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Universita’ degli Studi di Napoli Federico II
Facolta’ di IngegneriaCorso di laurea in Ingegneria Aerospaziale Dipartimento 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
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
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3
Index of the presentation:
Solar cell and the characteristic curve
Analogical differential sun sensor
Simulation program
Results and conclusions
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%.
Electric field
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.
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]
Cor
rent
e [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/6teta=pi/4
teta=pi/3
n
θ
In particular the cells 1,2,5 combine to determine the angle αs that the projection of solar
direction in plane YsZs shape with axis Zs.
The cells 3,4,5 instead combine to determine the angle βs that the projection of solar direction in
plane XsZs shape 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
αs
Zs
Xs
Ys
ŜYsZsŜ
βs
The formulas needed to determine the angle αs 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
-π/2 π/2
-π/2+α0 π/2-α0
C
E
D
BA
5
21n2n1
Sun in the fields of view of cells 1,2,5
stg0sin25scI
1scI2scI
Sun in the fields of view of cells 2 e 5
s00
5sc
2sc tgsincosI
Is00
5sc
1sc tgsincosI
I
Sun in the fields of view of cells 1 e 5
In a similar way the formulas are written for the calculation of the angle βs in plane XsZs.
Zs
Xs
-π/2 π/2
-π/2+α0 π/2-α0
C
E
D
BA
5
43n2n1
Sun in the fields of view of cells 3,4,5
stg0sin25scI
3scI4scI
Sun in the fields of view of cells 4 e 5
s00
5sc
4sc tgsincosI
I
Sun in the fields of view of cells 3 e 5
s005sc
3sc tgsincosI
I
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 satellite’s orbit.
A propagator of the dynamics of attitude.
A propagator of the apparent motion of the sun.
X
Y
ZZs
YsXs
The simulation program is implemented using Simulink
The general scheme is:
Sun orbital parameters
Sun sensor
Orbital propagator
X,Y,Z satellite in IRF
X,Y,Z sun in IRF
satellite in IRF
Solar propagator
Orbital parameters
X,Y,Z sun in BRF
Matrix
IRF to ORF
Propagator of the
dynamics of attitude
Initial attitude Matricx
ORF to BRF
Z,Y,X
,,
,,
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
Ω
w
ν
a
cose1
psinwcosicossinwsincoscoswsinicossinwcoscosrX
cose1
psinwcosicoscoswsinsincoswsinicoscoswcossinrY
cose1
psinwcosisincoswsinisinrY
Equatorial plane
n
Descending node
Ascending node
xp
zp
yp
Perigee
r
Simulink diagram for orbital propagator
MATLABFunction
velocita' angolaremedia
MATLABFunction
semilato retto
6778
semiasse maggiore
MATLABFunction
periodo orbitale
3.98*(10^5)
mu terra
45
inclinazione
0
eccentricita'
MATLABFunction
conversione
40
ascensione retta
30
argomento perigeo
MATLABFunction
anomalia vera
MATLABFunction
anomalia eccentrica
In1
Sottosistema velocita'
In1
Sottosistema posizione
Clock
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
tk3Msink31k3
e2tMsin
k31
e2tk3Msin
k3Mtk3Mcost 2
2222
2
020
tkMsinkM
tkMcost 33
030
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]
MATLABFunction
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]
MATLABFunction
roll e rollpunto
roll [rad]
roll [gradi]
pitch punto [gradi/s]
MATLABFunction
pitch e pitchpunto
pitch [rad]
pitch [gradi]
3.98*(10^5)
mu terra
MATLABFunction
gradi yaw e yawpunto
0
eccentricita'
2
Out2
1
Out1
MATLABFunction
roll punto
MATLABFunction
roll
0.94299
k1
clock
8.7266*10^-6
alfazeropunto
0.297
alfa0
1
In1
2
Out2
1
Out1
MATLABFunction
pitch punto
MATLABFunction
pitch
0.11141
kdue
8.7266*10^-6
beta0punto
0.262
beta0
Clock
2
In2
1
In1
2
Out2
1
Out18.7266*10^-6
yaw0punto
0.279
yaw0
MATLABFunction
yaw punto
MATLABFunction
yaw
0.92920
ktre
Clock
1
In1
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.
MATLABFunction
ricostruzione versore sole
In1 Out1
determinazione angoli alfa e beta sole
corrente cella 5 [A]
MATLABFunction
corrente cella 5
corrente cella 4 [A]
MATLABFunction
corrente cella 4
corrente cella 3 [A]
MATLABFunction
corrente cella 3
corrente cella 2 [A]
MATLABFunction
corrente cella 2
corrente cella 1 [A]
MATLABFunction
corrente cella 1
componenti versore sole ricostruito dal sensore
MATLABFunction
componenti versore sole nel sistema sensoriale
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 radiantiMATLABFunction
versore sole BRF
sensori solari
roll radianti
propagatore solare
propagatore orbitale e dinamica d'assetto
pitch radianti
modulo posizione sole [km]
MATLABFunction
eclisse
componenti versore sole BRF
componenti sole in BRF [km]
componenti posizione [km]
componenti posizione sole [km]
componenti velocita' [km/s]
MATLABFunction
ORF to BRFMATLABFunction
IRF to ORF
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), Ω = 40°, w = 30°.
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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]
CO
MP
ON
EN
TI
VE
RS
OR
ERICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componenteterza 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]
CO
MP
ON
EN
TI
VE
RS
OR
E
RICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componenteterza 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]
CO
MP
ON
EN
TI
VE
RS
OR
E
RICOSTRUZIONE DEL VERSORE SOLE
prima componente
seconda componenteterza 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]
CO
MP
ON
EN
TI
VE
RS
OR
E
COMPONENTI VERSORE SOLE IN BRF
prima componente
seconda componenteterza componente
TIME OFFSET:6.7391e+006
Eclipse
Eclipse
Eclipse
yo
zo
xo
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3
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AM
PIE
ZZ
A [
grad
i]RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AM
PIE
ZZ
A [
grad
i]
RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AM
PIE
ZZ
A [
grad
i]
RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
300
350
400
tempo [s]
AM
PIE
ZZ
A [
grad
i]
COELEVAZIONE ED AZIMUTH SOLE IN BRF
coelevazione
azimuth
TIME OFFSET : 6.7391e+006
Eclipse
Eclipse
Eclipse
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), Ω = 40°, w = 30°.
Keplerian circular orbit at the spring equinox,with 400 km altitude and inclination 45°, Ω =
40°, w = 30°.
Keplerian circular orbit at the summer solstice,with 800 km altitude and inclination 90°( polar
orbit ), Ω = 40°, w = 30°.
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.
Thank you for your kind attention
