The attached pdf compares Zach Patrick's BSC-ISI model against measurements of all H1 BSC-ISIs. Overall, the magnitudes are pretty good fits. Some of the TFs have right half plane zeros which throw the phase off. This will be a problem when trying to close loops around the model. Thus, I think we need to refit the model. I think this model was fit with frequency domain data in N4SID, but we now know that time domain is best (for good coherence). We also don't have any ground to stage motion fits, so we could add those in at that time.

I spent some hours trying to correct the right half plane zeros without success. My conclusion is that it is easy to fix in a SISO system by simply reflecting the right half plane zeros around the imaginary axis in the complex plane; but it is not feasible to do this with a MIMO system with dozens of poles and zeros. To do this you have to convert the state space to a zpk, which is fine. The problem is converting from zpk back to ss. For systems with multiple outputs, matlab does not have a numerically stable way to convert from zpk to ss. In fact it warns you about this in the comments to zp2ss.m. You could leave the model in zpk form, but it runs extremely slowly. Generally, state space is the best form for MIMO systems, since it permits the use of a lot of MIMO tools and analysis.

The model is located on the svn at

/ligo/svncommon/SeiSVN/seismic/BSC-ISI/Common/BSC_ISI_Model/N4SID_Model/L1BS/BuildFullL1BSmodel.m

To compare the model to data, run

/ligo/svncommon/SeiSVN/seismic/BSC-ISI/Common/BSC_ISI_Model/N4SID_Model/L1BS/CompareModel_to_data.m