I committed an update to ^/trunk/Common/MatlabTools/SingleModel_Production that optionally corrects (for the single model only at this point) a long-standing known error with the B matrix in the Matlab state space for all models (single, double, triple, quad), whereby the coupling from structure pitch to optic longitudinal was zero.

The trouble is that the SS matrix elements have been derived for infinitely flexible wire. For realistic, stiff wire, the wire flexure correction would ideally be implemented with code like the following

where dblade, dpitch, dyaw1 and dyaw2 are the vertical and horizontal offsets to the wire attachment points, flex0 is the vertical component of the flexure length, and si0 and c0 are sine and cosine of the angle of the wire to the vertical. This amounts to insetting the ends of the wire by one flexure length at each end. However for historical reasons there is no dblade or analogous quantity defined in any of the Matlab models for the very top wire attachment, so that line has had to be left out. The A matrix turns out completely OK because it only depends on the shortening of the wire - the pendulum has effectively been hitched up by flex0 because dblade couldn't be increased, but it retains all the same pendulum resonances. However it has the effect of zeroing out the structure pitch to optic longitudinal coupling in the B matrix, because even with dblade=0, there's supposed to be a lever arm of flex0.

The impetus to fix this is that Fabrice has been doing a series of experiments with a seismometer mounted as an pendulum with the same structure as for HAUX/HTTS (two blades, two wires), and is seeing a coupling from pitch of the structure. Therefore it is of interest to have a debugged model with the proper pitch-to-longitudinal coupling for comparison purposes.

To implement the fix, I created a new Mathematica model with an explicit dblade parameter, ^/trunk/Common/MathematicaModels/TwoWireSimpleBladesED (ED=extra "d"), updated the Matlab-export code to match, and exported a new set of Matlab matrix elements symbexport1bladesEDfull.m. I then hacked ssmake1MBf.m to use these elements when pend.dblade is defined. The usual use case will be pend.dblade=0, but other values also work. The attached plot is generated by edplot.m and shows the P to L transfer function for the default case of the TwoWireSimpleBladesED model which has dblade=0.001 and flex0=0.0009687. The plot generated from the Matlab model is in blue, and is exactly overlain by comparison data exported from the equivalent Mathematica in red.

As might be hoped, the value at f=0 is -(dblade+flex0)= -0.0019687. The sign is negative because +pitch is right-handed around +y=left, i.e., nose down, so as pitch increases the effective flexure point moves backwards. See the attached diagram.