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September 2004
www.gmv.com
Transfer Analysis Design Tool (focusTrento)
A. Pérez, M.A. Molina, F. Martínez (GMV S.A.)
2nd ESA Workshop on Astrodynamics Tools and Techniques
ESTEC 13-15 September 2004
GMVSA 4118/04
FOCUSTRENTO
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Presentation Contents
Introduction to focusTrentoMathematical formulation
Apogee/Perigee ManoeuvresGeosynchronous transfer (GTO)Supersynchronous transfer (SSTO)
Station Acquisition ManoeuvresOptimisation analysis
Software implementation and descriptionNumerical simulations and resultsfocusTrento Demonstration
September 2004
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Introduction to focusTrento
FOCUSTRENTO
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Introduction to focusTrento (1)
General Description
focusTrento is a SW tool designed and developed by GMV S.A., Spain.
It is a transfer design optimisation tool devoted to the analysis of transfer orbits for geostationary satellites, it allows to identify optimal transfer orbit strategies for geostationary satellites.
It supports impulsive (chemical) manoeuvres and low thrust (electrical) manoevres.
It supports two kind of tranfer strategies: geosynchronous transfer (GTO) and supersynchronous transfer (SSTO)
It performs an optimisation of the selected strategies using a full dynamic model.
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Introduction to focusTrento (2)
Software description – Main components
Sequencer : study a group of cases defined by the user
Kepler solution : theoretical cost to reach the geostationary orbitSimulation solution :
trajectory computation considering also station acquisition cost
Analyser : global optimisation of a particular case selected by the user
September 2004
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Mathematical formulation
FOCUSTRENTO
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Mathematical formulation (1)
Orbit Transfer Analysis for geostationary satellites
Geosynchronous transfer : apogee of transfer orbit at geostationaryaltitude
Supersynchronous transfer : apogee of the transfer orbit at very high altitude. The inclination correction correction is performed at very high altitude, this correction is proportional to the orbit velocity at this point.
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Mathematical formulation (2)
Sequencer Mathematical formulation
Apogee Manoeuvres _
11
1 expn laef
jLAEFs j
sp
vm m
I g−
−∆∆ = −
∑
The loss due to the thrust extension can be estimated using the Robbins penalty formula:
Robbins penalty:
ii
R VrtVtV ∆⋅⋅⋅
=∆⋅⋅
=∆ 3
222
2424µω
RV∆ : penalty due to the thrust extension
ω : orbital revolution rotation rate for a circular orbit at burn altitudet : burn duration
iV∆ : impulsive burn magnitude
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Mathematical formulation (3)
Station Acquisition manoeuvres
The total mass consumption to achieve station acquisition is the sum of the out of plane and the in plane consumptions. They can be computed as functions of the apogee radius, perigee radius, inclination and longitude at the end of the last apogee manoeuvres and the maximum drift duration up to the final on-station longitude.
Out of plane cost (CN/S )= residual inclination correction
In plane cost (CE/W )= residual eccentricity correction + rendezvous correction
Total STACQ Consumption: = CE/w + CN/SΦ
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Mathematical formulation (4)
Analyser Mathematical formulation (I)
The apogee manoeuvre optimisation problem is a non-linear optimisation problem subject to equality and inequality constraints. It can be formulated in the following way :
Φ+∆= LAEFsmxF )(Minimise
0)( =xgi i=1,....,me
0)( ≥xgiSubject to :
i=me+1,....,m
where x is the array of optimisation parameters, F is the objective function or cost function to be minimised (the propellant mass consumed) and gi are the targets to be achieved and the mission constraints to besatisfied.
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Mathematical formulation (5)
Analyser Mathematical formulation (II)
The cost function has been defined as the mass consumption due to the AEF manoeuvre and the station acquisition manoeuvres (inclination correction + apogee-perigee correction + station rendez-vous), this software optimises the cost function using the following optimisation variables for each apogee manoeuvre:
Initial time of the manoeuvreDuration of the manoeuvreRight ascension and declination of the manoeuvre thrust direction
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Software implementation and description
FOCUSTRENTO
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Software implementation and description (1)
Software implementation
focusTrento interface and Sequencer have been developed in Matlab/Simulink.
The Analyser is a GMV piece of software (AEFOS: Apogee Engine Firing Optimisation Software) developed in FORTRAN. AEFOS was developed originally to support the Artemis mission and has been used in other missions, currently is under customisation to support also ATV mission.
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Software implementation and description (2)
Software description – Input dataSatellite dataOrbit dataPropagation dataSequencer cases definitionAnalyser case definition
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Software implementation and description (3)
Software description – Input data
Total DeltaV
3 Splits
Case1: 0%, 100%
Case2: 33%, 67%Case3: 67%, 33%%Case4: 100%, 0%
2nd impulse
1rst impulse
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Software implementation and description (4)
Software description – Sequencer solution
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Software implementation and description (5)
Software descriptionAnalyser Input data Analyser Graphical simulation
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Numerical Simulations and results
FOCUSTRENTO
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Numerical Simulations and results (1)
Numerical Simulation : 3 impulses strategySequencer Results
Minimum cost :1182.9733 kg
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Numerical Simulations and results (2)
Numerical Simulation : 3 impulses strategyAnalyser Results ( AEFOS )
Analyser output after optimisation process
Analyser input from sequencer
1182.9733Cost (kg)
20AEF3 %∆V
40AEF2 %∆V
40AEF1 %∆V
1165.364Cost (kg)
24.4AEF3 %∆V
38.7AEF2 %∆V
36.9AEF1 %∆V
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Numerical Simulations and results (3)
Numerical Simulation : 4 impulses strategySequencer results
Minimum cost : 1171.6586 kg11.31 kg have been economised compared to the 3-impulse solution
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Numerical Simulations and results (4)
Numerical Simulation : 4 impulses strategyAnalyser Results ( AEFOS )
Analyser output after optimisation processAnalyser input from sequencer
1171.6586Cost (kg)
10AEF4 % ∆V
30AEF3 %∆V
30AEF2 %∆V
30AEF1 %∆V
1163.696Cost (kg)
9.7AEF4 % ∆V
35.5AEF3 %∆V
28.4AEF2 %∆V
26.6AEF1 %∆V
After optimisation process only 1.668 kg are saved with respect to the 3 impulses strategy.
September 2004
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focusTrento Demonstration
FOCUSTRENTO
