I used a recent measurement of the DHARD pitch transfer function done by Jenne, to extract the plant transfer function and fit it. The idea was to identify why there is that spurious phase rotation around 1 Hz.

It turns out that the phase rotation is not due to a right-half-plane zero (that would have resulted in a phase rotation in the other direction) but it is due to a right-half-plane pole at 0.96 Hz.

In a ideal case, the plant should have two stable (left-half-plane) double poles corresponding to the two mechanical resonances (we are actuating from L2). Those two double poles are indeed there at 0.95 Hz and 2.0 Hz. But there is also a close  double-pole / double-zero pair at about 1 Hz. This can be due to cross-couplings from other loops. In normal, stable conditions, this pair would produce a small wiggle in the phase, since a stable double pole would induce a phase rotation of -180 degrees and a double zero a phase rotation of +180 degrees. But the double pole in this case is unstable, so its phase rotation is +180 degrees, and this cancels out the -180 from the 0.95 Hz stable double pole.

Interestingly, if I use the plant fit and the control filter, and simulate the system stability with MATLAB's sisotool, I find out that the loop is indeed stable. So the situation seems to be that cross-coupling of DHARD with another loop creates a unstable pole/zero pair at about 1 Hz. And the current DHARD design is good enough to stabilize it. This is not that surprising, since the unstable pole has reasonably large Q, so it's not that hard to stabilize. Also I think that once the cross-coupling is fixed, the current loop shape should still give a stable feed-back (assuming we just remove the pole/zero pair).

For reference, see below the fit parameters