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Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
High PerformanceSpacecraft Dynamics Simulator
Dr.-Ing. Stephan TheilZARM / University of Bremen
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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– ...
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
• 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)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
Modeling of Density Variations (2/3)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
Modeling of Density Variations (3/3)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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:
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
General Simulator Structure
Satellite &Test MassDynamics
DisturbanceModels
ActuatorModels
Environment
ControllerSensorModels
• Dynamics simulation:– Numerical integration of equations of motion – Implementation of force and torque models
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
• 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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
Numerical Issues (2/2)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
Simplification and Analytical Solution (3/3)
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
Verification due to Comparison with the Simplified Analytical Solution
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
GP-B: Simulator Cross-Check
• Comparison of gyro positionATC off
• Comparison of gyro positionATC on
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
GP-B: Control Module Validation
Attitude TranslationFlight
Simulated
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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.
Workshop: Virtuelle Produktentwicklung für Raumfahrtsysteme, Köln, 12.06.2007
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
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