Requirements

The accuracy of longitudinal control loops can be defined as the RMS value of residual fluctuations of degrees of freedom around the working position.

Original requirements can be found for example in Lisa's Ph.D. thesis:

DARM: RMS < 2  x 10^-12 m

MICH: RMS < 5 x 10^-10 m

PRCL: RMS < 2 x 10^-10 m

For CARM (not frequency noise) there is no stringent requirement, since it is mainly used only for global inverted pendulum control.

Calibration of error signals

Longitudinal error signals have been calibrated using three different techniques:

• using the optical matrix recontruction described in the "Locking characterization" note
• comparing the amplitude of calibration lines (24, 62 and 379 Hz) in correction and error signals and using the actuator response measured by the calibration group
• Measuring the open loop transfer function of each loop and factoring out the mechanical and digital corrector responses

All three measurement gave similar results:

Gc_Differential = 1.5 x DARM
Gc_Michelson = 5.7 x 10⁶ x MICH
Gc_Recycling = 8.7 x 10⁵ x PRCL

The reference cavity signal calibration has been obtained from the frequency calibration explained in logbook entry number 14397.

Results

The following plots show the residual motion of all four degrees of freedom, together with the integrated RMS:






The resulting total residual RMS fluctuation are

DARM: RMS = 1.1 x 10^-15 m      (1/2000 of req.)

PRCL:  RMS = 1.2 x 10^-12 m      (1/200 of req.)

MICH:   RMS = 3.4 x 10^-11 m     (1/15 of req.)

CARM: RMS = 1.9 x 10^-8 m