Spacecraft Dynamics and Control Chris Hall Associate 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

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

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

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

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

*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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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)

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 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

ADCS Hardware Magnetometer Camera Torque Coils Camera Camera Rate Gyros

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

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

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

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

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

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

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

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

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

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)

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