8.6 The Lock Acquisition Procedure for the Caltech 40 m Interferometer
8.6.4 Adaptive compensation filter: the moving zero
power must be adjusted to keep the loops stable. This includes the CM servo, as the gain in the AO path (sensed byREF LDC) will increase. The gain in the AO path can be reduced to compensate, or it can be set in step F such that there is enough headroom to accommodate the increase.
Step H: Hand off CARM to RF
Once the CARM offset has been reduced to the point where the buildup of power in the IFO is greater than half its final value, the standard, RF, PDH-style signals designed for sensing CARM will come within their linear range, and can be used for controlling CARM. Care must be taken at this stage to understand (through modeling) the frequency response of the DC and RF signals to ensure that they have compatible frequency response (the MCL-AO crossover must be stable for both signals). The MCL feedback can be transitioned to an RF based signal digitally, while the MCF feedback (which uses an analog signal) must be transitioned using a cross-fade amplifier; the latter is available in the common mode servo electronics.
These transitions should happen approximately simultaneously; the scripts used at the 40 m transition the digital portion halfway, then transition the analog portion halfway, finish the digital portion and then finish the digital portion. Only the digital path has gain at DC, so it is not difficult to add an offset to the RF error signal to ensure a smooth signal transition without actually changing the offset in CARM; because the analog path has no gain at DC, it does not require an offset.
Step I: Remove CARM offset
Once the CARM loop (including the CM servo) is using the RF signal, the remaining CARM offset is removed and the IFO is brought to its operating point. At this stage the controls system is in its final configuration. All that remains is to apply any low-frequency boost stages that are not already engaged.
During this whole procedure, the primary observable change is a steady ramp in the power circulating in the interferometer, as shown in figure8.8.
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Frequency [Hz]
CARM optical response magnitude [dB]
CARM optical springs at different CARM offsets
Arm power = 6 Arm power = 8 Arm power = 10
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Frequency [Hz]
CARM optical response magnitude [dB]
CARM optical springs at different CARM offsets
Figure 8.7: The optical response (magnitude only) of the CARM DOF at several CARM offsets. As the CARM offset is reduced and the circulating power increases, the peak in the optical response moves toward lower frequencies while the opto-mechanical spring resonance moves toward higher frequencies. Experimental data are shown in dots; the solid line is a simulation.
As the CARM offset is reduced, the detuning of the CARM degree of freedom changes, causing a change in the optical plant. This change takes the effect of a complex pole in the response function (the peak in the optical response) moving from a relatively high frequency (at∼1 kHz) towards the on-resonance common mode coupled cavity pole (at ∼100 Hz). The digital control system at the 40 m (cf. section5.4) generally limits UGFs to a maximum of about 400 Hz, so this particular sweep of frequencies carries this complex pole right through the UGF of the CARM loop. This creates an excess phase delay which degrades the stability of the control loop. To prevent this, a digital filter which adapts to the changing response was implemented. This filter is composed of a flat path summed with a path rising likef2. The flat path is gain adjusted by being divided by the current buildup of power in the arm cavities. Thus, as the power builds in the interferometer, this division compensates the increasing optical gain. The path which rises like f2 is not gain compensated, however, and so as the power builds in the interferometer the crossover frequency of the f0 path and thef2 path moves downward in frequency along with the pole in the coupled cavity response.
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Power Buildup (%)
time (minutes)
Initial Acquisition at acquisition point, a large CARM offset
(Step A)
Operating point (Step I) CARM to RF signal
(Step H)
Removing CARM offset CARM on REFL DC signal
(Step G) Signal transitions
(Steps B through F)
Figure 8.8: The power in the interferometer gradually increases as the CARM offset is reduced during the lock acquisition procedure. This plot is a time trace of the power in an arm cavity; compare to the top of figure8.5.
Figure 8.9: dB magnitude of the CARM (sensed atREF LDC) open-loop opto-mechanical frequency response to input laser phase noise shown as a function of CARM offset.
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phase (degrees)
f (Hz)
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magnitude
TF from PM to REFL DC at multiple CARM offsets (pm)
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phase (degrees)
f (Hz)
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10−5 100
magnitude
TF from PM to REFL DC at multiple CARM offsets (pm)
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Figure 8.10: Bode plots of the opto-mechanical frequency response ofREF LDC to input laser phase noise, at various CARM offsets. This selection shows a series of offsets which lead to spring behavior in CARM;
offsets from resonance in the other direction would exhibit anti-spring behavior.
Figure8.12shows the action of this compensating filter with several transfer function measurements detailing the CARM cavity optical response at different CARM offsets, along with open-loop transfer functions which show the action of the compensation filter (since they do not change significantly).
This technique is limited however; eventually the rising control signal amplitude at high frequen- cies will saturate the digital to analog converters. Thus, this compensation filter is only used until the AO path (Step F in section8.6.3) has increased the CARM servo bandwidth enough that the phase delay at a few hundred Hz no longer impacts the overall loop stability. The period where it is applied is shown in figure8.5.