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Ae105c Term Project PDR Team reports from Structures and Thermal Dynamics Metrology

Ae105c Term Project PDR Team reports from Structures and Thermal Dynamics Metrology. Dynamics Team. Derek Chan Inki Choi Silas Hilliard Prakhar Mehrotra Kevin Watts. Review Board. Greg Davis Yunjin Kim Sergio Pellegrino Marco Quadrelli Virendra Sarohia Mike Watkins.

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Ae105c Term Project PDR Team reports from Structures and Thermal Dynamics Metrology

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  1. Ae105c Term ProjectPDRTeam reports fromStructures and ThermalDynamics Metrology

  2. Dynamics Team Derek Chan Inki Choi Silas Hilliard Prakhar Mehrotra Kevin Watts

  3. Review Board Greg Davis Yunjin Kim Sergio Pellegrino Marco Quadrelli Virendra Sarohia Mike Watkins

  4. Dynamics Task Overview Up to PDR - division into two groups • 1) Development of dynamic spacecraft model • Accurately describe spacecraft behavior over time • 2) Modeling of disturbances • J2 • Atmospheric drag • Solar pressure • Effect on orbital elements • Post-PDR – combine efforts • PI Controller • Create initial framework for further development • Integrate dynamic model and disturbance model

  5. Level 1 Requirements • Pointing accuracy • 120 microradian knowledge • 300 microradian control • .0075 radian orientation about z-axis • Orbital requirements • 27 degree inclination • Beginning of life 550 km circular orbit • End of life 425 km circular orbit

  6. Functional Requirements • Response time • Torque required • Maintain orbit for duration of mission 6

  7. Interfaces Receivables: From Structures/Thermal: Vibration mode From Metrology: Mapping from position to measurement From Project: Pointing requirements, S/C configuration Deliverables: To Structures/Thermal: Libration, dynamic frequencies To Metrology: Dynamic model and controllability To Project: Dynamic model, modes, response time

  8. Baseline Approach Utilizes two reference frames 8

  9. Dynamic Model Assumptions • Keplerian circular orbit • Two point masses connected by spring • Boom as linear damped spring • Earth’s gravity only external force • No drag, J2, solar pressure, etc. • Model parameters • Earth-centered inertial frame (X,Y,Z) • Moving reference frame (x,y,z) • R0 connects reference frame to inertial frame • ρ connects mass to reference frame origin • Allows “zoom in” on spacecraft 9

  10. Dynamics Equations • State: [ρ1 v1ρ2 v2 R0 R0]’ • ρ1 = r1 – R0 • a1 = r1 – R0 – Ω x Ω x ρ1 - 2Ω x v1 • Fs = -K (l-l0)* ρ1 /|ρ1| - C (v1 –v2) • Derek’s Changes Here 10

  11. Dynamics Parameters • Orbit model • 500 km circular orbit • Inclination 27 degrees • Gravity only external force • Drag, J2 terms can be integrated with extended model • S/C model • K = 8e5 N/m, (spring constant) • C = 1e3 N/m/s, (damping constant) • 17.40 Hz is first modal frequency of boom • M1 = 200 kg, M2 = 100 kg • K and C derived from given modal frequency 11

  12. Dynamics Analysis Boom strain over time – slightly underdamped BOLDIFY – fix graph 12

  13. Dynamics Analysis Vibrational Power Spectrum – peak at 17.40 HzBOLDIFY – fix graph 13

  14. Disturbances Assumptions • Orbital Elements • Earth-Centered Inertial (ECI) inertial reference system • Two-Body system with Spacecraft as the point mass • Gaussian Planetary Equations of Motion (Gauss VOP) • Disturbances • Solar pressure, Atmospheric drag, and Earth’s Oblateness • Forces resolved in RSW system (radial-tangential-normal)

  15. Baseline Approach - Disturbances • Formulation • Eccentricity approx. to 0.0001 • Ballistic Coefficient B(= A/m) ~ 0.019. • Time Marching Algorithm with Δt = 50 (~ 1/100th of Time Period) • Forces • Solar Pressure • Neglected seasonal variations • Nominal Solar Pressure Radiation constant fp = 4.5*10-6 (N/m2) • Fsolar = fp ( 1+ref)*B (N/Kg) • Reflectivity ref = 0 ( worst case i.e Black Body) *References: • Fundamentals of Astrodynamics – David A Vallado • Integrated Orbit, Attitude, and Structures Control System Design for Space Solar Powered Satellites – Bong Wie, Carlos M. Roithymayr , NASA/TM – 2001-210854.

  16. Baseline Approach - Disturbances • Forces (cont.) • Earth’s Oblateness • J2 Effect • Periodic effects ignored. • Atmospheric Drag • Cd = 2.2 • Exponential Model for the Density *References: • Fundamentals of Astrodynamics – David A Vallado • Integrated Orbit, Attitude, and Structures Control System Design for Space Solar Powered Satellites – Bong Wie, Carlos M. Roithymayr , NASA/TM – 2001-210854.

  17. Technical Status - Disturbances Orbit Inclination in degREMOVE BEFORE WEDNESDAY Eccentricity 17

  18. Technical Status - Disturbances Height in Km Semi-Major Axis in KmREMOVE 18

  19. Technical Status - Disturbances Ω degREMOVE ω deg 19

  20. Disturbances Analysis Drag Force (N) ~ 10-3 - BOLDIFY Earth’s Oblateness (N) ←Solar Pressure (N) ~ 10-5 20

  21. Incorporating changing cross-sectional area Accuracy of the atmospheric model Using ODE45 & ODE15s to integrate the dynamic model Orbital radius drop to 425 km quickly Open Issues and Concerns 21

  22. Summary • Initial model of spacecraft behavior completed • Oscillation at 17.40 Hz • Librations are difficult to model • Can extend model to incorporate more advanced orbital elements • Initial analysis of disturbances completed • Dominated by oblateness

  23. Back-up Material

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