Synchronization of a variable frequency source with a fixed frequency source using a sliding-mode controller

The authors show the synthesis of a sliding-mode controller using Lyapunov stability theory. One way of synchronizing the Superconducting Super Collider (SSC) low energy booster with the medium energy booster is by matching the longitudinal phase of the designated RF buckets of two machines throughout acceleration to a pre-programmed trajectory. This makes the synchronization predictable in advance. The model associated with the phase-locking is time-varying and model parameters are subjected to disturbance due to errors in the bending magnetic field. Also, the disturbance could be due to other feedback loops such as a B-field loop or a beam phase loop in the system. The measured phase error between the two reference waves may not be accurate. The design of a sliding-mode controller for such an application is considered. In the absence of measurement errors and parameter uncertainties and with no disturbance, the controller reduces to a classical gain feedback.<>