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

• bservation: 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 Sar SATellite)

The mission deals with a SAR of bistatic type (bistatic SAR - Synthetic Aperture Radar), equipped with receiving

• nly antenna

(microwave system), for Earth

• bservation.

Mission Features

The BISSAT will fly in formation tandem with one of the satellites from the COSMO/SkyMed

• constellation. The

proposed system does will not require any modification of existing COSMO design and

• perations.

The proposed system will carry some meaningful

advantages which:

• Low cost of the mission,

thanks also to the drastic reduction of the weight and the dimensions of the satellite (uses only receiving antenna);

• Added value to the

COSMO mission.

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
• bservation in real time in the hypothesis
• f being able to realize compatible

baseline with the maintenance of the interferometric coherence.

COSMO/ SkyMed

• COSMO (COnstellation
• f Small satellite in the

Mediterranean basin Observation) is an ASI space program for Earth observation, for scopes: 1. Management of the environmental risks; 2. Commercial applications; 3. Military applications.

• I t is a constellation of 7

satellites:

• 4 equipped with SAR;
• 3 with optical instruments.

I t offers: 1. High and highest resolution images ; 2. Fast system’s response time; 3. Ability of acquisition in every moment; 4. Ability to acquire data of immense areas with single passage; 5. Ability of along-track stereoscopic vision and interferometry; 6. Total accessibility also 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

• rder to avoid every

eventual danger of collision between them near the poles.

Orbital requirement of the two Satellites

COSMO

• Altitude:

hC = 619 km

• Inclination:

iC = 98.5°

• Right ascension of the

ascending node:

C = 0° (reference orbit)

• Off-nadir sighting angle
• f the antenna:

 = 35°

BI SSAT

• Altitude: hB= 619 km
• Inclination: iB= 98.5°
• Right ascension of the

ascending node :

B = 1.5°

• Angular delay:

B = 0.8°

• Minimum safety range

from COSMO: 100 km

Minimal and Maximum Distance Produced

The previous orbital elements produce the following minimal and maximum distances:

Dmin = 97.7348 km Dmax = 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

• SLC = 774.5718 km

(constant for all orbital period since it always aims with the same angle- shot)

SLB(min) = 690.216 km SLB(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 (m1, m2, m3) that generate the assigned outputs (, , , ’, ’, ’).

The optimal solution, called reference, will be

• btained 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:

) 1 ( ) ( ) , , ( T x B t x x f x   

  

I f  a constraint on its solutions:

) 2 ( , 1 ) , ( n i con t t x

i

    

) 3 ( ) , (           

 

t x x t x

i

) 4 ( 2 ) , (

2 2

                    

      

t x t x x x x x x x t x

j i j i i

And they are:

Then, necessary and sufficient condition so that the constraint (2) is satisfied t, is that

• ne 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).

t t x

i

   ) , (

t t x t x t x

i t i t i

      

    

) , ( ) , ( ) , (

2 } ) ( ) , , ( { ) , , ( ) (

2 2

                                  

    

t x t x x x x x T x B t x x f x t x x G T x B x

j i j i

Where the last one is obtained replacing (1) in the (4):

 

t t x x G T x B x t x x n i con t x

t t

                             

   

) , , ( ) ( , , 1 ) , ( 

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

• rder 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.

• 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.

Periodic Solution

Family of Periodic Solutions

• It is possible in exact way to determine the periodic
• solutions. They are those in correspondence of the

intersections of the curve of unitary value of ’final/’0 with that one of the number of the turns completed from the BISSAT.

• -18°  0  0°

(101)

• 0.111* vB  ’0  0.511* vB

(1 5)

• In absolute, the periodic solution is not said to be the

best one, also introducing the mentioned advantages

• already. In fact specific problems can exist in which

to consider a family of aperiodic solutions, with magnetic moment particularly low, is particularly convenient.

 I found approximate periodic solution, somewhat

interesting for values of:

0 = -10° ’0 = 0.311* vB

(vB = BISSAT angular speed)

Max| m| = 3.547 [A·m2] min| m| = 1.882 [A·m2] B = 1.5° B = 0.8 [°/ sec] 0 = -10°

’0 = 0.311* vB

Dimensioning and choice of the TORQRODS

Magnetic torquers are generally planar coils of uniform

wire (sometimes copper) rigidly placed along the attitude axes of the spacecraft. When a voltage is applied across a coil winding, a current is created, setting up a magnetic dipole. This dipole interacts with the Earth’s magnetic field, causing the coil to attempt to align its own magnetic field in a direction

• pposite to that of the Earth’s.

For the approximated periodic solution:

Max| m| = 3.547 [A·m2]

+ 50% of

• ver-sizing

M = 5.32 [A·m2]

The chosen model is:

“TR10CFN”

that amply satisfies our requirements.

• Dia. (1)

• f

x

TR1UPN

• weight. (5)

TR10CFN

• case. (5)

• weight. (5)

• case. (5)

2x

• weight. (5)

• weight. (5)

• case. (5)

2

2

• weight. (5)

• weight. (5)

• weight. (5)

• weight. (5)

• weight. (5)

Conclusions

• I t is possible to realize a system that

advantageously turns out economic, as regards traditional realizations, since they can be utilized:

• One sun sensor and
• One magnetometer,

in order to determine the attitude;

• Three magnetic-torquers as

actuators, for the restoration of the attitude, one for every body axis.

End of Presentation