High Performance Spacecraft Dynamics Simulator · 2007-08-27 · • Dynamics simulation: ... :...

Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007

High PerformanceSpacecraft Dynamics Simulator

Dr.-Ing. Stephan TheilZARM / University of Bremen


Background

• Past Missions: Requirement(s)– Hipparcos (1989 – 1993)

• Attitude accuracy after data reduction ~20 mas– Gravity Probe B (2004 – 2005)

• Pointing accuracy ~90 mas• Residual acceleration <10-10 m/s²

• Future Missions– MICROSCOPE <10-11 m/s²– LISA Pathfinder <10-13 m/s²– Gaia (relative/post mission) <5mas / <20µas– LISA <10-14 m/s²– STEP <10-14 m/s²– ...


Motivation

• Background:– Future missions require a high performance of dynamics control:

• Pointing accuracies: << 1arcsec … 1µas• Disturbance acceleration rejection: < 1.0E-14 m/s²

• Goals:– Allow simulations of high performance control systems (precision

pointing, drag-free) for:• feasibility analysis• design and• verification

– Enhance data reduction of scientific space missions by providinghigh performance simulations of spacecraft dynamics


The Force and Torque Free Satellite

• First suggested and analyzed by B. Lange (1964)• First generation: TRIAD I (1971), TIP II (1974)• Second generation: Gravity Probe-B (2004), GOCE, LISA,

MICROSCOPE, STEP, LISA Pathfinder

Aerodynamic force is main disturbance:Engl. „air drag”

Force free satellite:„drag-free satellite”

Control for compensation:„drag-free control”

TM

DisturbanceForce

Control Force

Control Force

Disturbance Force

Satellite Body

TM

DisturbanceForce

Control Force

Control Force

Disturbance Force

Satellite Body

TM

DisturbanceForce

Control Force

Control Force

Disturbance Force

Satellite Body

TM

DisturbanceForce

Control Force

Control Force

Disturbance Force

Satellite Body

TM

DisturbanceForce

Control Force

Control Force

Disturbance Force

Satellite Body


Forces and Torques• Forces and torques acting on the satellite and test

masses because of :– Gravitation– Control (forces and torques applied by the control system)– Interaction with the upper layers of the Earth atmosphere– Electromagnetic radiation (heat, radio communication, sun light)– Solar wind, plasma, dust– Interaction with the magnetic field

• Problem:– Standard models lack some details– No standard models available for specific effects

• Solution:– Develop new models– Enhance standard models


• Processing of data from CHAMP mission:– Orbit data: position, velocity– Sensor data: star tracker, accelerometers– Further data: geometry, area, mass

• Computation of density:

• Analysis of the frequency spectrum• Design of a form filter in order to create the

difference spectrum from white noise

Modeling of Density Variations (1/3)


Modeling of Forces from Electromagnetic Radiation (1/2)

• Effects:– EM radiation incident:

• Sun light• Albedo light• Infrared (thermal) radiation of Earth

– EM radiation emission:• Thermal radiation emission• Radio frequency emission

• Basic equations:


Modeling of Forces from Electromagnetic Radiation (2/2)

• Implementation:– Definition of elements

representing the satellite surface

– Determination of visibility• Back face determination• Shadowing

– Computation of force for each element

– Summation of total force and torque

– Creation of look-up tables for total force and torque

(Method also applicable for atmospheric drag)


Heat dissipation

• Luminosity-Force relation:

• Total force:

cL

F globselemheat

,Re, =

∑=i

elemheattot iFF )(,

• Total force is disturbance input for simulator• Look-up table used to simulate different heating conditions

Payload on Payload off


Radio beam reaction force model

• Radio beam reaction force:cP

F rpRadiobeam

⋅=β

)(sinmax

0

θθθθ

PdPrp ∫=

∫=max

0

)(cossin1 θ

θθθθβ dPPrp

Radiation pattern can be modeled withFE-model

Look-up table for different Power states


General Simulator Structure

Satellite &Test MassDynamics

DisturbanceModels

ActuatorModels

Environment

ControllerSensorModels

• Dynamics simulation:– Numerical integration of equations of motion – Implementation of force and torque models


Simulator Architecture

• Modular Design in Matlab/Simulink and C/Fortran– Matlab/Simulink is wrapper for development and analysis.– Major blocks are coded in C/Fortran.– Modules are available as library.– Simulator for each mission is assembled from modules.– Initialisation and set-up through data files

• Possibility to integrate into data reduction process needed– A transition to pure C/Fortran code or different wrapper software

(e.g. Java) needed– Interfaces for estimation algorithms needed


• User Interface in Matlab/Simulink• Dynamics/Environment/Disturbances: Fortran/C code compiled as S-function• GSS/ATC/Sensors/Actuators: Simulink models

GP-B: End-to-End Simulation


Numerical Issues (1/2)• Differences of large numbers result in small numbers

⇒ Limitation of computation due to numerical resolution

• For spherical potential:

• Not applicable for gravitational fields of higher order


Numerical Issues (2/2)


Verification of Simulator

• Comparison to analytical solution of simplified system– Simplified model renders ODE in Mathieu-Form– Verification by comparison of stability boundaries

• Comparison to Hill‘s Equation– Analytical description of uncoupled relative movement– Verification by comparison to

• Comparison to other orbit propagators• Verification of uncoupled attitude motion• Test of dynamic coupling between satellite and test

masses


Simplification and Analytical Solution (1/3)

• Circular orbit

• Constant satellite rotation

• Spherical gravitational potential

• One-dimensional test mass motion only

• Linear spring coupling

• No back coupling to the satellite

xxii

yyii

xxtm

θθ

ϕϕ

rriii,b


Simplification and Analytical Solution (2/3)• One-dimensional equation of motion:

• With:

• Transformation with:

• Result = differential equation in form of Mathieu equation

• Analytical solutions of Mathieu equation are well-known


Simplification and Analytical Solution (3/3)


Verification due to Comparison with the Simplified Analytical Solution


Validation with Flight Data

• Goal:1st European flight data validated simulation for drag-free

and high-performance attitude control missions

• Approach:– Acquire flight data with high accuracy attitude/position

measurements– Acquire further mission/spacecraft data

• Geometry, mass properties, control system characteristics– Model spacecraft dynamics, disturbances and control system– Compare with flight data and adapt simulation models– Problem:

• Detailed information about spacecraft and its control system are often restricted!

– Missions selected for validation: Hipparcos, Gravity Probe B


GP-B: Simulator Cross-Check

• Comparison of gyro positionATC off

• Comparison of gyro positionATC on


GP-B: Control Module Validation

Attitude TranslationFlight

Simulated


Application of Simulator

• Hipparcos• Gravity Probe B• LISA Pathfinder• MICROSCOPE• Gaia• LISA• STEP• DARWIN• XEUS• ...• Pioneer 10/11 / ENIGMA

Re-simulation for validationRe-simulation for validationReference for cross checks

Post-processingPost-processing

DFC verification / post-proc.DFC verification / post-proc.

??

Modules used for Post-proc.


Summary

• Goal: High-performance Nx6DOF spacecraft simulation– Allow simulations for feasibility analysis, design and verification of

high performance control systems– Enhance data reduction of scientific space missions

• Satellite and test masses dynamics:– multi-body mechanical system– represented by a set of coupled ODEs (13 per body)

• Modeling of disturbances must include small effects• Simulator implementation may render issues with

numerical precision.• Status:

– Validation of simulator with flight data on-going– First validated version available in 2008

High Performance Spacecraft Dynamics Simulator · 2007-08-27 · • Dynamics simulation: ... :...

Documents

Transcript of High Performance Spacecraft Dynamics Simulator · 2007-08-27 · • Dynamics simulation: ... :...