Spacecraft Dynamics and Control
Chris HallAssociate Professor
AeroSpace and Ocean Engineering
Virginia Polytechnic Institute and State University
Chris HallAssociate Professor
AeroSpace and Ocean Engineering
Virginia Polytechnic Institute and State University
Overview
• Aerospace and Ocean Engineering Dept• Spacecraft Dynamics and Control
Projects– Rotating tethered interferometer– Formation flying– Distributed Spacecraft Attitude Control
System Simulator– Base motion effects on magnetic bearings– HokieSat– HokieSat Attitude Determination and
Control
• Aerospace and Ocean Engineering Dept• Spacecraft Dynamics and Control
Projects– Rotating tethered interferometer– Formation flying– Distributed Spacecraft Attitude Control
System Simulator– Base motion effects on magnetic bearings– HokieSat– HokieSat Attitude Determination and
Control
Virginia Polytechnic Institute and
State University•Founded as a Land Grant College in 1872
•Offers 200 degree programs to 25,000 students
•100 buildings on a 2600 acre campus in Blacksburg
•1500 full-time faculty•$500M annual budget•8 different colleges
•Founded as a Land Grant College in 1872
•Offers 200 degree programs to 25,000 students
•100 buildings on a 2600 acre campus in Blacksburg
•1500 full-time faculty•$500M annual budget•8 different colleges
Burruss Hall is the main administration building
College of Engineering• Twelve departments offer 15 degree
programs at B.S., M.S., and Ph.D. level
• Graduate program ranked 16th in the nation by professional engineers and recruiters
• ~30 different Research Centers, e.g.:– Commercial Space Communications– Intelligent Materials, Systems, and
Structures– Multidisciplinary Analysis and Design
Center for Advanced Vehicles (MAD)
• More than 300 full-time faculty• Annual research expenditure of
more than $60M• 570 M.S. & 99 Ph.D. degrees
awarded in 1998
• Twelve departments offer 15 degree programs at B.S., M.S., and Ph.D. level
• Graduate program ranked 16th in the nation by professional engineers and recruiters
• ~30 different Research Centers, e.g.:– Commercial Space Communications– Intelligent Materials, Systems, and
Structures– Multidisciplinary Analysis and Design
Center for Advanced Vehicles (MAD)
• More than 300 full-time faculty• Annual research expenditure of
more than $60M• 570 M.S. & 99 Ph.D. degrees
awarded in 1998
Norris Hall is the main Engineering building
Aerospace Engineering at Virginia Tech
• Aerospace and Ocean Engineering Department Overview
• Space Design Projects• Space Systems Research• HokieSat!
• Aerospace and Ocean Engineering Department Overview
• Space Design Projects• Space Systems Research• HokieSat!
Randolph Hall houses AOE,
as well as Engineering Fundamentals, Mechanical Engineering, and Chemical Engineering
• 19 Faculty in – aerodynamics and hydrodynamics– structural mechanics– dynamics and control– design
• Yearly graduation rate of approximately– 50 Bachelor of Science– 25 Master of Science– 10 Doctor of Philosophy
• $3.5 million annual research funding• Extensive research facilities
– Innovative wind tunnels– Water tunnels– Full-scale flight simulator– Spacecraft simulator
• 19 Faculty in – aerodynamics and hydrodynamics– structural mechanics– dynamics and control– design
• Yearly graduation rate of approximately– 50 Bachelor of Science– 25 Master of Science– 10 Doctor of Philosophy
• $3.5 million annual research funding• Extensive research facilities
– Innovative wind tunnels– Water tunnels– Full-scale flight simulator– Spacecraft simulator
Aerospace and Ocean Engineering
National Ranking*1. Massachusetts Institute of Technology 2. Stanford University (CA)3. Georgia Institute of Technology 4. University of Michigan–Ann Arbor 5. California Institute of Technology 6. Purdue University–West Lafayette (IN)7. University of Texas–Austin 8. University of Illinois–Urbana-Champaign 9. Princeton University (NJ)10. Cornell University (NY)11. Pennsylvania State University
12. Virginia Tech
*Aerospace Engineering Departments in U.S. News and World
Report
1. Massachusetts Institute of Technology 2. Stanford University (CA)3. Georgia Institute of Technology 4. University of Michigan–Ann Arbor 5. California Institute of Technology 6. Purdue University–West Lafayette (IN)7. University of Texas–Austin 8. University of Illinois–Urbana-Champaign 9. Princeton University (NJ)10. Cornell University (NY)11. Pennsylvania State University
12. Virginia Tech
*Aerospace Engineering Departments in U.S. News and World
Report
Senior Design at VT
• All seniors complete one year of “capstone” design– two semesters with 3 credit hours each semester
• Choose between Aircraft and Spacecraft(Ocean Engineering students choose Ship Design)
• Students work in groups of 6 to 12 students– typically include freshmen in second semester
• Access to “Senior Design Lab”– PCs, Workstations, Printers, Plotters, Software
• Typically compete in national and international design competitions – In 1998, two 1st Place, one 2nd Place, one 3rd
Place
• All seniors complete one year of “capstone” design– two semesters with 3 credit hours each semester
• Choose between Aircraft and Spacecraft(Ocean Engineering students choose Ship Design)
• Students work in groups of 6 to 12 students– typically include freshmen in second semester
• Access to “Senior Design Lab”– PCs, Workstations, Printers, Plotters, Software
• Typically compete in national and international design competitions – In 1998, two 1st Place, one 2nd Place, one 3rd
Place
Space Design Projects ‘99• Single-Stage-to-Orbit Reusable Launch Vehicle
Using Rocket-Based Combined Cycle Technology– 8 AE seniors + 2 Georgia Tech students– took 1st Prize in AIAA Design Competition
• Virginia Tech Ionospheric Scintillation Measurement Mission– 9 AE seniors, 2 AE freshmen, 2 AE juniors, 20+ EE
juniors/seniors– also called “HokieSat” - 1st VT-built spacecraft– 15 kg “nanosatellite” will launch on shuttle in 2003– funded by Air Force and NASA
• Leonardo — a small group of Earth-sensing satellites flying in formation– 8 AE seniors, 1 AE freshman– supporting research sponsored by NASA Goddard
• Single-Stage-to-Orbit Reusable Launch Vehicle Using Rocket-Based Combined Cycle Technology– 8 AE seniors + 2 Georgia Tech students– took 1st Prize in AIAA Design Competition
• Virginia Tech Ionospheric Scintillation Measurement Mission– 9 AE seniors, 2 AE freshmen, 2 AE juniors, 20+ EE
juniors/seniors– also called “HokieSat” - 1st VT-built spacecraft– 15 kg “nanosatellite” will launch on shuttle in 2003– funded by Air Force and NASA
• Leonardo — a small group of Earth-sensing satellites flying in formation– 8 AE seniors, 1 AE freshman– supporting research sponsored by NASA Goddard
Space Design Projects ‘00
• Three tethered space systems projects – two involve collaboration with Technical
University of Vienna• tether system based on Space Station• free-flying tether system
– one involves cooperation with Next Generation Space Telescope program office at NASA Goddard
• Rotating tethered interferometer at L2– eventually became research project funded
by NASA
• Continued work on HokieSat
• Three tethered space systems projects – two involve collaboration with Technical
University of Vienna• tether system based on Space Station• free-flying tether system
– one involves cooperation with Next Generation Space Telescope program office at NASA Goddard
• Rotating tethered interferometer at L2– eventually became research project funded
by NASA
• Continued work on HokieSat
Space Design Projects ‘01
• PowerSail– Large deployable flexible solar array
connected to the host spacecraft by a flexible umbilical
– Sponsored by USAF, team traveled to Edwards AFB, CA to present design
• SOTV – Solar Orbit Transfer Vehicle– Solar thermal engine powers a reusable
space tug– Sponsored by USAF, collaboration with BWX
Technologies
• Venus Sample Return Mission– AIAA Undergraduate Team Space Design
Competition– Travel to Venus and return a 1 kg sample
• PowerSail– Large deployable flexible solar array
connected to the host spacecraft by a flexible umbilical
– Sponsored by USAF, team traveled to Edwards AFB, CA to present design
• SOTV – Solar Orbit Transfer Vehicle– Solar thermal engine powers a reusable
space tug– Sponsored by USAF, collaboration with BWX
Technologies
• Venus Sample Return Mission– AIAA Undergraduate Team Space Design
Competition– Travel to Venus and return a 1 kg sample
VT-Zero G Reduced Gravity Experiment
• Four VT Juniors designed, built experiment to fly on “Vomit Comet”
• Effects of Microgravity on a Human’s Ability to Control Remote Vehicle
• Eliminate visual and vestibular cues
• Goggles allow “pilot” to see 3D environment with crosshairs and illuminated targets
• Microgravity impedes inner ear equilibrium processes
• Pilot uses joystick to navigate between targets
• Four VT Juniors designed, built experiment to fly on “Vomit Comet”
• Effects of Microgravity on a Human’s Ability to Control Remote Vehicle
• Eliminate visual and vestibular cues
• Goggles allow “pilot” to see 3D environment with crosshairs and illuminated targets
• Microgravity impedes inner ear equilibrium processes
• Pilot uses joystick to navigate between targets
Space Systems Research• Formation Flying
– attitude and orbit dynamics and control
• Spacecraft Dynamics and Control– with gimbaled momentum wheels (GMWs)
• Integrated Energy Storage and Attitude Control– using high-speed flywheels as “batteries” and GMWs
• Optimal Continuous Thrust Orbit Transfer– approximations for indirect methods
• Supported by Air Force, NASA, and NSF• Graduated 31 M.S. students and 4 Ph.D.
students• Currently advising 7 M.S. students and 1 Ph.D.
student
• Formation Flying – attitude and orbit dynamics and control
• Spacecraft Dynamics and Control– with gimbaled momentum wheels (GMWs)
• Integrated Energy Storage and Attitude Control– using high-speed flywheels as “batteries” and GMWs
• Optimal Continuous Thrust Orbit Transfer– approximations for indirect methods
• Supported by Air Force, NASA, and NSF• Graduated 31 M.S. students and 4 Ph.D.
students• Currently advising 7 M.S. students and 1 Ph.D.
student
Control of a Rotating Tethered Interferometer
• In Halo orbit about L2• 3 infrared mirror satellites,
1 central collector• 10 m to 1 km tethers
• In Halo orbit about L2• 3 infrared mirror satellites,
1 central collector• 10 m to 1 km tethers
Stowed configuration
Deployedconfiguration
Formation Flying
• Ionospheric Observation Nanosatellite Formation (ION-F)– HokieSat will fly in formation with
nanosatellites being built by UW and USU– Uses micro pulsed plasma thrusters
• Leonardo– Earth-science remote sensing mission– Six small satellites in large formation to
study radiative forcing of Earth atmosphere
• Ionospheric Observation Nanosatellite Formation (ION-F)– HokieSat will fly in formation with
nanosatellites being built by UW and USU– Uses micro pulsed plasma thrusters
• Leonardo– Earth-science remote sensing mission– Six small satellites in large formation to
study radiative forcing of Earth atmosphere
Distributed Spacecraft Attitude Control System Simulator
• Two spherical air bearings, “floating” a spacecraft-like system
• One stationary “spacecraft”
• The three spacecraft communicate via radio modems, and “fly in formation” with integrated pointing maneuvers
• Two spherical air bearings, “floating” a spacecraft-like system
• One stationary “spacecraft”
• The three spacecraft communicate via radio modems, and “fly in formation” with integrated pointing maneuvers
Base Motion Effects on Magnetic Bearings
• Proposed applications for magnetic bearings involve use in moving vehicles
• Most research literature on magnetic bearings is for static systems
• Base motion effects have not yet been thoroughly investigated
• Will “Fly” magnetic bearing system as payload on Spacecraft Simulator
• Proposed applications for magnetic bearings involve use in moving vehicles
• Most research literature on magnetic bearings is for static systems
• Base motion effects have not yet been thoroughly investigated
• Will “Fly” magnetic bearing system as payload on Spacecraft Simulator
NASA Shuttle Hitchhiker Experiment
Launch System (SHELS)
AFRL Multi-Satellite
Deployment System (MSDS)
University Nanosatellites
HokieSat• Virginia Tech Ionospheric
Scintillation Measurement Mission (VTISMM) aka HokieSat
• Ionospheric Observation Nanosatellite Formation (ION-F)– Utah State University– University of Washington
– Virginia Tech• University Nanosatellite Program
– 2 stacks of 3 satellites
• Sponsors: AFRL, AFOSR, DARPA, NASA GSFC, SDL
The ION-F Mission• The Ionospheric Observation Nanosatellite
Formation mission addresses the following science topics:• Evolution of ionospheric plasma structure, irregularities
and scintillations• Spectral characteristics of ionospheric plasma waves• Global latitudinal distribution of ionospheric plasma
structures and irregularities
• Accomplished using• Plasma Impedance Probe (PIP)• Global Positioning System (GPS)
• Uniqueness of measurements lies in the ability to vary satellite separation
• Complement data collected with ground-based radar and concurrent observations from other satellites
• The Ionospheric Observation Nanosatellite Formation mission addresses the following science topics:• Evolution of ionospheric plasma structure, irregularities
and scintillations• Spectral characteristics of ionospheric plasma waves• Global latitudinal distribution of ionospheric plasma
structures and irregularities
• Accomplished using• Plasma Impedance Probe (PIP)• Global Positioning System (GPS)
• Uniqueness of measurements lies in the ability to vary satellite separation
• Complement data collected with ground-based radar and concurrent observations from other satellites
T4T1 = TSafe, All Systems ExceptRecontact Hazards
= 20 minutes
= 0:00 T3 = T SEP
= T0 + 96 hours, 4 secs
= TSEP, Nanosat
Stack separation signalreleases both stacks
Intersatellite separationMSDS is 20 minutes outfrom Orbiter,timers
time-out
T0
Safety inhibits removedfor all MSDS systems
without recontacthazards.
Safety inhibits removedfor Nanosat systems
without recontacthazards.
MSDS released fromOrbiter/SHELS
MSDS timers initiatedRecontact hazard inhibits
removed aboardNanosats
Recontact hazard inhibitsremoved aboard MSDS
T2 = TSafe,Recontact Hazards
= T0 + 96 hours
INHIBITS STATUS MSDS AND NANOSAT
RecontactHazards
All othersystems
In-place
In-place
In-place
Removed
Removed
Removed Removed
Removed
Removed
Removed
= T0 + 102 hours, 4 secs
3CSION-F
USUSat
Dawgstar
HokieSat
Multiple Satellite
Deployment System
T4T1 = TSafe, All Systems ExceptRecontact Hazards
= 20 minutes
= 0:00 T3 = T SEP
= T0 + 96 hours, 4 secs
= TSEP, Nanosat
Stack separation signalreleases both stacks
Intersatellite separationMSDS is 20 minutes outfrom Orbiter,timers
time-out
T0
Safety inhibits removedfor all MSDS systems
without recontacthazards.
Safety inhibits removedfor Nanosat systems
without recontacthazards.
MSDS released fromOrbiter/SHELS
MSDS timers initiatedRecontact hazard inhibits
removed aboardNanosats
Recontact hazard inhibitsremoved aboard MSDS
T2 = TSafe,Recontact Hazards
= T0 + 96 hours
INHIBITS STATUS MSDS AND NANOSAT
RecontactHazards
All othersystems
In-place
In-place
In-place
Removed
Removed
Removed Removed
Removed
Removed
Removed
= T0 + 102 hours, 4 secsT4T1 = TSafe, All Systems ExceptRecontact Hazards
= 20 minutes
= 0:00 T3 = T SEP
= T0 + 96 hours, 4 secs
= TSEP, Nanosat
Stack separation signalreleases both stacks
Intersatellite separationMSDS is 20 minutes outfrom Orbiter,timers
time-out
T0
Safety inhibits removedfor all MSDS systems
without recontacthazards.
Safety inhibits removedfor Nanosat systems
without recontacthazards.
MSDS released fromOrbiter/SHELS
MSDS timers initiatedRecontact hazard inhibits
removed aboardNanosats
Recontact hazard inhibitsremoved aboard MSDS
T2 = TSafe,Recontact Hazards
= T0 + 96 hours
INHIBITS STATUS MSDS AND NANOSAT
RecontactHazards
All othersystems
In-place
In-place
In-place
Removed
Removed
Removed Removed
Removed
Removed
Removed
= T0 + 102 hours, 4 secsT4T1 = TSafe, All Systems Except
Recontact Hazards
= 20 minutes
= 0:00 T3 = T SEP
= T0 + 96 hours, 4 secs
= TSEP, Nanosat
Stack separation signalreleases both stacks
Intersatellite separationMSDS is 20 minutes outfrom Orbiter,timers
time-out
T0
Safety inhibits removedfor all MSDS systems
without recontacthazards.
Safety inhibits removedfor Nanosat systems
without recontacthazards.
MSDS released fromOrbiter/SHELS
MSDS timers initiatedRecontact hazard inhibits
removed aboardNanosats
Recontact hazard inhibitsremoved aboard MSDS
T2 = TSafe,Recontact Hazards
= T0 + 96 hours
INHIBITS STATUS MSDS AND NANOSAT
RecontactHazards
All othersystems
In-place
In-place
In-place
Removed
Removed
Removed Removed
Removed
Removed
Removed
= T0 + 102 hours, 4 secs
ION-F Mission
Configuration:
Scenario:
Data Port
Crosslink Antenna
Uplink Antenna
Downlink Antenna
SciencePatches
LightBand
GPS Antenna
Pulsed PlasmaThrusters
Solar Cells
Camera
External Configuration
Torque Coils (3)
Rate Gyros (3)
Downlink Transmitter
Cameras
Camera
Electronics Enclosure
Battery Enclosure
MagnetometerCamer
a
PowerProcessing Unit
Crosslink Components
Internal Configuration
Pulsed PlasmaThrusters (2)
Overview of HokieSat’s DCS
Attitude Determination Hardware
• Three-axis magnetometer (TAM)– Measures Earth’s magnetic field
• Four CCD Cameras– Determine nadir vector from Earth
horizon– Determine Sun vector
• Solar array Sun measurements– Determine Sun vector
• Three single-axis rate gyros– Measure body-fixed angular
velocity
• Three-axis magnetometer (TAM)– Measures Earth’s magnetic field
• Four CCD Cameras– Determine nadir vector from Earth
horizon– Determine Sun vector
• Solar array Sun measurements– Determine Sun vector
• Three single-axis rate gyros– Measure body-fixed angular
velocity
Attitude Control Hardware
• Three torque coils– Generate magnetic moment (0.9
Am2)– Orthogonally mounted
• Torque coil sizing
• Three torque coils– Generate magnetic moment (0.9
Am2)– Orthogonally mounted
• Torque coil sizingnM ˆμINA
Number of turns SizeHexagonal coil 80 5.7" radiusRectangular coil 133 7" x 9"
ADCS Hardware
Camera
Magnetometer Camer
aTorque Coils
Rate Gyros
Camera
Hardware Summary
• Mass: 2.7 lbs (1.2 kg)• Power: 4.4 W (during control maneuvers)
• Mass: 2.7 lbs (1.2 kg)• Power: 4.4 W (during control maneuvers)
Component Mass (g) Voltage (V) Power (W)Torque Coils 570 3.3 0.45
Cameras 381 5.0 0.06Magnetometer 69 15.0 0.30
Rate Gyro 232 5.0 3.60
Attitude Determination Algorithms
• Nadir, sun, and magnetic field vector sensors
• Rate gyros
• Multiple cases– Rate gyros with >1 vector sensors– Rate gyros with 1 vector sensor– Rate gyros not available
• QUEST least-squares solution using vector measurements
• Extended Kalman Filter incorporates rate measurements
• Nadir, sun, and magnetic field vector sensors
• Rate gyros
• Multiple cases– Rate gyros with >1 vector sensors– Rate gyros with 1 vector sensor– Rate gyros not available
• QUEST least-squares solution using vector measurements
• Extended Kalman Filter incorporates rate measurements
Attitude Control Synthesis Algorithm
• Develop equations of motion nonlinear system
• Linearize about nadir-pointing linear time-varying system, periodic effects of magnetic field
• Average over one orbit linear time-invariant system
• Determine candidate control torque gains using LQR and LTI system
• Check stability of linear time variant system using Floquet theory
• Check stability of nonlinear system using simulation
• Develop equations of motion nonlinear system
• Linearize about nadir-pointing linear time-varying system, periodic effects of magnetic field
• Average over one orbit linear time-invariant system
• Determine candidate control torque gains using LQR and LTI system
• Check stability of linear time variant system using Floquet theory
• Check stability of nonlinear system using simulation
Magnetic Attitude Control
• Nonlinear equations of motion are
• Control input is based on linear feedback
where K is the gain matrix calculated from the linear quadratic regulator
• Nonlinear equations of motion are
• Control input is based on linear feedback
where K is the gain matrix calculated from the linear quadratic regulator
BMIoIoIIωωIω 133
11 ˆˆω3 c
ωq
1qq
T
q4
2
1
)()(~
tt KxM
Magnetic Moment
• Magnetic moment is most effective when it is perpendicular to magnetic field
• The mapped magnetic moment is the ideal desired moment, and M is the moment of the same magnitude that can feasibly be applied
• Magnetic moment is most effective when it is perpendicular to magnetic field
• The mapped magnetic moment is the ideal desired moment, and M is the moment of the same magnitude that can feasibly be applied
B
BMMMM
~
:~
Attitude Control Synthesis
KQ LQR
Stable Linear Time-Invariant Equations
Floquet TheoryStable Linear Time-Varying Equations
Nonlinear Simulation to Check Stability
Linear Time-
Invariant Equations
Linear Time-
Varying Equations
Nonlinear Equations
Linearize about
equilibrium
Average periodic
magnetic field terms
Conventional Control Results
Initial attitude error: ~14° from nadir pointing
0 0.5 1 1.5 2 2.5 3 3.5
x 104
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
time, sec
Mag
neti
c M
omen
t, A
-m2
Magnetic Moment vs Time
M1M2M3
0 0.5 1 1.5 2 2.5 3 3.5x 10
4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Nonlinear, LQR Controller with Gravity-Gradient Stability
time, sec
qbo
q1q2q3q4
Conventional Control ResultsReorienting an inverted spacecraft
0 0.5 1 1.5 2 2.5 3 3.5
x 104
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3Magnetic Moment vs Time
time, sec
Mag
netic
Mom
ent,
A-m
2
M1
M2
M3
0 0.5 1 1.5 2 2.5 3 3.5
x 104
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1qbo vs Time for Inverted Case
time, sec
qbo
q1
q2q
3q4
Conventional Control ResultsRequired magnetic moment is periodic
with period of approximately one day
0 1 2 3 4 5 6 7 8 9 10
x 105
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04Magnetic Moment vs Time
time, sec
Mag
netic
Mom
ent,
A-m
2
M1M2M3
Modal Testing of Structure (Without Skins)
Dynamic Testing
Mode 1fn = 245 Hz
(vs 249 Hz predicted)
Mode 2fn = 272 Hz
(vs 263 Hzpredicted)
Acknowledgements
•Air Force Research Lab•Air Force Office of
Scientific Research•Botstiber Foundation•Defense Advanced
Research Projects Agency•Georgia Tech•NASA Goddard Space
Flight Center•NASA Wallops Flight
Facility Test Center•National Science
Foundation•Technical University of
Vienna•University of Washington•USRA•Utah State University•Virginia Tech
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