In order to accomplish CARM control with the PSL laser frequency, we use two actuators.

One is the longitudinal direction of one of the MC mirrors. The londitudinal motion of the MC induces
the laser frequency control via the MC servo. As we move the mirror, the range is sort of big,
but the BW is limited by the mechanical response.

The other is the additive offset path. We inject a signal to the additional input port of the MC.
The MC servo supresses this injection by giving the same amount but oppsite sign offset to
the error signal (before the addtion of the inputs). The bandwidth of this AO path is limited
by the bandwidth of the MC servo. Basically the BW of the AO path is about 1/10 of that of the MC servo.

In order to confirm the capability of the AO path as a frequency actuator, 1) OLTF of the MC servo
2) TF of the AO input to the servo error was measured.

Attachment 1 shows the openloop TF of the MC servo. The UGF seems just little bit higher than
100kHz. The OLTF is empirically modelled by LISO as seen in the figure.

Attachment 2 shows the TF from the additive input (In2) to the error monitor (MC Servo module Q error mon).
The gain setting of the MC servo box was: In1 +18dB, In2 0dB. The measured TF has arbitorary gain 
due to the gain setting, the measuemrent data was multiplied by 4 to mach the DC value to the unity.
This is to compare the measurement with the prediction from the OLTF.

The AO path TF is expected to show the character of -G/(1+G) where G is the OLTF. In my case,
G = 0.75*OLTF showed the best maching. There might have been some misalignment of the MC
upon the AO path measurement as I found after the measurement.

From the plot , we can see that the response is flat up to 20kHz. Above that it rapidly raises.
This should be dealt with the CM servo filter as the bump may hit the unity gain. Since we have to use
strong roll off to avoid the bump, this will eat the phase margin at low frequency.

In the case that we don't like this bump:
This bump is caused by low phase mergin of the OLTF at 30~40kHz. If the total gain
is increased, the bump is reduced. Or, we can decrease the PZT loop gain in order to
reduce the dip at the crossover ferquency between the PZT and PC loops. In both cases,
the PC path suffers more actuation. We may need to think about the HV actuation option
for the PC (Apex PA85).

Well, let's see how the CM servo can handle this.
The key point here is that we have enough data to start the design of the CM servo.