The measured openloop TF of the ALS servo for each was characterized by a ZPK model.
The openloop TF can be modeled by:
1) Filter TF obtained from foton
2) Actuator response with appropriate assumption
3) Phase tracker closed loop TF
4) Delay caused by the digital control
5) anything else
For 1) ZPK models of the servo filter was obtained from foton. It turned out that the TF of FM5 doesn't match with the ZPK model in foton.
Therefore the TF was exported and fitted with LISO. This seems to be related to the pole frequency (3kHz) which is too close to Nyquist frequency (8kHz).
FM(:,1) = zero1(f,5).*pole1(f,0.001)*5000;
FM(:,2) = zero1(f,1).*pole1(f,0.001)*1000;
FM(:,3) = zero2(f,4.5,1.4619).*pole1(f,0.001).*pole1(f,0.001)*20.2501*1e6;
FM(:,4) = zero2(f,35,2).*pole2(f,3,3).*zero1(f,3000).*pole1(f,1).*pole2(f,3000,1/sqrt(2)).*pole1(f,700).*zero1(f,10).*zero1(f,350).*136e1;
FM(:,5) = zero1(f,1).*pole1(f,4.010e3).*pole2(f,17.3211e3,1.242).*zero2(f,18.865e3,100e3);
FM(:,6) = zero2(f,3.2,0.966775).*pole2(f,3.2,30.572);
FM(:,7) = zero2(f,16.5,2.48494).*pole2(f,16.5,78.5807).*zero2(f,24.0,2.22483).*pole2(f,24.0,7.03551);
FM(:,8) = 1;
FM(:,9) = zero2(f,7.50359,1.07194).*pole2(f,1.43429,0.717146)*27.5653;
FM(:,10) = 1;
dc_gain = 14;
FM1/2/3/5/6/7/9 are used for the control.
For 2), a resonant freq of 0.97 with Q of 5 was assumed.
The model for 3) was obtained by the previous entry.
Now the measured TF was divided by the known part of the model 1) ~ 3) and empirically fitted in LISO.
### XARM ###
pole 392.5021429051 698.1992431753m
zero 42.3128869460k 31.0954443799m
pole 589.2716424428 2.8325268375
factor 8.3430140244
delay 34.7536691023p
### YARM ###
pole 416.2463334253 743.2196174175m
zero 97.9161062704M 114.6703921876m
pole 626.0463515310 2.7671041771
factor 9.0045911761
delay 34.0945727358p
These compensation TF have weird TF. Probably the frequency response of the delay and the analog AA/AI filters without the high frequency data
led the LISO make up this. I'm requesting Masayuki to provide the AA/AI data to make the estimation more reasonable.
For the servo modeling, this is sufficient and we'll go a head.
The results of the OLTF modeling are attached. |