Enomoto, Nakano, Ballmer

More on last night's TM feed-back work:
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- We were able to increase the DAMR1 gain to -60000, which led to the reported suppression of some length peaks.
- For this we had a simple control filter in DARM1 FM8:p40^2,z1 : zpk([1],[40;40],1,"n")

- For the MN stage, we initially used a simple 1/f integrator and notch at .63Hz. That worked fine for a very low frequency bleed-off.

But naturally we tried to increase the gain to the MN stage.
- This rang up the fundamental Pendulum resonance at 0.63Hz, so we started designing the plant compensation filter. Details are below.
- We successively tested the first two pole compensations, i.e. with the 0.63Hz compensation, the 1.53Hz rang up, with the 0.63Hz and 1.53Hz compensations, the 2.49Hz rang up.
- We haven't tested the full compensation filter yet.
- given the almost 90dB of drive enhancement needed for the MN drive, we will also try the IM stage as an intermediate actuator.

- Filter design strategy
- We know the MN to TM feed-back has three main resonances. We found them by increasing the MN stage gain and ringing them up:
0.63Hz, 1.53Hz, 2.49Hz
- In other words, the MN->TM transfer functions has 3 high-Q pole pairs at those frequencies (and no zeros, since it has to be 1/f^6 at high frequencies).
- Since these resonances have high, not well known Q, there is no chance of exactly compensating them. That's especially true since additional damping will change the effective Q.
- In addition, high-Q digital filters are never a good idea from an operational point of view.
- So we need to compensate these high-Q poles with lower-Q zeros. But putting the compensating low-Q zero-pair at the same frequency as the pole results in a huge phase-drop just above the pole frequency.
- Therefore we need to move the compensating low-Q zeros to a slightly lower frequency, effectively generating a complex pole-zero lead filter, recovering some of the phase.
- However we can't be too aggressive with that strategy, as the multiple lead filters will increase the gain above resonances.
- This design strategy leads to filters that are relatively robust against changes in the Q of the mechanical plant.
- The attached bode plot of the compensation filter illustrates that.

Filter details:
- Fundamental (0th) Pendulum (0.63Hz) inversion:
zero pair: z=0.55Hz, Q=5 (pendulum compensation); pole pair: z=4Hz, Q=3 (roll-off)
zpk([0.055+i*0.547243;0.055-i*0.547243],[0.666667+i*3.94405;0.666667-i*3.94405],1,"n")

- 1st Pendulum (1.53Hz) inversion:
zero pair: z=1.46Hz, Q=5 (pendulum compensation); pole pair: z=4Hz, Q=3 (roll-off)
zpk([0.146+i*1.45268;0.146-i*1.45268],[0.666667+i*3.94405;0.666667-i*3.94405],1,"n")

- 2nd Pendulum (2.49Hz) inversion:
zero pair: z=2.31Hz, Q=5 (pendulum compensation); pole pair: z=5Hz, Q=4 (roll-off)
zpk([0.231+i*2.29842;0.231-i*2.29842],[0.625+i*4.96078;0.625-i*4.96078],1,"n")