1. Spacecraft Dynamics and Control
Chris Hall Associate Professor
AeroSpace and Ocean Engineering
Virginia Polytechnic Institute and State University

2. 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

3. 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
Burruss Hall is the main administration building

4. 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
Norris Hall is the main Engineering building

5. Aerospace Engineering at Virginia Tech
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

6. Aerospace and Ocean 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

7. *Aerospace Engineering Departments in U.S. News and World Report
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)
Cornell University (NY)
Pennsylvania State University
12. Virginia Tech
*Aerospace Engineering Departments in U.S. News and World Report

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. Control of a Rotating Tethered Interferometer
In Halo orbit about L2
3 infrared mirror satellites, 1 central collector
10 m to 1 km tethers
Stowed configuration
Deployed configuration

15. 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

16. 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

17. 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

18. AFRL Multi-Satellite Deployment NASA Shuttle Hitchhiker
HokieSat
University Nanosatellites
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
AFRL Multi-Satellite Deployment
System (MSDS)
NASA Shuttle Hitchhiker
Experiment Launch
System (SHELS)

19. 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

20. Multiple Satellite Deployment System
ION-F Mission
Configuration:
3CS
ION-F
USUSat
Dawgstar
HokieSat
Multiple Satellite Deployment System
Scenario:

21. External Configuration
GPS Antenna
Crosslink Antenna
Solar Cells
LightBand
Pulsed Plasma
Thrusters
Data Port
Camera
Downlink Antenna
Uplink Antenna
Science
Patches

22. Internal Configuration
Crosslink Components
Cameras
Power
Processing Unit
Torque Coils (3)
Magnetometer
Camera
Pulsed Plasma
Thrusters (2)
Camera
Battery Enclosure
Downlink Transmitter
Electronics Enclosure
Rate Gyros (3)

23. Overview of HokieSat’s DCS

24. 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
Three single-axis rate gyros
Measure body-fixed angular velocity

25. Attitude Control Hardware
Three torque coils
Generate magnetic moment (0.9 Am2)
Orthogonally mounted
Torque coil sizing

26. ADCS Hardware Magnetometer Camera Torque Coils Camera Camera
Rate Gyros

27. Hardware Summary Mass: 2.7 lbs (1.2 kg)
Power: 4.4 W (during control maneuvers)

28. 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

29. 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

30. 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

31. 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

32. Attitude Control Synthesis
Linearize about equilibrium
Average periodic magnetic field terms
Linear Time-Invariant Equations
Linear Time-Varying Equations
Nonlinear Equations
Stable Linear Time-Invariant Equations
Stable Linear Time-Varying Equations
Floquet Theory Q
LQR K
Nonlinear Simulation to Check Stability

33. Conventional Control Results
Initial attitude error: ~14° from nadir pointing
0.5 1
1.5 2
2.5 3
3.5
x 10 4 -1
-0.8
-0.6
-0.4
-0.2
0.2
0.4
0.6
0.8
Nonlinear, LQR Controller
with Gravity-Gradient Stability
time, sec q bo
0.5 1
1.5 2
2.5 3
3.5
x 10 4
-0.05
-0.04
-0.03
-0.02
-0.01
0.01
0.02
0.03
0.04
time, sec
Magnetic Moment, A-m
Magnetic Moment vs Time M 1 M 2 M 3

34. Conventional Control Results
Reorienting an inverted spacecraft
0.5 1
1.5 2
2.5 3
3.5
x 10 4 -1
-0.8
-0.6
-0.4
-0.2
0.2
0.4
0.6
0.8 q bo
vs Time for Inverted Case
time, sec
0.5 1
1.5 2
2.5 3
3.5
x 10 4
-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
Magnetic Moment vs Time
time, sec
Magnetic Moment, A-m M

35. Conventional Control Results
Required magnetic moment is periodic with period of approximately one day 1 2 3 4 5 6 7 8 9 10
x 10
-0.05
-0.04
-0.03
-0.02
-0.01
0.01
0.02
0.03
0.04
Magnetic Moment vs Time
time, sec
Magnetic Moment, A-m M

36. Dynamic Testing Modal Testing of Structure (Without Skins) Mode 1
fn = 245 Hz
(vs 249 Hz predicted)
Mode 2
fn = 272 Hz
(vs 263 Hz predicted)

37. 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