The last set of updated controllers in log post [11731], needs to be updated because it did not include two important things. First the plant needs to have delay added to it. The second is that the inverse of P_compliment needs to be added to the F3 path.

For the delay, I added a delay of 10 milliseconds. In future this will be easier, I added a few ways to do this. You can use the delay block, you can use the makeSPOFF function to add delay as an argument which adds this delay to the plant, or there is a new add_delay function to add delay to an existing SS or ZPK model. When I added the delay to the ZPK of the plant. It is also now possible to pass a ZPK of the plant into the makeSPOFF function.

I also needed to add the inverse of P_compliment to the third FOM (F3). P_compliment is the part of the plant that is move to the environmental noise. Inverse of P_compliment does not need to be added because it is just weighting the pure unmeasured output. In order to make the output of a FOM added after the controller equal to a FOM added to the augmented system F3' = P_c^-1 * F3. In the previous log post [11731] I was only using F3 and not F3'. I fixed this.

With these two improvements the solver threw errors because F3' has more zeros than poles making it a descriptor state space i.e. a state space that has an E matrix. To fight this I added a warning or error for when an E matrix is detected. To fix F3 I made the roll off after the bandpass in F3 steeper to get it to cancel out the extra zeros in inverse of P_compliment. Note that pretty much all plants have roll offs which means that P_compliment pretty much always rolls off which means P_compliment inverse will have an E matrix. Canceling out this E matrix while both of the systems is in zpk form is important because buzz does not handle the E matrix and will simply ignore it. Because of this it is important to have a steep enough roll off to cancel out the extra zeros in P_compliment.

When the fix to F3 so that it has an appropriate roll off, the H2 solves (with a warning about how the SS to ZPK is showing inconsistencies). The RMS plot (AIC_H2_FOM_RMS_Scatter.pdf) shows roughly the same values for total RMS but has higher values for the band pass RMS. I have also attached the open (AIC_H2_OL_BODE.pdf) and closed loop (AIC_H2_CL_BODE.pdf) plots for the H2 results.

The H infinity bounded LQG solver fails because it encounters an E matrix. I haven't fully investigated this yet. I haven't attached the H2 results yet because I want to take a closer look at them.

In addition to this here are some additions made to buzz in no particular order.

• vega plotter added so that it can be used with a single function call. I didn't add much functionality hoping to add more when I have less pressing issues to address.
• added a balance kwarg to multiconnect and makeSPOFF to allow the parts of the SPOFF to be balanced before getting appended
• added assert to check the stability of the parts of SPOFF to ensure the parts are correct
• added F3 to the ASC solver to test the solver to see if it is better. (still working on it. I think there is a numerical bug)

Things to still do:

• Verify the K_usable
• semi-standardize the names of SPOFF (this is partly done. I mainly want to add a check to make sure that the name spaces are not reused)
• calibrate the FBNS