Simulation

Based on the previously discussed model a simulation of the feedback loop has been performed based on a PID controller model in order to determine the detailed specifications for the feedback. It has been found that the feedback has to operate at a sampling rate of 4 kHz in order to provide a -20 dB orbit noise attenuation at 90 Hz (see Figure 7). The statistical monitor noise should be not larger than 0.5 $\mu$m rms. The same holds for the tolerable granularity of the corrector power supplies. For a maximum kick of 1 mrad per corrector the analogue resolution should not exceed 15 ppm in amplitude.

  

Figure 7: Noise attenuation of the feedback loop at a sampling rate of 4 kHz

If these prerequisites are fulfilled an rms orbit stabilization to 1 $\mu$m and an rms residual angle distortion of 0.1 $\mu$rad at the location of the insertion devices can be achieved.