[Ian, Lee]

Given a C-HARD Pitch plant as well as the related noise spectra with seismic (environmental) noise and sensing (measurement) noise, we calculated a number of optimal linear controllers for different weightings of two figures of merit. The code for this can be found in the github buzz dev branch in the AIC folder (with commit SHA). The outline of the system is given in the attachments as AIC_layout.pdf. This layout shows the the overall layout of the system we used to calculate our controller. The bandpass FOM, plotted in F1_plot.pdf, which we constructed using a 8th order bandpass and a 16th order high pass filter combined. The different roll offs on the different sides of the bandpass filter is better for our solver to process and is more like the real noise drop off on the SNR integral. In order to compare this controller with others made for this DOF, we are using a FOM that picks off right after the controller. This FOM is marked F3 on the layout attached. The Flat FOM (marked F2) remains right after the plant because it needs to hold a non zero D-matrix across the plant FOM combination. The original bandpass (F1) is not used here. A plot of the noises and plants is in noise_plant_bode.pdf. To meet solver requirements the measurement noise is modeled as flat. 

Results:

The RMS results are plotted in AIC_Hib_FOM_RMS_Scatter.pdf. In this plot, each point represents a controller, where its inner color is how heavily it is weighting the Bandpass FOM (F3) and the outside color is its phase margin in degrees. The red line is the H2 results which show the lowest possible performance RMS for a linear controller. The x-axis shows that controllers RMS after the bandpass FOM (F3) and the y-axis shows the RMS performance after the flat filter (F2). One set of controllers with a constat F3 weight of about 3e4 but increasingly more stable phase margins has been used in the HiB open loop bode plot (AIC_Hib_OL_BODE.pdf) and closed loop bode plot (AIC_Hib_CL_BODE.pdf).

I have included the H2 RMS plot in AIC_H2_FOM_RMS_Scatter.pdf, which shows just the H2 results as well as the associated open loop bode plot (AIC_H2_OL_BODE.pdf) and closed loop bode plot (AIC_H2_CL_BODE.pdf).