[Alexa, Evan, Sheila, Gabriele]

The attached MATLAB file is a model of how the ITM/ETM plant changes due to radiation pressure. I considered the actuation from the PUM and radiation pressure reaction on the test mass. I used the QUAD model to obtain the mechanical transfer functions I need. I checked that the modeled PUM to test mass transfer functions matches very well a measurement I took this morning. The optical stiffness matrix is computed following Sidles Sigg PLA 354, 167.

The laser input power and recycling gain are parameters of the model.

The first attached plot shows how the ETM actuation transfer function changes when we have 2.8 W in inupt of the IFO. The main low frequency peaks in both pitch and yaw are splitted, but the important thing to note is that the higher frequency features do not change significantly. This is expecially important for yaw: the 2-3 Hz structures don't move. My understanding is that those structures are parallel resonances coming from the upper stages of the QUAD, which are not affected by radiation pressure. It seems therefore that a reasonable strategy to implement larger bandwidth DHARD/CHARD loops is to compensate for the high frequency features, since they shouldn't change significantly with radiation pressure. Then we can develop a controller that works for both pitch and yaw, without a complete plant inversion.

The second attached plot shows the effect of radiation pressure in the hard/soft basis. Peaks move as expected.