Ushiba, Hirose, Tanaka

We succeeded in transitting from 1f signals to 3f signals for the DRMI lock just after initial alignment. Maybe we can lock DRMI with 3f sensors with good alignment. Current lock duration is less than 10 mins. Robust ASCs for all of DRMI DoFs are necessary. 

## What we did

(Conclusively, following work seems not to work for some reasons...)

• We remeasured the sensing matrix for DRMI 3f signals with the good configration as reported in klog37295. Fig.1,2,3 show the results of PRCL, SRCL, and MICH, respectively. There seem to be good coherences at the excitation frequency, 150.125 Hz
• From these results, we calculated the sensing matrix with the following procedure.
  • We assumed that PRM motion contributes only PRCL, and also, the SRM motion contributes only SRCL. On the other hands, the BS motion changes the distances of BS-IX and of PRM-BS, that is, BS changes not only MICH but also a half of PRCL and a half of SRCL. Moreover, the direction of PRCL change by BS is inverse from other two DoFs. 
  • Therefore, each length changes delta L_{PRCL, SRCL, MICH} can be written by using each mirror displasement delta x_{PRM, SRM, BS}
    $\begin{pmatrix} \delta L_{\mathrm{PRCL}} \\ \delta L_{\mathrm{SRCL}} \\ \delta L_{\mathrm{MICH}} \end{pmatrix} = \begin{pmatrix} 1 & 0 & -0.5 \\ 0 & 1 & 0.5 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} \delta x_{\mathrm{PRM}} \\ \delta x_{\mathrm{SRM}} \\ \delta x_{\mathrm{BS}} \end{pmatrix}$
  • we can derive the relation between the cavity length change and sensor response by using measured response from a mirror displacement to a sensor H
    $\begin{pmatrix} S_{\mathrm{51I}} \\ S_{\mathrm{51Q}} \\ S_{\mathrm{135I}} \\ \end{pmatrix} = \hat{H} \begin{pmatrix} \delta x_{\mathrm{PRM}} \\ \delta x_{\mathrm{SRM}} \\ \delta x_{\mathrm{BS}} \\ \end{pmatrix} = \hat{H} \begin{pmatrix} 1 & 0 & -0.5 \\ 0 & 0 & 0.5 \\ 0 & 0 & 1 \\ \end{pmatrix}^{-1} \begin{pmatrix} \delta L_{\mathrm{PRCL}} \\ \delta L_{\mathrm{SRCL}} \\ \delta L_{\mathrm{MICH}} \\ \end{pmatrix}$ 
  • Then, we can obtain the sensing matrix S,
    $S = \left[ \hat{H} \begin{pmatrix} 1 & 0 & -0.5 \\ 0 & 1 & 0.5 \\ 0 & 0 & 1 \\ \end{pmatrix}^{-1} \right]^{-1} = \begin{pmatrix} 1 & 0 & -0.5 \\ 0 & 1 & 0.5 \\ 0 & 0 & 1 \\ \end{pmatrix} \hat{H}^{-1}$
• After that, we used the K1:LSC-{CARM,XARM,YARM}_IN1 channels as virtual 3f sensors for {PRCL, SRCL, MICH} by using the obtained sensing matrix, respectively. And we normalized the each virtual sensor by the response of the corresponded DoF. Then, we measured the responses between mirror displacements and virtual sensors. Fig.4, 5, and 6 show the results. Their virual sensor could see the motions of corresponded mirros. Therefore, they seems to be decoupled.
• Then, we tried with the decoupled 3f sensors by the guardian, one by one. Before this, we modified the LOCKING_DRMI_3F state so that the guardian input the values of sensing matrix to LSC_INPUT_MATRIX. However, PRCL began to oscillated.

(Following work seems to work.) 

• Previously, as for PRCL and SRCL, we succeeded in transitting 1f sensors to 3f sensors just by using REFL51I for SRCL and REFL135I for PRCL (klog37228). So we tried to check the reproducebility of that results. At first, we adjusted the gains and signs of REFL135I and REFL51I by using the ratios of RF135I/PRCL 1f error and of REFL51I/SRCL 1f error. And we decided the offset of 3f signals by using the DC values when DRMI was locked with 1f signals. Then, we tried the transition, one by one. PRCL was succeeded in the transition. SRCL was also suceeded in the transition but the lock seems not to be unstable.
• After the lock was failed, DRMI lock seems to become difficult even with 1f sensors.  Actually, POP90 seems to be not already maximum because BS alignments are not controlled from this moring. So we assumed the alignment already became worse. We decided to perform initial alignment.
• After the initial alignment, we prepared the state for the transition (DRMI_TRANSITION_TO_3F) in the VERTEX guardian. Then, PRCL and SRCL transition to each 3f sensor with their offsets were succeeded by the guardian. The lock seems to be stable. Then, we tried to transitting MICH control from 1f to 3f sensor (REFL51Q) with the offset. It failed but we observed the error signal became far from the setpoint. So we flipped the sign and retried it. Then, we succeeded in transitting MICH control from 1f to 3f. 
• Fig.7, 8, and 9 show the measured OLTFs of PRCL, SRCL, MICH with 3f. The UGFs seems to be the same as the ones with 1fs.
• Current lock duration of DRMI 3f seems to be less than 10 mins. We need robust ASCs for all of DRMI DoFs to expand the duration.