On the choice of method to cancel 60 Hz disturbances in beam position and energy

Because the voltage applied to magnets in accelerators is likely to be rectified, there can be 60 Hz related fluctuations in beam position and energy. Correcting such errors as well as other less repeatable errors can be done with combinations of feedback, feedforward, real time repetitive control, and batch update repetitive control. This paper studies how to mix these approaches for optimized performance. It is shown that use of feedback control can be counterproductive because of the waterbed effect operating on errors such as BPM noise. Also, it is seen that iterative repetitive control updates can produce significantly better error levels than pure feedforward control. Making corrections of errors for harmonics of 60 Hz that are above the Nyquist frequency can be accomplished, and this can save the expense and integration effort to produce fast beam sampling