Thesis - Beaver simulation

See figures F-38 and F-39. Type help locerr o r help gserr for on-line help a t the MATLAB command line.

Both blocks have been created with the Mask utility of SIMULINKEvery. time a simulation is started, these blocks will be initiated. The following Mask initialization commands have been included:

LOCERR: xloc = @4; slot = 1.4*xloc; cat = @I;

if cat ==	1
D-iloc	=	Sloc*atan(10.5/xloc);
KSloc	=	1 +	(@2/100)*0.17;
elseif cat == 2
D-iloc	=	Sloc*atan(7.5/xloc);
K S ~ O C =		1 +	(@2/100)*0.17;
else
D-iloc =		Sloc*atan(3/xloc);
KSloc	=	1 +	(@2/100)*0.10;
end	D-iloc		* @3/100;
D-iloc =

81 is the performance category (1, 2, or 3), Q2 is the percentage of the maximum allowable error in localizer sensitivity, 8 3 is the percentage of the maximum allowable localizer misalignment, and @4is the distance from the runway treshold to the localizer transmitter.

See table C-1 from appendix C (section C.2.2) for the ICAO guidelines concerning localizer steady-state errors. The arctan commands are used to transfer the maximum deviation of the localizer reference plane from the runway centerline a t runway treshold into a n error-angle NL,.

GSERR: gangs = -abs(@4*pi/180); ~ g s= 625/abs(gamgs); cat = @I; if cat == 1

D-igs = Sgs*0.075*gamgs; KSgs = 1 + (@2/100)*0.25;

elseif cat == 2

D-igs = Sgs*O.075*garngs; KSgs = 1 + (@2/100)*0.20;

e l s e

D-igs = Sgs*0.040*gamgs; KSgs = 1 + (@2/100)*0.15;

end

D-igs = D-igs * @3/100

81is the performance category, 8 2 is the percentage of the maximum allowable error in the glideslope sensitivity, 03 is the percentage of the maximum glideslope misalignment, and 0 4 is the nominal glideslope elevation angle. The maximum permissible glideslope steady-state errors are listed in table C-2 of appendix C (section C.2.2).

3 - LOCNOISE and GSNOISE. These blocks are used to compute ILS noise. There are two types of ILS noise blocks, see appendix C, section C.2.3.

LOCNOISEl and GSNOISEl calculate the localizer and glideslope noise according to AGARD R-632 (ref.[l]), using a fixed (user-specified)value for the approach speed. The scale length and standard deviation of the localizer and glideslope noise must be specified.

Inputsignal: none

Outputsignal: localizer noise or glideslope noise in [$A]

See figures F-40 and F-41.

	iloc	+		iloc
	(nominal)	D-iloc -	KSloc = 1 if localizer sen-
				(real)
	Error signal due to difference		sitivlty has the nominal value.
			KSloc = 1.xx if the offset in
	between runway centerline and		Sloc is 1OO%%
		localizer reference plane

Figure F-38. Internal structure of the block LOCERR.

NAVLIB

(nominal)

D-igs

Error signal due to deviation of nominal glideslope elevation angle

KSgs = 1 if glideslope sen-	(real)
sitivity has the nominal value.
KSgs = 1.xx if the offset in
Sgs is 1OO%%

Figure F-39. Internal structure of the block GSERR,

NAVLIB

	K
	-
	tau.s+1
White Noise	loc noise out
	noise fitter

Figure F-40. Internal structure of the block LOCNOISEI.

NAVLIB

Figure F-41.Internal structure of the block GSNOISE1.

NAVLIB

5(s+l.5)

I

(s+0.35)(~+10)

ri
White Noise	Localizer
noise filter	noise WA]

Figure F-42. Internal structure of the block LOCNOISE2.

NAVLIB

	3.9875
	(s+0.25)	-
	White Noise		Glideslope
	noise filter		noise WA]

Figure F-43. Internal structure of the block GSNOISE2.

NAVLIB .

	GS-noise	-
	AGARD R-632
	Glideslope steady
r)l	state errors
	AGARD R-632
Nominal --.+	Localizer steady	[igs-t rue
	state errors	iloc-true]'
	AGARD R-632
	LOC-noise
	AGARD R-632

Figure F-44.Internal structure of the block ILSXMPL.

NAVLXB (also contained as separate system in directory EXAMPLES)

Appendix F

261

LOCNOISE2 and GSNOISE2 create localizer and glideslope noise according to NASA CR-2022 (ref.[20]).

Inputsignal: none

Outputsignal: localizer noise or glideslope noise in [pA]

See figures F-42 and F-43.

On-line help for the localizer and glideslope noise blocks is available from the MATLABcommand line (type help locnoise or help gsnoise, respectively).

4 - ILSXMPL. This block demonstrates the practical use of the ILS blocks. It uses the blocks ILS, LOCERR, GSERR, LOCNOISEI, and GSNOISEI. Only the localizer and glideslope currents, including noise and steady-state errors, are returned as block-outputs, to which other systems can be connected. But all output signals from ILSXMPLE are sent to the vector yils in the MATLABworkspace.

Inputs: Uils

Outputs: y,,,,(including errors)

See figure F-44.

5 - VOR. This block contains the equations, necessary to compute the nominal VOR signal. It also contains a To/From test, a Cone of silence flag, and a Range flag. The output from the To/From indicator equals 1if the aircraft flies TO the VOR transmitter; it equals 0 if it flies FROM the VOR transmitter. The Cone of silence flag is set to 1 if the aircraft has entered the Cone of silence; the Range flag is set to 1if the distance from the aircraft to the VOR station is too large (see section C.3.2).

The user must specify the coordinates of the VOR-station, xVoRand yvoR, its altitude above sea level HvoR,and the course datum CD.

Type help uor a t the MATLABcommand line for on-line help. The internal structure of VOR is shown in figure F-45.

6 - VORERR. This block can be used to implement a steady-state error in the VOR signal. The user must specify the error percentage. Type help vorerr a t the MATLABcommand line for on-line help.

Inputsignal:	,,T	(nominal value)
Outputsignal:	,,T	(nominal value + steady-state error)

See figure F-46 for the internal structure of this block.

		1 = to, 0= from
	atan((u[2]-yVOR)l(u[l]-xVOR))		Gamma-VOR
[xe ye HI'	QDR	+/- 10 deg
	f-xTl		yVOR1
	w
	CD (const.)

Mux

Cone of silenceflag

VOR-Range approximation

I

Figure F-45. Internal structure of the block VOR.

NAVLIB

Gamma-VOR		Gamma-VOR
(nominal value)	KVORerr	(actual value)

Figure F-46. Intermal structure of the block VORERR.

NAVLIB

Appendix F

263

F.5 Conclusions.

This appendix contains all details of the nonlinear 'Beaver' model, the VOR and ILS models, and wind and turbulence models. The equations have all been implemented in block-diagrams, using the Function blocks of SIMULINK(see also appendx G). Flexibility has been obtained by grouping small sets of equations into 'basic' SIMULINKblocks. With the Mask utility, the internal structure of the blocks has been hidden from the user, and sometimes dialog boxes have been included (black-boxapproach). The user is encouraged to use the models for hisher own experiment. Don't be impressed too much by the detailed description in this appendix! Chapters 4 and 6 will often give sufficient information for using the current models if it is not necessary to change the models, but if more details are needed, this appendix gives all information.

Table F-1. Parameters of the aerodynamic model of the 'Beaver' in the format used by the S ~ U L I NsimulationK model.

Appendix F

265

Table F-2. Parameters of the engine model of the 'Beaver' in the format used by the SIMULINKsimulation model.

Table F-3. Aircraft geometry and mass distribution data in the format used by the SIMULINKsimulation model.

= [	Cxa Cya CG					'ma	C n a IT
= [	Cxt		C y t Czt		Clt	Cmt	C n t IT
= [ X a Ya Z a L a M a 'a I
= [ x,		ygr I, I
= [ x, v, z t Lt					M t N t 1
= [ F,		F,		Fz I
=rw,v , GIT
= [ L		M #lT
= [ 6,		S,		6, S,]	(inputs to the aerodynamic model)
= [ n p,]				(inputs to the engine model)
= [ uw vw ww uw Ci,						vVw ] (wind and turbulence inputs)
= [ V		a p p q			r yl	8 cp	xe ye z e l T (statevector)
= [ ~ a f ~ p q i \ i r e + Hx ~] y~~
= [ Ax							1
= [ a M qdwlT
= [ 9c		Ve		Vc I
= [ T, R e				RClT
= [ P		Ps		T P g l T
= [ U		V	w l T
	p b		q F r b ] T
= [ m - n T
= [ $		e		@lT

= i r @a x @ I T

= [cos(a) sin(a) cos(p) sin@) tan@) sin(y) cos(y) sin(0) cos(0) sin(cp) cos(cp) IT

	Inputs:
Atmosph, element of: Airdata Group	X
Airdatal, element of: Airdata Group	X ,	Yatm
Airdata2, element of: Airdata Group	Yatm 9		Yad1
Airdata3, element of: Airdata Group	X , Yatm 9 Yad1
Dimless, element of: Aerodynamics Group	X
Aeromod (Beaver), element of: Aerodynamics Group	X l	u a 9 Ydl
FMdims, element of: Aerodynamics Group1Engine Group	Yadl		'a Or 't
Power (Beaver), element of: Engine Group	X ,	U t , Yatm
Engmod (Beaver), element of: Engine Group	X I	Ypow
Gravity	x ,	Yaim
Fwind	x ,	uw
FMsort	Fa F t Fgr,Fw
Hlpfcn, element of: Equations of motionlstate derivatives	X
Vabdot, element of: Equations of motionlstate derivatives
pqrdot, element of: Equations of motion\State derivatives
xyHdot, element of: Equations of motionlstate derivatives
uvw, element of: Equations of motionlstate derivatives
xdotcorr, element of: Equations of motion	X ,	x	(uncorrected), ya,
Flpath	x ,	x
Accel	Ftot 9		Fgr
uvwdot	x,	x

Outputs:

Yatm

Y a d l

Yad2

Yad3

Ydl

Ca

Faor F,

Ypow

ct

F,r

Fw

Ftot , Mtot

Yhip

YV a b

ypqr

Ye u ~

Ybvel

x (corrected)

YI,

Y a m

Y u w

Table F-4. List of basic blocks within the 'Beaver' model, including their inputs and outputs.

Appendix F

267

Sub-	Definition of the matrix Out (the numbers correspond with the columns
vector	which contain the time-trajectories of the specified variables)

x

................

x

................

Ybvel

................

Y U " w

................

Ydl

................

J'Ik

................

Ypow	dpt	P
	38	39

................ .......................................................................................................................................................................................................

Yaw

................

C a

................

ct

................

F a

................

F t

................

FB'

...............8

Fw

, ...............

Yatm

................

Yadl

................

Y a d

................

Y a a

Table F-5.List of all outputs from the system BEAVER which are sent to the MATLABworkspace (continued on next page).