Design of Radio Frequency Acceleration System for Ion Synchrotron Based on Theory of Linear Quadratic Problem

This report describes an optimal control system design of a radio frequency acceleration for an ion synchrotron. The theory of linear quadratic prdblem (LQP) is applied to minimize the deviation (ΔR) of the ion beam from the central orbit. Chapter II explains the formulation of LQP, with which the feedback gains are calculated. The solution also shows that the principal (ΔR) and the subsidiary (Δφ: longitudinal oscillation of beam) controllers are of PI (proportional+integral terms)-type and P-type, respectively. Chapter III presents discussions taking into account the noises superposed on ΔR and Δφ feedback signals. The noise reduction filters necessarily included in the detecting circuitries produce phase lags in the loops and may deteriorate the damping of the longitudinal oscillation. The effects are examined by simulations. Moreover, applying the stochastic control theory, dispersion of ΔR due to white noises is evaluated. Appropriate control parameters are settled as a compromise between quick responsiveness and noise-insensitiveness. The design method described here shows the complementary charaeter to the classical apploach.