MICROSCOPE instrument in-flight characterization
Ratana Chhun, Emilie Hardy, Manuel Rodrigues, Pierre Touboul, Gilles Métris, Damien Boulanger, Bruno Christophe, Pascale Danto, Bernard Foulon, Pierre-Yves Guidotti, Phuong-Anh Huynh, Vincent Lebat, Françoise Liorzou, Alain Robert
MMICROSCOPE instrument in-flight characterization
Ratana Chhun , Emilie Hardy , Manuel Rodrigues , PierreTouboul , Gilles M´etris , Damien Boulanger , BrunoChristophe , Pascale Danto , Bernard Foulon , Pierre-YvesGuidotti ‡ , Phuong-Anh Huynh , Vincent Lebat , Fran¸coiseLiorzou , Alain Robert DPHY, ONERA, Universit´e Paris Saclay, F-92322 Chˆatillon, France Universit´e Cˆote d’Azur, Observatoire de la Cˆote d’Azur, CNRS, IRD, G´eoazur, 250avenue Albert Einstein, F-06560 Valbonne, France CNES, 18 avenue E Belin, F-31401 Toulouse, FranceE-mail: [email protected], [email protected],[email protected]
January 2021
Abstract.
Since the MICROSCOPE instrument aims to measure accelerations aslow as a few 10 − m s − and cannot operate on ground, it was obvious to have a largetime dedicated to its characterization in flight. After its release and first operation, thecharacterization experiments covered all the aspects of the instrument design in orderto consolidate the scientific measurements and the subsequent conclusions drawn fromthem. Over the course of the mission we validated the servo-control and even updatedthe PID control laws for each inertial sensor. Thanks to several dedicated experimentsand the analysis of the instrument sensitivities, we have been able to identify a numberof instrument characteristics such as biases, gold wire and electrostatic stiffnesses, nonlinearities, couplings and free motion ranges of the test-masses, which may first impactthe scientific objective and secondly the analysis of the instrument good operation. Keywords : MICROSCOPE, accelerometer, control laws, electrostatic stiffness, in-orbitcharacterization
1. Introduction
The goal of the Microscope mission is to test the Equivalence Principle in orbit,measuring and comparing the fall in the Earth gravitational field of two concentricmasses [1] with an accuracy of 10 − . The Microscope satellite embarks two differentialaccelerometers, T-SAGE, which compare the accelerations needed to maintain the twomasses on the same orbit. A non null differential signal collinear to Earth’s gravity field ‡ Current address: AIRBUS Defence and Space, F-31402 Toulouse, France a r X i v : . [ a s t r o - ph . I M ] F e b ICROSCOPE T-SAGE characterization
2. Test-mass clamping, release and first control
Fearing damage at the core level of the instruments due to the launch vibrations,the whole instrument is maintained hyperstatic by clamping the four test-masses witha blocking mechanism consisting of 6 fingers or stops slightly inserted at each oppositetest-mass faces (3 at each end as shown in Fig. 1). Once the satellite was in orbit onthe 26 th of April 2016 and well operating, the first switch-on of the four inertial sensorswas realized on the 2 nd of May 2016. The global commissioning phase started then. Figure 1.
Left: open core during integration showing inner test-mass resting onlower stops, upper clamp not present. Right: Axes representation for one test-masssurrounded by the two X control electrodes.
After checking the thin 7 µ m gold wire connecting electrically the test-masses [4], ICROSCOPE T-SAGE characterization X axis, the controlaccelerations trying, in vain, to bring the masses back to their equilibrium position. Onother axes, acceleration and position outputs are different from zero when taking intoaccount machining and integration defaults for each test-mass. The general behavioris that it is pretty much aligned with its surrounding electrode cage, as deduced fromobserving the radial Y , Z , Θ and Ψ axes, but twisted around its axial axis as observedfrom Φ axis measurement (the reference frame is described in Fig. 1). This is likely dueto the misalignment between all 6 clamping fingers no matter which end they are at. Figure 2.
First control of IS1-SUREF (inner test-mass), accelerations and positionsof all 6 degrees of freedom converge to zero at first switch on of the instrument
Once retracted by a few tens of microns, the fingers act as stops which limit themotion range of each test-mass. Indeed the fingers do not clamp anymore the test-massbut do remain slightly inserted to limit the mass motion along and around all axessimultaneously. The observation of their 48 acceleration and position outputs lifts alldoubts: the test-masses are servo-controlled to the center of their respective electrodecages, as shown in Fig 2 for the SUREF (IS1 for inner test-mass, IS2 for the outertest-mass). SUEP presents the same behavior. Φ rotation is the axis which convergesthe slowest. The X axis displacement converges from its initial 75 µ m position. Theradial axes Y , Z , Θ and Ψ converge following a common pattern from an uncontrolledinitial position. All these observations of the proof-mass meet the expected behavior ofthe servo-control performed by simulation.Still subsequent frequency analyses of the acceleration outputs over the course of thefollowing few months, have shown that the control laws initially defined before launch ICROSCOPE T-SAGE characterization
3. Control laws optimization
The electrostatic sensor control loop is schematized in Fig. 3. The test-mass issurrounded by a set of electrodes, so that a test-mass motion induces a variation of thegaps between the mass and the electrodes in regard, and therefore a variation of thecorresponding capacitance. This variation is measured by a capacitive detector whoseoutput signal is digitized. By combining the outputs of the different electrode couples,the test-mass position and rotation are deduced along the six degrees of freedom. Acorrector computes the voltage to be applied onto the electrodes in order to compensatefor the test-mass motion and to keep it centered. The computed voltage is convertedback into an analog signal before being amplified. An electrical potential is appliedasymetrically by the electrodes in order to develop an actuation force opposed to the test-mass displacement. The electrostatic actuation keeps the test-mass motionless insidethe satellite, and therefore provides a measurement of the acceleration necessary tocompensate all other “natural” accelerations of the test-mass relatively to the satellite.Ref. [4] gives the detailed operation and equations of the electrostatic accelerometeralong all axes.
Figure 3.
Representation of an SU test-mass servo-control
The corrector is a PID-type (proportional-integral-derivative) controller imple-mented into a Digital Signal Processor (DSP). The digital controller operates at 1027 Hzand delivers data to the satellite at a 4 Hz rate. The PID blocks are modelized by aparallel scheme as in Fig. 4. It is surrounded by a second order low-pass filter upstreamand a first order low-pass filter downstream.The choice of the control loop parameters is constrained by the electrostaticconfiguration, the mission operational specifications and the instrument performanceobjectives.
ICROSCOPE T-SAGE characterization Figure 4.
Representation of the controller, as implemented in the ICU. The value ofthe gain and frequencies are presented in table 1
The satellite Drag-Free Attitude Control System (DFACS, [1, 5]) compensates theenvironmental perturbations applied to the satellite. The resulting residual accelerationaffects in common mode both concentric test-masses. The DFACS is started with theaccelerometers in their Full Range Mode (FRM) and performs a fine control of thesatellite attitude making use of the star sensors in order to reduce the angular motiondisturbances. Then the accelerometers are switched to their High Resolution Mode(HRM) in order to allow the DFACS to control the 6 degrees of freedom. Ref. [5] detailsthe DFACS operation and performances. As the output of the accelerometers are usedby the DFACS to control the satellite, the accelerometer servo-loop is designed to allowsufficient gain margins and stability to the DFACS loop. The accelerometer range designtakes into account the maximum applied acceleration in both modes (FRM and HRM)within the measurement bandwidth and takes into account some margins for out-of-the-band transients due to satellite cracking, micro-meteorites and cold gas propulsionpotential defects. Micrometeorite impacts are possible within the orbital environment,the accelerometer must sustain sudden shocks without the mass hitting the stops: thePID has been designed to counteract a debris momentum transfer of a few 1 . × − N sequivalent to a satellite instantaneous velocity variation of 5 × − m/s.Within the control range, the measurement range corresponds to the domain inwhich the output data provided by the instrument is not saturated. The predictedinstrument noise and bias constrain the test-mass measurement range, as the sum ofthe bias and the noise spectral density integration shall fit with margin within the range.The PID parameters for the control loop of the two identical internal test-massesof SUEP and SUREF have been defined while taking into account these requirements.The parameters of the external test-masses were then deduced by adjusting the controlloop gain in proportion to the mass in order to keep the same bandwidth properties.The parameter set has been tested on ground during the free-fall test of theinstrument in the drop tower of the ZARM institute [4], with a modified electronicsconfiguration with respect to the flight configuration in order to take into accountthe short free-fall duration of less than 10 seconds and higher disturbing environment. ICROSCOPE T-SAGE characterization − Hz , out of the measurement frequency band. Theseresonances in the control loop (Fig. 5) have a larger impact on SUEP than SUREF.This lines can disturb the calibration tests during which a stimulus signal needs tobe injected into the DFACS or instrument loop. It was therefore decided to adjustthe controller parameters in flight in order to decrease the amplitude of those spectrallines. This was achieved by decreasing the PID gain in this frequency range that leadsto reduce the frequency bandwidth. For that purpose the performances of the PIDcontroller have been computed for different sets of parameters. The set providing themaximal attenuation of the gain around 10Hz, while keeping acceptable values for thegain and phase margins, was selected. The drawback of this new PID adjustment is thephase shift higher than the requirement. As the accelerometers measurements are usedin the DFACS loop, it results in a delay in the DFACS loop. However, thanks to theremarkable performances of the DFACS [5], this additional delay remains acceptable.The new PID adjustment was tested in flight during dedicated sessions, enabling usto confirm that the test-masses were servo-controlled at the center of their electrostaticcages and that the attenuation of the components at high frequencies was highlyimproved (see figure 5). Figure 5.
Acceleration spectrum density before (left)/after (right) the change of PIDon SUEP X axis, inner (red line) and outer (blue line) test-masses Each axis of the four test-masses has its own well-tuned PID. The final set of
ICROSCOPE T-SAGE characterization
X Y /Z
Φ Θ / ΨUpstream cutoff frequency f P reLP (Hz) 10 30 10 15Gain K p for SUEP and SUREF internal test-masses -2 18.5 -35.2923 50.87Gain K p for SUEP external test-mass -1.9957 2.22 -1.7222 5.86Gain K p for SUREF external test-mass -3.0025 5.0129 -7.7635 13.1390Integral cutoff frequency f I (Hz) 0.004 0.1 0.01 0.1Low derivative cutoff frequency f D (Hz) 0.05 0.25 0.08 0.25High derivative cutoff frequency f D (Hz) 1 20 5 7Low-pass cutoff frequency f C (Hz) 5 25 5 10Downstream cutoff frequency f P ostLP (Hz) 10 30 10 15
Table 1.
Parameters of the instrument control loop PID controller (see figure 4) forthe four test-masses in HRM mode
The controller performance has been evaluated on ground before the mission usinga software simulator of the instrument dynamics (see Fig. 6) on the basis of the schemain Fig.4. The instrument model, designed in Matlab ® /Simulink, simulates the motionof a test-mass along each axis, and the rotation about each axis. The input of thesimulator is the external non-gravitational acceleration applied on the test-mass. Adouble integrator computes the test-mass displacement or rotation along the chosenaxis, taking into account the potential rebounds of the mass if it hits the stops. Thesimulation of a velocity step as specified for a piece of debris is performed by adding asignal in the double integrator box, between the two integrators.The capacitive detector is modeled by a first order transfer function followed bya saturation representative of the electronics and provides a voltage proportional tothe measurement of the test-mass position and converted to a digital number by ananalog-to-digital converter [4]. The PID block uses this measurement to compute thevoltage to be applied onto the electrodes in order to control the test-mass motionless.Its output is converted into an analog voltage amplified by the Drive Voltage Amplifier(DVA) represented by a first order transfer function and a saturation. The computedvoltage is applied to the electrodes surrounding the test-mass and results in an additionalelectrostatic force. The stiffness of the instrument (see section 4.1) is modeled by a gainintroducing an effect on the test-mass position offset in the electrostatic actuation. Theclosed loop transfer function of the instrument, computed by the software simulator, isrepresented in Fig. 7. Its corresponding characteristics are presented in table 2. Thetransfer function at low frequency has been optimized in order to keep a phase shift lowerthan 28 ◦ at 0.1Hz for the DFACS stability needs. The noise and bias of the instrument ICROSCOPE T-SAGE characterization . × − m/s which corresponds to the impact of a micrometeorite with a momentumof 10 − N s considering the mass of the satellite: such event was expected to occur twicea month by CNES and thus during most of the science sessions. The response to themaximum momentum of 1 . × − N s was also simulated but corresponds to a smallerprobability (twice a year). As specified the test-mass does not reach the stops. SUEPfeatures the same performance as SUREF except for the autosaturation of IS2-SUEPbeing half the IS2-SUREF values because of the bias voltages applied on electrodes [4]that modify the range.
Figure 6.
Representation of the instrument control loop in the Simulink tool
Figure 7.
Bode diagram of the closed-loop transfer functions of the accelerometeralong the different axes. The transfer functions are identical for the four test-masses
ICROSCOPE T-SAGE characterization
X Y /Z
Φ Θ / ΨBandwidth (Hz) 0.62 1.8 1.0 1.6Overshoot ( a ) (dB) 1.3 1.0 1.2 1.4Gain margin (dB) 16.4 19.2 15.0 14.9Phase margin ( ◦ ) 53.9 60.6 60.3 47.9Phase shift ( ◦ ) ( b ) ( c ) IS1 9.3 47.0 44.2 53.9IS2-SUEP / SUREF 5.0 / 6.3 12.5 / 27.9 4.4 / 9.5 11.7 / 20.4(% of the range)
Table 2.
Performance of the instrument control loop computed by the simulationsoftware: bandwidth is calculated at -3dB; (a): the maximum overshoot gain in thefrequency range [0.005Hz-0.2Hz]; (b): the phase shift is considered at 0.1Hz of theaccelerometer output for the DFACS, it takes into account the PID transfer function,the anti-aliasing filter and the mean filter; (c): the saturation in the control loop isevaluated as the sum of the bias and of the 5 σ -noise. IS2-SUEP has better phase shiftand autosaturation performance than its SUREF counterpart. Figure 8.
Step response of the accelerometer X axis control loop when undergoingan impact with a 10 − N s momentum
4. Instrument characterization
The mission did not only consist of scientific measurements. In order to improvethe knowledge on all the aspects of the instrument and potentially understand anumber of observations on the measurements, several characteristics of the electrostatic
ICROSCOPE T-SAGE characterization meas i = Γ i + K i Γ app i + k i m d i + K i Γ app i + (cid:88) j Ct j,i Γ app j + (cid:88) j Cr j,i ˙Ω j + n i (1)Γ i is the measurement bias along “ i ” axis, Γ app i is the actual acceleration closeto Γ meas i by a scale factor K i , k i m is the stiffness inducing an additional bias when thetest-mass is displaced at a distance d i with respect to its equilibrium position ( m beingthe mass of the test-mass), K i is the quadratic factor, Ct j,i represent the couplingswith the linear accelerations Γ app j along “ j ” axes, Cr j,i represent the couplings with theangular accelerations ˙Ω j about “ j ” axes and n i represents the measurement noise. One important characteristic of the electrostatic accelerometer is the electrostaticstiffness. This characteristic induces into the acceleration measurement a biasproportional to an offcentering of the test-mass with respect to its electrostaticequilibrium or zero position.By introducing a periodic motion signal successively along each test-mass axis(equation 2), it is possible to measure a periodic acceleration proportional to themotion because of the stiffness. The stiffness was assessed in flight during thecommissioning phase then assessed again at the end of the mission with a differentelectrical configuration (see figures 9 and 10) using a least-square method on thedisplacement and the corresponding acceleration sines in equations 2 and 3. d i ( t ) = d i sin(2 πf cal t + ψ ) , d (cid:54) = i = 0 (2)Γ i = Γ exc i + Γ i + k i m d i (3)where Γ exc i = [ T − In ] i,i d i − ¨ d i (4)Γ exc i includes the kinematic effect of the displacement in the satellite reference frameand the Earth gravity gradient effect: the definition of the matrix of inertia [In] and ofthe gravity gradient matrix [T] is detailed in Ref. [1]. At the oscillation frequency f cal ,the angular velocity Ω is inferior to 4 × − rad/s . Considering the mass excenterings (afew µm ), the effect of [In] on the acceleration measurement is negligible with respect tothe stiffness effect. The term in ˙ d i is missing in equation 4 because the resulting effectis orthogonal to the “ i ” axis. Disturbing terms could potentially occur with the DFACSresidual angular acceleration lower than 4 × − rad/s at f cal and by considering thestatic offcentering of a few tens of micrometers, but this effect leads to a negligible effect. ICROSCOPE T-SAGE characterization d i (about 2 × − m/s − )has to be considered and is indeed corrected from the measurement before stiffnessassessment. The results in table 3 take these considerations into account. Figure 9.
Stiffness measurement on SUEP IS1 X (axial) axis in High ResolutionMode: a sine signal input sets the mass in motion, displacement and correspondingacceleration are compared to obtain the stiffness, signals are in phase, interpreted asmain gold wire influence By design the electrostatic stiffness, or torsion constant in rotation, is expectedto be very low on the sensitive axes X and Φ because of the principle of capacitivesensing on these axes based on the variation of overlap of electrode over test-mass. Tobe accurate the control of Φ axis is a mix of gap variation and overlap. However theactual stiffness measurements (see table 3) turn out being higher than expected (exceptaround Φ axis of IS1-SUREF). Do note that these results, while approximated withrespect to [6] remain comparable and compatible.Along the X axis this is likely due to the gold wire which induces a mechanicalstiffness. The influence of the gold wire is indicated by the positive sign of thestiffness indicating a stabilizing effect in reaction to a displacement of the test-mass.On the external mass of SUREF, the effect of the gold wire is very strong while thetorsion constants around Φ axis are negative on the masses of SUEP, which means theelectrostatic stiffness is greater than expected, and compensates the effect of the goldwire. The internal mass of SUREF is the only one featuring a stiffness compatible withthe theory. From one mass to another, the stiffness due to the gold wire is subject tovary a lot because it is dependant on its mechanical integration inside the core. Giventhe nature of the 7 µm diameter gold wire and the procedure to glue it by both ends,the mechanical behavior of the gold wire when the mass is displaced is quite difficult topredict beforehand and to reproduce. By considering the free motion ranges presentedin table 5, especially in SUEP, it can also be argued that the proof-mass is quite close to ICROSCOPE T-SAGE characterization mV instead of 15 mV . InSUREF, these patch effects would have to be 20 times greater, which is highly unlikely.Axis IS1-SUREF IS2-SUREF IS1-SUEP IS2-SUEPX( × − N m − ) 0.84 ± ± ± ± ∼
0) ( ∼
0) ( ∼
0) ( ∼ × − N m − ) -1.52 ± ± ± ± × − N m − ) -1.52 ± ± ± ± × − N m rd − ) 0.0 ± ± ± ± × − N m rd − ) -1.75 ± ± ± ± × − N m rd − ) -1.85 ± ± ± ± Table 3.
Measured and expected (between brackets) stiffnesses and torsion constantsin High Resolution Mode; theoretical values have been computed before flight assuminga perfect and simple electrostatic configuration and a negligible stiffness of the wire
On the radial axes Y , Z , Θ and Ψ, the capacitive sensing is based on the variationof distance between test-mass and electrode thus generating a negative stiffness whichtends to destabilize the equilibrium of the test-mass as opposed to the gold wire stiffnesseffect. On this basis, the stiffness only depends on the geometrical configuration and thevoltages applied on the electrodes and the test-mass. The results obtained (see table 3)are quite comparable between the two internal masses of each SU since their electrostaticconfigurations are identical. They are slightly different between the two external massesbecause the voltages applied on the electrodes are also slightly different. The discrepancybetween the results and the expected values is explained by the simplification of thetheoretical electrostatic model and configuration.The electrostatic main origin of the stiffness on the radial axes is also pointedout by the differences between the values measured during the campaigns led in HighResolution Mode and in Full Range Mode, meaning the polarization voltage applied onthe mass is different with respect to the mode (respectively 5V and 40V). In Full RangeMode, the stiffnesses see their amplitude increased although not by a factor strictlyequal to the square of the potential difference between the mass and the electrodes asthe gold wire also has an influence independent of the electronics configuration albeitless impacting.On the contrary, the stiffness along X axis and the torsion constant around Φaxis are hardly affected by the change of the polarization voltage value, indicating the ICROSCOPE T-SAGE characterization Figure 10.
Stiffness measurement on SUREF IS2 Y (radial) axis in High ResolutionMode: a sine signal input sets the mass in motion, displacement and correspondingmeasured acceleration are compared to obtain the stiffness, signals are in opposition,interpreted as main electrostatic influence electrostatic part represents a minor contribution to the global stiffness essentially dueto the gold wire. The bias of each axis is periodically measured in order to be fed to the DFACS andminimize gas consumption among purposes, by biasing the DFACS so that it does notpointlessly compensate the instrument linear biases. Figure 11 presents the evolution ofthe bias along the X axis of each inertial sensor. For this axis but more globally alongall axes, the bias is quite stable over the whole mission, especially over the second halfof the mission when the electronics configuration has attained its pretty much final formas opposed to the first half and especially around the first few months of the mission,when the biases were prone to variation as we were still adjusting the electronics. Thisis particularly observable towards the end of August 2016 on the external SUREF test-masses. The test of the equivalence principle has been performed several times over thecourse of the mission. The test performance is limited for an important part by thenoise of the acceleration measurement. The spectra of the residual accelerations fromall the test sessions, with the gravity field signal removed, have been plotted to comparethe quality of the different sessions. Fig. 12 shows the spectra for the SUEP, smoothedusing sliding frequency windows and linear interpolation between the central points of
ICROSCOPE T-SAGE characterization Figure 11.
Bias evolution over the course of the 2-year-long mission along the X axisof each inertial sensor linear regressions applied on each of these windows. Since the duration of the sessionsvaries a lot from one to another, they are all normalized to 120 orbits.In the measurement bandwidth [10 − − − ] Hz , we can observe that all but 3sessions have a similar spectrum level in Fig. 12. The first 2 sessions, numbers 80 and86, feature a higher noise level than the pack, the very first test being the noisier. Session430 is characterized by a different configuration as both differential accelerometers areswitched on and thus the operating temperature is higher. Albeit shorter in duration,once normalized, the spectrum is much lower than in the other sessions.By comparing the noise value at a given frequency for every session, it is even moreapparent that, over the course of 2 years of mission, the noise level decreases while thespectrum keeps the same shape.The improvement starts at the time the measurement frequency is chosen to behigher in rotating mode, around 3 × − Hz instead of around 10 − Hz . But it is notestablished whether the improvement is due to this new configuration or to environmentand more general mission conditions less favorable during the first months of thescientific mission.This behavior is observable on both SUREF and SUEP accelerometers. Theimprovement starts around the same time rejecting the potential influence of the changeof the control laws, which occurred at very different dates for each SU. Improvementof noise with time has been observed in Lisa Pathfinder [7] due to pressure diminutionwith time. In MICROSCOPE, the core is enclosed in a hermetic vessel and cannot takeadvantage of a reduction of pressure due to the residual gas escaping to space vacuumas in Lisa Pathfinder. It is probably due to a different phenomenon. ICROSCOPE T-SAGE characterization Figure 12.
Noise comparison between all EP test sessions with SUEP, normalized to120 orbits
When dissymmetries of geometrical or electronic nature are taken into account,a disturbance acceleration depending on the square of the acceleration applied on theelectrodes has to be considered. This term is proportional to the coefficient defined asthe quadratic factor, K .To estimate this term, a periodic acceleration signal is input inside the accelerometercontrol loop (along the investigated degree of freedom) in order to generate a periodicterm due to K (see figure 13). This signal is based upon a sine signal at a frequency f s higher than the measurement bandwidth and of amplitude A s , modulated by a squaresignal of which the frequency f c is well inside the bandwidth. Due to K , a signalproportional to it is generated and its components are at 2 f s and DC . By selecting f s outside the measurement bandwidth, both components at f s and 2 f s are not visible inthe output measurement. But by modulating the sine signal with the square signal, the DC component is measurable in the output as a periodic square signal at frequency f c and of amplitude proportional to K and the square of A s as expressed in equation 5. ICROSCOPE T-SAGE characterization Figure 13. K measurement: expected acceleration input and output signals Fig 14 shows a measurement example and the resulting fit by a square signal estimatedby a least-square method. The summary results for the linear axes are presented intable 4. Γ meas = Γ + 12 K A s (5)Axis IS1-SUREF IS2-SUREF IS1-SUEP IS2-SUEP X ( s /m ) 2520 ±
796 1250 ±
868 7260 ±
344 565 ± Y ( s /m ) 770 ±
27 -120 ± Z ( s /m ) -5560 ±
313 22.5 ± Table 4.
Quadratic factors estimated with a least-square method compared tospecification between brackets, SUEP radial axes measurements did not give anysignificant result
For calibration purpose it is necessary to displace one of the test-mass along oraround one of its degree of freedom by a few microns. Dedicated sessions have beenset up in order to estimate the range margins for the amplitude of the displacementand to better evaluate the disturbances related to the distance test-mass/finger stops.The clamping fingers used during the launch are retracted from their initial position
ICROSCOPE T-SAGE characterization Figure 14. K measurement on IS1-SUREF Y (radial) axis: a square modulated sinesignal input in acceleration generates a square signal, the amplitude is proportional to K , identified by a least-square fit at +75 µ m for SUEP and +90 µ m for SUREF to a new theroretical position of -75 µ m.Thus after launch these stops limit the motion range of the mass to prevent any electricalcontact with the electrodes. Because of the ball-point shape of the finger stops tips andthe conic-shaped holes on the test-mass section facing the stops, and because of theaccuracy of the realization and the assembly of these parts, the range can be reducedby several tens of microns.On top of that the capacitive equilibrium due to the servo-control may be differentfrom the geometrical equilibrium.The dedicated sessions for motion range evaluation have been performed in orbitwith a triangle signal injected as a position secondary input along or around each axissuccessively for each mass. The input signal starts from zero and takes 5 minutes toreach a peak which is set to a value over the maximum of the detector range. Performedin Full Range (FR) mode, the detector range is much higher than the theoretical physicalrange and allows to observe the actual free motion range. Performed in High Resolution(HR) mode, we observe the saturation of the detector near 30 µ m which is the HRMrange lower than the free motion. The measurements in HR mode are still interestingbecause it is the mode commonly used for scientific measurements and give valuableinformation on the mass behavior when it is excentered.So in FR mode, each mass is displaced towards one direction then the opposite.The maximum range in one direction is considered attained when the test-mass is notfree of motion anymore along or about at least one of its degrees of freedom, observed ICROSCOPE T-SAGE characterization X axis by about 30 µ m for IS1-SUREF and 25 µ m for IS2-SUEP, deducedfrom ground test capacitance measurements. This leads to recenter a little IS1-SUREFand IS2-SUEP test-masses. Then, only IS1-SUEP proof-mass presents a critical freemotion of only 8.1 µ m in the X axis positive direction, which increases the noise and biasdue to patch effects. However, the bias effect is quite negligible when considering a fewtens of mV for this phenomenon. The others axes are less sensitive to capacitive bordereffects. However, SUEP has a narrower cage in which the mass can move freely which islimiting for scientific measurements requiring excentered sessions (some characterizationsessions or even scientific sessions could have benefited from a greater offcentering, tomagnify some disturbing effects). The SUREF meets most integration expectations (ifnot the design values).Axis IS1-SUREF IS2-SUREF IS1-SUEP IS2-SUEP X ( µm ) -78.9 33.7 -36.1 39.2 -32.7 8.1 -55.2 11.3(-34) (39) (-34) (51) (-44) (37) (-49) (24) Y ( µm ) -43.8 63.7 -69.6 57.3 -21.2 24.1 -18.5 25.3(-34) (39) (-34) (51) (-44) (37) (-49) (24) Z ( µm ) -66.2 44.0 -62.0 47.0 -10.8 29.0 -23.1 17.5(-34) (39) (-34) (51) (-44) (37) (-49) (24)Φ( µrad ) -2430 3225 -2290 1120 -6085 515 -457 1350(-1932) (2216) (-1043) (1564) (-2500) (2102) (-1503) (736)Θ( µrad ) -717 1567 -952 852 -577 2028 -519 1228(-1567) (1797) (-852) (1278) (-2028) (1705) (-1228) (602)Ψ( µrad ) -1450 1567 -1095 852 -630 2028 -617 1228(-1567) (1797) (-852) (1278) (-2028) (1705) (-1228) (602) Table 5.
Measured and best guess from mechanical geometry (between brackets) freemotion ranges in both directions per axis. The best guess free motion is computedtaking into account cumulated metrological deviances without taking into accountpotential signs and without taking into account capacitive defects which might biasthe measured position.
On the bright side these results demonstrate that in regular operation (massescentered or with less than 5 µm excursion during calibration), the instrument worksnominally with no mechanical hindrance. ICROSCOPE T-SAGE characterization
The couplings between the three translation axes and the three rotation axes of theinstrument introduces a dependency between the six ideally completely independentaxes. The couplings disturb the measurement by creating an additional term tocompensate for the projection of the test-mass motion along the other axes. Withthe six axes working simultaneously, coupling from a first axis will cause the controlvoltage on a second axis to react, which in turn creates a coupling effect on a third axis(for a negligible effect though).Dedicated technical sessions have been performed in order to characterize thecouplings in flight [3]. A sine signal is applied in the instrument control loop toforce an oscillation of the test-mass position along the X axis during 100 s with alow frequency f tech = 0 . Hz outside the control bandwidth of the DFACS systemwhich is set to compensate for the motion of the other test-mass. Then a sinusoidwith the same frequency but a different amplitude is induced in the satellite motionalong the Y axis during 100 s , and finally along the Z axis during 100 s . The impacton the measurement of the other axes (see figure 15) of this excitation at a well-knownfrequency is studied in order to extract the coupling values. Do note that specificscientific sessions are dedicated to the estimation of linear couplings towards the X axis differential acceleration though since these couplings are an important part of thecalibration described in [2].In order to extract the coupling values, a software simulator is used that modelizesthe DFACS and accelerometer servo loops. It is based on the one-axis model of theinstrument control loop presented in [1]. This model is duplicated for the three linearaxes of the internal sensor IS1 and the three linear axes of the external sensor IS2. Foreach axis, the DFACS control loop is represented. The DFACS control block, modelizedby a fourth order transfer function and a phase delay, is set to compensate the motion ofthe external test-mass. The acceleration of both test-masses along each axis is injectedon the other axes through the coupling parameters.The acceleration measurement is fitted with a sinusoidal function at f tech with aleast-square method in order to determine its amplitude along each axis for the threeexcitation periods. The value of the simulated coupling factors is adjusted so that theamplitude of the simulated acceleration is as close as possible to the amplitude measuredin flight. The adjustment is made to determine first the impact of the acceleration alongthe X axis on the Y and Z axes using the first excitation period, then Y on X and Z using the second period and finally Z on X and Y using the third one. As eachaxis impacts the others, the adjustement process is repeated until convergence of thecoupling factor values. The results are presented in table 6. ICROSCOPE T-SAGE characterization Figure 15.
Accelerometer measurements during technical session 516 along the linearaxes of the internal sensor (IS1) and the external sensor (IS2) for the SUEP. A sineexcitation signal is introduced during 100 s first on the X axis, then on the Y axis andfinally on the Z axis. The impact of this excitation on the other axes is due to thecouplings between the axes. This characterization is useful to use the acceleration measurement in common
ICROSCOPE T-SAGE characterization ( ∗ ) IS2-SUEP ( ∗ ) X → Y . × − ± × − − . ± × − X → Z . × − ± × − − . ± × − Y → X − . × − ± × − − . × − ± × − Y → Z . × − ± × − . × − ± . × − Z → X − . × − ± × − − . × − ± × − Z → Y − . × − ± × − − . × − ± × − Table 6.
Linear to linear coupling factors determined by an iteration process forthe internal sensor (IS1) and the external sensor (IS2) for the SUEP and associatedleast-square error. ( ∗ ) A few % error of the simulation models also has to be takeninto account and leads to a systematic error of the order of 0.05 to be added to theleast-square error. mode for other applications of the data. In differential mode, the calibration sessionsare much more accurate and show in particular a very small coupling from radial axestoward the X axis (less than 10 − ) [2]. The coupling factors in table 6 are establishedat 0.1 Hz. The consequence is that these estimated couplings have to be corrected fromthe transfer function to get estimated values near EP frequencies of interest [0.0009 Hz- 0.0065 Hz]. Furthermore, the DFACS loop has been simplified and its parametersestimated on the basis of a fit response to particular signals. The error of the modelshould represent a maximum of 0.05 (depending on the measurement axis, frequencyof stimuli and model error). When using the calibration sessions, the couplings indifferential mode are compatible with table 6 results within the presented accuracy.The strong coupling of acceleration along X upon Y or Z is explained by the impactof the applied voltage for X electrodes to compensate the bias on the stiffness of Y or Z control forces. The equations are detailed in Ref. [4] and can be summarized for theelectrostatic control acceleration along Y as an example :Γ y ∼ k v y + α y ( V py + v y + v ψ ) y + α z ( V pz + v z + v θ ) y + α x ( V px + v x ) y + α φ ( V pφ + v φ ) y (6)where k is the physical gain for the Y control, V pw is the difference of reference voltagesbetween test-mass and electrodes controlling the w degree of freedom, α w is a geometricalfactor, v w is the voltage calculated by the digital controller for each degree of freedomand y the displacement along Y as the one resulting from the bias of the electronics.In the case of SUEP, the gold wire stiffness is quite large and leads to have a controlvoltage v x = v x + v x t while on others axes v w has a mean value close to zero. At firstorder, the acceleration along Y presents a term 2 α x v x v x t y . That means that an appliedacceleration along X will induce a controlled voltage variation of v x t proportional tothe acceleration which will be also measured along Y with the scale factor 2 α x v x y .As a small offcentering exists along all axes, this effect is not so negligible as shown intable 6. The on-ground metrology of the different parts give an order of magnitude of ICROSCOPE T-SAGE characterization X towards all others axes. The measurement of the couplings from the angular axes to the linear axes hasbeen performed on each SU with a different approach. The principle is to induce anangular oscillation in the instrument environment and observe its influence on the linearacceleration measurements. The amplitude of the sine signal along the linear axis isestimated by a least-square method and compared to the estimated oscillation signal tofinally give the angular to linear axis coupling for that axis (the results are presented intable 7).With the drag-free and attitude control centered on the external mass, the satelliteis summoned to perform a sine oscillation motion around each of the three axesconsecutively. During each oscillation, we estimate the amplitude of that motion throughthe external mass acceleration around the oscillation axis. This acceleration is then usedas a base of comparison with each linear axis acceleration measurement of the internalmass, which actually is the differential acceleration along that axis given the drag-free setting. This measurement Γ meas is corrected from the effect of the relative massexcenterings ∆ coupled to the satellite angular motion and the Earth gravity tensor.Once this term [( T − In )∆] is corrected from, the actual coupling C j,i for each axis isevaluated (see equation 7).Γ meas,i = Γ ,i + C j,i ˙ ω osc,j + [( T − In )∆] i (7)where i designates a linear axis, j an angular axis and ˙ ω osc,j the angular accelerationdue to the satellite motion around axis j .( m/s ) / ( rad/s ) SUREF SUEPΦ → X − . × − ± . × − . × − ± . × − Θ → X × − ± . × − − . × − ± . × − Ψ → X × − ± . × − − × − ± . × − Φ → Y . × − ± . × − − . × − ± . × − Θ → Y − . × − ± . × − − . × − ± . × − Ψ → Y − . × − ± . × − − . × − ± . × − Φ → Z . × − ± . × − . × − ± . × − Θ → Z − . × − ± . × − . × − ± . × − Ψ → Z . × − ± . × − . × − ± . × − Table 7.
Angular to linear differential couplings computed by comparison of least-square method estimations of acceleration measurement during dedicated satelliteoscillation sessions.
Considering a restitution error of the angular acceleration control of 10 − rad / s at ICROSCOPE T-SAGE characterization f EP [1] , the maximum effect on X axis is less than 2 . × − m / s which is compatible with the EP test resolution objective of 10 − .
5. Conclusion
While not a direct part of the scientific extraction of the EP signal, thecharacterization of the instrument helps better understanding the instrument andits measurements especially at times when they do not behave as expected. Theconsequences of this knowledge acquired thanks to the characterization range fromorienting the scenario or modifying the instrument parameters (during the mission) toimprove its behavior to simply going towards the validation of the EP test. In the endeverything learned about the instrument during the MICROSCOPE mission is valuableknowledge for the use of data by others teams to test the EP or any other physics andfor the development of future accelerometer instruments.
Acknowledgments
The authors express their gratitude to all the different services involvedin the mission partners and in particular CNES, the French space agency incharge of the satellite. This work is based on observations made with the T-SAGE instrument, installed on the CNES-ESA-ONERA-CNRS-OCA-DLR-ZARMMICROSCOPE mission. ONERA authors’ work is financially supported by CNESand ONERA fundings. Authors from OCA, Observatoire de la Cˆote d’Azur, have beensupported by OCA, CNRS, the French National Center for Scientific Research, andCNES. ZARM authors’ work is supported by the DLR, German Space Agency, withfunds of the BMWi (FKZ 50 OY 1305) and by the Deutsche ForschungsgemeinschaftDFG (LA 905/12-1). The authors would like to thank the Physikalisch-TechnischeBundesanstalt institute in Braunschweig, Germany, for their contribution to thedevelopment of the test-masses with funds of CNES and DLR.
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