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7/31/2019 Presentazione En
1/22
Universita degli Studi di Napoli
Federico II
Facolta di Ingegneria
Corso di laurea in Ingegneria AerospazialeDipartimento di Ingegneria Aerospaziale
Analogical-differential sun sensor simulator
Academic Year 2007/2008
Teacher Supervisor: Ch.mo Prof. Ing. Candidate: Claudio Bove
Michele Grassi matr. 347/436
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The aim of the thesis is the development of modeling and a numerical code that simulates the
operation of an analogical-differential sun sensor instead on a satellite in orbit.It consists of five
solar cells arranged on a truncated pyramid with square base and allows to determine the direction
of the sun through a combination of short-circuit currents.
The comparison between this direction and that reconstructed from the know apparent motion of
the sun allows to estimate the satellite attitude.
Analogical differential sun sensor Satellite attitude
yo
zo
xo
12
3
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The key element of an analogical differential sun sensor is the solar cell,a device capable of
trasforming the energy of light radiation into electrical energy.
The most common solar cell consists of a silicon sheet, a non-reflective glass and two electrical
contacts.
The efficiency of the solar cell is obtained by evaluating the relationship between provided
energy and the energy of light which invests its entire surface.Typical values for specimens of
crystalline silicon on the market is around 15%.
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Electricfield
p-type silicon
Anti-reflection coating
Top electric contact
Junction
n-type silicon
Low electric contact
Solar radiation
Putting a load in parallel there is the passage of electric current due to a concentration gradient of
charges.
Electrical
resistance
+ -
-
++
Principle of operation of the photovoltaic cell
Doping pure silicon with group III atoms as boron (p-type silicon) and group V such as phosphorus
(n-type silicon) an electrical field that favors the separation of charge carriers is obtained at the
junction when an electron is removed from atom due photoelectric effet.
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4Curva caratteristica della cella solare Silicon K7700A
Tensione [V]
Corrente[A]
The diagram showing the current as a function of the voltage is called characteristic curve .In it
there are two parameters that depend on the construction of the cell:
Short -circuit current Short- circuit voltage
In addition there is a dependence on the angle of solar radiation incidence.
teta=0
teta=pi/6
teta=pi/4
teta=pi/3
n
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In particular the cells 1,2,5 combine to determine the angle s that the projection of solar directionThe cells 3,4,5 instead combine to determine the angle s that the projection of solar direction in
lane XsZs sha e with the axis Zs.
Analogical differential sun sensor combines the short-circuit currents of five cells to determine the
direction of the sun in sensory reference XsYsZs.
4
3
1
2
5
Xs
Ys
Zs
s
Zs
Xs
Ys
YsZs
s
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The formulas needed to determine the angle s in plane YsZs are achieved by combining short-
circuit currents of cells 1,2,5.This angle can be calculated only in three cases:
Zs
Ys
-/2 /2
-/2+0 /2-0
C
E
D
BA
521
n2n1
Sun in the fields of view of cells 1,2,5 stg0sin25scI
1sc
I
2sc
I
=
Sun in the fields of view of cells 2 e 5
s005sc
2sc
tgsincosI
I
+=s005sc
1sc
tgsincosI
I
=
Sun in the fields of view of cells 1 e 5
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In a similar way the formulas are written for the calculation of the angle s in plane XsZs.
Zs
Xs
-/2 /2
-/2+0 /2-0
C
E
D
BA
543
n2n1
Sun in the fields of view of cells 3,4,5 stg0sin2
5sc
I
3scI4scI =
Sun in the fields of view of cells 4 e 5
s005sc
4sc
tgsincosI
I
+=
Sun in the fields of view of cells 3 e 5
s005sc
3sc
tgsincosI
I
=
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Simulation program
Simulate the operation of the analogical differential sun sensor means to predict the short-circuit
currents produced by the five cells at any instant of the time if it is placed on a satellite in orbit.
A block that calculates short-circuit currents and rebuild the direction of the sun in the sensory
system XsYsZs.
So it is necessary to design:
An orbit propagator to simulate the satellites orbit.
A propagator of the dynamics of attitude.
A propagator of the apparent motion of the sun.
X
Y
ZZs
YsXs
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The simulation program is implemented using Simulink
The general scheme is:
Sun orbitalparameters
Sun sensor
Orbitalpropagator
X,Y,Z satellite in IRF
X,Y,Z sun in IRF
satellite in IRF
Solarpropagator
Orbital parameters
X,Y,Z sun in BRF
Matrix
IRF to ORF
Propagatorof the
dynamics of
attitude
Initial attitude Matricx
ORF to BRF
Z,Y,X
,,
,,
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Orbital propagator
Input:inclination, right ascension of the ascending node, argument of perigee,true anomaly, semi-
major axis maggiore,eccentricity.
Output:componenti della posizione del satellite nel riferimento inerziale.
By derivation the velocity components can also be obtained.
Z
X
Y
i
w
a
( ) ( )[ ]
+
+=cose1
psinwcosicossinwsincoscoswsinicossinwcoscosrX
( ) ( )[ ]+
+++=cose1
psinwcosicoscoswsinsincoswsinicoscoswcossinrY
[ ]+
+=cose1
psinwcosisincoswsinisinrY
Equatorialplane
n
Descendingnode
Ascending
node
xp
zp
yp
Perigee
r
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Simulink diagram for orbital propagator
M A T L A B
Fu n ct io n
ve l o ci ta ' a n g o la re
m e d ia
M A T L A B
F u n ct i o n
se m il a to re tt o
6 7 7 8
se m i a sse
m a g g io re
M A T L A B
Fu n ct io n
p e rio d o o rb i ta le
3 .9 8 *(1 0 5 )
m u te rra
4 5
in cl in a zio n e
0
e cce n t r ic i ta '
M A T L A B
Fu n ct i o n
c o n ve rsio n e
4 0
a sc e n sio n e re tta
3 0
a rg o m e n to p e ri g e o
M A T L A B
Fu n ct io n
a n o m a l i a ve ra
M A T L A B
Fu n ct io n
a n o m a l ia e cce n tr ic a
I n 1
S o tto siste m a ve lo ci ta '
I n 1
S o tto siste m a p o siz io n e
C l o ck
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Propagator of the dynamics of the attitude
The equations of dynamics of attitude ,in case of small eccentricity and small angles ,are:
( ) 0k1MkM4 112 =+
( )tMsinMe2kM3 22 =+
( ) 0k1MkM 332 =++
The obtained solutions by integration are the following:
( ) ( ) ( )tkM2sinkM2
tkM2cost 11
010
+=
( ) ( ) ( ) ( ) ( ) ( ) ( )tk3Msink31k3e2
tMsink31
e2tk3Msink3Mtk3Mcost
2222
22
020
+
+=
( ) ( ) ( )tkMsinkM
tkMcost 33
030
+=
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So the propagator of dynamics of satellite attitude is created by a block that produces in output
these solutions giving in input the initial angles ,the initial angle speed,the eccentricity,medium
angle speed,details of the moments of inertia mass.
yaw punto [gradi/s]
yaw [rad]
yaw [gradi]
MATLAB
Function
velocita' angolare
media
In1
Out1
Out2
sottosistema yaw
In1
Out1
Out2
sottosistema roll
In1
In2
Out1
Out2
sottosistema pitch
6778
semiasse
maggiore
roll punto [gradi/s]
MATLAB
Function
roll e rollpunto
roll [rad]
roll [gradi]
pitch punto [gradi/s]
MATLAB
Function
pitch e pitchpunto
pitch [rad]
pitch [gradi]
3.98*(10^5)
mu terra
MATLAB
Function
gradi yaw e yawpunto
0
eccentricita'
2
Out2
1
Out1
MATLAB
Function
roll punto
MATLAB
Function
roll
0.94299
k1
clock
8.7266*10^-6
alfazeropunto
0.297
alfa0
1
In1
2
Out2
1
Out1
MAT LAB
Function
pitch punto
MAT LAB
Function
pitch
0.11141
kdue
8.7266*10^-6
beta0punto
0.262
beta0
Clock
2In 2
1
In 1
2
Out2
1
Out18.7266*10^-6
yaw0punto
0.279
yaw0
MATLAB
Function
yaw punto
MATLAB
Function
ya w
0.92920
ktre
Clock
1
In1
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Simulink model of the analogical differential sun sensor
The simulink diagram that models the analogical differential sun sensor has in input the
components of the solar unit vector in the sensory reference and output short-circuit currents of the
five solar cells.
MATLAB
Function
ricostruzione
versore sole
In1 Out1
determinazione angoli
alfa e beta sole
corrente cella 5 [A]
MATLAB
Function
corrente cella 5
corrente cella 4 [A]
MATLABFunction
corrente cella 4
corrente cella 3 [A]
MATLAB
Function
corrente cella 3
corrente cella 2 [A]
MATLAB
Function
corrente cella 2
corrente cella 1 [A]
MATLAB
Function
corrente cella 1
componenti versore sole
ricostruito dal sensore
MATLAB
Function
componen ti versore sole
nel sistema sensoriale
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The simulink diagram is:
In the simulation program five solar sensors were considered ,each placed on one side of the
satellite except the one facing the earth,in order to increase the chances of reconstruction of the
solar direction.Then the ideal operation of the sensors with perfectly same cells and that real with
cells having short-circuit currents equal to less than 1% were simulated.
yaw radiantiMATLAB
Function
versore sole BRF
sen sori sol ari
rol l radianti
propagatore solare
propagatore orbitale e dinam ica d'assetto
pitch radianti
modulo posizione
sole [km]
MATLAB
Function
eclisse
compo nenti versore
sole BRF
componenti sole
in B RF [km]
comp onenti po sizione [km]
componenti posizione
sole [km]
compon enti velocita' [km/s]
MATLAB
Function
ORF to BRFMATLAB
Function
IRF to ORF
RICOSTRUZIONE DEL VERSORE SOLE COMPONENTI VERSORE SOLE IN BRF
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Simulation results
The simulator works for any type of Keplerian orbit having small eccentricity.In this thesis
simulations have been carried out for three types of orbits,showing the trends of short-circuit
currents of all the solar cells and the reconstructions of the solar unit for each sensor in terms both
of components both of coelevation and azimuth sun angles.
Keplerian circular orbit at the spring equinox,with 400 km altitude,inclination 0 (equatorial
orbit), = 40, w = 30.
yo
zo
xo
1 2
3
0 1000 2000 3000 4000 5000 6000-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
tempo [s]
COMPONE
NTIVERSORE
RICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componente
terza componente
TIME OFFSET:6.7391e+006
0 1000 2000 3000 4000 5000 6000-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
tempo [s]
COMPONENTIVERSO
RE
RICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componente
terza c omponente
TIME OFFSET:6.7391e+006
0 1000 2000 3000 4000 5000 60-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
tempo [s]
COMPONENTIVERSO
RE
RICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componente
terza componente
TIME OFFSET:6.7391e+006
0 1000 2000 3000 4000 5000 60-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
tempo [s]
COMPONE
NTIVERSORE
COMPONENTI VERSORE SOLE IN BRF
prima componente
seconda c omponente
terza componente
TIME OFFSET:6.7391e+006
Eclipse
Eclipse
Eclipse
RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE COELEVAZIONE ED AZIMUTH SOLE IN BRF
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yo
zo
xo
1 2
3
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AMPIEZZA
[gradi]
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AMPIEZZA
[gradi]
RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 600
50
100
150
200
250
300
350
400
tempo [s]
AMPIEZZA
[gradi]
RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 6000
50
100
150
200
250
300
350
400
tempo [s]
AMPIE
ZZA
[gradi]
coelevazione
azimuth
TIME O FFSET : 6.7391e+006
Eclipse
Eclipse
Eclipse
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Simulation results
The simulator works for any type of Keplerian orbit having small eccentricity.In this thesis
simulations have been carried out for three types of orbits,showing the trends of short-circuit
currents of all the solar cells and the reconstructions of the solar unit vector for each sensor in terms
both of components both of coelevation and azimuth sun angles:
Keplerian circular orbit at the spring equinox,with 400 km altitude ,inclination 0 ( equatorial
orbit), = 40, w = 30.
Keplerian circular orbit at the spring equinox,with 400 km altitude and inclination 45, =
40, w = 30.
Keplerian circular orbit at the summer solstice,with 800 km altitude and inclination 90( polar
orbit ), = 40, w = 30.
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Conclusions
The aim of the thesis have been the creation of a program that simulates the operation of five
solar sensors placed on the satellite faces.
The combination of the short-circuit currents determines in each sensory reference the sun
direction which ,compared with that known by sun apparent motion,can estimate the satellite
attitude.So it possible choose the best placement of the sensors.
The numeric code have been created using Simulink and has given satisfactory results ,that could
be improved by modeling the main causes perturbations of the orbit.
The program could be used in the design of future spece missions ,for prediction calculations on
the satellite attitude and to obtain useful informations for development of the best design of
attitude control.
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Thank you for your kind attention