POLYTECHNI C of BARI FACULTY of ENGI NEERI NG COURSE of DEGREE in - PowerPoint PPT Presentation

POLYTECHNI C of BARI FACULTY of ENGI NEERI NG COURSE of DEGREE in ELECTRONI C ENGI NEERI NG

GRADUATION THESIS Bistatic SAR for Earth observation: application of the “Dynamic I nversion” technique to the orbital and attitude control

Chairman : Prof . Luciano GUERRI ERO (Polytechnic of Bari) Co-chairman : Eng . Leonardo MAZZI NI (Alenia Spazio – Rome) Student: Andrea TEDESCO

Thesis Aim To verify the feasibility and, in which case, to plan a low cost orbital and attitude control system, even using some magnetic- torquer.

“BI SSAT “ Mission ( BI static S ar SAT ellite) The mission deals with a SAR of bistatic type (bistatic SAR - Synthetic Aperture Radar ), equipped with receiving only antenna (microwave system), for Earth observation.

Mission Features The BISSAT will fly in The proposed system will formation tandem carry some meaningful advantages which: with one of the satellites from the • Low cost of the mission, COSMO/SkyMed thanks also to the drastic constellation. The reduction of the weight and the dimensions of the proposed system satellite (uses only does will not require receiving antenna); any modification of existing COSMO • Added value to the COSMO mission. design and operations.

Scientific Purposes The bistatic mission allows the simultaneous acquisition of two set of data of the same area under different angles of view, that allows to obtain:  A digital elevation model (DEM) of the ground of observed area, which can be useful: 1. to map the topography of the territory and to characterize eventual crumbling (liable to slide down) motions; 2. to correct the data of the satellite master.

 Low rugged images (lakes, seas,…), allowing: 1. The implementation of new models for the location of algae or superficial pollution.  Stereoscopiche images;  Techniques of interferometric observation in real time in the hypothesis of being able to realize compatible baseline with the maintenance of the interferometric coherence.

COSMO/ SkyMed   I t is a constellation of 7 COSMO ( CO nstellation satellites: of S mall satellite in the • 4 equipped with SAR; M editerranean basin 3 with optical instruments. • I t offers: O bservation) is an ASI 1. High and highest resolution space program for images ; Earth observation, 2. Fast system’s response time; 3. Ability of acquisition in every for scopes: moment; 1. Management of the 4. Ability to acquire data of immense areas with single environmental risks; passage; 5. Ability of along-track 2. Commercial stereoscopic vision and applications; interferometry; 6. Total accessibility also 3. Military applications. through mobile reception stations.

Choice of the Type of Formation Type of formation that allows parallel orbits of the two satellites to introduce a difference between the right ascensions of the ascending nodes (  ) and a difference between the transit times of the same ascending nodes (  t), in order to avoid every eventual danger of collision between them near the poles.

Orbital requirement of the two Satellites COSMO BI SSAT • Altitude: Altitude: h B = 619 km • h C = 619 km Inclination: i B = 98.5° • • Inclination: • Right ascension of the i C = 98.5° ascending node : • Right ascension of the  B = 1.5° ascending node: • Angular delay:  C = 0° (reference orbit)  B = 0.8° • Off-nadir sighting angle of the antenna: • Minimum safety range from COSMO:  100 km  = 35°

Minimal and Maximum Distance Produced The previous orbital elements produce the following minimal and maximum distances: D min = 97.7348 km D max = 276.604 km

Distance and Slant-Range Orbital Period: 97.084 min (the same one for both satellites inasmuch as it is considered the same altitude) • Periodic course of the distance between BISSAT and the COSMO SL C = 774.5718 km • (constant for all orbital period since it always aims with the same angle- shot) SL B(min) = 690.216 km SL B(Max) = 895.488 km (because of its continuous pursuit of the trace on the earth)

Propagation of the two Satellities

Nominal Attitude Angles • Bissat, in order to follow the trace to COSMO earth, needs of two angles: “Azimuth” angle : •  B(min) = 23.924 °  B(max) = 43.261 ° “Elevation” angle : •  B(min) = 24.977 °  B(Max) = 43.559 °

DYNAMI C I NVERSI ON The Dynamic I nversion is a technique developed for the plan of control systems for high performances, proposed especially for non-linear dynamic systems. This is a methodology for the use of continuous- time dynamics in order to supply an estimate of the variable roots in the time of functions dependents from the time. I n other words, the basis idea is to define a prior the wished functions of time on the outputs of the controlled system, in order to use,after, an inversion of the dynamic system to determine the inputs (m 1 , m 2 , m 3 ) that generate the assigned outputs (  ,  ,  ,  ’,  ’,  ’).

The optimal solution, called reference , will be obtained through a feedforward branch. Moreover, a feedback will become necessary to stabilize the dynamic around the same reference solution. Such feedback branch limits the sensors noise effects and effects of the non-modelling disturbance pair.

Advantages of the D.I . The technique of the Dynamic I nversion, from the point of view of continuous-time systems, allows to describe wished solutions that respect determined constraints and to describe the structure of such solutions. The use of total stabilizing feedback in non-linear field requires the demonstration, preliminary matter, of the stability and can converge on non optimal solutions. The Dynamic I nversion allows to realize a ring of feedforward inner the one of feedback, in order to this one become simpler, obtaining, normally, greatly advanced performances.

D.I . Technique Given a esprimibile system by means of:       x f ( x , x , t ) B ( x ) T ( 1 ) I f  a constraint on its solutions:      ( x , t ) 0 t con i 1 , n ( 2 ) i            And they are: ( x , t ) 0 x 0 ( 3 )   i x t                2        ( x , t ) 0 x x x 2 x 0 ( 4 )       i j 2 i x x x x t t i j

Then, necessary and sufficient condition so that the constraint (2) is satisfied  t, is that one dynamics such is had that the eq. (4) it is verified  t and that the eq. (3) and (2) they are satisfied in the initial conditions (t= 0).    ( x , t ) 0 t i   ( x , t ) 0  i t 0    ( x , t ) 0 i  t 0      ( x , t ) 0 t i

      ( x , t ) 0 con i 1 , , n  t 0          x 0       x t  t 0          B ( x ) T G ( x , x , t ) t      x Where the last one is obtained replacing (1) in the (4):          B ( x ) T G ( x , x , t )      x             2         { ( , , ) ( ) } 2 0 f x x t B x T x x x       i j 2 x x x x t t i j

Attitude Determination  The plan for the attitude control is guided from the idea to make so that it is independent from the yaw angle (  ), that is, it is free of rotate round z axis (yaw axis) of the body reference of the BI SSAT, which is directed towards the Earth.  The problem has been dealed with considering the equations that govern dynamics and the cinematic of the “rigid body”, simplifying therefore the modelling of the real system, even if can be present flexible elements (solar panels, antennas,…).  The rotation sequence of the Euler angles choice is 3-1-2 (  -  -  “ Type 1 ”).

I mplementation of the D.I .

Final Result In the hypotheses made previously (  B = 1.5° ;  B = 0.8° ) and for values of  0 = 0° and  ’ 0 = 0 [°/ sec] , I have obtained following graphs relative to the Euler angles and the terrestrial magnetic field (necessary in order to use the magnetic-torquer):

In order that, I shall use the torqrods, I estimated also the orders of the control torques and the necessary magnetic moments to produce demanded attitude.

Periodic Solution • I searched “periodic solutions” , that is those solutions for which the values of the Euler angles and their derivatives, turn out to be equal, after the completion of one orbit, to the respective initial values (  0 =  finale ;  0 =  finale ;  0 =  finale ;  ). • They are attractive since guarantee the same behavior, of the satellite, for every orbit and therefore it is sure that the maximum magnetic moment made on one orbit is still the maximum after a sure number of orbits.