Message ID: 16031
Entry time: Wed Apr 14 17:53:38 2021
In reply to: 16020
Reply to this: 16035

Author:

Anchal

Type:

Update

Category:

SUS

Subject:

Plan for calculating filter banks for output matrix aka F2A aka F2P

Plan of action

Get the transfer functions of the suspension plant from actuated DOF to sensed DOF. We'll verify Bhavini's state-space model and get these transfer functions. Use the model TFs, not measured.

For each of POS->POS, PIT->PIT, and YAW->YAW, we'll get the resonant frequency and Q of the resonance from these models. No, forget about the Q.

We can correct the resonant frequencies from the measured ones in our free swinging data.

Now, we'll repeat the following for each column of output matrix filters (inspired from scripts/SUS/F2Pcalc.py, but not fully understood how/why):

Select col (eg. POS)

Set f_{0} to the resonant frequency.

Calculate where G_{UL} is the corrected DC gain we got after output matrix optimization earlier. (Not sure how, why?). No, use the SS model.

Calculate f_{UR}, f_{LL}, and f_{LR} like above.

Set (This just seems like a way of keeping some approximately low Q, ideally we should keep this same to what we got above but that might cause saturation issues like Rana mentioned in the meeting)

Then, set the following filter in the output matrix element for UL:

which is in zpk form equivalent to:

Repeat the above for UR, LL, LR.

Note that this filter function takes values G_{UL} at DC and at high frequencies while it would dip at the resonant frequency for POS with depth and narrowness directly proportional to Q_{UL}.No, the DC gain is different from the AC gain.

However, the F2P filter plots we found in several places on elog look a bit different. Like here: 40m/4719. One important difference is that the filter magnitude always become 1 after the resonance at higher frequencies. Yes, this is what we want, since you already did the balancing at high frequencies.

A preliminary plot of the above calculation for the 1,1 output matrix filter bank (POS -> UL) is attached in Attachment 1.

Discussion:

We can make 12 such filters for the 12 numbers we got for the optimized output matrix. Is that the aim or should we do it only for the POS column as has been done in past?

We are not sure how the choice of Q is made in setting the above filter function. We'll think more about it to understand this.

We are also not sure how the choice of f_{UL} is made above. It looks like depending on the correction gain, we want to slide the zero positions with respect to the pole positions which are fixed at the resonant frequency as expected. This seems to have some complex explanation.

Please let us know if we are planning this right before we dive into these calculations/script writing. Thanks.

Edit Thu Apr 15 08:32:58 2021 :

Comments are from Rana.

Corrected the plot in the attachment. It shows the correct behavior at high frequencies now.