE (sphi*sthe*spsiE+cphi*cpsiE) (cphi*sthe*spsiE-sphi*cpsiE)
-sthe sphi*cthe cphi*cthe]
# CG location
xcg=ur[13]
ycg=ur[14]
zcg=ur[15]
# linear accelerations
Vxbdot=ur[16]
Vybdot=ur[17]
Vzbdot=ur[118]
# angular acceleration inputs
pdot=ur[19]
qdot=ur[20]
rdot=ur[21]
# rotor acceleration
Omega_dot=ur[23]
# wind gusts
VgNED=reshape(ur[24:23+NB*NSEG*3],3,NB*NSEG)
# coupling gain to fade out inflow model
InflowFade=ur[23+NB*NSEG*3+1]
# convert gusts to shaft axes
Vgs=Tshaft*Tbody2NED'*VgNED;
Vgxs=reshape((Vgs[1,:])',NSEG,NB)'
Vgys=reshape((Vgs[2,:])',NSEG,NB)'
Vgzs=reshape((Vgs[3,:])',NSEG,NB)'
# accelerations at Rotor Hub
gx=G*sthe
gy=-G*sphi*cthe
gz=-G*cphi*cthe
# moment arms from fuselage CG to main rotor hub
Xh=(FSCGB-FSMR)/12.0
Yh=(BLCGB-BLMR)/12.0
Zh=(WLCGB-WLMR)/12.0
# acceleration of the hub
Vxhdot=Vxbdot-r*Vyb+q*Vzb-Xh*(q^2+r^2)+Yh*(p*q-rdot)+Zh*(p*r+qdot)+gx
Vyhdot=Vybdot-p*Vzb+r*Vxb+Xh*(p*q+rdot)-Yh*(p^2+r^2)+Zh*(q*r-pdot)+gy
Vzhdot=Vzbdot+p*Vyb-q*Vxb+Xh*(p*r-qdot)+Yh*(q*r+pdot)-Zh*(p^2+q^2)+gz
# non-dimensional advance ratios
muxh=(Vxb+q*Zh-r*Yh)/(OMEGA*R)
muyh=(Vyb+r*Xh-p*Zh)/(OMEGA*R)
muzh=(Vzb-q*Xh+p*Yh)/(OMEGA*R)
# non-dimensional advance ratios derivatives
muxhdot=(Vxbdot+qdot*Zh-rdot*Yh)/(OMEGA*R)
muyhdot=(Vybdot+rdot*Xh-pdot*Zh)/(OMEGA*R)
muzhdot=(Vzbdot-qdot*Xh+pdot*Yh)/(OMEGA*R)
# shaft axes transformations
temp=Tshaft*[Vxhdot;Vyhdot;Vzhdot]
Vxsdot=temp[1]
Vysdot=temp[2]
Vzsdot=temp[3]
#
temp=Tshaft*[pdot;qdot;rdot]
psdot=temp[1]
qsdot=temp[2]
rsdot=temp[3]
rsdotmomd=rsdot-Omega_dot
#
temp=Tshaft*[muxh;muyh;muzh]
muxs=temp[1]
muys=temp[2]
muzs=temp[3]
mu=sqrt(muxs^2+muys^2)
betawind = atan2(muys, muxs)
#
temp=Tshaft*[muxhdot;muyhdot;muzhdot]
muxsdot=temp[1]
muysdot=temp[2]
muzsdot=temp[3]
betawind_dot=(muxs*muysdot-muys*muxsdot)/(mu^2)
#
temp=Tshaft*[p;q;r]
ps=temp[1]
qs=temp[2]
rs=temp[3]
rminusO=rs-OMEGA
# blade pitch
thetab = zeros(4)
thetab_dot = zeros(4)
for i=1:NB
thetab[i]=theta0+theta1c*cos(psi[i]+DELSP)+theta1s*sin(psi[i]+DELSP)-
tan(DELTA3)*beta[i]
thetab_dot[i]=-theta1c*OMEGA*sin(psi[i]+DELSP)+theta1s*OMEGA*
cos(psi[i]+DELSP)
end
# dynamic Twist Component
Veq=sqrt(RHO/rhoSLSTD)*sqrt(Vxb^2+Vyb^2+Vzb^2)/1.688
KVDT=min(max(1.4e-4-(4.4e-6*Veq),-0.00052),-0.0003)
theta_DTtip=KVDT*xr[21]
theta_DT=vec(ones(4,1))*vec(DynTwistMode)'*theta_DTtip*pi/180.0
# segment pitch
theta=vec(thetab)*ones(1,NSEG)+ones(NB,1)*vec(twist)'*pi/180+theta_DT
# gust velocities, transform to blade system
Utg=1/(OMEGA*R)*( (spsizeta*ones(1,NSEG)).*Vgxs + (cpsizeta*ones(1,NSEG)).*Vgys)
Urg=1/(OMEGA*R)*( ((-cpsizeta.*cbeta)*ones(1,NSEG)).*Vgxs +
((spsizeta.*cbeta)*ones(1,NSEG)).*Vgys - (sbeta*ones(1,NSEG)).*Vgzs )
Upg=1/(OMEGA*R)*( ((-cpsizeta.*sbeta)*ones(1,NSEG)).*Vgxs +
((spsizeta.*sbeta)*ones(1,NSEG)).*Vgys + (cbeta*ones(1,NSEG)).*Vgzs )
# for Pitt-Peters Model
Upd_pp=(-lambda0*vec(cbeta)*ones(1,NSEG)-lambda1c*(e*vec(cbeta).*vec(cpsi)*ones(1,NSEG)+
vec(cbeta).*vec(cpsizeta)*vec(RSEG)')-lambda1s*(e*vec(cbeta).*vec(spsi)*ones(1,NSEG)+vec(cbeta).*
vec(spsizeta)*vec(RSEG)') )*(1-InflowFade)
Urd_pp=(-lambda0*vec(sbeta)*ones(1,NSEG)-lambda1c*(e*vec(sbeta).*vec(cpsi)*ones(1,NSEG)+
vec(sbeta).*vec(cpsizeta)*vec(RSEG)')-lambda1s*(e*vec(sbeta).*vec(spsi)*ones(1,NSEG)+vec(sbeta).*
vec(spsizeta)*vec(RSEG)') )*(1-InflowFade)
Upd_ph = zeros(NB,NSEG)
Urd_ph = zeros(NB,NSEG)
# blade segment velocities
Up=(-muxs*vec(sbeta).*vec(cpsizeta)+muys*vec(sbeta).*vec(spsizeta)+muzs*vec(cbeta))*ones(1,NSEG)+
(e/OMEGA)*(vec(cbeta).*(qs*vec(cpsi)+ps*vec(spsi))-vec(sbeta).*vec(szeta)*rminusO)*ones(1,NSEG)+
(-vec(beta_dot)+qs*vec(cpsizeta)+ps*vec(spsizeta))*vec(RSEG)'/OMEGA+Upd_pp+Upg+Upd_ph
Ut=(muxs*vec(spsizeta)+muys*vec(cpsizeta)-(e/OMEGA)*vec(czeta)*rminusO)*ones(1,NSEG)+
((vec(zeta_dot)-ones(4)*rminusO).*vec(cbeta)+(ps*vec(cpsizeta)-qs*vec(spsizeta)).*vec(sbeta))*vec(RSEG)'/OMEGA+
Utg
Ur=(muxs*vec(cbeta).*vec(cpsizeta)-muys*vec(cbeta).*vec(spsizeta)+muzs*vec(sbeta))*ones(1,NSEG)+
(e/OMEGA)*(vec(sbeta).*(qs*vec(cpsi)+ps*vec(spsi))+vec(cbeta).*vec(szeta)*rminusO)*ones(1,NSEG)+
Urd_pp+Urg+Urd_ph
Utot=(Up.^2+Ut.^2+Ur.^2).^(1/2)
# local angles of attack, Mach, skew
cosgam=abs.(Ut)./((Ut.^2+Ur.^2).^(1/2))
acosgam=abs.(cosgam)
alphay=(180.0/pi)*atan2.((Ut.*tan.(theta)+Up).*acosgam,(Ut-Up.*tan.(theta).*
cosgam.*cosgam))
Mach=((Ut.^2+Up.^2).^(1/2))*OMEGA*R/VSOUND
Machtab=max.(min.(Mach,1.0),0.0)
# GenHel rotor model
atrans0=cosgam.*alphay
atranslow=(alphay+ones(4,10)*180.0).*cosgam-ones(4,10)*180.0
atranshigh=ones(4,10)*180.0+(alphay-ones(4,10)*180.0).*cosgam
#
atrans1=((1.0-ACL1/90.0)*atrans0-ACL1*(ones(4,10)-cosgam))./(-ACL1/90.0*ones(4,10)+cosgam)
atrans2=((1.0-ACL2/90.0)*atranshigh+ACL2*(ones(4,10)-cosgam))./(2.0*ones(4,10)-ACL2/90.0*ones(4,10)-cosgam)
atrans3=((1.0+ACL3/90.0)*atrans0-ACL3*(ones(4,10)-cosgam))./(ACL3/90.0*ones(4,10)+cosgam)
atrans4=((1.0+ACL4/90.0)*atranslow+ACL4*(ones(4,10)-cosgam))./(2.0*ones(4,10)+ACL4/90.0*ones(4,10)-cosgam)
#
atrans=atrans0.*(atrans0.<=ACL1).*(atrans0.>=ACL3).*(abs.(alphay).<90.0)+
atrans1.*(atrans0.>ACL1).*(alphay.<90.0)+(atrans2.*(atranshigh.<ACL2)+
atranshigh.*(atranshigh.>=ACL2)).*(alphay.>=90.0)+atrans3.*
(atrans0.<ACL3).*(alphay.>=-90.0)+(atrans4.*(atranslow.>ACL4)+
atranslow.*(atranslow.<=ACL4)).*(alphay.<-90.0)
atransBtab=max.(min.(atrans,32.0),-32.0)
alphayBtab=max.(min.(alphay,32.0),-32.0)
#
CL=interpp1(vec(AOAUTAB),vec(CLR0UTAB),atrans).*(abs.(atrans).>32.0)+
interpp2(vec(AOABTAB),vec(MACHTAB),CLR0BTAB,atransBtab,Machtab).*
(abs.(atrans).<=32.0)
CD=interpp1(vec(AOAUTAB),vec(CDR0UTAB),alphay).*(abs.(alphay).>32.0)+
interpp2(vec(AOABTAB),vec(MACHTAB),CDR0BTAB,alphayBtab,Machtab).*
(abs.(alphay).<=32.0)+ones(4,10)*DCDMR
# lift array specific to Peters-He inflow form
BLSEGLIFT=((0.5*(ones(NB,1)*vec(CHORD)'))./R).*CL.*sign.(Ut).*Utot.*
sqrt.(Ut.^2+Ur.^2)
# blade segment forces
Fp=(0.5*RHO*OMEGA^2*R^3)*(ones(NB,1)*vec(CHORD)').*Utot.*
(CL.*Ut./acosgam+CD.*Up).*(ones(NB,1)*vec(delseg)')
Ft=(0.5*RHO*OMEGA^2*R^3)*(ones(NB,1)*vec(CHORD)').*Utot.*
(CD.*Ut-CL.*Up.*acosgam).*(ones(NB,1)*vec(delseg)')
Fr=(0.5*RHO*OMEGA^2*R^3)*(ones(NB,1)*vec(CHORD)').*Utot.*
(CD-CL.*Up.*acosgam./Ut).*Ur.*(ones(NB,1)*vec(delseg)')
# total shear force at each blade hinge
Fpb=zeros(4,1)
Ftb=zeros(4,1)
Frb=zeros(4,1)
for i=1:NB
Fpb[i]=sum(Fp[i,:])
Ftb[i]=sum(Ft[i,:])
Frb[i]=sum(Fr[i,:])
end
#Fpb=sum(Fp,2)
#Ftb=sum(Ft,2)
#Frb=sum(Fr,2)
# sum total blade forces for dynamic twist model
Fp_DT=sum(sqrt.(Fpb.^2+Ftb.^2))/NB
# total aero moment about each hinge
Mf_aero=zeros(4,1)
Ml_aero=zeros(4,1)
for i=1:NB
Mf_aero[i]=R*sum(rseg.*Fp[i,:])
Ml_aero[i]=R*sum(rseg.*Ft[i,:])
end
#Mf_aero=R*sum((ones(NB,1)*vec(rseg)').*Fp,2)
#Ml_aero=R*sum((ones(NB,1)*vec(rseg)').*Ft,2)
# aero moments
Lha=-sum(Mf_aero.*spsizeta) # maybe a mistake here?
Mha=-sum(Mf_aero.*cpsizeta)
# aero shear forces at each hinge
Fxa=Frb.*cbeta.*szeta-Ftb.*czeta-Fpb.*sbeta.*szeta
Fya=Frb.*cbeta.*czeta+Ftb.*szeta-Fpb.*sbeta.*czeta
Fza=-Frb.*sbeta-Fpb.*cbeta
# total aero thrust
Tha=-sum(Fza)
# aero force and momemnt coefficients (used by Pitt Peters model)
CTa=Tha/(pi*RHO*OMEGA^2*R^4)
CLa=Lha/(pi*RHO*OMEGA^2*R^5)
CMa=Mha/(pi*RHO*OMEGA^2*R^5)
# lag damper kinematics
thetald=thetab-THETALDGEO*ones(4)
xld=ALD*sbeta+ones(4)*CLD+(BLD*cos.(zeta+ones(4)*ZETA0)+DLD*
sin.(zeta+ones(4)*ZETA0)).*cbeta
yld=-RLD*cos.(thetald)-BLD*sin.(zeta+ones(4)*ZETA0)+DLD*
cos.(zeta+ones(4)*ZETA0)
zld=ALD*cbeta-RLD*sin.(thetald)-(BLD*cos.(zeta+ones(4)*ZETA0)+
DLD*sin.(zeta+ones(4)*ZETA0)).*sbeta
daxld=sqrt.(xld.^2+yld.^2+zld.^2)
#
xld_dot = ALD*beta_dot.*cbeta-beta_dot.*sbeta.*(BLD*cos.(zeta+ones(4)
*ZETA0)+DLD*sin.(zeta+ones(4)*ZETA0))+(-BLD*sin.(zeta+ones(4)*
ZETA0)+DLD*cos.(zeta+ones(4)*ZETA0)).*zeta_dot.*cbeta
yld_dot = RLD*sin.(thetald).*thetab_dot-(BLD*cos.(zeta+ones(4)*ZETA0)+DLD*
cos.(zeta+ones(4)*ZETA0)).*zeta_dot
zld_dot = -ALD*sbeta.*beta_dot-RLD*cos.(thetald).*thetab_dot -cbeta.*
beta_dot.*(BLD*cos.(zeta+ones(4)*ZETA0)+DLD*sin.(zeta+ones(4)*
ZETA0))-(-BLD*sin.(zeta+ones(4)*ZETA0)+DLD*cos.(zeta+ones(4)*
ZETA0)).*zeta_dot.*sbeta
raxld = (xld.*xld_dot+yld.*yld_dot+zld.*zld_dot)./daxld
# lag damper force (linear lag damper)
Fld=CLAG*raxld
# flap and lag moments due to lag damper force
Mf_ld=-Fld.*((zld*CLD)+(xld.*sin.(thetald)*RLD))./(12.0*daxld)
Ml_ld=-Fld.*(RLD*cos.(thetald).*(xld.*cbeta-zld.*sbeta)+yld.*
(CLD*cbeta+RLD*sin.(thetald).*sbeta))./(12.0*daxld)-
KLAG*(zeta+ones(4)*ZETA0)
# notional flap sping /damper
Mf_fd=-KFLAP*beta-CFLAP*beta_dot
# flap and lag acclerations
beta_ddot = zeros(NB)
zeta_ddot = zeros(NB)
for i=1:NB
beta_ddot[i]=(MBETA/IBETA)*(cbeta[i].*(Vzsdot+HOFFSET*(2*OMEGA*(ps*cpsi[i]-qs*spsi[i])+
psdot*spsi[i]+qsdot*cpsi[i]))+sbeta[i].*czeta[i].*(Vysdot*spsi[i]-Vxsdot*cpsi[i]-
HOFFSET*rminusO^2)+sbeta[i].*szeta[i].*(Vysdot*spsi[i]-Vxsdot*cpsi[i]-
HOFFSET*rsdotmomd))+(cbeta[i].^2).*(czeta[i].*(psdot*spsi[i]+qsdot*
cpsi[i]-2*(zeta_dot[i]+OMEGA).*(qs*spsi[i]-ps*cpsi[i]))-szeta[i].*(2*(OMEGA+
zeta_dot[i]).*(ps*spsi[i]+qs*cpsi[i])+(qsdot*spsi[i]-psdot*cpsi[i])))+
cbeta[i].*sbeta[i].*(2*zeta_dot[i]*rminusO-rminusO^2-zeta_dot[i].^2)+
(Mf_aero[i]+Mf_ld[i]+Mf_fd[i])/IBETA
zeta_ddot[i]=(MBETA./(IBETA*cbeta[i])).*(szeta[i].*(Vysdot*spsi[i]-Vxsdot*cpsi[i]-
HOFFSET*rminusO^2)-czeta[i].*(Vxsdot*spsi[i]+Vysdot*cpsi[i]))+rsdotmomd+
(sbeta[i]./cbeta[i]).*(2*beta_dot[i].*(OMEGA+zeta_dot[i]-rs)+qsdot*spsizeta[i]-
psdot*cpsizeta[i])+2*beta_dot[i].*(czeta[i].*(qs*spsi[i]-ps*cpsi[i])+szeta[i].*
(ps*spsi[i]+qs*cpsi[i]))+(Ml_ld[i])./(IBETA*cbeta[i].^2)-
Ml_aero[i]./(IBETA*cbeta[i])
end
# inertial shear at each hinge
Fxi = zeros(NB)
Fyi = zeros(NB)
Fzi = zeros(NB)
for i=1:NB
Fxi[i]=MBETA*(cbeta[i].*czeta[i].*(rsdotmomd-zeta_ddot[i])+2*sbeta[i].*czeta[i].*(zeta_dot[i].*
beta_dot[i]-rminusO*beta_dot[i])+cbeta[i].*szeta[i].*(zeta_dot[i].^2+beta_dot[i].^2-2*
rminusO*zeta_dot[i]+rminusO^2)+2*beta_dot[i].*cbeta[i].*(ps*cpsi[i]-qs*spsi[i])+
sbeta[i].*szeta[i].*beta_ddot[i])-WBLADE/G*(Vxsdot*spsi[i]+Vysdot*cpsi[i])
Fyi[i]=MBETA*(cbeta[i].*czeta[i].*(zeta_dot[i].^2+beta_dot[i].^2-2*rminusO*zeta_dot[i]+
rminusO^2)+sbeta[i].*czeta[i].*beta_ddot[i]+cbeta[i].*szeta[i].*zeta_ddot[i]-2*beta_dot[i].*
cbeta[i].*(ps*spsi[i]+qs*cpsi[i])+WBLADE*HOFFSET/(G*MBETA)*rminusO^2)+WBLADE/G*
(Vxsdot*cpsi[i]-Vysdot*spsi[i])
Fzi[i]=MBETA*(beta_ddot[i].*cbeta[i]-(beta_dot[i].^2).*sbeta[i] + 2*sbeta[i].*czeta[i].*
beta_dot[i].*(ps*spsi[i]+qs*cpsi[i])+cbeta[i].*szeta[i].*(2*(OMEGA+zeta_dot[i]).*
(ps*spsi[i]+qs*cpsi[i])+qsdot*spsi[i]-psdot*cpsi[i])-cbeta[i].*czeta[i].*(2*(OMEGA+
zeta_dot[i]).*(ps*cpsi[i]-qs*spsi[i])+psdot*spsi[i]+qsdot*cpsi[i])+WBLADE*HOFFSET/
(G*MBETA)*((2*OMEGA*(ps*cpsi[i]-qs*spsi[i])+psdot*spsi[i]+qsdot*cpsi[i])))-
WBLADE/G*Vzsdot
end
# total shear force
Fxt=Fxi+Fxa
Fyt=Fyi+Fya
Fzt=Fzi+Fza
# total rotor forces and moments
Thrust=-sum(Fzt)
Hforce=sum(Fyt.*cpsi-Fxt.*spsi)
Jforce=-sum(Fxt.*cpsi+Fyt.*spsi)
Lhub=sum(HOFFSET*Fzt.*spsi+Mf_ld.*spsizeta)
Mhub=sum(HOFFSET*Fzt.*cpsi+Mf_ld.*cpsizeta)
Qhub=-sum(HOFFSET*Fxt-Ml_ld)
# iteration to solve for quasi-steady lambda0
lambda0_qs=lambda0
delta_lambda=10.0
iter=0
while ((abs(delta_lambda)>1e-9) && (iter<70))
lambda0_qsn=CTa/(2*sqrt(mu^2+(lambda0_qs-muzs)^2))
delta_lambda=lambda0_qsn-lambda0_qs
lambda0_qs=lambda0_qs+0.5*delta_lambda
iter=iter+1
end
# angle of attack and mass flow parameters
mutot=sqrt(mu^2+(muzs-lambda0_qs)^2)
Vmpp=(mu^2+(lambda0_qs-muzs)*(2*lambda0_qs-muzs))/mutot
# wind to shaft transformation
cbetawind=muxs/mu
sbetawind=muys/mu
Ts2w=[1 0 0
0 cbetawind sbetawind
0 -sbetawind cbetawind]
Tw2s=Ts2w'
Tw2sdot=[0 0 0
0 -sbetawind -cbetawind
0 -cbetawind sbetawind]*betawind_dot
Ts2wdot=Tw2sdot'
#
lambda_w=Ts2w*[lambda0;lambda1s;lambda1c]
#
omega_w=Ts2w*[rs;ps;qs]/OMEGA
beta1c_dot=xr[NB+3]
beta1s_dot=xr[NB+4]
beta0_dot=xr[NB+1]
betastar_w=Ts2w*[beta0_dot;beta1s_dot;beta1c_dot]/OMEGA
# Pitt-Peters with quasi-steady wake curvature effects. Based on Zhao 2004
Xpp=xr[4*NB+6]
kcpp=xr[4*NB+7]
kspp=xr[4*NB+8]
# limit the denominator to be positive
kcqs=(omega_w[3]-betastar_w[3])/max((lambda0_qs-muzs),0.001)
ksqs=(omega_w[2]-betastar_w[2])/max((lambda0_qs-muzs),0.001)
chi=atan2(mu,(lambda0_qs-muzs))
#
Xqs=tan(0.5*chi)
#
Xpp_dot=OMEGA*(15.0*pi*Vmpp)/32.0*(Xqs-Xpp) # a bit off
kcpp_dot=OMEGA*(15.0*pi*mutot)/32.0*(kcqs-kcpp)
kspp_dot=OMEGA*(15.0*pi*mutot)/32.0*(ksqs-kspp)
#
Vpp=[mutot 0.0 0.0
0.0 Vmpp 0.0
0.0 0.0 Vmpp]
Lpp=[0.5 0.0 -15*pi/64*Xpp
0.0 2*(1+Xpp^2) 0
15*pi/64*Xpp 0.0 2*(1-Xpp^2)]
# use constant value of KR>=0, otherwise use airspeed schedule
#if KR<0
# ciao=interp1(vec(KRVsched),vec(KRsched),Veq)
#end
# assume no wake curvature for now
delL1=zeros(3,3)
delL1[2,1]=0.5*KR*kspp
delL1[3,1]=0.5*KR*kcpp
delL1[1,2]=0.5*KR*kspp
delL1[1,3]=0.5*KR*kcpp
delL2=zeros(3,3)
delL2[2,1]=0.75*KR*kspp*Xpp^2
delL2[3,1]=-0.75*KR*kcpp*Xpp^2
delL3=zeros(3,3)
delL3[2,1]=1.25*mu*kcpp*Xpp*KR
delL3[2,2]=(-2.5*kcpp*Xpp-1.5*mu*kspp*(1.0+1.5*Xpp^2))*KR
delL3[2,3]=-2.5*kspp*Xpp*KR
delL3[3,1]=1.25*mu*kspp*Xpp*KR
delL3[3,2]=(-2.5*kspp*Xpp-1.5*mu*kcpp*(1.0-1.5*Xpp^2))*KR
delL3[3,3]=-0.3*kcpp*Xpp*KR
#
ciao=OMEGA*[(75*pi)/128 0.0 0.0
0.0 (45*pi)/16 0.0
0.0 0.0 (45*pi)/16]
ciao2=Ts2w*[CTa;-CLa;-CMa]-(inv(Lpp+delL1+delL2+delL3)*Vpp)*lambda_w
lambda_dot_w=ciao*ciao2
#lambda_dot_w=ciao*(Ts2w*[CTa;-CLa;-CMa]-Vpp/(Lpp+delL1+delL2+delL3)*lambda_w)
lambda_dot=Tw2s*lambda_dot_w+Tw2sdot*lambda_w
# build rotor derivatives vector
xrdot=zeros(NRSTATES)
xrdot[1:NB]=LIBC2MBC*beta_dot+LIBC2MBCdot*beta
xrdot[NB+1:2*NB]=LIBC2MBC*beta_ddot+2*LIBC2MBCdot*beta_dot+LIBC2MBCddot*beta
xrdot[2*NB+1:3*NB]=LIBC2MBC*zeta_dot+LIBC2MBCdot*zeta
xrdot[3*NB+1:4*NB]=LIBC2MBC*zeta_ddot+2*LIBC2MBCdot*zeta_dot+LIBC2MBCddot*zeta
xrdot[4*NB+1:4*NB+3]=lambda_dot
xrdot[4*NB+4]=OMEGA
# added state for filtered dynamic twist force
xrdot[4*NB+5]=(1.0/TauDT)*(Fp_DT-xr[4*NB+5])
xrdot[4*NB+6]=Xpp_dot
xrdot[4*NB+7]=kcpp_dot
xrdot[4*NB+8]=kspp_dot
# rotor forces and moments in body frame at aircraft CG
Fmrb=Tshaft'*[-Hforce;-Jforce;-Thrust];
Mmrb=Tshaft'*[Lhub;Mhub;Qhub]+[0 -Zh Yh;Zh 0 -Xh;-Yh Xh 0]*Fmrb
# main rotor forces and moments
Fr=Fmrb
Mr=Mmrb
Qr=Qhub
# EQUATIONS OF MOTION
# total forces and moments
Ftot=Fr+Ff+Fht+Fvt+Ftr
Mtot=Mr+Mf+Mht+Mvt+Mtr
Qreq=Qr+Qtr*GEARTR
# equations of motion
xfdot=eqnmot(xf,Ftot,Mtot)
# STATE DERIVATIVE
xdot=zeros(NSTATES)
xdot[1:NFSTATES]=xfdot
xdot[NFSTATES+1:NFSTATES+NRSTATES]=xrdot
#xdot[NFSTATES+NRSTATES+1:NFSTATES+NRSTATES+NTRSTATES]=xtrdot[1]
xdot[NSTATES]=xtrdot
return xdot
end