presentazione en

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


2/22

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


3/22


4/22

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%.


5/22

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.


6/22

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


7/22

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


8/22

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

=



9/22

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 =


s005sc

4sc

tgsincosI

I

+=


s005sc

3sc

tgsincosI

I

=


10/22

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


11/22

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

,,

,,


12/22

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


13/22

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


14/22

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

+=


15/22

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


16/22

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


MATLABFunction

corrente cella 4


MATLAB

Function

corrente cella 3


MATLAB

Function

corrente cella 2


MATLAB

Function

corrente cella 1

componenti versore sole

ricostruito dal sensore

MATLAB

Function

componen ti versore sole

nel sistema sensoriale


17/22

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


18/22

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


prima componente

seconda componente

terza c omponente


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


prima componente

seconda componente

terza componente


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


Eclipse

Eclipse

Eclipse

RICOSTRUZIONE COELEVAZIONE ED AZIMUTH DEL SOLE COELEVAZIONE ED AZIMUTH SOLE IN BRF


19/22

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


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


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


20/22

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.


21/22

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.


22/22

Thank you for your kind attention

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