An extremum seeking control system for control of RF cavity resonators

RF cavity resonators are one of the key structures in particle accelerators. They provide accelerating field for a beam of charged particles passing through them. An RF source transmits required power for acceleration to cavity through waveguides. Due to impedance mismatch, some amount of available power generated by the RF source reflects back from the cavity. To save power and provide the maximum accelerating field, it is desirable to minimize this reflected power by equalizing the frequencies of the cavity and source. A mechanical tuner mounted on top of the cavity moves a tuner plate in or out of the cavity, thereby changing cavity’s resonance frequency. In this thesis, first a mathematical dynamic model of the cavity in terms of its transient and steady state signals is provided. Then based on the dynamic model, an extremum seeking (ES) algorithm is developed to automatically reach the minimum value of the reflected power and maintain this condition by keeping the resonance frequency of the cavity equal to the source frequency. The ES algorithm is derived through a Lyapunov-based analysis and uses only reflected power as feedback signal. A gradient estimation is performed to determine the direction of movement. The proposed ES controller is further compared with classical perturbation-based ES methods. Simulation and experimental results are presented to evaluate stability and the response behavior of the algorithms in reaching the minimum condition. While both algorithms successfully minimize reflected power in finite time, the results obtained from the Lyapunov-based algorithm are faster and smoother. However, if the cavity is not perfectly coupled and the minimum reflected power is greater than zero, the performance of the proposed controller degrades due to appearance of steady state oscillation. This problem can be solved by adding an initialization phase to the controller, to track the minimum value of reflected power and update the control law with the new value of the minimum.