[Continuing 11217]

The environmental noise (SEI) must be stable and the plant must have a nonzero D matrix. Because the controller I added in [11217] was unstable it made the seismic section unstable causing the failure we saw in the last post. To fix this issue I manipulated the poles and zeros in this way;

1.  Copy all unstable poles into the plant as new poles of the plant
2.  Make the real part of all the unstable poles in the SEI negative, thus stabilizing the SEI.
3.  Copy all the newly stabilized poles from the SEI and make them zeros of the plant. Make sure you are only copying the poles that were unstable before step 2 and not all the now stable poles.

This process keeps the SEI stable and keeps the plant's D matrix non-zero all while keeping the characteristics of the system. The stable poles in the SEI are canceled out by the zeros in the plant leaving only the unstable zeros in the plant. 

When running this modified model, the solver runs no problem and gives the attached RMS plot. This plot has all the features that we are looking for; the margins increase as we move away from the H2 limit and it does not seem to have any numerical errors. 

There are two things that bother me about this plot. The first is that the current controller (red center in the top left of the plot) seems to be in the outside the theoretical H2 bound for optimality, i.e. it is to the left of the dotted red line. One possible explanation is that this might be some numerical thing, for example, it is not unusual for the solver to return controllers that were below the theoretical limit when the controllers seemed to have numerical issues like the BNS FOM being weighted too high. The second of which is that the current controller does not seem to be particularly stable with this new model. It is only reporting 0.55dB of gain margin and under 10 degrees of phase margin. I'm not sure why either of these things is true and I haven't investigated yet.

There are a few things that are new with the plot. The first of which is that there is an H2 optimal bound on the plot. This is the red line. The second is that there is text to describe what the numbers next to the points are. This is ground breaking tech

Next Steps:

1.  Talk to Lee and finalize the ASC model for the paper. This involves deciding on the SEI and measurement noise levels are that make sense.
2.  Add the getSPOFF() to buzz and add the new pole/zero manipulation to it in case of unstable environmental noise.
3.  Update the solver with the slightly better solver from Lee.