h igh p erfor m anc e s im ulation of a ttitude and t rans...

3rd International Workshop on Astrodynamics 3rd International Workshop on Astrodynamics

tools and Techniques, Noordwijk, 2 - 5 October tools and Techniques, Noordwijk, 2 - 5 October

2006200611

High Performance Simulation of Attitude

and Translation Dynamics

Ivanka Pelivan, Stefanie Grotjan,

Michel S. Guilherme, Silvia Scheithauer, Stephan Theil

ZARM / University of Bremen



2006200622

Outline

• Motivation

• Objectives

• Simulator Target Missions

• Simulator– Architecture

– Core Features

– Dynamics

– Disturbance Models

– Verification

• Summary and Outlook



2006200633

Motivation (1/2)

Future scientific space missions (LISA/LISA

Pathfinder, Gaia, MICROSCOPE, STEP, etc.) are

scientifically and technically a new generation.

Reasons:

– expected improvement of measurement accuracy by

several orders of magnitude

– utilisation of new key technologies

– very close link between spacecraft dynamics and scientific

measurements



2006200644

Motivation (2/2)

• S/C developers and engineers need a tool for:

– Analysis and engineering of AOCS

– Performance validation of S/C systems

• Scientific users need a tool for:

– Error analysis and budgets

– Development of the scientific data reduction

– Development of scientific in-flight monitoring tools

Development of a high-fidelity S/C dynamics simulator:

! Very accurate dynamics modelling

! Enhanced models of environment and disturbances



2006200655

Simulator Objectives

• Provide comprehensive simulation of the real system

including science signal and error sources

• Provide simulation environment for control system

performance validation

• Generate data needed to test data reduction methods

• Provide capability for identification of the satellite and

instrument



2006200666

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

Satellite is forced to

follow the proof mass

! Distance between

satellite and proof

mass is controlled

! Introduction of

coupling forces and

torques

Control ForceDisturbance Force

Satellite Body

TM

Drag-free concept: Shield satellite payload (proof mass) from all external

non-gravitational disturbances ! payload follows a purely gravitational

orbit

Control Force

Disturbance Force



2006200677

Target Missions

• Intended application to:

– Drag-Free Missions:

• Gravity Probe B – as a reference and for validation

• MICROSCOPE – satellite dynamics model for independent

scientific data reduction

• LISA – simulator elements for the scientific data reduction

• STEP – analysis and engineering tool

– Astronomy missions:

• Hipparcos – as a reference and for validation

• Gaia – simulator elements for the scientific data reduction

– Other missions:

• Pioneer 10/11 – utilization of disturbance models for the re-

analysis of the Doppler data



2006200688

General Simulator Structure



2006200699

Simulator Architecture

• Modular Design in Matlab/Simulink and C/Fortran

– Matlab/Simulink is wrapper for development and analysis.

– Major blocks shall be 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

– A transition to pure C/Fortran code necessary

– Interfaces for estimation algorithms



200620061010

Simulator Architecture• Modules: Dynamics Core, Environment and Disturbance, Sensor,

Controller, Actuator, Transformations

• User Interface: Matlab/Simulink

• Core and most Environment/Disturbance modules: s-function blocks



200620061111

Satellite and Test Mass Dynamics

• Satellite dynamics described in inertial and satellite body-fixed frame

• Test mass dynamics described in sensor and test mass frame

" Objects are treated as rigid

bodies

" 6 satellite degrees of freedom

" 3 for translation

" 3 for rotation

" 6 degrees of freedom per test

mass

" Driving force:

" Gravitation

GTM1 GTM2

GSat

FControl

FDist



200620061212

Coordinate Frames

inertial frame (ECI, i), body/satellite frame (b), mechanical/structural frame (m), accelerometer frame (a), sensitive axis frames for test masses 1 and 2 (sens1, sens2), test mass body frames for test masses 1 and 2



200620061313

Satellite Equations of Motion

• Translation of Satellite:

– Motion of a rigid body in a gravity field

– Additional force = coupling force

• Rotation of Satellite:



200620061414

Test Mass Equations of Motion• Definition in sensor coordinate frame: satellite-fixed, non inertial

Considers accelerations and rotations of system

• Translation:

• Rotation: - Approach: Conservation of angular momentum



200620061515

Simulator Core Features• Simulation of full satellite and test mass dynamics in six degrees of freedom by

numerical integration of the equations of motion (13 states: attitude rate, quaternion, position, velocity)

• Up to four differential accelerometers utilizing two test masses each (8 (TMs) + 1 (Satellite) = 9x13 states = 117 states)

• Consideration of linear and nonlinear coupling forces and torques between satellite and test masses as well as between test masses

• Modelling of cross-coupling interaction

• Earth gravity model up to 360th degree and order,

influence of Sun, Moon and planets can be included

• Gravity-gradient forces and torques

• 5th order Runge-Kutta numerical integration

• 128 bit numerical precision (`quad precision') on an ALPHA processor

Several error sources are considered in the model:

+ misalignment and attitude errors

+ coupling biases

+ displacement errors



200620061616

Force & Torque Modeling (1/2)

• Modeling of forces and torques acting on the satellite and

test masses because of:

– Gravitation and Gravity Gradients

– Control (forces and torques applied by the control system)

– Interaction with the upper layers of the Earth atmosphere

– Electromagnetic radiation

• heat, radio communication emission

• Absorption and reflection of radiation incident (sun, Albedo, etc.)

– Interaction with the magnetic field

– Interaction (coupling) between satellite and test masses

• Test mass sensing and actuation systems

• Gravitational coupling



200620061717

Force & Torque Modeling (2/2)

• Modeling approaches:

1. Utilization AND extension of standard models

2. Derivation of parametric models from detailed FEM

analysis of specific effects

• Standard models used:

– International Geomagnetic Reference Field (IGRF, IAGA)

– Earth Gravity Model (EGM, NASA)

– Mass Spectrometer Incoherent Scatter Model (MSIS, NRL)

• Short-term variations of Earth atmospheric density (analysis of

CHAMP mission data)



200620061818

Attitude Dependency of Gravitational Acceleration

• Origin: Gradient of gravity field

• Center of Mass and Center of Gravity do not coincide.

• Effects:– Gravity gradient torque

– Attitude dependent gravity force

CoM

CoG

CoM

CoG

Earth

CoGCoMgg



200620061919

Gravity-Gradient Forces and Torques

• Force from Earth potential field

• Gravity-gradient Torque:

1)

2)

dF dm d= !F

T dFr=

mono GGF F F= +

T Gr r=



200620062020

• 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)



200620062121




200620062222




200620062323

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:



200620062424

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)



200620062525

Modeling of Torques from the Interaction with the

External Magnetic Field (1/3)

• Computation of magnetic dipole from element data:

• Derivation of a parametric model

– !-Metal-Shield (STEP)

– Core of magnetic coils

; ;

- Analytic simplified derivation of the torque assuming the shape of an

ellipsoid

- Numerical computation using Finite Elements (FEM)



200620062626





200620062727





200620062828

General Modeling of Coupling Forces

• Specific coupling forces:

• Coupling torques:

• Definition of general force:



200620062929

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

• Comparison to other orbit propagators

• Verification of uncoupled attitude motion

• Test of dynamic coupling between satellite and test masses

• Verification with flight data



200620063030

Summary and Outlook• Multi-body mechanical system simulator (satellite and test masses).• Satellite and test mass dynamics is represented by a set of coupled

ordinary differential equations (13 per body).• Modeling of disturbances include also smaller effects such as:

– Density variation

– Torques from magnetization of components

– Radiation incident and EM radiation emission

• Outlook:– Validation of simulator with flight data

– Post-mission analysis of GP-B and Hipparcos

– Model improvement based on post-mission analysis and flight data

– Adaptation to STEP, MICROSCOPE, Gaia

• Future additions:– Adaptation of dynamics core to L2-orbits

– Implementation of Earth Albedo

– Structural effects (thermo-elastic)

h igh p erfor m anc e s im ulation of a ttitude and t rans...

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