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NGGM Assessment Study Progress Meeting 3TAS-I, Torino, 26 May 2010

This agenda outlines the topics to be discussed in the NGGM Assessment Study progress meeting, including observing techniques, mission analysis, mission architecture, and simulation tool. The text language is English.

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NGGM Assessment Study Progress Meeting 3TAS-I, Torino, 26 May 2010

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  1. NGGM ASSESSMENT STUDYProgress Meeting 3TAS-I, Torino, 26 May 2010

  2. Agenda • 9.15 Introduction and Agenda • 9.30 Task 2: Observing techniques • WP 2120 Instrument Concepts TAS-I • WP 2121 Measurement Technologies ONERA • WP 2110 Observing Techniques DEOS [IAPG] • 11.00 Task 3: Mission analysis and attitude and orbit control concepts • WP 2220 Attitude and Orbit Control Concepts TAS-I • WP 2210 Mission Analysis TAS-I [DEIMOS] • 12.00 Task 5: Mission Architecture Outlines • WP 2420: Mission Architecture DEOS [GIS] • WP 2410: Architecture Definition and Trade-Off TAS-I • 13.30 Lunch break • 14.30 Task 4: Simulation Tool • WP 2310 End-to-End Simulator Design and Implementation TAS-I • WP 2320 Variable Gravity Model DEOS [IAPG] • WP 2330 Backward Module DEOS • 16.15 Discussion, Planning • 16.30 Adjourn

  3. WP 2120 Instrument Concepts (TAS-I)

  4. Top-level requirements • From science requirements to measurement requirements • Geoid cumulative error 1 mm at SH 200, 10 mm at SH 250 is achievable with: • orbit altitude = 300 km • satellite-satellite distance = 100 km • satellite-to-satellite distance variation relative error SD 210-13 1/Hz • non-gravitational acceleration measurement error SD 10-11 m/s2/Hz

  5. Satellite-Satellite distance error tree Satellite-to-satellite distance measurement error SD 20 nm/Hz relative error 210-13 1/Hz at satellite-to-satellite distance d = 100 km. Error breakdown (for the metrology without BSM) defined to relax as far as possible the requirements on laser beam frequency stability and pointing (satellite relative orientation).

  6. Laser frequency stability Relative stability for d = 100 km Measurement error if laser frequency stability = 300 Hz/Hz (10x LISA): 107.5 nm/Hz (relative error = 1.07510-12 1/Hz at d = 100 km)

  7. Laser metrology performance requirements Measurement noise of the Satellite 2 (Satellite 1) orientation to S-S line, provided by the angle (lateral) metrology on Satellite 2 • Interferometer measurement noise requirement [m/Hz] 2 µrad/Hz 10 nm/Hz • Optical power on the interferometer sensor (pd2) required for 10 nm/Hz =0.8 pW  OK from link budget. • Optical power on the PSD of the angle metrology on S2 for 2 µrad/Hz = 70 nW OK from link budget

  8. Reference accelerometer layout choice Z US axis LS axis • Concept 1: excluded since it doesn’t provide any GGT component measurement. • Concept 2: excluded since it doesn’t measure the linear acceleration along each direction with accelerometer US axes (the linear acceleration Z is measured with LS axes only). • Both Concept 3 and 4 provides the VYY and VZZ components of the GGT and measures two angular accelerations with US axes. • Concept 3 is preferred to Concept 4 because the linear acceleration along X (nominally aligned to the satellite-to-satellite line) is measured with four US axes (two in the Concept 4). • Warning: due to the lack of accelerometers along X, the measurement of the Y, Z angular accelerations is unavoidably contaminated by the off-diagonal GGT components VXZ, VXY. Y X Concept 1 Concept 2 Concept 3 Concept 4

  9. Reference accelerometer layout choice • Linear acceleration X: aX = (a1X + a2X + a3X + a4X)/4 (US axes only) • Linear acceleration Y, Z: aY = (a1Y + a3Y)/2 , aZ = (a2Z + a4Z)/2 (US axes only) • Angular acceleration X: dX/dt = [(a1Z – a3Z)/L – (a2Y – a4Y)/L]/2 (LS axes only) • Angular acceleration Y: dY/dt = (a2X – a4X)/L + VXZ - XZ(US axes only) • Angular acceleration Z:dZ/dt = (a3X – a1X)/L - VXY + XY(US axes only) • GGT components:VYY = (a3Y – a1Y)/L - X2 - Z2; VZZ = (a4Z – a2Z)/L - X2 - Y2

  10. Acceleration measurement error tree Error breakdown updated for the 4-accelerometer reference layout and defined to match the satellite pointing requirements with those from the S-S distance measurement 10-11 m/s2/Hz

  11. Accelerometer performance requirements Requirements applicable to the 4-accelerometer reference layout. • Accelerometer noise: 310-12 m/s2Hz (US axes) • Accelerometer noise: 310-10 m/s2Hz (LS axis) • Accelerometer bias: 210-7 m/s2 (all axes) • Common and differential scale factors knowledge: 210-4 for X axis (from calibration):  110-3 for Y, Z axes (from calibration) The requirement of the common SF is more stringent than in GOCE (210-3) where the differential accelerations and not the common-mode ones are the main observables. • Accelerometer scale factor stability (all): 10-6 1Hz Note: for the ll-SST purposes, it is not required for the accelerometer noise to be flat till 0.1 Hz, since the metrology measurement error is dominant above 0.01 Hz. However, a low noise level till 0.1 Hz (achievable with the GOCE accelerometers) can be useful for the GGT components measurements. ll-SST GGT

  12. Derived control requirements • Satellite X-axis alignment to the satellite-to-satellite direction: Satellite 2: 1 (thanks to the use of a retro-reflector) Satellite 1:  210-5 rad (driven by the laser beam pointing) • Satellite X-axis pointing stability relative to the satellite-to-satellite direction (Merging of the needs of the satellite-to-satellite distance measurement and of the non-gravitational acceleration measurement): Driven by the laser beam pointing 10µrad/Hz 2µrad/Hz

  13. Derived control requirements Linear acceleration control (drag-free level) of each satellite along each axis. 10-8 m/s2/Hz Angular acceleration and angular rate control of each satellite about each axis. 10-6 rad/s/Hz • Formation control: • 10% on the relative distance • 510-3d along transversal directions 10-8 rad/s2/Hz

  14. Laser metrology budgets

  15. WP 2121 Measurement Technologies (ONERA)

  16. Input for accelerometer technology review (1/1) ACC2 ACC3 ACC1 ACC4 Concept 3 Linear acceleration Cross-track axis Y Radial axis Z Sat-Sat axis, X Scale factor stability Sat-Sat axis, X Cross-track axis Y Radial axis Z Linear acceleration bias Bias along Y < 210-7 m/s2 Bias along Z < 210-7 m/s2

  17. Input for accelerometer technology review (2/2) ACC2 ACC3 ACC1 ACC4 Angular acceleration • Angular acceleration around X: • from aZ1 – aZ3 et aY2 – aY4, • Angular acceleration around Y: • from aX2 – aX4 , • Angular acceleration around Z: • from aX1 – aX3

  18. Proposed concept of accelerometer X Z Y g • Short-term solution with TRL 9 • with levitation on-ground • GOCE/GRACE concept • 2 ultra-sensitive axes • 1 less-sensitive axis • 1 angular acceleration measure • Analogic or Digital control loop

  19. Improved GOCE solution Linear Acceleration • With 4 accelerometers: • aX given by ¼(aX1+aX2+aX3+aX4) • aY given by ½(aY1+aY3) • aZ given by ½(aZ2+aZ4) • Improvement wrt GOCE: • Temperature stability

  20. Improved GOCE solution X Z Y Angular Acceleration From linear accelerations From angular accelerations in spacecraft reference frame in S/C ref. frame in accelerometer reference frame

  21. Improved GOCE solution Angular Acceleration From Linear acceleration From Angular acceleration • Limitation LS axis: • Detector noise (limited by range = ±6 µm) • Contact Potential Difference • Gold wire damping

  22. Improved GOCE solution Temperature stability Scale factor Mechanical Temperature driven by accelerometer noise Tmec = 40 mK/Hz1/2 (1 mHz / f) Grad Tmec = 4 mK/Hz1/2 (1 mHz / f) Electronic Temperaturedriven by scale factor stability Telec = 40 mK/Hz1/2 (1 mHz / f) Range Control range 3.1 10-5 m/s2 Measurement range 6.4 10-6 m/s2 Bias • Improvement wrt GOCE: • Reference voltage of ADC2 Along Y (ACC 1, 3) 1.2 10-7 m/s2 Along Z (ACC 2, 4) 1.2 10-7 m/s2

  23. New concept for angular acceleration 55 mm (GOCE 70 mm) X Y Z • Cubic proof-mass for having 3 angular accelerations: • Proof-mass in PtRh10: 25x25x25 mm3, 0.315 kg • no more testable on ground • one linear & one angular freedom controlled by axis Other design Other design Additional studies are necessary

  24. Analogic control loop (GRACE) Advantages Consumption Size (FEEU electronic around ASH) Mass ASH with FEEU : 7.6 kg x 4 => 30.4 kg ICU* 3.7 kg x 4 => 14.8 kg 45.2 kg Consumption ASH with FEEU : 2.1 W x 4 => 8.4 W ICU* 7.1 W x 4 => 28.4 W 36.8 W * Could be reduced Digital control loop (GOCE) Advantages Detector/action redundancy K2 correction easy Mass ASH 5.2 kg x 4 => 20.8 kg FEEU 6.3 kg x 2 => 12.6 kg GAIEU 6.6 kg x 1 => 6.6 kg 40.0 kg Consumption FEEU 15 W x 2 => 30 W GAIEU 16.5 W x 1 => 33 W 63 W Improved GOCE solution Mass and power budget

  25. WP 2220 Attitude and Orbit Control Concepts (TAS-I)

  26. Activities since PM2 • Performed activities since PM2 and presentation content. • Answer to the PM2 TAS-I AI#1 : to identify the main effects driving the formation control. • Improvement of the formation flying control algorithm to reduce the init transient time. • Preliminary results of the algorithms to track Sat2 by Sat1 (in-line and pendulum geometries). • Support for system level analysis (e.g. fuel budget, presented elsewhere) and integration of the control laws in E2E simulator.

  27. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (1/6) AI#1: TAS-I to identify the main effects driving the formation control (are the causes of cross-track, radial bias driven by the spacecraft systems or by natural perturbations?) Pictures from PM2

  28. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (2/6) • The main effects driving the formation control performances are differential linear accelerometers biases. In particular, the worst effect come from the X-axis (along track) differential linear acceleration. This has been already addressed by Deimos at PM2. New results from E2E simulator will be presented hereafter. • These effects have been considered driver for algorithm design phase. • Taking into account the very low-control bandwidth that shall be considered for formation flying control design to do not corrupt to much the differential gravity acceleration, the Clohessy-Wiltshire equation in Hill reference frame are good enough to address the effects of differential bias on formation.

  29. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (3/6) • CWH model puts in evidence coupling between XZ axes (along-track/ radial), Y axis (across track) is uncoupled. Since the model is linear, the superposition principle may be applied. • If we apply a bias on X linear axis (along-track) only, then: • X-axis relative position grows in quadratic way; • Z-axis relative position grows in linear way. • If we apply a bias on Z linear axis (radial) only, then: • X-axis relative position grows in linear way; • Z-axis relative position remains bounded with an amplitude related to the applied bias. • If we apply a bias on Y linear axis (across-track) only, then: • Y-axis relative position remains bounded with an amplitude related to the applied bias.

  30. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (4/6) • As consequence of previous statements, the proposed formation control for the observation phase may be very simple. • The along track (X-axis) relative position shall be controlled. The controller shall embed the capability to estimate the differential bias and shall provide compensation for it (i.e. PID like controller). • Radial (Z-axis) and across-track (Y-axis) may be left without any specific control law. The observed formation drift is still compatible with the requirement up to 60 or more days mission. • The observation phase shall be preceded and followed by formation acquisition phases (based for instance on already available control algorithms developed during the previous study phases).

  31. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (5/6) No bias applied Differential bias X-axis 2e-7m/s2 About 12 days simulation time

  32. Answer to the TAS-I AI#1 Answer to the TAS-I AI#1 (6/6) Differential bias X-axis 2e-7m/s2 About 12 days simulation time

  33. FF algorithm update • Results for in-line formation (1/4) • Satellites’ relative position (PM2 result)Satellites’ relative position (now)

  34. FF algorithm update • Results for in-line formation (2/4) • Relative position (X-axis) Sat1 linear acceleration

  35. FF algorithm update • Results for in-line formation (3/4) • Relative position (X-axis) Relative position (YZ-axes)

  36. FF algorithm update • Results for in-line formation (4/4) • Sat1 linear acceleration

  37. Laser beam steered by attitude control Sat2 tracked by Sat1 (1/9) • Preliminary algorithms have been designed to implement the Sat2 tracking by Sat1 attitude control. The objective is to eliminate the Beam Steering Mechanism. • They have been designed considering the following attitude control objectives: • Satellite 1 • X-axis to null the laser beam mispointing (nP unit vector associated to the relative position Sat2-Sat1); • Y-axis normal to the plane constituted by ZLORF and nP • Z-axis in the remaining direction of the right hand orthogonal triad • Satellite 2 • LORF tracking • As expected, good results have been obtained for in-line formation. In the pendulum-case, the low-frequency angular accelerations are very high.

  38. Laser beam steered by attitude control Sat2 tracked by Sat1 (2/9) – In- line formation results • Angular acceleration Sat1 Angular acceleration Sat2

  39. Laser beam steered by attitude control Sat2 tracked by Sat1 (3/9) – In- line formation results • Linear acceleration Sat1 Linear acceleration Sat2

  40. Laser beam steered by attitude control Sat2 tracked by Sat1 (4/9) – In- line formation results • Relative position - Sat1 ref. frame Relative position – Sat1 ref. frame - zoom

  41. Laser beam steered by attitude control Sat2 tracked by Sat1 (5/9) – In- line formation results • Relative position – Sat2 ref. frame Relative position – Sat2 ref. frame - zoom

  42. Laser beam steered by attitude control Sat2 tracked by Sat1 (6/9) – Pendulum formation results • Angular acceleration Sat1 Angular acceleration Sat2

  43. Laser beam steered by attitude control Sat2 tracked by Sat1 (7/9) – Pendulum formation results • Linear acceleration Sat1 Linear acceleration Sat2 Y-axis linear acceleration control on Sat1 shall be modified in-order to increase the provided rejection.

  44. Laser beam steered by attitude control Sat2 tracked by Sat1 (8/9) – Pendulum formation results • Relative position – Sat1 ref. frame Relative position – Sat1 ref. frame - zoom

  45. Laser beam steered by attitude control Sat2 tracked by Sat1 (9/9) – Pendulum formation results • Relative position – Sat2 ref. frame Relative position – Sat2 ref. frame - zoom

  46. Activities from now to MAR • Activities from PM2 to Mission Architecture Review • Consolidation of the algorithms for the tracking of Sat2 by Sat1. • Definition of the actuators requirements for in-line and pendulum formations. • Definition of the star-trackers mounting architecture and accuracy. • Preparation of the TN4: “Candidate scenarios and AOCS concepts”. • Support for system level analysis.

  47. WP 2210 Mission Analysis (DEIMOS, presented by TAS-I)

  48. Atmospheric Density and Drag Study of Jacchia-Bowman new atmospheric model Spectral analysis Drag levels for polar orbits, function of LT and date Assessment of differential drag for Pendulum and In-line formations Formation Flying Stability Cartwheel formation 1-month open-loop simulations Gravity only Gravity + 3rd bodies Gravity + 3rd bodies + thruster bias 2 cases: Worst case: sat-2-sat line vertical over the Equator Best case: sat-2-sat line vertical over the Poles MA Activities since PM2

  49. Jacchia-Bowman 2006 Model (JB2006) Required by ECSS-E-ST-10-04C (Nov.2008) Better and more accurate mean total atmospheric density Valid for altitudes over 120 km Key novel features: New formulation of semi-annual density variation in thermosphere New formulation of solar indices Indices: F10.7 : radio energy flux S10.7: EUV radiation M10.7: MUV radiation Ap Atmospheric Density Example: densityWinter, 10:00 UTC Sun

  50. Influence of Orbital Parameters on Drag Assumptions Altitude: 250 km Fixed values of the solar/geomagnetic indices → Study the influence of other parameters Date / inclination: light influence Atmospheric Density Example: densityWinter, 10:00 UTC Sun

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