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Satellite Attitude Control with Dual Reaction Wheels

Satellite Attitude Control with Dual Reaction Wheels. Enkh Mandakh – AERO 625 Final Project. Introduction. Design satellite attitude controller NZSP-LQG PI-NZSP (SDR) PIF-NZSP-CRW (SDR) Goals T rack a given direction Orbital mechanics and long-term perturbations not considered

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Satellite Attitude Control with Dual Reaction Wheels

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  1. Satellite Attitude Control with Dual Reaction Wheels EnkhMandakh – AERO 625 Final Project

  2. Introduction • Design satellite attitude controller • NZSP-LQG • PI-NZSP (SDR) • PIF-NZSP-CRW (SDR) • Goals • Track a given direction • Orbital mechanics and long-term perturbations not considered • Applications • Orienting imaging, star tracking cameras • Orienting solar arrays • Orienting antennas, etc.

  3. Performance Specs – Time Domain • Step input specifications • Overshoot: 20% • Steady state error: 1% • Departure time: 1s • Rise time: 3s • Settling time: 10s

  4. Satellite Setup • Actuators: dual orthogonal reaction wheels • Simpler dynamics than control moment gyroscopes • More practical than gas or ion thrusters • High precision • Assumptions • Reaction wheels centered on satellite C.M. • Each reaction wheel axis coincident to satellite principal axis • Satellite is axially symmetric about instrument axis • Instrument axis and each reaction wheel axis are orthogonal • Rotation about instrument axis is irrelevant

  5. Satellite Setup • Coordinate Frame

  6. Satellite Setup • Attitude • Dynamics

  7. Satellite Setup • Attitude • Dynamics

  8. Satellite Setup • Attitude Dynamics • A = B = • C = D = • eigenvalues eigenvectors

  9. Satellite Setup • Singular Values = • 2 non-minimal dimensions • sigma_max = 1.25, amplification • sigma_min = 1.25, attenuation

  10. Satellite Setup

  11. Satellite Setup • Reaction Wheels • Speed range: -9000rpm to 9000rpm • -54000deg/s to 54000deg/s • Speed tracking error <1rpm = 6deg/s = 0.1047 rad/s (assume 3*sigma boundary) • Measurement noise mean = 0 • Measurement noise standard deviation = 0.1047/3 = 0.0349 rad/s • Measurement noise variation = 0.0349^2 = 0.0012 rad/s • No info on acceleration limits, electric motors most likely very fast

  12. Controllability and Observability • C = • rank(C) = 4, controllable • O = rank(O) = 4 • observable • if x1 or x3 not • measured, becomes • unobservable

  13. Open Loop Response

  14. SDR – Preliminary Testing • w1 sensitivity • Q = R = x0 = T = 0.01s • w1 = 0 > unstable • w1 low => long period wobbling • w1 high => high frequency on angular velocities • Rate of convergence not highly dependent on w1

  15. SDR – Preliminary Testing w1 = 0.00005 rad/s

  16. SDR – Preliminary Testing w1 = 0.0025 rad/s

  17. SDR – Preliminary Testing w1 = 0.1 rad/s

  18. SDR – Preliminary Testing • Initial condition sensitivity • Q = R = w1 = 0.01 rad/s • T = 0.01s • Rate of convergence not highly dependent on initial state

  19. SDR – Preliminary Testing x0 = degrees

  20. SDR – Preliminary Testing x0 = degrees

  21. SDR – Preliminary Testing x0 = degrees

  22. SDR – Preliminary Testing • Sample rate sensitivity • Q = R = w1 = 0.01 rad/s • x0 = • Angle weights increased for faster convergence and easier to see sample delay • sample step becomes detrimental above 1s, not much change in behavior below 1s

  23. SDR – Preliminary Testing T = 0.01s

  24. SDR – Preliminary Testing T = 0.1s

  25. SDR – Preliminary Testing T = 1s

  26. SDR – Preliminary Testing T = 5s

  27. NZSP (LQG) conditions • Q = R = w1 = 0.01s • T = 0.1s • x0 = ym = • G = xh0 = • Process error: mean = 0, variance = 1e-7 • Measurement error: mean = 0, variance = 0.0012

  28. NZSP (LQG)

  29. PI-NZSP (SDR) conditions • Q = R = w1 = 0.01s • T = 0.1s • x0 = ym = • Qy =

  30. PI-NZSP (SDR)

  31. PI-NZSP (SDR) conditions • Q = R = w1 = 0.01s • T = 0.1s • x0 = ym = • Qy = • Process error: 0.1deg • Goes divergent with process error 1deg

  32. PI-NZSP (SDR)

  33. PIF-NZSP-CRW (SDR) conditions • Q = R = w1 = 0.01s • T = 0.1s • x0 = ym = • Qy = Rd = • Process error: 2deg • Handles large constant process errors well

  34. PIF-NZSP-CRW (SDR)

  35. PIF-NZSP-CRW (SDR)

  36. PIF-NZSP-CRW (SDR) conditions • Q = R = w1 = 0.01s • T = 0.1s • x0 = ym = • Qy = Rd = • Process error: 2deg • Handles large constant process errors well

  37. PIF-NZSP-CRW (SDR)

  38. PIF-NZSP-CRW (SDR)

  39. References • J. Crassidis, J. Junkins, “Optimal Estimation of Dynamic Systems” 2004. • H. Schaub, J. Junkins, “Analytical Mechanics of Space Systems” 2003. • J. Valasek, AERO 625 Notes • http://www.satserv.co.uk/ReactionWheel.pdf • www.wikipedia.org

  40. Questions?

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