Development Status of the ESA Micro-Newton Thrust Balance IEPC-2011-011 Presented at the 32nd International Electric Propulsion Conference, Wiesbaden • Germany September 11 – 15, 2011 J. Pérez Luna1, C.H. Edwards2 and J. Gonzalez del Amo3 European Space Agency, ESTEC, Noordwijk, 2201 AZ, The Netherlands. B. Hughes4 National Physical Laboratory, Teddington, Middlesex, United Kingdom.
Abstract: A number of future space missions require low-noise micro-thrusters in order to guarantee accurate spacecraft attitude and position control with stringent requirements. In order to develop and qualify thrusters which fulfill these requirements, missions need a high performance measurement system capable of making dynamic thrust measurements in the µN range. The European Space Agency (ESA) is developing a MicroNewton Thrust Balance (µNTB) to improve measurement coverage of the mission requirements and to offer measurements accredited to ISO 17025 in the µN range with traceability to international standards and rigorous uncertainty evaluation. An engineering model has already been extensively tested in different environments. The first accreditation test is planned for first quarter 2012. In this paper we describe the instrument and present some results of recent tests. Nomenclature a E ka kamp kc kd kp lp Me R t T
τc τd
TFA Ti Va 1
= = = = = = = = = = = = = = = = =
Width of the flexures Young modulus Force actuator sensitivity Displacement sensor amplifier gain PID proportional gain Differentiator constant Displacement sensor sensitivity Distance between pivot points of the pendulum Effective mass of pendulum Flexure radius Flexure thickness Measured thrust PID integration time PID differentiation time Thrust produced by the force actuator Step height Command of force actuator
Research Fellow, TEC-MPE,
[email protected]. Electric Propulsion Engineer, TEC-MPE,
[email protected]. 3 Electric Propulsion Section Head, TEC-MPE,
[email protected]. 4 Principal Research Scientist, Engineering Measurement Division,
[email protected]. 1 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011 2
y κ ω0
= = =
Displacement of pendulum Stiffness of flexures Resonant frequency of pendulum
I.
E
Introduction
uropean scientists are pursuing a number of unique science missions which require extremely high performance micro-propulsion systems to perform precision attitude control to meet their challenging scientific goals. These missions include planned and possible missions such as GAIA1, LISA Pathfinder2, Microscope3 and Euclid4. A number of different propulsion systems are under development to try and meet the needs of these missions, including systems based on FEEP, mini-ion and cold gas thruster technologies. The critical performance requirements for the thrusters are related to thrust accuracy, dynamic response and noise, where very challenging requirements are set. For instance, LISA Pathfinder requires 0.3 µN to 150 µN with resolution below 0.3 µN and thrust noise below 0.1 µN/√Hz between 10-2 Hz and 10 Hz and below 1 µN/√Hz between 10-3 Hz and 10-2 Hz. Although it is anticipated that the thruster technologies can meet these challenging requirements, verification of these performances by test presents its own difficulties, since the magnitude of the thrust noise requirements is close to the limit of available measurement devices and the practicalities of testing thrusters under vacuum provide their own challenges such as disturbances due to external vibration sources and thermal issues. Two measurement facilities already exist within European industry, one at Thales Alenia Space5 and one at ONERA6. These facilities have already been used to make measurements for the ongoing projects (GAIA and LPF), but have limitations in performance (particularly in terms of measurement bandwidth). At present measurements fully meeting mission requirements are not possible. The ESA is developing in the ESA Propulsion Laboratory (EPL) a Micro-Newton Thrust Balance (µNTB)7 to improve measurement coverage of the mission requirements and to offer measurements accredited to ISO 170258 in the µN range with traceability to international standards with rigorous uncertainty evaluation. An accredited measurement, including an ISO GUM9 (Guide to the expression of uncertainty in measurement) compliant uncertainty budget, is vital considering the difficulty of such measurements. For several years the ESA has been working on the µNTB project with the National Physical Laboratory (NPL), the UK’s national measurement institute. The result of this joint work is an engineering model which has already been extensively tested both in the EPL and at NPL. These recent tests show the validity of the design concept but also the extensive challenges related to ground testing. The present paper will first describe the µNTB system in detail, the set-up of the device in the EPL will then be described and finally, some preliminary performance results and uncertainty calculations will be presented.
II.
µNTB system description
The µNTB consists of two null-displacement, force-feedback folded pendulum balance assemblies: the tilt compensation assembly (TCA) and the measurement balance assembly (MBA). The thruster is placed on the MBA and a dummy mass is placed on the TCA. For each balance assembly a capacitive displacement sensor measures the
Figure 1. Schematic of the µNTB measurement concept (for the MBA only). 2 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
displacement of the pendulum (shown as y in Fig. 1). This displacement is used as the feedback signal to a controller which commands a calibrated solenoid/magnet force actuator so that the displacement of the pendulum from its equilibrium position is zero (null displacement) when the thruster fires. The commanded thrust of the force actuator, Va in Fig. 1, is a direct measurement of the thrust applied to the pendulum, and can be calibrated with direct reference to international standards. In order to compensate for tilt and low frequency (< 2 Hz) vibration sensitivities of the balances, the output of the tilt compensation assembly can be subtracted from the output of the measurement balance assembly to minimize these effects. The resultant subtracted signal provides the desired thrust measurement. The concept of the measurement is illustrated in Fig.1. The main components of the system, their transfer functions and the overall measurement system transfer function are described below. A. Monolithic Folded Pendulum The balance design is based on the Folded Pendulum (FP) concept which was first proposed by Blair et al.10 for the purpose of ultra-low vibration isolation of a laser interferometer gravitational wave detector. Later work by co-workers Liu et al.11 focused on the use of the FP as a high-sensitivity, low frequency seismometer for the detection of near shore ocean wave activity. The idea of using an FP as a seismometer was developed further by Bertoloni et al.12 who employed it as the primary sensor in a vibration isolation system for a gravitational wave detector. In addition to the numerous technical refinements of the FP as a measurement system, Bertolini et al.’s primary contribution to the work presented in this paper is Figure 2 Kinematic diagram of the folded the design of the FP as a monolithic structure eliminating alignment and repeatability issues associated with a pendulum concept. multipart construction. An FP consists of a mass suspended at one end by a positive pendulum and at the other by an inverted pendulum such that the positive gravitational restoring force of the inverted pendulum balances the negative gravitational force of the positive pendulum. A basic conceptual sketch of the system kinematics is shown in Fig. 2. The FP is illustrated as an ideal positive pendulum of length L1 connected to an ideal inverted pendulum of length L2 by a massless rigid beam. The counteracting influence of the positive and negative gravitational restoring forces results in a very low effective stiffness and thus a high sensitivity to external forces. If the pendulum arms are assumed to have the same mass and length, the natural frequency of the pendulum can be expressed by:
ω0 =
κ M el p
2
(1)
where lp is the distance between the pivot points of the pendulum arms, Me is the effective mass of the pendulum and κ, the effective cumulative stiffness of the flexures, given by the Tseylin13 formula:
κ=
Eat 2 ⎡ 0.43R ⎤ 16⎢1 + 1 + ⎥ t ⎦ ⎣
(2)
where E is the Young’s modulus of the FP material, a is the cumulative width of the flexures, t is the flexure thickness and R is the flexure radius. The FP has the transfer function: 3 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
1/ M e y = 2 T s + ω0 2
(3)
where y is the displacement of the pendulum resulting from the force component T in the measurement direction and s = iw is the Laplace operator. By cutting the FP from a single block of material using a monolithic design, shear effects at contact surfaces between separate mechanical parts are eliminated, mitigating hysteresis and dissipation. The use of a single material also reduces the instrument’s thermal sensitivity. Moreover, single process machining effectively eliminates all directional crosstalk due to misalignment. The manufacturing details of the FP are given in Ref. 6. B. Displacement sensor The displacement sensor is an MTI capacitive displacement transducer comprising an Accumeasure 5000 with an ASP-5-PCR sensor. This has a displacement sensitivity, kp, of 0.157 V/mm. The transfer function of the displacement sensor is:
Vp y
=
kp ⎛ s ⎜1 + ⎜ 2πLPF cutoff ⎝
⎞ ⎟ ⎟ ⎠
5
(4)
Where Vp is the output voltage and y is the input displacement, and the internal low-pass filter cut-off frequency, LPFcutoff, can be set to 10 Hz, 100 Hz or 1000 Hz. In this case, LPFcutoff is set to 1000 Hz. C. Force Actuator The force actuator is a key element in the system. It is the component which defines the sensitivity of the system. The force actuator comprises a current source driving a solenoid, which in conjunction with a rare-earth magnet produces a known force for a given input voltage to the current source. The transfer function is given by,
TFA = ka Va
(5)
where TFA is the force produced for a given input voltage Va. ka is the force actuator sensitivity. The force actuators are calibrated with their precision current source to international standards by NPL. D. PID A PID controller is required to allow for control of the system bandwidth through the proportional gain and to provide integrating action to eliminate steady-state error. The algorithm chosen is the academic form shown below:
⎛ sτ d 1 PID = k c ⎜1 + + ⎜ sτ (1 + sτ f i ⎝
⎞ ⎟ ) ⎟⎠
(6)
where kc is the proportional gain, τi and τd are the integration and differentiation time constants respectively and τf is a filter time constant used to limit the action of the differentiator at higher frequencies to reduce the tendency to
amplify noise.
E. Velocity feedback The displacement sensor output is differentiated to produce a signal proportional to velocity. This signal is fed back to the pendulum via the force actuator to provide active damping of the pendulum’s natural resonance The transfer function is given by, 4 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
Vd = kd s Va
(7)
where Vd is the velocity feedback signal and kd is the differentiator constant. F. Measurement transfer function Following the description of the system shown in Fig. 1, the closed loop transfer function as modeled in this section is:
k amp k p k c ⎛ ⎞ 1 ⎜⎜1 + + sτ d ⎟⎟ M e ⎝ sτ i Output ⎠ = 5 T ⎛ 2 k k ⎞⎛ ⎞ k amp k p k c k a ⎛ ⎞ s 1 ⎜ s + d a s + κ ⎟⎜1 + ⎟ + ⎜⎜1 + + sτ d ⎟⎟ 2 ⎜ Me Me M e l p ⎟⎠⎜⎝ 2πLPFcutoff ⎟⎠ ⎝ sτ i ⎠ ⎝
(8)
V a s →0 1 ⎯⎯⎯→ . In other words the low frequency sensitivity of the balance is T ka dependent only on the sensitivity of the force actuator. This feature of the design assures traceability of the measurement to international standards via the calibration of the force actuator.
In steady state this reduces to
III.
Set-up description
The µNTB thrust measurement system has been installed in the GALILEO vacuum facility in the EPL. GALILEO is a 1.2 m high 1 m diameter chamber. Its pumping system is composed of primary pumps and a turbomolecular pump (450 L/s N2). A damper feedthrough is added to the turbopump to limit vibration transmission. Lowest achievable pressure is 10-6 mbar. This facility has a flat bottom on which the balance can easily be installed. Figure 3 shows a picture of GALILEO. Figure 4 shows a design drawing of the µNTB on top of its baseplate (left) and a picture of the set-up in GALILEO (right).
A. Balance mounting Both balance assemblies (MBA and TCA) are screwed to a tilt adjustment platform made of aluminium. These platforms are equipped with motorized micrometers which can be controlled remotely via a controller connected to the Data Acquisition System (DAS). Both tilts are adjusted separately to bring the equilibrium position of each assembly within the operating range of the displacement sensors. These platforms stand on an aluminium baseplate. A steel plate interfaces kinematically the baseplate and the tilt adjustment platforms. An IMI 626A04 seismometer is also mounted on the aluminium baseplate in the thrust measurement direction. B. Seismic isolation Figure 3. Picture of the GALILEO vacuum facility in the ESA Propulsion Laboratory.
5 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
Figure 4. Design view (left) and picture (right) of the µNTB system set-up. The picture shows the balance installed on the isolation platform in GALILEO. Since the µNTB has been designed to measure very low thrust levels and operates in a similar way to a seismometer, it is equally sensitive to environmental vibration noise. One of the challenges of the measurements is to be able to distinguish the output signal components due to thrust from those generated by environmental vibration noise. The first step is to reduce as much as possible the environmental noise. At lower frequencies this is taken care of by the compensation system of the balance (MBA-TCA). In order to reduce vibration noise at higher frequencies (above 1 Hz) the aluminium baseplate of the µNTB is positioned on top of a six degrees-of-freedom commercial vibration isolation platform manufactured by Minus-K14. This isolation platform acts as a mechanical low pass filter based on negative stiffness principles. The natural frequencies of the platform without damping are: 0.25 Hz for horizontal, 1.25 Hz for tilt and 0.5 Hz for vertical. Damping material is used to limit the peak at the resonant frequency. Figure 5 shows the Noise Spectral Densities (NSD) of the accelerations measured by two identical seismometers; one on the floor of GALILEO and the other on the isolation platform (picture in Fig. 4).Accelerations were recorded during 15 minutes at 128 Hz. It can be seen that the platform effectively damps vibrations above 1 Hz.
IV.
Acceleration NSD, µg/√Hz
1000
Floor 100
The µNTB has been extensively characterized both at NPL and in the EPL. An effort has been made to reduce as much as possible external vibrations in the EPL during testing. In this section are presented the latest results obtained with the balance installed with the full set-up in GALILEO. All data acquisition is performed at 128 Hz.
MinusK
10 1 0.1 0.01 0.01
Preliminary performance results and uncertainty calculations
A. System transfer functions The main characterisation test of the Frequency, Hz balance consists of determining the open loop Figure 5. Acceleration Noise Spectral density (µg/√Hz) transfer function of each pendulum and the recorded by the seismometer on the floor of GALILEO and closed loop transfer functions of each balance by the seismometer on the isolation platform in the thrust assembly (MBA and TCA). These transfer functions allow us to: verify that the system is measurement direction. working as expected; check the similarity of 0.1
1
10
6 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
80
Amplitude, dB
-40
-20
120
TCA
80
-40
40 -60
0
-80
-40 -80
-100
Amplitude Phase
-120 -140 0.1
40 -60
0
-80
-40 -80
-100
-120 -160 1
10
-120 -120
-160
-200 -140 0.1
1
Frequency, Hz
20 0
Amplitude, dB
10
-200
Frequency, Hz
MBA
100
20
50
0
100
TCA
50
-20
0
-20
0
-40
-50
-40
-50
-100
-60
-150
-80 -100 0.1
-200 1
Phase, degrees
120
MBA
10
-100
-60
-150
-80
Phase, degrees
-20
-200
-100 0.1
1
Frequency, Hz
10
Frequency, Hz
Figure 6. Experimental (grey) and modeled (red-blue) amplitudes and phases of different transfer functions. Top: pendulum open loop transfer functions for MBA (left) and TCA (right). Bottom: Close loop transfer functions. the MBA and the TCA; have access to essential information such as the bandwidth or the DC gain of the system. The experimental closed loop transfer function of the pendulum is obtained by applying a known mechanical excitation to the pendulum and recording the output of the balance. A thrust noise signal is applied by the force actuator (using the Digital-to-Analogue-Converter of the DAS). The control system is left in open loop (no feedback). The ratio between the displacement of the balance (output) and the force of the force actuator (input) gives a measurement of the transfer function of the pendulum. An example is given in Fig. 6 (left for MBA and right for TCA). The signal of the balance was recorded for 20 minutes at 128 Hz. As described in section II.A, the theoretical transfer function of the pendulum is:
1/ M e y where, ω 0 = = 2 T s + ω0 2
κ M el p
2
In this model the length of the pendulum is known (manufactured value) as are estimates for Me and κ. This model can be fitted to match the experimental transfer functions presented above. The results presented here show that the resonant frequency of the pendulums of the MBA and the TCA are 2.36 Hz and 2.32 Hz, respectively. An identical approach is used to determine the experimental closed loop transfer function of the system and fit a model to it. The system is set to closed loop mode with the PID properly tuned in the control loop. The force actuator is used to generate an input force on the pendulum. The ratio between the measured thrust (output) and the generated noise (input) gives the closed loop transfer function. As mentioned in section II. F, the theoretical transfer function of the system is: 7 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
40
1000
a Thrust NSD, µN/√Hz
Thrust, µN
20 0 -20 -40 -60 -80 375 376 377 378 379 380 381 382 383 384 385
b
MBA TCA MBA-TCA
100 10 1 0.1 0.01 0.001
0.01
Time, s
0.1
1
10
Frequency, Hz
Figure 7. a) Thrust noise (µN) measured by the MBA (red), the TCA (blue) and difference of both (black). b) Corresponding thrust Noise Spectral Densities (µN/√Hz).
k amp k p k c ⎛ ⎞ 1 ⎜⎜1 + + sτ d ⎟⎟ M e ⎝ sτ i ⎠
Output = Thrust ⎛ ⎞⎛ s ⎜ s 2 + k d k a s + κ ⎟⎜1 + 2 ⎜ ⎜ ⎟ Me M e l p ⎠⎝ 2πLPFcutoff ⎝
5
⎞ k amp k p k c k a ⎟ + ⎟ Me ⎠
⎛ ⎞ 1 ⎜⎜1 + + sτ d ⎟⎟ ⎝ sτ i ⎠
This model is fitted to match the measured transfer function. Both experimental and modeled transfer functions are plotted in Fig. 6 for the MBA and TCA. The bandwidth of the closed loop system is close to 7 Hz.
B. Performance of balance 1. Noise cancellation The primary reason for having two matched balance pendulums was to facilitate some form of tilt and vibration noise compensation. The MBA and TCA have to be as similar as possible over the full measurement bandwidth for the noise compensation to work. The closed loop transfer functions presented above show that this is the case up to about 2-3 Hz. Above this frequency the magnitude and phase response of both assemblies differ as frequency increases (this is by definition). Figure 7 above shows the force noise on the balance recorded in the GALILEO vacuum facility under vacuum with the turbopump running. Thrust was recorded by the MBA and TCA for 20 minutes. On the left graph are plotted ten second samples of the thrusts measured by the MBA (red), the TCA (blue) and the difference between the two (black). After being compensated the noise drops from 21 µN rms to 7 µN rms. The effect of TCA compensation can also be seen in the frequency domain. The NSD of the difference between MBA and TCA drops almost and order of magnitude below 2 Hz. 2. Step tests and uncertainty calculation A thrust measurement can be simulated by using the force actuator of the system as an input. This is achieved by simply adding a voltage signal to the demand signal to the force actuator. This has the advantage the magnitude of the step introduced by the calibrated force actuator is known exactly. The difference between the measured thrust and the commanded thrust can provide information on the uncertainty of the measurement but is also a way to validate the post-processing method and uncertainty budget calculation. The following test was carried out in GALILEO, with the whole set-up described earlier, under vacuum. Ten steps were generated using the force actuator of the MBA. Each step was 100 µN high, 20 seconds long and separated by 20 seconds. The results of this test are presented in Fig. 8. A model-based approach was used to extract the thrust signal from the underlying drift and noise. The advantage of the model-based approach is that it takes all data into account and obtains the best possible value for each parameter and provides an uncertainty estimate for each fitted parameter that takes into account the noise on the signals. The experimental data (grey plot) was 8 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
a
125
Thrust, µN
1
Raw Stim Fit
Thrust error, µN
150
100 75 50 25
b
0.5
0
-0.5
0 -25 0
100
200
300
400
500
-1
0
1
2
Time, s
Thrust error, µN
4
3
4
5
6
7
8
9
10
Step number
c
2
0
-2
-4 0
10
20
30
40
50
60
70
Step number
Figure 8. a): Raw (grey), fitted (red) and generated thrusts for the MBA (µN) b) Error and expanded uncertainties (2σ) on the height of each step for the data set presented in figure a. c) Error and uncertainties (2σ) on the height of each step for a longer data set with different step lengths. modelled as a number of steps of height Ti and an underlying drift polynomial (4rd order Chebychev polynomial). This model was fitted to the experimental data with a least-squares method. The solution of the model fit to the data automatically compensates for drift and the effects of noise and provides the height of each step (red plot) and the uncertainty associated with each step height value due to the noise and drift compensation process. However, standard least-squares theory assumes that noise is Gaussian, white i.e. the same power at all frequencies, stationary (does not change with time) and uncorrelated. The nature of the feedback control system that the measurement signal is derived from means that the output signal is correlated and band-limited; examination of the noise spectra has shown that it is not white or stationary. It was therefore necessary to examine the validity of the uncertainty estimates provided by the standard least-squares fit of the model to the data. This was done by comparing the observed errors on each step with the calculated uncertainties. The error on each thrust step is the difference between the stimulus (force generated by the force actuator, blue plot) and the calculated thrust. The uncertainty calculation can be considered correct if 95% of the observed thrust errors are equal to zero within the expanded calculated uncertainty (with coverage factor, k = 2 or 2σ) and the calculated uncertainty is equal to the standard deviation of the errors. Figure8b shows the error on each step and the expanded uncertainty (k = 2). The errors are all below 0.2 µN. For step number 6 the error is not zero within the expanded uncertainty. Moreover, the mean calculated uncertainty is 0.11 µN and the standard deviation on the error is 0.14 µN. The uncertainty is underestimated by the model. Figure 8c gives the errors and expanded uncertainties for a series of seventy 100 µN steps of different lengths: ten 1 second long steps, ten 5 second long steps, ten 10 second long steps, ten 20 second long steps, ten 30 second long steps and twenty 20 second long steps (in this order). The uncertainties increase for shorter steps (statistical error). Also, even for long steps (20 or 30 second long) the error on more than half of the steps is not zero within the expanded uncertainty. In theory, this should only occur for 5% of the steps, for an expanded uncertainty with k = 2. The standard deviation of the error is 0.77 µN but the 9 The 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11 – 15, 2011
mean uncertainty is only 0.15 µN. Again, the uncertainty was underestimated. This particular case is a good example that shows the importance of understanding the properties of noise when applying statistical analysis to determine uncertainty. As previously stated, the approach used makes the assumption that the noise on the system is Gaussian, white, stationary and unfiltered. In reality this is not true and consequently the calculated uncertainty does not match the standard deviation of the observed errors. The degree to which the calculated uncertainty is in error increases with narrower thrust steps. Longer thrust steps could be used to reduce the effect of the properties of the noise on the uncertainty calculation, but longer steps could potentially be subject to greater drift. So shorter duration steps are preferred for drift compensation. Given this limitation, the approach taken for now is to intersperse thruster steps with force actuator steps and determine the uncertainty on the real thrust using the errors observed on the force actuator generated steps. The next step will be to develop a new post-processing method which provides a correct uncertainty estimate taking into account the properties of the noise on the signals. In addition, system identification methods will be used to measure the transfer functions of both assemblies. The transfer functions will then be used to design inverse filters which will be used to deconvolve the frequency dependent effect of the balance assemblies and control systems on the output signals. In this way, it will be possible to reconstruct the input signals within some uncertainty limits that will need to be determined. Differencing of the reconstructed signals should provide better vibration noise cancellation over a wider frequency range that is currently achieved. Even though the transfer functions of each balance are similar (see Fig. 6) there are some differences which explain why the differencing of MBA and TCA has less effect above 2 Hz and does not completely eliminate noise components due to vibration in the output signal. Work on deconvolution and the uncertainty implications of the signal processing of the output signals is on-going.
V.
Conclusion
This paper has presented the current development status of the ESA Micro Newton Thrust balance. An engineering model of the system is already available and extensive testing has shown that low thrust measurements in the EPL with this system are possible. The new isolation platform effectively damps vibrations above 1 Hz. The closed-loop approach offers a wide bandwidth (7 Hz proved, 10 Hz expected) and the compensation mechanism reduces considerably noise due to vibration at lower frequencies. A model-based approach has been deployed to extract the thrust signal from the noise and drift on the signal as well as to provide an uncertainty estimate associated with the fitted parameters. However, it has been shown that the assumptions made regarding the properties of the noise on the signal when applying standard least-squares theory are not valid in this case. This has led to the calculated uncertainties being optimistic. Further work is already planned in the frame of the collaboration between the ESA and NPL. An enhanced compensation between MBA and TCA using deconvolution is planned which will not only reduce even more noise in data but will consequently offer a more accurate uncertainty calculation method. In parallel to this work, a new testing sequence has already started in the EPL. The purpose of this test is to characterize all uncertainty factors in the set-up other than the uncertainty related to data processing. These include gas-line pressure, thermal and electrical effects. The first thrust measurements using a cold gas thruster have also been performed. The first accreditation test is planned for first quarter 2012.
Acknowledgments The authors would like to thank David Robinson (Psi-Tran Ltd), Trevor Esward (NPL) and Matteo Appolloni (ESA) for their help on the project.
References 1
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4 Laureijs, R., “Euclid: an ESA mission to map the geometry of the Dark Universe”, JENAM 2010, Joint European and National Astronomy Meeting, 6-10 September, Lisbon, Portugal, p.166, 2010. 5 Cesare, S., Musso, F., D’Angelo, F., Castorina, G., Bisi, M., Cordiale, P., Canuto, E., Nicolini, D., Balaguer, E., Frigot, P.E., “Nanobalance: the European balance for micro-propulsion”, Proceedings of the 31st International Electric Propulsion Conference, University of Michigan, Ann Arbor, Michigan, USA, September 20 – 24, 2009, 182. 6 Packan, D., Bonnet, J., and Rocca, S., “Thrust Measurements with the ONERA Micronewton Balance”, Proceedings of the 31st International Electric Propulsion Conference, University of Michigan, Ann Arbor, Michigan, USA, September 20 – 24, 2009, 185. 7 Sutherland, O., Appolloni, M., O’Neil, S., Gonzalez del Amo, J., and Hughes, B., “Advances with the ESA Propulsion Laboratory µN Thrust Balance”, Proceedings of the 5th International Spacecraft Propulsion Conference, Crete, Greece, 5-9 May, (2008). 8 ISO/IEC 17025:2005 General requirements for the competence of testing and calibration laboratories. 9 ISO/IEC Guide 98-3:2008 Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995). 10 Blair, D.G. et al., “Performance of an ultra low frequency folded pendulum”, Physics Letters A, 193:223-226, 1994. 11 J. Liu et al., “Near-shore ocean wave measurement using a very low frequency folded pendulum”, Measurement Science Technology, 9:1772-1776, 1998. 12 Bertolini, A. et al, “Mechanical design of a single-axis monolithic accelerometer for advanced seismic attenuation systems”, Nuclear Instruments and Methods in Physics Research A, 556:616-623, 2006. 13 Tseytlin, Y.M., “Notch flexure hinges: an effective theory”, Review of Scientific Instruments, 73(9):3363-3368, 2002. 14 Platus, D. L., “Negative-Stiffness-Mechanism Vibration Isolation Systems”, Optomechanical Engineering and Vibration, Control, SPIE, Denver, Colorado, 20-23 July, Volume 3786, 1999.
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