System modeling and control of resonance frequency for an RF cavity using reflected power measurements

This paper presents a motion control system based on reflected power measurements to stabilize the natural resonance frequency of an RF cavity. Control of the natural resonance frequency of an RF cavity is essential for superconducting accelerator structures due to their high cavity sensitivity to internal and external vibrations and dependency on temperature changes. Due to the relatively high radio frequencies involved (MHz to GHz), direct measurement of the resonant frequency for real-time control is not possible with conventional microcontroller hardware. To address the control problem, this paper presents a nonlinear control scheme that relies on the measurement of the reflected power instead of the well-known phase comparison technique. The control scheme will be used in a motion control system to stabilize the resonance frequency of the cavity. The control algorithm is based on performance index minimization using the steepest descent method. A Lyapunov based stability analysis is presented that provides necessary conditions for closed-loop stability with the error reaching a bounded region in the state space of error dynamics. Simulations for the mechatronic system are presented to evaluate the performance of the proposed controller.