Some Considerations of Feedback Loop Design for the SRS Storage Ring R.F. System

A stability analysis has been made of the electron beam/r.f. cavity system for a high current storage ring under closed loop feedback conditions, using a variety of control theory techniques. A linearized, state variable model is formulated in terms of small changes in amplitude and phase of r.f. cavity voltage and generator drive. Modern multivariable design techniques are applied to the state space model. It is found that a multivariable root-locus method is more suited to this particular problem than is the inverse Nyquist array technique. Several cases are considered for both accumulation and storage modes of operation, with and without reactive mismatch between r.f. generator drive current and effective cavity volts. Amplitude and phase responses are obtained corresponding to step changes and several possible feedback options, involving proportional or integral action, are presented.