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