Minimizing the Resonant Frequency of MGAS Springs for Seismic Attenuation System in Low Frequency Gravitational
Waves Interferometers
Maddalena Mantovani, Juri Agresti, Erika D’Ambrosio, Riccardo De Salvo, Barbara Simoni
Motivations
Ground Based Interferometer are Limited by Newtonian Noise under 10 Hz
Recent Calculations Show the Possibility of Suppression of Newtonian Noise by Suspending the Test Masses in Deep Caves
Seismic Attenuation was Designed to Match that Limit
Suppression of NN by a Factor of 10-6 in Amplitude, 30 in Frequency Seismic Attenuation Must be Redesigned to Match the New Limit
Giancarlo Cella Draft
Horizontal Achievable with Longer Wires in WellsVertical Attenuation Requires New Development
Cella Suppression of Newtonian Noise
*1/100 Underground Seismic Amplitude
Horizontal Attenuation
Filter
Inverted Pendula
Existing MGAS Spring
Control LVDT
Magnet
Coil
Practical Limit 200mHz
LIGO-T010006-00-R
Frequency Tuning
Method to Lower the Resonant Frequency below the Mechanical Limitations
Apparatus Schematics
Load
Blade
Control CircuitLVDT Driver
Signal 1
Signal 3
Spectrum Analyzer
Control LVDT
Signal 2
Source
Filter to ground LVDT
Mechanical Actuator
Ground to Payload LVDT
Actuator
Simulated Noise
Control CircuitLVDT Driver
Source
Ground to Payload LVDT
Mechanical Shaking Actuator
Spectrum Analyzer
Filter Actuator
Control LVDT
Load
Filter to ground LVDT
Signal 3
Signal 2
Signal 1
Mechanical Setup
Blades
Variable Gain
Control Circuit
MGAS already neutralize > 90% of cantilever spring stiffness
Circuit corrects the last few per cent of stiffness and stabilizes performance
Actuator
MGAS Blade
Control LVDTThermal
Compensation
• LVDT
• Variable Gain
• Amplificator-Voice Coil
Tunable spring in parallel with MGAS spring
100÷300 sec
Set Point Integrator Thermal Drift Correction( )
Payload
Characterization Work
• Determination of the Working Point
• Circuit Calibration
• Frequency behavior as a function of the Gain
• Q Factor Analysis
Impulse Response
Frequency Response
After fixing the vertical height to the minimum frequency point we change the Gain to find the frequency behavior vs.
gain
0
0.1
0.2
0.3
0.4
0.5
-10 -5 0 5 10
Gain
Frequency [Hz]fit
gain [turns]
y = m2*(m0-m1)^0.5
ErrorValue
0.016428-8.8043m1
0.000261590.11096m2
NA0.00035801Chisq
NA0.9997R
326
0
mHz
G
8.8043
0
G
Hz
Q Factor Analysis; Two Methods
Fitting the Damped Exponential in Free Oscillations
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-5 0 5 10 15 20
Waveform G=2.5
Voltage [V]
time [sec]
Q
Fitting the Resonant Width in the Transfer Function
0fQf
-50
0
50
0.01 0.1 1 10
Transfer Function
Frequency [Hz]
y = 20*log(m1*m2 ̂2/((m2 ̂2-...
ErrorValue
0.0249861.8764m1
0.00112860.43352m2
20.1362.096m3
NA6362.2Chisq
NA0.97913R
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-5 0 5 10 15 20
Waveform G=9
Voltage [V]
time [sec]
-0.6
-0.55
-0.5
-0.45
-0.4
-0.35
-0.3
-5 0 5 10 15 20
Waveform G=-3.5
Voltage [V]
time [sec]
-0.65
-0.6
-0.55
-0.5
-0.45
-0.4
-0.35
-0.3
0 5 10 15 20
Waveform G=-8.3
Voltage [V]
time [sec]
/0 1 cos 2 ty c c t e
0
50
100
150
200
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
Q Factor
Frequency [Hz]
y = m1*m0^m2
ErrorValue
59.684585.74m1
0.107461.8393m2
NA3132.9Chisq
NA0.97901R
factorQ
Impulse Response
-50
-40
-30
-20
-10
0
10
20
30
0.01 0.1 1
Frequency [Hz]
y = 20*log(1*m2^ 2/((m2 ̂2-m...
ErrorValue
0.0028150.47752m2
4.000516.259m3
NA1897.6Chisq
NA0.98421R
Transfer Function Measurement
(filter body to payload)
20 0
2 222 2 0
0 2
20logH
f
Q
Lowering the system stiffness
As the Transfer Function is shifted to lower frequencies,
The Q factor decreases
-30
-20
-10
0
10
20
30
40
0.04 0.06 0.08 0.1 0.3 0.5
dB (G=1)dB (G=5)dB (G=4)dB (G=3)dB (G=2)dB (G=8.5)dB (G=-1)dB (G=-2)dB (G=-2.5)dB (G=-2.8)dB (G=-3)
Frequency [Hz]
Transfer Function with Different Gain values
0
5
10
15
20
25
30
35
40
0.06 0.08 0.1 0.3 0.5
Transfer Function G=8.5
Frequency [Hz]
y = 20*log(m1*m2 ̂2/((m2 ̂2-...
ErrorValue
0.0136671.7675m1
0.000274620.36361m2
3.443945.173m3
NA40.974Chisq
NA0.99659R
-10
0
10
20
30
40
0.2 0.3 0.4 0.5 0.6
Transfer Function G=3
Frequency [Hz]
y = 20*log(m1*m2 ̂2/((m2 ̂2-...
ErrorValue
0.023071.8548m1
0.000450120.27612m2
1.972124.354m3
NA51.879Chisq
NA0.99664R
-25
-20
-15
-10
-5
0
5
10
15
0.01 0.1 1
Transfer Function G=-3
Frequency [Hz]
y = 20*log(m1*m2 ̂2/((m2 ̂2-...
ErrorValue
0.986063.5196m1
0.0103940.079989m2
0.158850.80982m3
NA298.29Chisq
NA0.97027R
1
2
3
1
2
3
0
10
20
30
40
50
0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4
Resonant Frequency [Hz]
y = m1*m0^m2
ErrorValue
41.092358.81m1
0.0933592.0882m2
NA24.881Chisq
NA0.99413R
Q Factor Analysis
0
50
100
150
200
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
Q Factor
Frequency [Hz]
y = m1*m0^m2
ErrorValue
59.684585.74m1
0.107461.8393m2
NA3132.9Chisq
NA0.97901R
0
10
20
30
40
50
0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4
Resonant Frequency [Hz]
y = m1*m0^m2
ErrorValue
41.092358.81m1
0.0933592.0882m2
NA24.881Chisq
NA0.99413R
Impulse Response Frequency Response
Both methods show a quadratic behavior for the Q factor
Implies structural, non viscous, damping
Need for Thermal Compensation
The large thermal dependence of the blade working point with temperature, at low stiffness, makes it practically
impossible to obtain very low resonant frequencies
2 Ey
dY g
dT L
Where is the thermal expansion coefficient given
by the Young’s modulus
E
Virginio Sannibale et al.
y
Y
Thermal Compensation Circuit
100÷300sec
Overnight Blade Tip Position stability Integrated on 10 Period
0
2
4
6
8
10
12
14
-615.6 -613.1 -610.6
Blade Position averaged on 10 Period
Range
Blade Position [micron] averaged 100 sec and decimated
-612.4834Mean
1.1317328Std Deviation
1.2808192Variance
0.08042875Std Error
-0.51884154Skewness
-0.25288313Kurtosis
0
2000
4000
6000
8000
1 104
-687 -667 -647 -627 -607 -587 -567 -547
LVDT Readout Histogram
LVDT Signal [micron]
Blade Position [micron]
LVDT Signal [micron]
351079Points
-611.72936Mean
17.369398Std Deviation
0.029314489Std Error
0.017346127Skewness
0.023316299Kurtosis
These residuals are mainly the r.m.s. 100 mHz oscillator resonance excited by the seismic activity
Power Considerations
The Power consumption is of the order of 10mW
-50
-40
-30
-20
-10
0
10
0.1 1
Frequency [Hz]
Two Anomalies at Low Frequency are Discovered
1/f
1/f 2-50
-40
-30
-20
-10
0
10
20
30
0.01 0.1 1
dB
Frequency [Hz]
Right 1/f2 Behavior
1/f 2
1. Slower Slope in the Lower Frequency Transfer Function Measurements
Transfer Function Measurements with different Excitation Amplitude
-60
-50
-40
-30
-20
-10
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Transfer Functions with Different Excitation Amplitude
dB (25mV)dB (10mV)dB (5mV)dB (70mV)
Frequency [Hz]
The slope does not change
-50
-40
-30
-20
-10
0
10
20
30
0.1 1
Transfer Function with Different Integration Times
dB (t=200sec)dB (t=100sec)dB (t=300sec)
Frequency [Hz]
Transfer Function Slope for Different Integration Times
The Slope does not depends on the integration time
Need for more investigations
-45
-40
-35
-30
-25
-20
-15
-10
-5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Transfer Function measurements for different vertical positions
dB (-.850V) nomrdB (-1.14V) normdB (-0.696V) normdB (-0.350V) normdB (-1.46V) normdB (0.003V) normdB (0.497V) normdB (1.25V) norm
Frequency [Hz]
Slope for Different Vertical Positions
-2.2 100
-2.1 100
-2 100
-1.9 100
-1.8 100
-1.7 100
-1.6 100
-1.5 100
50 100 150
y = -1.1119 - 0.0072851x R= 0.98337
Resonant Frequency [mHz]
Second anomaly founded
50
100
150
200
250
300
350
400
450
-4 -3 -2 -1 0 1 2 3 4
Vertical Position [V]
• So far the working point to frequency dependence has always been observed to be hyperbolic, getting narrower at lower frequency
• At lower frequency we find a departure from the hyperbolic behavior (the fit in the bottom data set is a fourth power polynomial)
• We suppose that higher order effect may be taking over when the anti-spring gets close to fully neutralize the spring constant
• The newly observed behavior is coincidental with the departure from 1/f2 of the attenuation transfer function
• We do not know yet if the two anomalous effects are correlated.
Is this useful for LIGO??
the LIGO Deep Fall Back solution prototype for one-pier preattenuators
Vertical Attenuation
Horizontal Attenuation
Bellow equivalent springs
Cantilevers
350 Kg Payload
DFBS prototype
Real time
DFBS Prototype
So far driven down to 120mHz despite the additional springs (4/3 of the equivalent bellow stiffness) in
fully passive configuration
Expect ≤ 30mHz if tuned with electromagnetic anti-spring
attenuation plateau at 10-3 proven on preceding prototypes (expect similar performance)
• This development of Electromagnetic Correction Springs was designed to boost the Low Frequency attenuation performance of Geometric Anti Springs for future Underground Low Frequency Gravitational Wave Interferometric Detectors (Horizontal Attenuation was always easily available)
• This development allows for further depression of seismic perturbations, beyond the performance of the Superattenuators, reaching down to 1 Hz and even below.
Conclusions
-50
-40
-30
-20
-10
0
10
0.1 1
Frequency [Hz]
• The retrofitting of this technology on existing system like the LIGO deep fall back pre-isolator solution may allow the introduction of attenuation factors as large as one thousand for frequencies above 1 Hertz
• Sizeable attenuation at the micro seismic peak at 150 mHz can be obtained as well
Conclusions
-50
-40
-30
-20
-10
0
10
0.1 1
Frequency [Hz]
• Find the source of the less then 1/f2 behavior
• Repeat the Measurements with Accelerometers
• Study and Reduce the Control Circuit Noise Improving some of its Performances (Yanyi Chen)
• Make a Mechanical Thermal Compensation
• Use this Seismic Attenuation System on the Mexican Hat Interferometer (Barbara Simoni)
Next Steps