We designed an optimal controller using H-inf synthesis (see, e.g., G1501583, T1800077) for MICH PIT ASC.
In the attached plot we show the comparison for between the original (blue) and the new, optimal control filters (red). The new controller provides 6 dB more suppression in both the microseismic band ~ 0.5 Hz and 4 dB more at the earthquake band ~0.003 Hz. At the same time the high-freq row-off is similar for the two configuration (as we already put a very aggressive LP filter for MICH ASC). At around the ugf ~ 1 Hz we lose only 10 deg of phase which should not affect the loop stability.
The new filters are now put in FM4 & 8. The old FM4 was unused and FM8 was simply a cheby2("BandStop", 4, 20,83,93). We will further optimize the weighting functions as well as our knowledge of the plant to improve the filter performance.
We are able to lock MICH pitch with the filter designed with mu-synthesis. Relative to the previous design we modified the weighting so that the high-freq cutoff was more sharp. See the first plot. The second plot showed the MICH P error signal and control signal. Right now there is some gain peaking at 1.1 Hz. This seemed to be due to that our knowledge on the plant was not good enough and our inversion of the secondary resonant peak was a bit off. Once we get some chance to do a detailed BS plant measurement we should be able to avoid the 1.1 Hz peaking.
