minimum-time problem resolution under constraints for low...

ASTRIUM

Minimum-time problem resolution under

constraints for low-thrust stage trajectory

computation

Nathalie DELATTRE

ASTRIUM Space Transportation

ASTRIUM

• Purpose :

– Taking into account new technology for upper stage and/or satellite like solar propulsion or electric propulsion, reassessthe satellite launcher task sharing

– The payload is considered at the telecommunications system on board satellite (usually considered as the satellite payload)

• Two tools are available to answer the question

Introduction

ASTRIUMLaunch analysis :Insertion by low thrust stage

• MIPELEC : resolution of minimum-time problem

– Quick optimisation tool, initially developed under a thesis

at CNES, then industrialised through EADS-ST and CNES

shared contract by LAAS (CNRS)

– finds the optimal command for minimum time transfer

(continuous thrust)

– applications: slow insertion from Earth orbit to escape

orbit by electrical, solar-thermal or nuclear propulsion

– very user-friendly tool

– very quick optimisation solving (~ 1 min)

– used for any advance-project, but does not consider

constraints like eclipses or visibility constraint by ground

station

ASTRIUMLaunch analysis:Insertion by low thrust stage (2)

• TOPE : resolution of minimum-time problem under constraints

– finds a quasi-optimal command for minimum time transfer

including constraints (quasi-continuous thrust)

– takes eclipses into account (burn interruption during

shadow period) and visibility constraint (burn possible

only during given set of ground station visibility)

– applications: slow insertion from Earth orbit to escape

orbit by electrical, solar-thermal or nuclear propulsion

– very user-friendly tool

– quick optimisation solving (a few minutes)

– successfully benchmarked with MIPELEC for the

unconstrained case

ASTRIUMELECTRIC PROPULSION FOR SATELLITES (1)

Satellites market analysis

-Payload characteristics

(required power system)

-Short and long terms scenarios (EP, mixed,

chemical satellites repartition)

Satellites model

LEO/MEO & GEO applications

-Architecture model

mass repartition = f(payload)

-Costs model (fabrication)

-Constraints (Van Allen,…)

Propulsion data

-Electric & mixed propulsion models

mass, thrust, Isp = f(power)

-Constraints

-Costs model (EP, mixed, chemical)

Launchers data

-Characteristics

-Launch costs models

Satellites associated costs

-Insurance

-Operator’s investment

-Satellite exploitation

-Maximum transfer duration

(operators constraint)

Reference satellites selection


-Propulsion characteristics

-Mass repartition

-Constraints

-Short term

Mission analysis


-Injection strategy trade-off

-Impact on launcher filling ratio

-Comparison with competitorsShort term economical aspects


-Global cost (operators point of view)

-Gain assessment (comparison with classic

chemical satellite)

Phase 2

Short term scenario synthesis

Europe launchers positioning vs competitors

(sensitivity wrt satellites market scenario)

Short term

Mission and Market considerations

Phase 1

Work logic

ASTRIUM

Satellite á propulsion électrique - Transfert en temps minimum de MEO (7 deg) vers GEO avec contrainte d’éclairement

-30000 -10000 10000 30000

-40000

-35000

-30000

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

km

Deformation de l’orbite avec zone d’eclipse

km

ELECTRIC PROPULSION FOR SATELLITES (2)

ASTRIUM

INJECTION ORBIT (ORBIT 1) ELECTRICAL PROPULSION

BEGINNING (ORBIT 2)

STRATEGY

designation Za / Zp / 7° designation Za / Zp / 7°

100% chemical GTO 200 / 35 786 / 7

MEO Za / Za / 7 = orbit 1100% electrical GTO+ Zp / 35 786 / 7 = orbit 1

GTO 200 / 35 786 / 7 GTO+ Zp / 35 786 / 7

subGTO 200 / Za / 7 MEO Za / Za / 7hybrid

supGTO 200 / Za / 7 supGTOZp / Za / 7

with (Za+Zp)/2 = 35786 km

ELECTRIC PROPULSION FOR SATELLITES (3)Scenarios

ASTRIUM

Satellite á propulsion électrique : masse initiale 3410 kg, poussée 1N, ISP 1700s

Transfert en temps minimum de GTO+ (14000km / 35786km / 0deg) vers GEO

Durée du transfert : 38.52j / Masse consommée : 199.56kg / Nombre de révolutions : 46.05

0 5 10 15 20 25 30 35

15000

20000

25000

30000

35000

40000

alt

itu

de (

km

)

Altitudes apogée et périgée (km)

date (j)0 5 10 15 20 25 30 35

3220

3240

3260

3280

3300

3320

3340

3360

3380

3400

masse (

kg

)

Masse totale (kg)

date (j)

ELECTRIC PROPULSION FOR SATELLITES (4)

ASTRIUMSTOTS (1)

� Propulsion system principles: 3 sub-systems

�Concentrator Array and Tracking System (CATS)

which collects and focuses the sun light

�Receiver Absorber Converter (RAC)

which converts the concentrated sunlight into usable heat used to vaporise LH2

�Propellant Feed and Storage System (PFSS)

which stores the propellant and feeds the engine

Solar-Thermal Orbital Transfer Stage

ASTRIUM

� Intermittent thrust mode

� Same architecture as described before, except that the RAC is now a Receiver

Accumulator Converter

� Introduction of a thermal storage mass heated by solar energy

� The heat is later extracted by the propellant for propulsion purpose

� The transfer is made of succession of thrusting and recharging phases, driven by the

RAC temperature

Highest admissible

temperature

Lowest admissible

temperature

Thrusting Thrusting Thrusting

Recharging RAC

(eclipse case)

Recharging RAC

(no eclipse)

Perigee

first

Apogee

next

� Goal of the study

� Design the optimal components of the solar-thermal engine together with the payload

optimisation process for the transfer from LEO to GEO

STOTS (2)

ASTRIUM

� One orbit model

inputs: � current orbit characteristics (apogee, perigee, inclination)

� sun relative location, solar flux

� state of the propulsive system thanks to a model (RAC temperature, PFSS state, …)

� control: mass flow, boost location (apogee or perigee) and duration, inclination correction

Solving process: � estimation of eclipse duration on the current orbit

� estimation of power at the entrance of RAC (CATS model)

� RAC heating during balistic sun lighted phase

� PFSS functionning

� RAC characteristics (temperature, phase change, Isp(t), F(t), ∆V delivered, Isp, F)� gravity losses estimation (see later)

� apogee, perigee and inclination modification after the boost

� To avoid large gravity losses, the boost durations have to be optimised depending

on the amount of heat accumulated by the RAC

� The sun lighted duration increases while raising the apogee, so the boost duration

may be increased

Use of a linear model Tboost(iorb) = Tboost (1) + T’boost . iorb

Where iorb = orbit number, Tboost (1) and T’boost are the optimised parameters (2 for apogee, 2 for perigee)

STOTS (3)

ASTRIUM

� The one orbit model is used several

times until the final conditions are

reached

Global performance of the system

� Design of the propulsion system:

The 3 most influent parameters have been selected:

� Energy storage mass (≈RAC mass)allows to increase Isp, but then mass balance penalised

� CATS area

� Mass flow

STOTS (4)

ASTRIUM

PFSS model

Input : pressure, external flux

Output : TVS, heater , self-

pressurization , going out

propellant characteristics (H prop),

mass (M PFSS), geometry

RAC model ( ballistic and boost )

Input : material , insulation , storage

mass, initial temperature

Output : final temperatures (GH2,

RAC), phase change, Isp(t), F(t),

MRAC

CATS model

Input : solar area , solar flux,

optical efficiency ,

concentration ratio

Output : power at the

entrance of RAC (P CATS),

mass (M CATS)

Orbit characteristics :

Input : Apogee ,

Perigee , Sun location

Boost

Input : propellant

flow rate (q prop)

Output : duration (t boost)

Ballistic phase :

Output:

eclipse durations , lit

ballistic phase (t sun)

PCATS

tsunqprop, tboost

qprop, tboosttsun

Hprop

Global performance :

Output : ∆V, duration , mass

budget, payload mass

MCATSMPFSS

MRAC

Orbit performance :

Output : ∆Vboost,

<Isp>, <F>

∆Vboost

ORBIT LOOP

� Whole optimisation process

Criterion: maximise payload

Parameters (7):

� MRAC

� Qprop

� CATS area

� Tboost(1) and T’boost for apogee

� Tboost (1) and T’boost for perigee

STOTS (5)

minimum-time problem resolution under constraints for low...

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