Universita’ degli Studi di Napoli Federico II

1. Universita’ degli Studi di Napoli Federico II Facolta’ di Ingegneria Corso di laurea in Ingegneria Aerospaziale Dipartimento di Ingegneria Aerospaziale Analogical-differential sun sensor simulator Academic Year 2007/2008

2. 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. yo 2 1 xo 3 zo Analogical differential sun sensor Satellite attitude

3. Index of the presentation: • Solar cell and the characteristic curve • Analogical differential sun sensor • Simulation program • Results and conclusions

4. 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. 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 Top electric contact Solar radiation Anti-reflection coating Electrical resistance n-type silicon Electric field Junction p-type silicon Low electric contact when an electron is removed from atom due photoelectric effet. - + - + + Putting a load in parallel there is the passage of electric current due to a concentration gradient of charges.

6. 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: n θ • Short- circuit voltage • Short -circuit current In addition there is a dependence on the angle of solar radiation incidence.

7. Analogical differential sun sensor combines the short-circuit currents of five cells to determine the direction of the sun in sensory reference XsYsZs. Zs 1 5 Zs 3 4 Xs 2 Ŝ ŜYsZs βs αs Ys Xs Ys 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. 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.

8. 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 -π/2+α0 π/2-α0 A E B -π/2 π/2 D C 5 n2 n1 1 2 Ys Sun in the fields of view of cells 1,2,5 Sun in the fields of view of cells 1 e 5 Sun in the fields of view of cells 2 e 5

9. In a similar way the formulas are written for the calculation of the angle βs in plane XsZs. Zs -π/2+α0 π/2-α0 A E B -π/2 π/2 D C 5 n2 n1 3 4 Xs Sun in the fields of view of cells 3,4,5 Sun in the fields of view of cells 3 e 5 Sun in the fields of view of cells 4 e 5

10. 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. Zs Z Xs Ys Y X

11. The simulation program is implemented using Simulink • The general scheme is: X,Y,Z satellite in IRF Orbital propagator Matrix IRF to ORF Orbital parameters satellite in IRF Solar propagator Sun orbital parameters X,Y,Z sun in IRF Sun sensor X,Y,Z sun in BRF Initial attitude Propagator of the dynamics of attitude Matricx ORF to BRF

12. 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. zp Perigee yp xp r Descending node Equatorial plane Ascending node n Z i ν w Y Ω X a

13. Simulink diagram for orbital propagator

14. Propagator of the dynamics of the attitude • The equations of dynamics of attitude ,in case of small eccentricity and small angles ,are: • The obtained solutions by integration are the following:

15. 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.

16. 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.

17. 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. The simulink diagram is:

18. 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°. yo 2 1 xo 3 zo Eclipse Eclipse Eclipse

19. yo 2 1 xo 3 zo Eclipse Eclipse Eclipse

20. 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°.

21. 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. Thank you for your kind attention