Danny, Stefan

We fitted the ring heater step response that we found in /ligo/home/aidan.brooks/OneArmTest/h2hwsey/2012_08_09_hws_rh_test/matlab_workspace.mat
in the frequency domain. The essential low frequency features are well captured by a
- zero at 5.45e-6Hz
- pole at 1.36e-5Hz
- pole at 6.00e-5Hz

We can therefore design an inverse filter that does not overshoot (high frequency gain equal low frequency gain equal 1) by using
- pole at 5.45e-6Hz
- zero at 1.36e-5Hz
- zero at 6.00e-5Hz
- pole at 1.497e-4Hz

The resulting lens step response is given in plot 1. Note that this inversion essentially shortens the full response to about 2h (at the 5% level), while never overshooting (i.e. there is no negative value problem).
I would imagine that some more tuning could even improve on that.