[Tanaka, Komori]

Abstract:

We are continuing the implementation of a new filter to enhance the unity gain frequency (UGF) of DHARD yaw.
Our next approach is to implement a moderate-bandwidth filter that controls only the first and second yaw resonances, while avoiding control of the third resonance.

Details:

In the first trial, we observed oscillations above 10 Hz immediately after enabling the new filter.
This is likely because the gain at high frequencies was too large due to the use of multiple phase compensation filters, causing amplified signals to couple into other degrees of freedom.
Therefore, we decided to abandon, for now, the strategy of controlling all three yaw resonances and instead focus on controlling only the first (0.3 Hz) and second (1.8 Hz) resonances.

We designed the openloop transfer function as shown in the figure.
Phase compensation was implemented using four zero–pole filters, and a notch filter was added to prevent the third resonance at 3.1 Hz from surpassing the unity gain.
When we enabled the new filter, we again encountered oscillations above 10 Hz on several occasions, so additional notch filters were implemented accordingly.

We have not yet successfully closed the DHARD yaw loop.
This is likely because the CHARD yaw loop is still using the conventional low-gain filter.
In the next step, we will apply the same new filter to CHARD yaw and attempt to close the {D, C}HARD yaw loops simultaneously using the new filter.

[Tanaka, Ushiba, Komori]

Today, we tried a hierarchical control scheme for the yaw modes.
We measured the transfer function from the input of DHARD yaw to each TM oplev signal with the newly designed filter, as shown in the figure.
Assuming that the optical gain is flat, this is regarded as the estimated openloop transfer function.

We designed this filter to achieve a similar response for each suspension, in particular by inserting additional gains in the TM lock filters to match the high-frequency response.
The crossover frequency between the MN and TM is approximately 0.8 Hz, and the overall unity gain frequency is 2 Hz.

We found significant coupling from the pitch mode into DSOFT Y.
Therefore, we will apply this new filter after further decoupling of the pitch and yaw degrees of freedom.

Komori, Tanaka

## Abstract

We tried to engaged {D, C}HARD_Y control with new filters and MN/TM actuators. We succeeded in engaging {D,C} HARD_Y with 2 Hz UGF. On the other hand, SOFT modes starts oscillating at 0.3- 0,4 Hz when the gain values got more than 0.4 maybe due to the reduction of phase margin around their frequencies by some coupling (D/C or HARD/SOFT or both).

Also, since gain peaking around 2 Hz seems to be too large, we can see the 2 Hz and the harmonics' peaks in DARM spectrum. So it is necessary to improve 2 Hz phase margin by modifing the filter design.

## What we did

After the IFO recovery, we attempted the new filter and actuator setting which Komori-san prepared in klog36323. The setting is following:

• {E,I}TM{X,Y}_MN_LOCK_Y: FM7(HBint) -> ON, FM10(LP1) -> OFF, gain=1,
• {ETMY,ITMX,ITMY}_TM_LOCK_Y: FM6(gain) > ON, gain=1,
• {D,C}HARD_Y: FM4 (HBtest3) -> ON, others -> OFF.

In this setting, we requested ASC_LOCK guardian to go to ENGAGE_HARD_LOOPS, where the guardian set the gain value of HARD loops to -0.2. However, CHARD Y started oscillating and IFO got down.

We considered the phase margin is smaller than we expected when gain was 0.2. According to the figure in klog36323, the expected UGF when gain was 0.2 seems to be around 0.3 Hz, but there is the damped resonance at 0.3 Hz. So each phase rotation around 0.3 Hz can be difference by difference damping situation in each suspension.  Therefore, we changed the gain set value from 0.2 to 0.1 to shift the expected the UGF to less than 0.3 Hz, at once. Then, we succeeded in engaging HARD_Y controls with less than 0.3 Hz UGF. 

We measured the OLTFs of HARD_Y controlls. Figure 1 and 2 show the results of DHARD_Y and CHARD_Y, respectively. The magenta line in the left upper panel in the figure is the TF when HARD_P gain = -0.2 and HARD_Y gain = -0.1. DHARD_Y UGF seems to be less than 0.1 Hz but CHARD_Y UGF seems to be more than 0.2 Hz even though gain value was reduced. This indicatd that CHARD_Y sensor efficiecy  may be larger than we expected. So, I adjusted the CHARD_Y gain by modifying the filter gain. On the other hand, both phase margin of {D,C}HARD_Y seems to be almost the same as our expectation from the TF in klog3623. Therefore, we attempted to increase the gains from 0.1 to 0.2. The oscillation did not occured at that moment.

Anyway, we increased the gain from 0.2 to 1. The oscillation did not occured. Then, we measured the OLTFs in this state. The cyan lines in the figure show the TF when HARD_P gain = -0.2, HARD_Y gain = -1, and SOFT_Y gain = -0.2. Each UGF reached to around 2 Hz as we expected. On the other hand, phase marging below 0.3 Hz seems to decrease compared with the one when HARD_Y gain = -0.2. According to the TF from actuator to sensor (OUT -> IN1) in right middle (gain) and lower (phase) panels, the TF below 0.6 Hz seems to be changed. This time, we increased only HARD_Y gain in terms of the region 0.1 Hz to 1 Hz. Therefore, the TF change seems to be caused by the coupling between Diff. and Comm. mode.

After that, we increased the HARD_P gains from 0.2 to 1. The orange lines show the TFs when HARD_P gain = -1, HARD_Y gain = -1, and SOFT_Y gain = -0.2. The TFs seem to be changed not so much.

Then, we tried to increased the SOFT_Y mode's gains but the SOFT mode started ot oscillating when the gain value got more than 0.4 at 0.3-0.4 Hz (fig.3:DSOFT, fig.4:CSOFT). So we stopped increasing the gain to 0.3 and measured the OLTFs. The red lines in the figure 1 and 2 show the TF when HARD_P gain = -1, HARD_Y gain = -1, and SOFT_Y gain =-0.3. the phase margin of OLTF around 0.2 Hz seems to be almost 0. So this indicates there is the coupling between HARD and SOFT in the 0.1 - 1 Hz region. Therefore, it is necessary to decouple them to solve this issue. 

Finally, since gain peaking around 2 Hz seems to be too large, we can see the 2 Hz and the harmonics' peaks in DARM spectrum. So it is necessary to improve 2 Hz phase margin by modifing the filter design like the fig.5.