J. Kissel, J. Betzwieser

No rocket science here, but I wanted to post to an aLOG such that we have a convenient reference to cite. Recall that the latest ESD linearization algorithm is described in G1500036, and we're using a simplified version of said algorithm because we do not compensate for charge, namely, when the ii'th linearized quadrant's output is
Vii = Vb * (1 - sqrt( 2 * ( (Fii / Vb^2) * G_ct + 1 ) ) )
where Vb is the bias voltage, Fii is the digitally requested ii'th quadrant's force input to the linearization algorithm, and G_ct is the EPICs record representing the linear force coefficient.

Since even this simplified linearization function is rather daunting to gather intuition about signs, I've made a few plots demonstrating how the algorithm plays with a 100 [Hz] frequency, 10 [ct] amplitude sine wave input request, showing both the output of the algorithm and the resulting force on the optic. The 10 [ct] was chosen because that's roughly what I see requested out of LOCK bank during low noise for both detectors. I've used LLO's numbers for the force coefficient EPICs record (G_{ct} = +/- 512000 [ct]) and bias voltage (Vb = +/- 127999 [ct]). 

As the title suggests, the sign of the output of the linearization algorithm signal gets flipped w.r.t. its input, regardless of the bias sign. 

This impacts the reconstruction of CAL-CS and therefore h(t),  in that LLO uses linearization and LHO does not, and it hasn't been included in the matlab model of the IFO to-date. It also is a piece to the missing sign puzzle (LHO aLOGs 21627 and 21703): there are therefore three polarity flips one must deal with in the ESD chain: the sign of the bias voltage, whether the linearization is on or off, and that the ESD itself is an inherently attractive actuator. It's those pieces that hadn't been considered in detail, which has result in the confusion between LLO and LHO's reconstruction of the actuation path -- at least on the TST / L3 stage.