To investigate the phase delay issues in DSOFT, I came back to check the each suspension hierarchical actuators.
What I did is the following three measurements:

1. Both MN_LOCK_Y and TM_LOCK_Y filter bank inputs are ON and FM9 of MN_LOCK_Y is ON (Same filter setting as those at OBSERVATION state).
2. Both MN_LOCK_Y and TM_LOCK_Y filter bank inputs are ON but FM9 of MN_LOCK_Y is OFF.
3. MN_LOCK_Y filter bank inputs are OFF.
Note that excitation signals were injected from K1:ASC-DHARD_Y_SM_EXC, and INPUT switches of MN_OLDAMP_{P,Y} filter banks were OFF for all measurements.

According to the MN2TM and TM2TM transger function measurement conducted on 9 February (fig1), 2 and 3 should be almost same because MN2TM transfer function was well below.
Figure 2 shows examples of TFs (ETMX and ITMX).
The setting of each transfer function measurement can be seen in the legend of the graph.

As expected,the measurement setting 2 and 3 did not change TFs so much though small (but significant) notch can be seen around 1 Hz, especially for ITMX somehow.
According to theTF measuremnt results, significant notch stracture appears when MN integrator was turned on.
This implies that cross-over frequency between MN and TM hierarchical actuators are not optimal, which was designed around 0.1 Hz.
Due to this issue, phase of ITMX hierarchical actuators are rotated by 360 degs around 0.5 Hz, which would be problematic for ASC controls.
So, it would be necessary to tune the hierarchical actuators, especialy cross-over frequency between MN and TM stages.