Stage 1 Feedforward (HEPI-L4C to coarse actuators (stage 1)):
Transfer functions from the coarse actuators (Stage 1) to the HEPI L4C were measured to evaluate the "feedback path" (on the HEPI-L4Cs) once the feedforward controller is engaged. Coherence is bad in the [100m;700m]Hz due to a weak drive (needs to be redone). Transfer functions were measured with:
- No HEPI control
- ISI damped  on both stages

In the attached figure H1_ISI_ETMY_TF_FF01_X_2012_11_06.fig, few TFs in the X direction are presented:
- the ground path (HEPI-L4C to ST1 T240) - No drive
- the force paths F11 and F10 (coarse actuators to Stage 1 T240 and coarse actuators to HEPI L4C)
- the feedforward filter (Ground/force + fit filter)
- the "Open loop" - Feedforward filter x Force path (F10)

The force path F11 (coarse actuators to Stage 1 T240) is pretty strong in comparison with the force path F10 (coarse actuators to HEPI L4C). Consequently, the risk of instability is low.  The reference signal (HEPI -L4C) is lightly changed by the feedback loop (F10 x FF). F10 x FF is always far below 1 (The peak at 0.14Hz is due to the low coherence in the initial measurement).
 

Stage 2 Feedfoward (Blend {L4C + T240} to fine actuators (stage 2)):
In a first step, the stage 1 L4C and the Stage 1 T240 are blended at 2Hz (cf H1_ISI_ETMY_TF_Blend_FF_X_2012_11_06.fig in the X direction). Then, some simulations were performed to set the feedforward controller. In attachment H1_ISI_ETMY_TF_FF12_X_2012_11_06.fig, TFs in the X direction are shown:
- the ground path (ST1->ST2) - No drive
- the force paths F22 and F21 (fine actuators to Stage 2 GS13 and fine actuators to the (L4C+HEPI) blend)
- the feedforward filter ((ST1->ST2)/F22 + fit filter)
- The "Open loop" - Feedforward filter x Force path (F21)

The force path F22 is pretty weak in comparison with the force path F21. Consequently, the risk of instability is high. The "Open loop" - Feedforward filter x Force path (F21) shows that the feedfoward controller from stage 1 to stage 2 won't be stable. In this case, the reference signal (stage 1 motion) is too much changed once the FF controller is engaged

To circumvent the problem, the contribution of the stage 1 motion created by the feedforward controller can be evaluated and removed from the reference signal (cf block diagram). The "open loop' becomes (F21-F21 fit) x FF. I fitted the F21 path and re-evaluated the "open loop" in the X direction. With this strategy, the controller is stable in simulations but probably would not be experimentally. This approach seems tricky too implement experimentally.