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Spacecraft Dynamics and Control

Spacecraft Dynamics and Control. Chris Hall Associate Professor Aero Space 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

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Spacecraft Dynamics and Control

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  1. Spacecraft Dynamics and Control Chris HallAssociate 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. 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 Deployedconfiguration

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

  21. External Configuration Solar Cells Crosslink Antenna GPS Antenna LightBand Pulsed Plasma Thrusters Data Port Camera Uplink Antenna Downlink 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 • Determine Sun vector • 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 Average periodic magnetic field terms Linearize about equilibrium 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. Nonlinear, LQR Controller with Gravity-Gradient Stability Magnetic Moment vs Time 1 0.04 q 1 q 0.8 0.03 2 q 3 2 q 0.6 4 0.02 0.4 0.01 0.2 0 bo Magnetic Moment, A-m 0 q -0.01 -0.2 -0.02 -0.4 -0.03 -0.6 -0.8 -0.04 -1 -0.05 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time, sec time, sec 4 x 10 x 10 Conventional Control Results Initial attitude error: ~14° from nadir pointing M 1 M 2 M 3

  34. bo q vs Time for Inverted Case Magnetic Moment vs Time 1 0.3 q 1 q 0.8 2 q 0.2 M 3 1 q 0.6 4 M 2 2 M 0.1 0.4 3 0.2 0 bo 0 q Magnetic Moment, A-m -0.1 -0.2 -0.4 -0.2 -0.6 -0.3 -0.8 -1 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 time, sec 4 x 10 4 time, sec x 10 Conventional Control Results Reorienting an inverted spacecraft

  35. Magnetic Moment vs Time 0.04 M 1 2 0.03 M 2 M 0.02 3 0.01 Magnetic Moment, A-m 0 -0.01 -0.02 -0.03 -0.04 -0.05 0 1 2 3 4 5 6 7 8 9 10 time, sec 5 x 10 Conventional Control Results Required magnetic moment is periodic with period of approximately one day

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

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