Today I tried to understand the reason for the instability of the blending strategy 30 mHz along the T direction. As already mentioned, the T TF shows a strange phase behaviour below 100 mHz, in spite of the phase compensator implemented to compensate it.
Figure 1 and Figure 2 show the TF: LVDT/IS{L,T}. It is clear that there is still a phase lag which introduces an instability into the loop. To mitigate the phase lag, I implemented a new phase compensator on the virtual inertial sensor and this seems to be able to stabilise the loop. I was able to successfully engage the inertial damping (blending frequency 30 mHz) along both L and T. Figure 3 shows the spectra taken when the following strategy was engaged:
1) IP_{L,T,Y}: DC control on (blue line)
2) IP{L,T} blending at 80 mHz, IP_Y blending at 110 mHz (red line)
3) IP{L,T} blending at 30 mHz, IP_Y blending at 110 mHz (magenta line).
It is clear from the figure that the 30 mHz strategy helps to reduce the rms by almost a factor of 18 at the microseismic peak.
Note: I still need to work on the shape of the control filter and the optimisation of the blending filters.
