Application of Extremum Seeking for Time-Varying Systems to Resonance Control of RF Cavities

A recently developed form of extremum seeking for time-varying systems is implemented in hardware for the resonance control of radio-frequency cavities without phase measurements. Normal conducting RF cavity resonance control is performed via a slug tuner, while superconducting TESLA-type cavity resonance control is performed via piezo actuators. The controller maintains resonance by minimizing reflected power by utilizing model-independent adaptive feedback. Unlike standard phase-measurement-based resonance control, the presented approach is not sensitive to arbitrary phase shifts of the RF signals due to temperature-dependent cable length or phasemeasurement hardware changes. The phase independence of this method removes common slowly varying drifts and required periodic recalibration of phase-based methods. A general overview of the adaptive controller is presented along with the proof of principle experimental results at room temperature. This method allows us to both maintain a cavity at a desired resonance frequency and also to dynamically modify its resonance frequency to track the unknown time-varying frequency of an RF source, thereby maintaining maximal cavity field strength, based only on power-level measurements.