A general control model for designing beam control feedback loops

To control the beam in the synchrotron there may be six different primary feedback loops interacting with the beam at a given time. To apply modern feedback controllers and study the interaction of all feedback loops, a good mathematical model of the beam should be developed. The derivation of a non-linear tracking model in terms of differential equations obtained from a set of time varying finite difference equations is presented. The model compares well with the results of thin element tracking codes. (G.P.) 3 refs.; 1 tab